Kwantitatieve bepaling van de invloed van experimenteel gevonden microstructurele veranderingen, geïnduceerd door neutronenstraling, op de hardheid van modellegeringen en staalsoorten
Experimental Quantification of the Effect of Neutron Irradiation Induced Microstructural Changes on the Hardening of Model Alloys and Steels
Marlies Lambrecht
Promotoren: Prof. Dr. Ir. Y. Houbaert en Dr. A. Almazouzi Proefschrift ingediend tot het behalen van de graad van Doctor in de Ingenieurswetenschappen: Materiaalkunde
Voorzitter: Prof. Dr. Ir. J. Degrieck Faculteit Ingenieurswetenschappen Academiejaar 2008-2009
ISBN 978-90-8578-294-0 NUR 971 Wettelijk depot: D/2009/10.500/52
Dit onderzoek werd uitgevoerd aan het onderzoekscentrum This research was performed at the research centre Structural Materials (NMA) group Laboratory for medium and high activity (LHMA) Nuclear Materials Science (NMS) Institute SCK•CEN Boeretang 200 2400 Mol
Onder begeleiding van Under guidance of Dr. Abderrahim Almazouzi Dr. Lorenzo Malerba
In samenwerking met In collaboration with Vakgroep Toegepaste Materiaalwetenschappen Faculteit Toegepaste Wetenschappen Universiteit Gent (UGent) Technologiepark 903
9053 Zwijnaarde
Met promotor With promoter Prof. Dr. Ir. Yvan Houbaert
Deels gefinancierd door Partially financed by
FI60-CT-2003-5088-40 FP6_PERFECT project
The European commision
Foreword
Foreword
I really enjoyed realizing this PhD thesis! The results presented in this thesis are the outcome of a fruitful collaboration between the University of Ghent and the research centre SCK•CEN and I was the chosen one to accomplish the work. I hereby had the possibility to combine pleasure with work. The proposal laid within the scope of my interest, as I could approach engineering problems (the hardening and embrittlement of the RPV steels) using fundamental physics (the defects visualized by the positron technique in model alloys). In addition, it allowed me to work in an international environment and in laboratories which earn a great amount of international respect. The subject of the thesis was part of a European project, allowing me to collaborate with other important laboratories in Europe. Moreover, the issue is an important research assignment for countries all over the world. I therefore was able to visit laboratories all over the world, even outside Europe. All these experiences imparted me with a lot of knowledge.
The realization of this PhD proved to be much more complex than just "doing research and writing the book". The obtained results needed to be analyzed, discussed and explained. For a successful accomplishment of all these matters, the knowledge, the experience, the thoughts and even just the listening ears and support of a lot of people were needed. I hereby want to thank each and every one of you.
At Ghent University, Prof. Dr. Ir. Bruno De Cooman initialized the project at the end of my master, and without him I would never have started this PhD. Unfortunately, he left the university only a few months later, but I was pleased to know that Prof. Dr. Ir. Yvan Houbaert agreed to take over the job of being my promoter. Despite his tight schedule, he was able to make some time for me, when needed. The support of the management of SCK•CEN was also needed for the realization of the project. Therefore, I would like to thank Prof. Dr. Eric van Walle, Dr. Leo Sannen, Dr. Ir. Steven Van Dyck and Dr. Rachid Chaouadi.
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The major part of the work was financed by the FP6-PERFECT project, under the professional leadership of Dr. Jean-Paul Massoud (EDF, Les Renardières, France).
The most important man for the realization of the work itself and for the obtained experiences is Dr. Abderrahim Almazouzi (Abdou), co-promoter of the PhD. Already the second week of my PhD, he took me to a PERFECT meeting in Paris, to get acquainted with the subject, as well as to meet important people in the field. It was hard in the beginning; he wanted me to master the subject as soon as possible, in order to follow the demands of the PERFECT project, which was initiated about 2 years before my arrival. But, he believed in me since the very first day. And together, we realized this very fine work. Dr. Lorenzo Malerba, mentor of the PhD, was a great help, especially on scientific matters. The lot of discussions helped me in the understanding of the observed results and his remarks and correction of papers and the thesis led to the publishing of high quality work.
Actually, I should thank the whole crew of motivated colleagues at SCK•CEN. Special thanks to Ing. Maarten Jardin, Ing. Yves Parthoens and Ing. Stefan Dekelver for their help with the PAS setup. Concerning my initiation with this setup, I also want to thank Dr. Andrey Rempel. Other people to be mentioned for their help are Marc Eykmans, Willy Claes, Henri Maussen (Rik), Eddy Kox, Kris Kaers, Dirk Quirijnen, Danny Penneman, Roger Mertens, Paul Wouters, Ludo Eysermans, Nancy Van der Borgt and Odette Wouters. Scientific support was given by many others, such as Milan Konstantinovic and Dmitry Terentyev. It was enjoyable to share the office with the other PhD students: Joris Van den Bosch, Giovanni Bonny, Katelijne Verhiest, Xiaoqiang Li, Gunter Coen, Nicolas Castin and Boris Minov. And pleasant distraction was provided during lunch breaks, by among others Ben, Kevin, Frédéric and Wendy. And during the coffee breaks, I made friends among all people of LHMA.
A great amount of thanks, I want to send to Prof. Dr. Yasuyoshi Nagai (Yasu). He was not only a great help for me in the positron community, but he also invited me to come to his laboratory in Oarai (Tohoku University, Japan). There, I could perform post-irradiation annealing experiments, using both the PAS and APT technique. Local help was provided by Dr. Takeshi Toyama.
- ii - Foreword
Another help within the positron community was Prof. Dr. Jan Kuriplach. Also he invited me to his lab in Prague (Charles University, Czech Republic), with the local help of Oksana Melikhova. I learned to work with the APT technique at the University of Rouen (France) with the help of Bertrand Radiguet. And I want to thank Prof. Dr. Philippe Pareige for this opportunity. Also the RPV-2 model was thought to me, and this was done by Gilles Adjanor at EDF (Les Renardières, France).
Furthermore, I need to thank all members of the PERFECT community for all discussion that led to the finishing of this PhD thesis. Special thanks to Estelle Meslin (University of Rouen, France), Frank Bergner (FZD, Germany) and Mercedes Hernandez- Mayoral (Merche) (CIEMAT, Spain) for their patience and collaboration in publishing the common results.
I should also thank my parents, sister and brothers for everything they taught me and helped me with, in order to get me this far! In addition, I want to thank my friends and family for their support. And finally, I send a big kiss to Peter, for the discussion in the car, for the fact that he read the PhD (although this was rather difficult for him) and for his patience when I was writing this book.
Marlies Lambrecht April 2009
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Samenvatting
De stralingsgeïnduceerde verharding en verbrossing van kuipstalen (reactor pressure vessel steels of RPV steels) zijn van uiterst belang voor de levensduurbepaling van de nucleaire energiecentrales. Deze centrales zijn al gedurende vele jaren onderhevig aan uitgebreide onderzoeken in het belang van hun behoud. Er is opgemerkt dat de materialen gebruikt voor kuipstalen geneigd zijn om te verbrossen door bestraling. De werkelijke aard van de stralingsschade, verantwoordelijk voor deze verbrossing, blijft nochtans onvatbaar en er is behoefte aan nauwkeurig onderzoek.
Stralingsgeïnduceerde verbrossing van RPV staalsoorten is traditioneel toegeschreven aan drie oorzaken: de precipitatie, de matrixschade en de korrelgrens segregatie. Terwijl precipitatie en segregatie al diepgaand bestudeerd zijn, is het nog steeds onduidelijk wat de aard en de voornaamste mechanismes achter de vorming van de matrixschade zijn. De vooruitgang verwezenlijkt in de gevorderde experimentele technieken, zoals transmissie elektronenmicroscopie (TEM), positron annihilatie spectroscopie (PAS), atoom sonde tomografie (atom probe tomography of APT) en kleine hoek neutronenverspreiding (small angle neutron scattering of SANS), maakt het tegenwoordig mogelijk om een diepgaand onderzoek uit te voeren op de nano-elementen geïnduceerd door straling in the RPV staalsoorten. Deze technieken worden gecombineerd gebruikt voor het onderzoek van dezelfde materialen (het "REVE" experiment). In het huidige werk zijn de experimenten, uitgevoerd door PAS, gebruikt voor de interpretatie van de overeenkomstige hardheidsresultaten, verkregen door trektesten, met de hulp van enkele computermodellen en theoretische overwegingen. De resultaten zijn gekwantificeerd en gebruikt in combinatie met de resultaten van de andere technieken om een volledig begrip te verkrijgen van het microstructurele gedrag onder neutronenbestraling. Ten slotte is deze kennis gebruikt om de wisselwerking tussen de gevonden defecten en de stijging van de hardheid te begrijpen in neutronenbestraalde modellegeringen en staalsoorten.
- iv - Samenvatting
Gedurende de laatste decennia is er een grote vooruitgang gemaakt in het detecteren van vacatureclusters met PAS. De nadruk wordt nu gelegd op de chemische omgeving van de clusters waaraan de positronen gevoelig zijn, om een betere kennis op te bouwen over de aard van de matrixschade. Daardoor zijn er substantiële inspanningen gedaan om deze techniek opnieuw te gebruiken voor de identificatie van de uiteindelijke redenen van verharding en verbrossing in RPV staalsoorten, in het bijzonder met het oog op de ontwikkeling van fysisch gebaseerde modellen. In dit werk zijn de resultaten, verkregen door de PAS onderzoeken van verschillende neutronenbestraalde modellegeringen, beschreven en besproken. De resultaten zijn dan in verband gebracht met de bestralingsgeïnduceerde hardheidsdata, verkregen op dezelfde materialen. Een westers type RPV staalsoort is toegevoegd om deze te kunnen vergelijken met de modellegeringen. De resultaten kunnen als volgt samengevat worden.
¾ De aanwezigheid van koolstof verkleint de grootte van zowel de vacature als van de zelf-interstitiële (self-interstitial atom of SIA) type defecten, terwijl het de dichtheid van deze defecten in het materiaal vergroot. De veranderingen in grootte en aantal van de vacatures kan rechtstreeks waargenomen worden door de PAS resultaten, daar waar het gedrag van de SIAs onrechtstreeks bepaald wordt. De stijgende concentratie aan defecten leidt tot een groter aantal obstakels voor de beweging van de dislocaties, waardoor een sterkere verharding kan teruggevonden worden in de materialen met een zeker koolstofgehalte.
¾ Door de hoge onderlinge bindingsenergie tussen de vacatures en de koperatomen, kunnen de mobiele vacatures de koperatomen meenemen volgens de richting van de vacaturebeweging. Aangezien zowel de koper-koper als de vacature-vacature bindingsenergieën belangrijk positief zijn, kunnen koper-vacature complexen gevormd worden. Deze zijn waargenomen door PAS. Deze koperverrijkte precipitaten, gevormd aan het begin van de bestraling, leiden tot een belangrijke stijging van de hardheid van de materialen. Deze verharding lijkt te stabiliseren met stijgende neutronendosis.
¾ Zowel de mangaan-mangaan als de nikkel-nikkel bindingsenergieën zijn negatief, waardoor er meer vacatures nodig zijn om analoge mangaan-vacature of nikkel-vacature complexen te vormen (zoals gevonden voor de koper-vacature complexen). Dit grote
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aantal vacatures is echter niet gevonden; enkel kleine vacature cluster zijn waargenomen in de materialen met mangaan en nikkel concentraties.
¾ Mangaan heeft anderzijds een sterke binding met zelf-interstitiële atomen. Er wordt dus verondersteld dat mangaan kleine SIA clusters kan stabiliseren, waarbij de mobiliteit van de gevormde clusters veel lager is dan van de zuivere SIA clusters. Als paren van vacatures gebonden met legeringselementen (zoals koper, nikkel en zelfs mangaan) een dergelijk cluster tegenkomen, kan er recombinatie optreden van de vacature met een van de SIAs. Het legeringselement zal dan in de cluster achterblijven. De invloed van deze clusters op de verharding van het materiaal is relatief klein bij lage bestralingsdosis, maar het kan overheersend worden bij hoger bestralingsdosissen.
¾ Ook chroom interageert sterk met de SIA clusters. Er wordt geloofd dat de vertraging van de mobiliteit van deze clusters zorgt voor een sterke verhoging van de recombinatie van vacatures met SIAs. Hierdoor blijven minder vacatures en SIAs over in de matrix, waardoor er minder obstakels zijn voor de dislocaties. Er wordt inderdaad een verminderd aantal vacatures waargenomen door PAS. Een hogere concentratie aan chroom zorgt voor meer vertraagde SIA clusters, waardoor een verminderde versteviging gevonden wordt voor een stijgende chroomconcentratie in de materialen.
De PAS resultaten verstrekken dus belangrijke kwalitatieve informatie. Maar ook de kwantitatieve schattingen van de gemiddelde grote en dichtheid van de annihilatieplaatsen zijn van belang. Deze resultaten kunnen namelijk beter vergeleken worden met de resultaten verkregen door andere technieken, zoals TEM, APT en SANS. De kwantitatieve bepaling van de PAS resultaten is echter niet eenvoudig. In dit doctoraat zijn er twee pogingen gedaan, welke tot realistische resultaten geleid hebben. De eerste poging lijkt een betere schatting van de vacaturehoudende clusters te maken, die een belangrijke invloed hebben op de hardheid. De tweede poging daarentegen lijkt een betere schatting te geven van de verhouding van het aantal kleine vacature clusters tot de grotere clusters.
- vi - Samenvatting
Door de vier verschillende technieken te gebruiken is het mogelijk meer inzicht in de defecten te krijgen. De defecten veroorzaakt door straling kunnen dan ingedeeld worden in 4 groepen.
1) In de meeste modellegeringen, uitgezonderd de binaire Fe-Cu legeringen, alsook in de staalsoort, zijn er kleine vacature houdende clusters gevonden door PAS. Deze defecten zijn onzichtbaar voor de andere technieken. De defecten gevonden door PAS in de binaire Fe-Cu legeringen werden geïdentificeerd als de koperrijke precipitaten (met vacatures), als ook gevonden door APT.
2) De modellegeringen en de staalsoort tonen de aanwezigheid van clusters en/of precipitaten van legeringselementen. Deze clusters zijn gevonden door APT en zijn ook aanwezig in de resultaten van de SANS metingen.
3) In sommige legeringen en het zuiver ijzer zijn er ook andere defecten gevonden door SANS, namelijk nanoholtes.
4) Ten slotte zijn er nog SIA loops gedetecteerd, die enkel zichtbaar zijn met de TEM techniek. Deze loops zijn teruggevonden in alle modellegeringen, maar niet in het staal.
Startend van de kwantitatieve resultaten is het nu mogelijk om de bijdrage van elk type van de geobserveerde defecten tot de gemeten stralingsgeïnduceerde verharding te bepalen in de onderzochte materialen. Om deze verbanden te vinden wordt een klassiek model gebruikt, namelijk gebruik makend van de Orowan vergelijking.
¾ Van de eerste groep defecten (namelijk de kleine vacature defecten) werd er verwacht dat ze verwaarloosbaar zouden zijn door hun extreem kleine grootte. Er werd niettemin gevonden dat ze toch een zekere bijdrage hebben tot de verharding van de bestraalde materialen door hun enorm aantal.
¾ Het was al gekend dat de precipitaten een belangrijke rol spelen in de verharding op lagere bestralingsdosissen. Dit was beaamd in dit doctoraat. Hier is bovendien
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gevonden dat hun rol secundair wordt bij hogere bestralingsdosissen, terwijl de literatuur op dit gebied nogal beperkt is.
¾ Terwijl de invloed van de holtes zeer belangrijk is in zuiver ijzer, is hun invloed beperkt in de gelegerde materialen, waar andere defecten een grotere rol spelen.
¾ De vierde groep defecten (de SIA loops) zorgen voor de belangrijkste hardheidsbijdrage in zuiver ijzer. In de gelegeerde materialen wordt hun invloed veel kleiner, maar een continue stijging is gevonden met stijgende stralingsdosis. Hun invloed wordt zelfs opnieuw overheersend in de Fe-Mn-Ni legering op de hoogste bestralingsdosis.
Er kan dus besloten worden, dat voor de verlenging van de exploitatie van deze RPV staalsoorten, extra aandacht vereist is voor de verschijning van mangaan gestabiliseerde SIA loops.
De bestraling van Fe-Cr legeringen toont een gereduceerd aantal overblijvende vacatures, in vergelijking met chroomvrije legeringen. Dit is verklaard door een stijgende recombinatie van de vacatures met de SIAs, die vertraagd zijn door de aanwezigheid van chroom. Dit kan leiden tot een verminderde zwelling van deze materialen bij hogere stralingsdosissen.
- viii - Summary
Summary
The irradiation-induced hardening and embrittlement of reactor pressure vessel (RPV) steels are a great concern for nuclear power plant (NPP) life assessment. For the sake of their preservation, NPPs have been the subject of extensive investigations for many years. It was observed that the materials used for the reactor vessels are prone to embrittle due to irradiation. However, the real nature of the radiation damage responsible for this embrittlement and its evolution with dose remain elusive and still require close examination.
Irradiation-induced embrittlement in RPV steels is conventionally ascribed to three main causes: precipitation, matrix-damage and grain boundary segregation. While precipitation and segregation have been profoundly studied, it is still unclear what the nature and the main mechanisms of the formation of matrix damage are. Presently, the progress achieved in advanced experimental techniques, such as, for example, transmission electron microscopy (TEM), positron annihilation spectroscopy (PAS), atom probe tomography (APT) and small angle neutron scattering (SANS), enables a detailed investigation of the nano- features induced by irradiation in RPV steels to be performed. These techniques have been used in a combined fashion to investigate the same materials (the "REVE" experiment). For the present work, the experiments conducted by PAS were used to interpret the corresponding hardening results that were obtained by tensile tests, with the support of a few computer-modelling results and theoretical considerations. The results have been quantified and combined with results from the other techniques to obtain a full understanding of the behaviour of the microstructure under neutron irradiation. Finally, this knowledge is used to correlate the observed defects with the increase of hardness in neutron irradiated model alloys and steels.
Significant progress in revealing potential vacancy clusters has been made by PAS during the past decades. The focus is now being put on the chemical surroundings of the clusters that are sensitive to positrons, to obtain a better understanding of the nature of the matrix damage. Therefore, a substantial effort is being re-deployed to use this technique to
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identify the ultimate causes of hardening and embrittlement in RPV steels, particularly with a view to developing physically based models. In this work, the results obtained from PAS investigations of different neutron- irradiated Fe and Fe-Cu alloys as well as of Fe-Mn-Ni and Fe-Mn-Ni-Cu alloys, are described and discussed. The results are then correlated to the irradiation-induced hardening data obtained from the same samples. For the sake of comparison, also a Western type RPV steel was examined. The results can be summarized as follows.
¾ The presence of carbon reduces the size of both vacancy and self-interstitial atom (SIA) type of defects, while it increases the number density of these defects. The changes in size and density of the vacancies can be observed directly by the PAS results, while the behaviour of the SIAs is deduced indirectly. The augmented number density of the defects leads to a higher amount of obstacles for the dislocation movement, and therefore a higher hardening can be found in materials containing a certain amount of carbon.
¾ Due to the high mutual binding energies of vacancies and copper atoms, the mobile vacancies can take the copper atoms along the direction of vacancy motion. As, in addition, the copper-copper and vacancy-vacancy binding energies are important as well, copper-vacancy complexes are formed and observed by PAS. These copper-rich precipitates, formed at early irradiation, induce an important increase of the hardening of the material. It is found that this hardening seems to saturate with increasing neutron dose.
¾ The manganese-manganese and nickel-nickel binding energies are negative, and therefore many more vacancies are necessary to stabilize manganese-vacancy or nickel- vacancy complexes compared to the copper-vacancy complexes. This great amount of vacancies is however not found; only small vacancy clusters are observed in manganese and nickel containing materials.
¾ Manganese shows, on the other side, a strong binding with self-interstitial atoms. It is therefore assumed that manganese can stabilize small SIA clusters. The mobility of such stabilized clusters will be much lower than the one of pure SIA clusters. When pairs of vacancies with alloying elements, such as copper, nickel, silicon and even
- x - Summary
manganese, meet such stabilized clusters, recombination may occur of the vacancy with one of the SIAs. The alloying element will then remain localized in the cluster. The effect of such clusters on the hardening is rather small at low irradiation doses, but it becomes dominant at higher irradiation doses.
¾ Also chromium interacts strongly with SIA clusters. It is believed that the slowing down of the mobility of such clusters leads to a strongly increased recombination of vacancies with SIAs. Therefore, less vacancies and SIAs remain in the matrix, which act as obstacles for dislocations. Indeed, PAS observes a reduced amount of vacancies. A higher chromium concentration induces more slowing down, and therefore a decreasing amount of hardening is observed with increasing chromium content.
The PAS results have thus imparted important qualitative knowledge. But, focus should also be put on the quantitative estimations of the average size and density of the positron annihilation sites, as this would lead to a better comparison with other techniques, such as TEM, APT and SANS. The quantification of PAS results is however not straightforward. In this thesis two attempts are made, which have been found to give reasonable results. While the first attempt seems to give a better estimation on the vacancy containing clusters, which could play a significant role in the hardening, the second attempt seems to be better in estimating the ratio of the amount of small vacancy clusters to bigger clusters.
From the combination of the four different techniques, the observed defects, produced during irradiation, can be classified within the following groups.
1) In most alloys, except the binary Fe-Cu alloys, as well as in the steel, small vacancy- containing clusters have been observed by PAS, which are invisible by any other technique. The defects observed by PAS in the binary Fe-Cu alloys have been found to be the same as the copper-rich precipitates (with vacancies), which are observed by APT.
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2) The model alloys and the steel show the appearance of clusters and/or precipitates of the alloying atoms. These clusters are observed by APT, and they are also present in the SANS results.
3) Some alloys and pure iron are found to have a remaining number of defects, observed by SANS. These defects are found to be nanovoids.
4) Finally, TEM is the only technique sensitive to SIA loops. These loops are observed in all alloys, except the steel.
In addition, the quantitative contribution of each type of the observed features to the measured irradiation-induced hardening, in the investigated alloys, can now be determined. Such correlations are attempted using classical models (i.e. the Orowan equation).
¾ The first group of defects (the small vacancy type of defects) were expected to be negligible due to their extremely low size. Nevertheless, due to their enormous number density, it is found that they are contributing to the hardening of irradiated materials.
¾ It was already known that precipitates play the major role in the hardening at lower irradiation doses. This is also found in this thesis. In addition, it is found here that their role becomes only secondary at higher irradiation doses, while the literature is very limited on these higher doses.
¾ While the influence of the voids is important in pure iron, it is only limited in the alloyed materials, where other defects are more important.
¾ The forth group of defects (the SIA loops) leads to the major hardening contribution in the pure iron. In the alloyed materials, however, their contribution is rather small, but increases continuously with increasing neutron dose. This component becomes even predominant in the Fe-Mn-Ni alloy irradiated at the highest dose.
For the prolongation of the operational time of RPV steels, special care should thus be taken in the appearance of manganese stabilized SIA loops.
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Irradiation of Fe-Cr alloys show a reduced number of remaining vacancies, compared to the chromium-free alloys. This is explained by an increased recombination of the vacancies with self-interstitials, which are slowed down by the presence of chromium. This feature is speculated to be responsible for the reduced swelling of such materials at higher irradiation doses.
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Acronyms, abbreviations and jargon
AFNOR Association Française de normalisation AGR Great Britain's advanced gas-cooled reactor (generation II) AFM Atom probe field-ion microscopy AMP Amplifier AP Atom probe APFIM Atom prove field ion microscopy APT Atom probe tomography ART Adjusted reference temperature ATSUP Atomic superposition at% Atomic percentage – a measure of concentration used in chemistry and spectroscopy bcc Body-centered cubic – a crystal structure of metals BR1 Belgian reactor 1 (generation I) BR2 Belgian reactor 2 (generation II) BWR Boiling water reactor (generation II) C Carbon Cr Chromium Cu Copper CALLISTO Capability for light water irradiation in steady state and transient operation – special experimental loop with PWR conditions in the BR2 reactor CANDU Canada deuterium uranium reactor (generation II) CDB Coincidence Doppler broadening CRP Copper-rich precipitates DB Doppler broadening DBTT Ductile to brittle transition temperature – an expression of embrittlement dpa Displacements per atom DSO Digital storage oscilloscope DSP Digital signal processor EBR-I Experimental Breeder Reactor I ECOTAP Energy compensated optical TAP EPR European pressurized water reactor (generation III) eV Electron volt – a unit of energy (the most common unit of energy within physics) – 1 eV = 1.602 × 10-19 joules fcc Face-centered cubic – a crystal structure of metals
- xiv - Acronyms, abbreviations and jargon
FBR Fast breeder reactor (generation IV) FIM Field ion microscopy FWHM Full width at the half of the maximum GCR Gas cooled reactor (generation I) GFR Gas-cooled fast reactor (generation IV) HPGe High-purity germanium detector HRTEM High-resolution TEM HV High voltage IC Ion channelling ICP-MS Induced coupled plasma mass spectroscopy IF Internal friction INT Interface card IPS In-pile section of the CALLISTO loop ITER International thermonuclear experimental reactor (fusion) JET Joint European Torus (fusion) keV Kilo-electron volt – a unit of energy (the most common unit of energy within physics) – 1 eV = 1.602 × 10-16 joules KMC Kinetic Monte Carlo model LEAP Local electrode atom probe LFR Lead cooled fast reactor (generation IV) LWR Light water reactor (generation II) MCA Multi-channel analyser MCNP Monte Carlo n-particle calculations MeV Mega-electron volt – a unit of energy (the most common unit of energy within physics) – 1 eV = 1.602 × 10-13 joules Mn Manganese MS Mössbauer spectroscopy MSMP Multi-scale multi-physics model MSR Molten salt reactor (generation IV) MW Megawatt – one million watts MWe Megawatt of electrical output µSR Muon spin resonance NEA Nuclear energy agency Ni Nickel NPP Nuclear power plant nS Neutron scattering OM Optical microscopy o-Ps Ortho-positronium
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PALS Positron annihilation lifetime spectroscopy PAS Positron annihilation spectroscopy PAW Projector augmented wave approximation PM Photomultiplier ppm Parts per million – a relative proportion in measured quantities p-Ps Para-positronium PWR Pressurized water reactor (generation II) RAFM Reduced activation ferritic-martensitic steel RMBK Russian high power channel type reactor (generation II) RPV Reactor pressure vessel
RTNDT Reference temperature for nil ductility transition S Line-shape parameter of a CDB spectrum SANS Small angle neutron scattering technique SCWR Supercritical water reactor (generation IV) SFR Sodium-cooled fast reactor (generation IV) SIA Self-interstitial atom SMD Stable matrix damage STEM Scanning transmission electron microscopy STM Scanning tunnelling microscopy TAC Time-to-amplitude converter TAP Tomographic atom probe TEM Transmission electron microscopy TTS Transition temperature shift TWh Terawatt hour – a unit of energy (usually for energy delivered by electric utilities) UMD Unstable matrix damage USPP Ultrasoft pseudopotential approximation V Vacancy VASP Vienna ab initio simulation package – modelling method VHTR Very high temperature reactor (generation IV) VVER Russian water-water energetic reactor (generation II) W Wing parameter of a CDB spectrum WATAM Wide angle TAP wt% Mass percentage – a measure of concentration used in chemistry and spectroscopy YS Yield stress – tensile test property
- xvi - Table of content
Table of content
Foreword...... i Samenvatting ...... iv Summary...... ix Acronyms, abbreviations and jargon...... xiv Table of content...... xvii
Chapter 1 Introduction...... 1 1.1. Nuclear power plant lifetime ...... 3 1.2. Surveillance of the reactors ...... 17 1.3. Microstructural changes...... 25 1.3.1. Defects...... 25 1.3.2. Influence of RPV steel parameters ...... 28 1.3.3. Influence of parameters on future generation reactor steels...... 39 1.4. Mechanistic correlations...... 41 1.5. Conclusions ...... 60
Chapter 2 Materials and irradiation conditions ...... 61 2.1. Materials ...... 63 2.2. Irradiation ...... 75 2.3. Conclusions ...... 82
Chapter 3 Techniques ...... 83 3.1. Introduction ...... 85 3.2. Positron annihilation spectroscopy...... 87 3.2.1. Theory of the positron annihilation ...... 87 3.2.2. Positron annihilation lifetime spectroscopy ...... 92 3.2.3. Coincidence Doppler broadening ...... 97 3.3. Atom probe tomography...... 103 3.4. Transmission electron microscopy...... 110 3.5. Small angle neutron scattering ...... 113 3.6. Tensile tests...... 117 3.7. Conclusions ...... 118
Chapter 4 Positron annihilation spectroscopy results...... 119 4.1. Positron affinitive sites in steels ...... 121 4.2. Positron lifetime results...... 123 4.2.1. Pure iron and the binary Fe-C alloy ...... 123 4.2.2. Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper...... 126 4.2.3. Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy ...... 127 4.2.4. Low-Cu RPV steel...... 129 4.3. CDB results...... 131 4.3.1. Pure iron and the binary Fe-C alloy ...... 131 4.3.2. Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper...... 133 4.3.3. Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy ...... 135
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4.3.4. Low-Cu RPV steel...... 138 4.4. Discussion...... 140 4.4.1. Binding energies of the investigated elements with Vs and SIAs...... 140 4.4.2. Hardening of the alloys ...... 143 4.4.3. Discussion of the PAS results...... 144 4.4.4. Influence of the defects observed by PAS on the hardening of steels...... 151 4.5. Flux effect...... 155 4.6. Fe-Cr alloys...... 158 4.7. Conclusions ...... 164
Chapter 5 Quantification of the results...... 165 5.1. Quantitative results...... 167 5.1.1. First attempt...... 168 5.1.2. Second attempt...... 175 5.2. Combination with other techniques...... 184 5.2.1. Limitations of the different techniques...... 184 5.2.2. Results ...... 188 5.3. Flux effect...... 194 5.4. Fe-Cr alloys...... 197 5.5. Conclusions ...... 200
Chapter 6 Influence of microstructural defects on the hardening ...... 201 6.1. Hardening results...... 203 6.1.1. Hardening trends with dose of the different model alloys...... 203 6.1.2. Hardening trend of commercial RPV steels ...... 210 6.2. Comparison with industrial trend curves...... 213 6.3. Influence of the defects on the hardening...... 216 6.3.1. Superposition of the effect of defect populations on yield strength increase.217 6.3.2. Primary calculations using the Orowan equation...... 221 6.3.3. Primary calculations using the best fit method...... 223 6.3.4. Hardening calculations using the newly developed analysis model...... 227 6.4. Conclusions ...... 230
Chapter 7 General conclusions and outlook...... 231 7.1. General conclusions...... 233 7.2. Future work...... 237
Appendix A History of the positron ...... 241 Appendix B The technical details on the positron lifetime setup...... 245 Appendix C The technical details on the coincidence Doppler broadening setup ...... 253 Appendix D The preparation of an adequate APT tip...... 257 Appendix E Post-irradiation annealing of an Fe-Cu alloy ...... 261 Appendix F Quantitative calculations of the PAS results ...... 275
References ...... 289
Author Biography...... 299 List of publications ...... 300
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Chapter 1 Introduction
“A single conversation across the table with a wise person is worth a month's study of books” Chinese Proverb
For the safe operation of the nuclear power plants (NPPs), it is mandatory to ensure the mechanical integrity of the reactor pressure vessels (RPV). This irreplaceable component is made of low alloy steels that are prone to embrittlement due to neutron irradiation. Neutrons, when colliding with the material, produce microstructural defects, such as vacancies, self- interstitials and both vacancy and self-interstitial clusters. The abundance of these defects is the origin of irradiation-induced precipitation and segregation. The study of defect formation under neutron irradiation and their thermal stability is therefore of paramount importance for the understanding of radiation damage of structural materials. Moreover, to extend the lifetime of the NPPs, there is an urgent need for predictive models based simultaneously on experiments and numerical computer simulation.
In the first section of this chapter, a brief overview is given on the history of NPPs, as well as an introduction to the most probable future installations. For the current state of nuclear energy, some examples of the Belgian reactors are given. The current surveillance procedures are introduced in the second section. As the hardening and embrittlement of RPV steels is of paramount importance for the maintenance of the reactors, these features are also introduced in this section. The third section focuses on the microstructural changes occurring inside the RPV material during neutron irradiation, to obtain an insight on the current know-how on this subject. First, the formation of the different types of defects is surveyed. However, the defect behaviour is known to depend strongly on the material composition. The second part of this section is therefore focused on the influence of the different alloying elements on the defects. Within the surveillance procedures, mechanical properties are compared to mechanistic correlations, such as those given in the fourth section of this chapter. The chapter ends by drawing the main conclusion from the former sections.
p. 1 Chapter 1
Table of content Chapter 1 Introduction...... 1 1.1. Nuclear power plant lifetime...... 3 Neutron ...... 3 Brief history...... 3 Different generations ...... 5 Generation I...... 6 Generation II ...... 6 Generation III...... 8 Generation IV...... 8 Fusion...... 11 Reactors in the world ...... 12 Reactor lifetime...... 15
1.2. Surveillance of the reactors ...... 17 Degradation of the reactor wall...... 17 Hardening and embrittlement ...... 18 Local surveillance...... 20 Surveillance specimens versus the actual steel ...... 23 Progresses ...... 24
1.3. Microstructural changes ...... 25 1.3.1. Defects ...... 25 Defect production...... 25 Influence of defects on embrittlement...... 26 1.3.2. Influence of RPV steel parameters...... 28 Chemical composition...... 29 Carbon...... 30 Copper...... 32 Nickel ...... 34 Manganese...... 34 Phosphorus ...... 35 Nitrogen...... 36 Silicon ...... 36 Tin ...... 36 Microstructure...... 36 Irradiation conditions ...... 37 Temperature ...... 37 Fluence ...... 37 Flux ...... 38 1.3.3. Influence of parameters on future generation reactor steels...... 39 Chemical composition...... 39 Chromium...... 40 Irradiation conditions ...... 40
1.4. Mechanistic correlations...... 41 First investigations...... 41 First mechanistic models...... 43 Influence of the flux...... 46 Recent updates ...... 51 Frequently used correlations...... 53 US NRC Regulatory Guide 1.99 Rev. 2 (May 1988)...... 53 US NRC NUREG/CR-6551 (November 1998)...... 54 ASTM E900-02 (2005) ...... 56 US NRC NUREG-1874 (2007)...... 56 USNRC Regulatory Guide 1.99 Rev. 3 (2007) ...... 57 FIS formula ...... 59
1.5. Conclusions ...... 60
p. 2 Introduction
1.1. Nuclear power plant lifetime
Neutron{ TC "Neutron" \f C \l "3" }
In 1935, James Chadwick (Figure 1) received the Nobel Prize in Physics for his discovery of the neutron in 1932. A neutron is a subatomic particle with no electric charge and a mass (1.6749 × 10-27 kg) slightly larger than the one of a proton (1.6726 × 10-27 kg). This particle, present in the atomic nuclei, can be released during atomic fission, as it occurs in nuclear power plants.
Figure 1 The discoverer of the neutron, James Chadwick [1].
Brief history{ TC "Brief history" \f C \l "3" }
Immediately after its discovery, a lot of investigations were performed using this "new" particle. During such experiments in 1934, Enrico Fermi et al. [2] achieved the first atomic fission by bombarding uranium with neutrons, but their results were only correctly interpreted a few years later. Otto Hahn and Fritz Strassmann further worked out this research and published, in January 1939, the first undeniable proof that uranium when bombarded with neutrons splits into a few isotopes of lighter elements [3]. Lise Meitner and Otto Robert Frisch correctly interpreted these results as being nuclear fission. Numerous scientists recognized in a conference, end January 1939, that if fission reactions release additional neutrons, a self-sustaining nuclear chain reaction could occur. This was the start of an era with numerous technological achievements in this subject.
p. 3 Chapter 1
Figure 2 Five important people in nuclear fission research: (from left to right) Enrico Fermi [1], Fritz Strassman, Lise Meitner and Otto Hahn (Meinz, 1956) [4] and Otto Robert Frisch [5].
This research led, with the aid of Enrico Fermi, to the creation of the first reactor, "Chicago Pile-1" (Chicago, United States), which achieved criticality in December 1942. In December 1951, in the experimental reactor, "EBR-I" (Idaho, United States), electricity was for the first time obtained by nuclear energy, i.e. about 100 kW was produced. And, the first commercial nuclear power plant was taken into service in June 1954 in Obninsk (USSR), which produced around 5 MW electric power.
Chicago Pile-1 EBR-I Obninsk power plant
Figure 3 The three most important installations at early nuclear energy production: (from left to right) Chicago Pile-1 [6], EBR-I [7] and the Obninsk nuclear power plant [8].
Belgium was very present in the area of nuclear energy, as the Belgian Congo possessed uranium mines. In 1952, a group of scientists founded the Belgian nuclear research centre. Already in May 1956, the first Belgian reactor BR1 (Figure 4) went critical, with a power of 4 MW. The reactor used graphite as moderator, natural uranium as nuclear fuel and air as coolant. The moderator thermalizes the neutron flux to allow the interaction with the nuclear fuel and to maintain, in this way, the chain reaction. The coolant, on the other hand, removes
p. 4 Introduction the heat generated by nuclear chain reactions, from nuclear fuel and provides the energy for the electric power generation.
Figure 4 The first Belgian reactor BR1, built in 1956 [9].
Different generations{ TC "Different generations" \f C \l "3" }
The present nuclear power plants have however another design. Nowadays, graphite is generally not used anymore as moderator, and in most cases a liquid coolant is chosen. The progress of the nuclear power design in time is expressed in generations, as illustrated in Figure 5. The first reactors, such as BR1, are called generation I type of reactors; most of the current active reactors are part of generation II; and the reactors that are presently being built or that are planned to be built in the near future consist mainly of generation III reactors. Nowadays however, new research focuses on even a next generation of reactors.
Figure 5 The survey of the different generations of nuclear reactors. As example of generation I, BR1 is given. A picture of the Doel domain is illustrating generation II. And the artist impression of the under-construction reactor, the European pressurized water reactor (EPR) in Finland, exemplifies the third generation.
p. 5 Chapter 1
Generation I{ TC "Generation I" \f C \l "4" }
The first generation of reactors were in general prototype reactors, which have been built in the fifties and sixties (until ca. 1965). A typical example of such a reactor is BR1, with a graphite moderator and an air coolant. No other reactors of this type have been built in Belgium.
Generation II{ TC "Generation II" \f C \l "4" }
By far, most of the existing commercial nuclear reactors are from the second generation. These reactors have been built in the seventies, eighties and nineties (in-between 1965 and 1995). As the world was in the grip of the Cold War during this time, nuclear programs were kept a national secret and many countries developed their own reactor types.
The United States built the light water reactors (LWRs), pressurized water reactor (PWR) and boiling water reactor (BWR). These were adopted by many other Western countries. The use of ordinary water makes it necessary to enrich the uranium fuel (to approximately 3 %), in order to maintain the criticality of the reactor. Figure 6 illustrates schematically the two types of LWRs. PWRs use ordinary water under high pressure as coolant and moderator. The primary coolant loop is kept under high pressure (around 150 bar) to prevent the water from boiling, at the operation temperature of about 300 °C. PWRs are the most common type of power producing nuclear reactors. About 60 % of the commonly used reactors is of this type. Also all 7 commercial reactors active in Belgium are PWRs. As the pressure is kept to ca 75 bar (and therefore too low to keep the water liquid at the operation temperature of about 300 °C), the BWRs are characterized by two-phase fluid flow (water and steam) in the upper part of the reactor core. The advantage of the lower pressure needed to operate this type of reactor results however in less moderation, lower neutron efficiency and thus lower power density. But, in contrast to the PWRs that utilize two separate loops, in BWRs the steam going to the turbine that powers the electrical generator is produced directly in the reactor core. Also this type of reactor is widely used in nuclear power plants (about 20 % of the used reactors).
p. 6 Introduction
Figure 6 The schematic diagram of the PWR (upper) and the BWR (lower) [7].
The former Soviet Union built reactors of the types water-water energetic reactor (VVER) and high power channel type reactors (RMBK). The VVERs are in fact a local type of PWRs, which are still used today by China, Finland and the present-day Russian Federation. The RBMKs are the bigger versions of the first commercial nuclear power reactor in Obninsk. Using light water for cooling and graphite for moderation, it is possible to use natural uranium in metallic form. In these reactors, power can thus be obtained without the need for expensive procedures. However, the reactor involved in the Chernobyl accident was also of this type. In 2008, at least 12 RBMKs are still operating in Russia and Lithuania, but there are no plans to build any new ones and there is even international pressure to close those that remain.
Canada developed deuterium uranium (CANDU) reactors, pressurized heavy water reactors, running on natural uranium. In heavy water, the deuterium isotope of hydrogen replaces the common hydrogen atoms in the water molecules (D2O instead of H2O, with a molecular weight of 20 instead of 18). All current power reactors in Canada (17 in use + 3
p. 7 Chapter 1 which are being refurbished) are of the CANDU type and 11 more are spread through the world.
Finally, Great Britain developed the advanced gas-cooled reactors (AGR), using graphite as neutron moderator and carbon dioxide as coolant. They operate at a higher gas temperature (reaching 640 °C at pressure of about 40 bar) for improved thermal efficiency. Currently, there are seven nuclear generating stations, each with two operating AGRs, in the United Kingdom.
Generation III{ TC "Generation III" \f C \l "4" }
Generation III reactors used the same design as was used in the second generation (especially the PWRs and BWRs were used as model), but they involved several innovations with respect to the previous generations. Therefore, the reactors from this generation are designed to have lower costs per kWh, simpler licensing, a higher reliability and a further enhancement of the safety. The first generation III reactors were built in Japan. Nevertheless, it is expected that this era will end in 2010 to make place for the Generation III+ reactors, which will make use to a certain extent of passive safety systems (no operation action or electronic feedback is required in order to shut down safely in the event of a particular type of emergency). Several reactors of this type are approved for construction in Europe, i.e. in Finland and France.
Generation IV{ TC "Generation IV" \f C \l "4" }
The future reactors, the so-called generation IV reactors, are a set of conceptional nuclear reactor designs currently being investigated. In the post-Cold War era, international efforts could be united for this purpose. Most of these designs are generally not expected to be available for commercial construction before 2030. Research into these reactor types is based on different technology goals. Substantial improvements are envisaged compared to the previous generations, concerning the nuclear safety, the proliferation resistance, the minimization of waste and natural resource utilization and the economics. In addition, these nuclear reactors can be used to transmute the produced nuclear waste, i.e. the waste will be converted into elements with much shorter half-life. It is however not possible to combine all these properties into one reactor type. A combination of
p. 8 Introduction reactor types is expected to produce a safe nuclear energy mix, with a maximal exploitation of the resources.
Within generation IV, six reactor types were selected for further investigation, which offer significant technological advances. Figure 7 gives the schematic overview of the six selected reactors. Three systems are nominally thermal reactors and three fast reactors. In the thermal reactors, almost all neutrons in the reactor core have a low energy, while in the fast reactors, the neutron energy is much higher. Fast reactors offer therefore the possibility of burning actinides to further reduce the long-life waste and of being able to breed more fuel. Nevertheless, these reactors need still more research in the field of safety and reactor materials.
The very high temperature reactor (VHTR) is a thermal reactor that uses a graphite moderator. This reactor design envisions an outlet temperature of about 1 000 °C. High operation temperatures increase the thermal efficiency, as known since the times of Carnot.
The maximum efficiency possible by any sort of engine has a limit defined by η =1 − TC TH , where TC and TH are the absolute temperature of the cold and hot reservoir, respectively.
Since TC is fixed by the environment, the only way for a designer to increase the theoretical efficiency is to increase TH . The high temperatures also enable additional applications such as hydrogen production. This design would be passively safe. The supercritical water reactor (SCWR) is also a thermal reactor, but it uses supercritical water (water at a temperature and pressure above its critical point, containing both properties of the liquid and the gas) as the moderating and cooling fluid. SCWRs are based on the light water reactors (PWR and BWR), but operating at higher temperatures and pressure. They are promising advanced nuclear systems due to their high thermal efficiency (i.e. about 45 % in comparison with the 33 % of the current LWRs) and considerable plant simplification. The last thermal reactor under consideration is the molten salt reactor (MSR). In many designs, the nuclear fuel is dissolved in the molten fluoride salt coolant, as uranium tetrafluoride (UF4). The fluid becomes critical in a graphite core, which serves as moderator. Other concepts rely on fuel that is dispersed in the graphite matrix. The salts are much more efficient at removing heat from the core, reducing the need for pumping, piping and reducing
p. 9 Chapter 1 the size of the core. On top of this, the low operation pressure makes the entire reactor core much simpler and lighter, while the high temperatures provide an efficient energy extraction.
Thermal reactors Fast reactors
Figure 7 The schematic diagram of the different types investigated for generation IV reactors [10].
The gas-cooled fast reactor (GFR) is a helium-cooled reactor, with closed fuel cycle and an outlet temperature of 850 °C and therefore it can obtain a high thermal efficiency. Helium is an inert gas, so it will rarely react with any material, except through its stored heat. Additionally, exposing helium to radiation does not make it radioactive, unlike most other possible coolants. The reactors are intended to produce electricity, while, at the same time, they are able to breed new nuclear fuel, via transmutation of fertile nuclides to fissile ones
p. 10 Introduction
(e.g. U238 to Pu239). Indeed, in the GFR design like in all other fast reactors, the unit operates on fast neutrons and thus no moderator is needed. A priori, also other nuclear fuels can be used (e.g. thorium which forms fissile uranium-233 when it absorbs epithermal or thermal neutrons) or minor actinides can be burned. The sodium-cooled fast reactor (SFR) is a fast neutron reactor, with a closed fuel cycle for efficient management of the actinides. In addition to the benefits of the augmented operation temperature and reduced half-life of the transuranics from the waste cycle, the SFR fuel expands when the reactor overheats and the chain reaction automatically slows down (as also happens in the generation II reactors). In this manner, it is passively safe. The main advantage of the SFRs above the other generation IV reactors is the fact that its technology is already present. Finally, the lead cooled fast reactor (LFR) features a fast neutron spectrum, molten lead or lead-bismuth eutectic coolant and a closed fuel cycle. It is cooled by natural convection with a reactor outlet coolant temperature of 550 °C, possibly ranging up to 800 °C with advanced materials. The LFR battery (one of the possible LFRs) is a small factory-built turnkey plant operating on a closed fuel cycle with very long refuelling intervals (15 to 20 years). This is however in the case the bred fuel is not withdrawn for use in other reactor types.
Fusion{ TC "Fusion" \f C \l "4" }
The aim of international research in fusion is the realization of prototypes of a fusion power station, fulfilling the expectations of the society, i.e. the security, the reliability, the availability of fuel, the relief of the environment and the economic profitability. The major problem in this research has always been the confinement and the self-sustainment of the reaction. Magnetic confinement is the mainstream road currently followed, but its implementation is a huge challenge.
In 1979, the construction of the Joint European Torus (JET) started in Oxfordshire (Great Britain) and, in 1983, it became operative. JET was the first tokamak in the world, which used real fusion fuel, i.e. deuterium and tritium. Currently, it is still the world's largest Tokamak. This unit was able to produce about 16 MW of power in 1997, but it still needed 25 MW. Nowadays, the JET facilities include plasma heating systems capable of delivering up to 30 MW of power, an active gas handling system and a beryllium handling facility.
p. 11 Chapter 1
Since 2006, the fusion community works on a large scale international fusion experiment, the international thermonuclear experimental reactor (ITER). Figure 8 shows a schematic overview of this reactor. It is a project including laboratories from Europe, Russia, the United States, China, India and South Korea. ITER is expected to become critical in 2018 and it should show the world that fusion is possible on Earth. ITER will generate 500 MW of fusion power (10 times more than the energy input needed to keep the plasma at the right temperature) in Cadarache (France).
Figure 8 The schematic overview of ITER [9].
Reactors in the world{ TC "Reactors in the world" \f C \l "3" }
An overview on the present state of the nuclear reactor application in OECD countries can be found on the website of the nuclear energy agency (NEA) (
p. 12 Introduction
Table 1 The nuclear electricity generation in TWh, the number of reactors and the percentage of the total electricity supply of all 30 NEA members. Number of nuclear Nuclear electricity Nuclear percentage Country units connected Generation of total electricity to the grid (end 2007) supply (net TWh) (%) Australia ------Austria ------Belgium 7 45.9 54.1 Canada 20 88.6 14.7 Czech Republic 6 26.2 32.2 Denmark ------Finland 4 22.5 29 France 59 418.6 76.8 Germany 17 133.2 23.2 Greece ------Hungary 4 13.8 37.2 Iceland ------Ireland ------Italy ------Japan 55 251.6 25.6 Korea 20 136.3 35.2 Luxembourg ------Mexico 2 10.4 4.4 Netherlands 1 4 4 New Zealand ------Norway ------Poland ------Portugal ------Slovak Republic 5 14.1 54.9 Spain 8 53.4 17.8 Sweden 10 64.3 47.4 Switzerland 5 26.3 39.9 Turkey ------United Kingdom 19 57.3 15.7 United States 104 806 19.4 346 TOTAL 2 172.5 21.6 (439 worldwide)
Figure 9 shows the amount of electricity supplied in the different European countries in 1999, separated between nuclear energy and others. It can be observed that, with the exception of Italy, in countries where more than about 60 TWh electricity is needed, a substantial part of the electricity is produced by nuclear power plants [12]. Moreover, France (by far the country with most nuclear energy production) is the only country that could deliver a high level of net exports of electricity [12].
p. 13 Chapter 1
Figure 9 The electricity supplied in European countries, showing the nuclear capacity [12].
As mentioned before, most of the current active reactors are of the light water type. This is also illustrated in Figure 10 [12]. About 60 % of the reactors consist of PWRs together with VVERs, and another 20 % are BWRs.
Figure 10 Number of different operating reactor types in the world on 31/12/2001 [12]. The gas cooled reactors (GCR) are generation I reactors and also some early generation IV reactors (fast breeder reactors (FBR)) are included.
All 7 commercial reactors in Belgium are PWRs, with a total electric power of 5 789 MW, i.e. about 55 % of the total electricity supply. These reactors are installed in two nuclear sites, i.e. Doel and Tihange (Figure 11). Table 2 lists the respective power of each reactor, as well as the year they became critical.
Table 2 The 7 Belgian reactors are given with their net capacity, the year they became operative and their designer. Doel 1 393 MWe 08/'74 Westinghouse Tihange 1 962 MWe 03/'75 Westinghouse Doel 2 420 MWe 08/'75 Westinghouse Tihange 2 1 008 MWe 10/'82 Framatome Doel 3 1 006 MWe 06/'82 Framatome Tihange 3 1 015 MWe 06/'85 Westinghouse Doel 4 985 MWe 04/'85 Westinghouse PWR 2 804 MWe PWR 2 985 MWe
p. 14 Introduction
Doel Tihange
Figure 11 The nuclear power sites of Doel [7] (left) and Tihange [13] (right) are shown respectively.
Reactor lifetime{ TC "Reactor lifetime" \f C \l "3" }
The plant operational life is not usually a predefined period. The initial aim is to operate for a period (plus a margin of sometimes 5 years) that allows the full recovery of capital costs and charges (the amortisation period). There are variations on the licensing processes. In the US, the initial license period is 40 years, which coincides with the design life period, but also arose from the "antitrust" laws. The initial considerations for this period were thus based on economic and "antitrust" factors, rather than safety, technical or environmental standards. Other countries (such as Belgium) need relicensing after 10 years, with a postulated end at about 40 years of operation. The reactors thus have been designed to have a life of about 40 years, as well. However, the first reactors (Doel 1 and 2 and Tihange 1) had a design life of 30 years, leading to renewal of certain components of the reactor, when they reached this age. The postulated end date is thus approaching for the reactors constructed in Belgium around 1975. Not only Belgian reactors are approaching this age. In Figure 12, it can be observed that an important portion of the nuclear reactors over the world are over 30 years old [14]. Nevertheless, political voices are raised for the prolongation of the reactor operation time. Therefore, it has to be demonstrated that the plant can operate safely for more years of operation, focussing on matters to do with the effect of ageing on systems, structures and components for the period of extension. Recently (2001), it has been reported that 8 units (e.g. Calvert Cliffs and Oconee nuclear power plants (USA)) had received licence renewal (up to 60 years of operation), 14 plants had registered licence renewal applications and 25 units have announced plans of
p. 15 Chapter 1 intent [12]. Moreover, it is predicted that 100 plants or more will eventually seek licence renewal over the next 10 to 20 years.
Figure 12 The age of the world's nuclear reactor fleet in 2005 [14].
Figure 12 also indicates that still new reactors are installed, up to about 5 reactors per year after the peak number of starts in the mid 1980s. This has been done to satisfy the increasing demand rather than for the replacement of old reactors.
p. 16 Introduction
1.2. Surveillance of the reactors As in the early years of the nuclear industry, the behaviour of materials under irradiation was not fully understood, a surveillance program was proposed to monitor the changes in the materials.
Degradation of the reactor wall{ TC "Degradation of the reactor wall" \f C \l "3" }
The degradation mechanisms for the metallic reactor pressure vessel (RPV) components are mostly common to all industrial plants. They include general and local corrosion, erosion- corrosion, fatigue, corrosion fatigue, creep and wear. In addition, NPPs are also susceptible to material changes due to irradiation and temperature. The non-irradiation induced degradation mechanisms are well studied in all types of industries, but the irradiation related mechanisms are specific and therefore rather new and not yet fully understood. During operation, the integrity depends on the initial quality of the vessel as designed and fabricated, but also on the degradation of mechanical properties with irradiation. The integrity of the design assumes the use of carefully specified and tested best quality materials. A comprehensive quality assurance programme is needed, as well as extensive and efficient inspection during fabrication. In addition, a hydrostatic pressure test is performed in order to verify the behaviour of the material in the reactor environment. During operation, the degradation of all the NPP materials has to be monitored and assessed. The operation history is recorded to ensure that the design's operational intent is met.
The observed material degradation in operation has highlighted the need to develop a methodology to allow an improvement in the understanding and management of degradation and ageing in a timely and planned way. This allows that safety and operational margins can be maintained while the plant's economic viability is protected. The safety of NPPs is usually periodically reviewed in order to confirm that the plant is not less safe than originally intended. In addition, it is possible to evaluate the current condition of structures, systems and components, with regard to ageing degradation and with the expected future requirements.
The first step for safety or reliability is to identify those key components whose failure would have a major impact on safety or plant operational life. Then, the components are
p. 17 Chapter 1 classified into four categories. Category 1 components are those which are generally considered to be irreplaceable. Examples of such components include the reactor pressure vessel and also the containment structure. It can be argued that even these structures could be replaced, but at a great cost. The probability of their failure is however very low. Category 2 components are those which are replaceable, but are costly in terms of capital expenditure and outage time requirements. Examples of this type of components are the steam generators, which have been replaced in many plants. Category 3 components are those, which are 'key' in terms of plant safety and reliability and are susceptible to ageing, but which are replaceable on a routine basis. Finally, category 4 components are all other components. They are not related to 'life' considerations. In this work, focus is put on the category 1 components. More specific, the work focuses on the RPV steel, as this structural component is obviously the most demanding one, being irreplaceable and subjected to non-negligible irradiation doses.
Hardening and embrittlement{ TC "Hardening and embrittlement" \f C \l "3" }
The reactor pressure vessel contains the reactor core and represents one of the main barriers separating the core from the outside. As this steel component cannot be replaced without the full decommissioning of the reactor, it needs special care to ensure its integrity and to prevent early close down of the reactor. Figure 13 gives a pictorial representation of the vessel.
Figure 13 A pictorial representation of a generation II light water reactor pressure vessel.
In order to guarantee their integrity and safety, NPPs have been the subject of extensive investigations for many years, with special attention to the reactor pressure vessels [15]. A vessel surveillance program has been foreseen for most NPPs. The surveillance procedure is meant to estimate material properties for the irradiated pressure vessels, based on Charpy-V p. 18 Introduction tests. The licenses are granted, based on the results of these impact tests. Capsules are usually installed at the inner shell of the reactor at the beginning of its life cycle and are extracted to perform tests according to a predefined schedule. Also using material test reactors, such as BR2 (Belgian Reactor 2) in Mol (Belgium), the influence of the neutron irradiation on these steels after 10, 20 and even 40 years has been studied. As a result of these investigations, it has been observed that the mechanical properties of the material used for the reactor vessels can substantially alter. The material is prone to harden due to the neutron irradiation. Hardening is revealed by an increase in both the yield strength and the ultimate tensile strength in tensile testing (see Figure 14). Hardening by itself may seem a positive change for material under tension. Nevertheless, the irradiation- induced hardening causes problems, due to the embrittlement that goes along. Embrittlement can be expressed as the shift of the ductile-to-brittle transition temperature (DBTT) (see also Figure 14). This transition temperature should be well below the operation temperature to avoid brittle fracture during operation. The irradiation-induced hardening and embrittlement of RPV steels, therefore, represent the main criterion to be used for NPP life assessment.
Figure 14 (left) the increase of hardening is shown with irradiation dose, as the increase of both the yield strength and the ultimate tensile strength in stress-strain curves, obtained by tensile tests. (right) The shift in DBTT illustrates the increase of embrittlement during irradiation.
When the oldest NPPs were constructed, it was already known that ferritic steels undergo a marked transition from ductile to brittle fracture behaviour and that this transition temperature may be affected by neutron irradiation. But the effect of irradiation variables and materials properties on this embrittlement was not understood. Therefore, surveillance procedures were set in place.
p. 19 Chapter 1
Local surveillance{ TC "Local surveillance" \f C \l "3" }
The ageing and degradation mechanisms are often plant specific, and therefore monitoring these mechanisms is very important in plant life management. This monitoring can be performed by continuous (or on-line) monitoring, in-service inspection or intermittent testing of specimens made from plant materials that can be installed inside components. Generally, monitoring of changes in material characteristics is based on destructive techniques. Therefore, the material of the reactor wall cannot be tested in a direct way. However, tests may be performed on specimens made from plant materials that are installed inside the wall. On the other hand, some techniques have been developed to measure non- destructively a parameter, which may be related to material characteristics. It remains however difficult to assess the relationship between the various parameters. In practice, the continuous non-destructive in-service inspection is verified by and supplemented with intermittent testing of material positioned at the inside of the reactor wall.
The material included in the surveillance program is representative of the beltline region of the reactor vessel, concerning its chemical composition as well as the undergone heat treatments. Figure 15 shows the beltline, specified as the zone directly surrounding the effective height of the fuel element assemblies.
Figure 15 Schematic view of the reactor internals.
p. 20 Introduction
Specimens fabricated from the representative material of the vessel and its welds are placed in capsules located between the core and the pressure vessel wall in the beltline region. The specimen irradiation history thereby duplicates the neutron spectrum, temperature history, and maximum neutron fluence experienced by the reactor vessel inner surface. The capsules, in which the surveillance specimens are positioned (Figure 16), are manufactured from thin austenitic stainless steel plate material to protect the specimens from oxidation at the temperature of the reactor coolant system. After insertion of the specimens and also dosimetry and temperature monitors, the capsules (25 × 25 × ~ 1 000 mm3) are welded two by two together. After welding, the capsules are hydrostatically pressurized in demineralised water to collapse the capsules on the specimens, so that optimum thermal conductivity between the specimens and the reactor coolant is obtained. By this way, it is ensured that the temperature history of the specimens duplicates, as closely as possible, the temperature experienced by the reactor vessel.
Figure 16 Surveillance capsules of a generation II reactor [16].
p. 21 Chapter 1
It is obviously seen in Figure 16, that there is only a limited amount of space for surveillance capsules. Therefore, the strictly minimum amount of material, necessary to evaluate the evolution of the base metal, the weld and the heat affected zone, is included.
The capsules are positioned in the reactor at the midplane of the core and at angular positions with respect to peak flux. As the specimens are located nearer to the core than the vessel wall, they experience accelerated exposure and the mechanical properties are representative of the vessel at a later time of life. Figure 17 shows a typical withdrawal schedule of the surveillance capsules in the Belgian NPPs. First the capsules irradiated at the highest flux are withdrawn, and once the capsules at highest flux are exhausted, the other capsules are chosen. It can be clearly observed that the predicted material properties correspond to an irradiation for longer times than the reactor vessel surface.
Figure 17 A typical surveillance capsule withdrawal schedule in the Belgian NPPs [16].
The ratio of the neutron flux at the specimen location to the maximum calculated neutron flux at the inside surface in the reactor vessel wall is called the "lead factor". This factor is usually within a range of 1 to 3.
Table 3 The lead factors of the Belgian units. Lead factors Reactor (according to capsule azimuthal position) Doel 1 and 2 1.5 to 2.9 Tihange 1 0.5 to 1.57 Doel 3 - Tihange 2 2.72 and 3.23 Doel 4 - Tihange 3 2.06 and 2.30
p. 22 Introduction
Table 3 gives examples of this factor for the Belgian reactors. For Tihange 1, some capsules are not in the peak flux area and the lead factor is here less than 1. These capsules have thus to be repositioned during the life of the reactor. { TC "Surveillance specimens versus the actual steel" \f C \l "3" }
Surveillance specimens versus the actual steel
The main difficulty in predicting the behaviour of the reactors generally comes from the fact that surveillance specimens are not exactly in the same environment and conditions as the part of the component to be monitored. Therefore, some kind of extrapolation must be operated, based on the physical understanding of the acting mechanisms.
Three main differences between the surveillance conditions and the conditions of the actual steel can be encountered.
¾ It was mentioned before that the lead factor of the surveillance specimens should be higher than 1, to predict the behaviour of the reactor pressure vessel, when they would reach the same fluence. Nevertheless, this difference in flux could lead to small fluctuations in the behaviour. As the lead factor is expressed as the ratio of the flux of the surveillance specimens to the highest possible flux of the reactor wall, higher differences are expected for the material irradiated to considerable lower fluxes, i.e. further away from the reactor core.
¾ The surveillance specimens have a maximal thickness of about 25 mm, while the thickness of the wall itself is ca. 300 mm. It is expected that changes occur in the neutron spectra, irradiation temperatures, and so on, throughout the wall thickness. This can however not be mimicked using the surveillance specimens.
¾ Casting big plates necessary for the construction of the reactor will lead to inhomogeneities in the chemical composition of the steel, as well as in its initial microstructure. Theses inhomogeneities cannot be reproduced by the capsules, either.
p. 23 Chapter 1
Progresses{ TC "Progresses" \f C \l "3" }
It is clear that still many mechanisms are not fully understood, concerning the behaviour of the reactor wall. Nevertheless, the experience obtained during the past operation of NPPs led to more safety at current times. This can be clearly observed by a decrease of the incident rate in the past years, as illustrated in Figure 18 [17].
Figure 18 (left) The safety accident rate (number of lost work hours per 200 000 man-hours worked, resulting from accidents) as a function of the time [17]. (right) The collective radiation exposure (the total amount of radiation the employees are exposed to) in PWRs as a function of time [17].
p. 24 Introduction
1.3. Microstructural changes The still available surveillance capsules are drastically decreasing in number, as many NPPs are reaching their postulated lifetime. To safely extend the operational lifetime of the RPV, empirical correlations may not be fully reliable. Predictive models enabling extrapolations to different conditions (flux and fluence) are thus needed based simultaneously on experiments and numerical computer simulation. These models must rely on a detailed knowledge of the microstructural changes induced by neutron irradiation and their thermal stability. The application of experimental techniques for the microstructural characterization of neutron-irradiated ferritic model alloys of increasing complexity and steels has indeed contributed to the mechanistic understanding of irradiation embrittlement [18]. These experimental results are also qualified for the calibration of the model parameters.
1.3.1. Defects
Defect production{ TC "Defect production" \f C \l "4" }
Intuitive and physical models show that the neutrons, when colliding with the atoms of a material, lead to the formation of point-defects, such as self-interstitial atoms (SIAs) and vacancies (Vs) via a sequence of atomic displacements that affect a small region only (displacement cascade). Small vacancy and self-interstitial clusters are also known to be produced directly in displacement cascades in metals [19]-[21]. These primary defects then further agglomerate to form larger defects, such as nanovoids and self-interstitial clusters and loops. This is the so-called matrix damage. At the same time, the abundance of the primary produced defects (vacancies and self- interstitials) is the origin of irradiation-induced solute atom diffusion. This leads to the formation of precipitates and complex defect-solute configurations, as well as to grain boundary segregation (an increased concentration of particular elements at extended defects). The formation of complexes and/or alloyed precipitates is observed in [22], such as copper- rich precipitates, which contain significant quantities of manganese and M3P-type precipitates (75 at% of a metallic element + 25 at% phosphorous). Also the presence of defect-solute
p. 25 Chapter 1 configurations is detected [19]. But, which solutes and how and why they stabilize the clusters, is still a debated matter.
Figure 19 shows schematically the production of defects in the reactor pressure vessels (or in any other metallic material). Left, the neutron strike is illustrated, with the creation of new vacancies, self-interstitials and small clusters of vacancies or self-interstitials. Part of them will annihilate or disappear at sinks. The remaining part then agglomerate to form larger SIA and V clusters, as shown in the middle part of the figure, thereby creating cavities and dislocation loops. The remaining free vacancies and self-interstitials will cause solute atom diffusion, thereby producing precipitates, defect-solute complexes and grain boundary segregation, as illustrated on the right side of the figure.
Figure 19 In a schematic overview the production of defects in the grains of the material is given. First (left), the creation of vacancies and self-interstitials due to the neutron strike is illustrated. Then (middle), the agglomeration to obtain clusters and loops of theses defects is shown. Finally (right), some solute atom diffusion will occur, and so precipitates, defect-solute complexes and grain boundary segregation appear. { TC "Influence of defects on embrittlement" \f C \l "4" }
Influence of defects on embrittlement
The irradiation-induced embrittlement in RPV steels is conventionally ascribed to only three main causes [19], [22]-[24], i.e. the formation of precipitates, matrix damage and grain boundary segregation of elements such as P, S, As, Sn and Sb [22], [25]. Whereas the former two also contribute to the hardening, the latter will lead to intergranular failure and non- hardening embrittlement. Since the segregation has only a limited effect, it is not added in most models, which are limited to predict the hardening under irradiation. Thus, available models are similar in
p. 26 Introduction considering two main irradiation-induced microstructural components to be of importance. Both components act as obstacles to the free movement of dislocations, thereby producing an increase of the yield stress and hardness. At these defects, where the dislocations are blocked, an accumulation of dislocations may occur. This leads locally to an increase of the tension in the material, thereby making the material more brittle, visible by the shift in the ductile-to- brittle transition temperature. While it is believed that the hardening due to precipitates saturates after a certain fluence, the effect of matrix damage should continue increasing, leading to a higher contribution at higher fluences. This has been illustrated in Figure 20. The nature of these effects has to be known for the better understanding of the interplay of the hardening and embrittlement phenomena.
Figure 20 A schematic illustration of the hardening increase caused by the presence of precipitates and matrix damage as function of the square root (sqrt) of the neutron fluence. While the effect of precipitates tends to saturate, that of the matrix damage continuously increases.
It is known that more than 70 % of the embrittlement is due to the hardening. The main contributions to the hardening are the precipitates, the defect-solute configurations and the matrix damage. This is illustrated in Figure 21, where the yield stress and the critical stress (for cleavage) are given as functions of temperature. The temperature, at which these two stresses cross, corresponds to the ductile-to-brittle transition temperature.
Figure 21 The yield stress and the critical stress for cleavage as function of the temperature. Hardening causes an increase of the yield stress, while segregation causes a decrease of the critical stress.
p. 27 Chapter 1
Hardening will manifest itself through an increase of the yield strength over the whole temperature range. And the critical stress is affected by the appearance of segregation; segregation causes a decrease of the critical stress. Both phenomena lead to an increase of the DBTT, but the major part of embrittlement is caused by the hardening phenomena, with simultaneous ductility decrease. The segregation in irradiated RPV steels is responsible for a minor portion of the radiation-induced DBTT shift, not exceeding about 10 to 20 % [26].
Matrix damage is thought to consist of small self-interstitial loops and vacancy clusters (voids). These features arise from the agglomeration of defect clusters formed in the displacement spike. A large fraction of the defects are expected to annihilate or to disappear at sinks. The remaining fraction of the clusters can grow until they reach microsizes. Matrix damage may thus be "sponges" (vacancy-rich regions), microvoids, dislocation loops (vacancy or self-interstitial), or solute-point defect clusters. The irradiation environment and material variables are known to be important, but the details of how these factors influence the processes are not fully understood. It is thus still unclear what the nature and the main mechanisms are, giving rise to the matrix damage. Lumping voids and loops into a single category of hardening features corresponds, however, to a very crude approach, as they interact very differently with dislocations. Today, while the dominant role of precipitates on hardening and embrittlement is well documented [15], [27]-[29], there is no clear perception of whether it is the voids or loops that mainly contribute to the hardening. The latter information may become of importance in connection with NPP lifetime extension, in consideration of the fact that, while the contribution to hardening of copper-rich precipitates saturates with dose, the contribution of matrix damage does not, at least in the range of dose of technological relevance [27].
1.3.2. Influence of RPV steel parameters Globally, DBTT shifts are controlled by the interaction between a large number of environmental variables, such as irradiation temperature, neutron flux and fluence, chemical composition (especially copper, nickel and phosphorous contents), microstructure and heat treatments [19]. The flux is defined as the amount of neutron irradiation that is received by a unit area (given both in m2 and in cm2) per second, while the fluence or the integrated flux is given by the number of neutrons that are received by a unit area.
p. 28 Introduction
Significant variation in embrittlement behaviour has been found between different steels, different heat treatments of the same steel and different irradiation conditions. This suggests the existence of an effect of chemical composition, microstructure and irradiation parameters on the mechanical behaviour of the steel under irradiation. The results of many studies are summarized in this section, but more detailed information can be found in [19], [30], [31].
Chemical composition{ TC "Chemical composition" \f C \l "4" }
The reactor vessels are made of high toughness, quenched and tempered, low-alloyed ferritic steels. Most of the base metals for generation II reactor pressure vessels are low- alloyed ferritic steels, typically 16MND5 steel (in the French AFNOR standard or referred to as A533-B Class 1 in the ASTM norm). Generation III uses the same type of steels. Table 4 lists the ASTM standard of the chemical composition for this steel [32], as well as the composition of the steel, used within this work. Class 1 corresponds to a strength level of 550 to 690 MPa (ultimate tensile strength) and ≥ 345 MPa (yield strength) and in 50 mm it has a total elongation ≥ 18 %.
Table 4(a) The chemical composition (in wt %) of the steel and its corresponding ASTM standard. C N Si P S ASTM A533-B ≤ 0.25 -- 0.15 - 0.40 ≤ 0.035 ≤ 0.035 RPV steel 0.14 0.07 0.195 0.007 0.006
Table 4(b) The chemical composition (in wt %) of the steel and its corresponding ASTM standard (continue). V Cr Mn Ni Cu Mo ASTM A533-B -- -- 1.15 - 1.50 0.40 - 0.70 -- 0.45 - 0.60 RPV steel -- -- 1.30 0.75 0.064 --
Depending on their solubility limit, the alloying elements will remain in solution or may precipitate or segregate to grain boundaries during steel making or heat treatments prior to irradiation. The solubility limit of each element depends, however, slightly on the whole chemistry of the steel. And the precipitation and segregation of each element, on the other hand, depends on manufacturing conditions, such as the tempering temperatures and times.
p. 29 Chapter 1
As a first approximation, Table 5 summarizes the solubility limits for some important elements in pure iron, for temperatures of about 300 °C (the reactor operation temperature) and 600 °C (a frequently used tempering temperature).
Table 5 The solubility limits (in wt %) of some chemical elements in α-iron at 300 °C and 600 °C, respectively. Temperature C N Si P Mn Ni Cu 300 °C 0.001 [33] 0.015 [33] 10 [33] 0.04 [34] 5 [35] 4.2 [34] 0.003 [19] 600 °C 0.011 [33] 0.1 [33] 12 [33] 0.48 [34] 3 [33] 5.4 [34] 0.17 [30]
Carbon{ TC "Carbon" \f C \l "5" }
Carbon is the basic component of steels. It is known from experiments that the interaction of interstitial carbon atoms with lattice defects affects the mechanical properties of ferritic steels [36]. But, the understanding of this process in irradiated material is still poor, even in the binary Fe-C alloy.
It is known that pure iron can exist in two crystal structures, i.e. body-centered cubic (bcc) and face-centered cubic (fcc). The bcc system has one lattice point at the centre of the unit cell in addition to the eight corner points. The fcc system, on the other hand, has lattice points on the faces of the cube, in addition to the corner lattice points.
bcc fcc
Figure 22 The two crystal structures of iron, bcc (left) and fcc (right) [7].
The possible phases present in the binary Fe-C system are given in the iron-carbon phase diagram given in Figure 23.
p. 30 Introduction
Figure 23 The iron- carbon phase diagram, showing the phases which are stable under certain conditions [7]. The terms ledeburite and perlite, given in this figure, correspond to bainite and pearlite, respectively.
Alpha iron, also known as ferrite, has a bcc structure and is the most stable form of iron at normal temperatures. It is a fairly soft metal that can dissolve only a small concentration of carbon (no more than 0.021 wt% at 723 °C). The carbon dissolves interstitially in α-iron with the carbon atoms being about twice the diameter of the interstitial holes, so that each carbon atom is surrounded by a strong compressive local strain field.
Above 912 °C, α-iron undergoes a phase transformation from bcc to the fcc configuration of gamma iron, also called austenite. This is similarly soft and metallic, but can dissolve considerably more carbon (as much as 2.04 wt% at 1146 °C), due to the larger interstitial cavities available in γ-iron. Above 1394 °C, up to the melting point of iron at 1538 °C, the bcc crystal structure is again the most stable form of the delta iron.
Mild steels (carbon steel with up to about 0.2 wt% C) consist mostly of ferrite, with increasing amount of pearlite with increasing carbon content. Pearlite is a fine two-phased, lamellar structure composed of alternating layers of ferrite and cementite (Fe3C). Bainite (shown as ledeburite in Figure 23) is a similar structure with lamellae much smaller than the wavelength of visible light and thus lacks the pearlescent appearance. Bainite is prepared by
p. 31 Chapter 1 more rapid cooling. Since bainite and pearlite each have ferrite as main component, any iron- carbon alloy will contain some amount of ferrite if it is allowed to reach equilibrium at room temperature.
If the carbon content is higher than the solubility limit of the ferrite or austenite structure, iron carbides can be formed. Cementite is a chemical compound with the formula
Fe3C. It is a hard, brittle material, normally classified as a ceramic in its pure form. Due to its high hardness, these carbides can limit the grain growth and serve as a strengthening mechanism by hindering or stopping the dislocation movement. It is thus obvious that also pearlite and bainite structures have a higher strength compared to α-iron.
Copper{ TC "Copper" \f C \l "5" }
Copper contents in recent RPV steels are lower than the solubility limit of this element in iron at the temperature of stress-relief heat treatments (see Table 5). More recently, also Perez et al. found a solubility limit of ca. 0.3 wt% at 600 °C [37]. Thus, it can be expected that in such steels a large part of copper atoms is in solid solution when the vessel is commissioned. As the copper solubility limit at the irradiation temperature is very low (see Table 5), copper atoms tend to form precipitates or clusters in RPV steels in operation.
Although it is nowadays well known that the solubility limit of copper at 300 °C is well below its concentration present in many steels, this was not known at the time of the production of early reactor pressure vessels. Indeed, the solubility limit of copper in iron at temperatures lower than 700 °C was not precisely known, because copper diffusion is too slow to reach equilibrium with classical experimental techniques involving long range diffusion. The copper solubility at lower temperatures was generally extrapolated from the higher temperature results, which may lead to important discrepancies. Annealing for instance at 300 °C for many hours did not results in precipitation of the copper in binary Fe- Cu alloys with a concentration below 0.1 wt%. Therefore, until recently, it was believed that the solubility level of copper in iron was about 0.1 wt% [38]. Moreover, copper concentrations in RPV steels were even increased up to this concentration, to obtain solute solution hardening (substitutional copper atoms in an iron matrix may cause some hardening, due to the different properties of the atoms).
p. 32 Introduction
Already starting from early irradiation, copper appears to precipitate, however. Therefore, more investigation was necessary concerning this solubility limit. It was found that the solubility limit is well below 0.01 wt%, inducing precipitation in alloys containing a higher concentration of copper [19]. But, it was also found that the kinetics in normal annealing is very slow. It is, on the other hand, commonly agreed that irradiation-enhanced diffusion greatly accelerates the normal precipitation kinetics in steels supersaturated with copper at irradiation temperatures of about 300 °C, causing the precipitation to occur much more easily. As at this temperature the solubility limit of copper is about 0.003 %, many embrittlement data trends can be quantitatively rationalized by simple precipitation models.
The radiation-enhanced diffusion and precipitation of impurity copper from solid solution in the steel results in the formation of small, typically about 2 nm diameter precipitates, with a coherent bcc structure [19]. The typical number densities are in excess of 1017 cm-3 [19]. Their significance increases with copper up to an effective maximum of about 0.25-0.35 %. This maximum is imposed by pre-precipitation at the final stress relief temperature (typically in the range 610-630 °C) in the form of large ε-phase (fcc) particles on dislocations and boundaries. The precipitates formed under irradiation are not pure Cu, but can be alloyed with Mn, Ni and Si, as well as P (e.g. [39], [40]). The levels of these elements in the precipitates depend on parameters such as the irradiation temperature and their alloy contents [19]. In addition, [25] showed that the rate of copper precipitation is very fast in the early stage of irradiation and quite independent of copper content. Only the strengthening magnitude increases with copper content. The maximum hardening due to copper precipitation seems to be reached after a neutron fluence of about 1 × 1019 n cm-2 (E > 1 MeV), in agreement with the high copper materials in [41]. Above 1 × 1019 n cm-2, the hardening becomes constant (about 10 MPa per 1019 n cm-2), independently of the copper content.
These copper precipitates play an important, and perhaps dominant, role in the irradiation hardening of RPV steels containing significant concentrations of this impurity (> 0.1 %). Figure 24 illustrates that with increasing copper content the hardening of the steels increases as well. Most of the hardening is already present at the start of irradiation. This effect appears from a copper content of about 0.04 % [25] and becomes very strong above 0.1 % (i.e. about 50 MPa compared to a hardening coming from other hardening mechanisms
p. 33 Chapter 1 of about 100 MPa at a fluence of about 1 × 1020 n cm-2). From the 70s, the total copper content in RPV steels and their welds has been limited to a maximal value of 0.1 %, and later even lower values were pursued, in most Western countries.
Figure 24 The yield stress increase is given for steels, found in literature, combined in three groups with different copper content.
Nickel{ TC "Nickel" \f C \l "5" }
Nickel contents in RPV steels were expected to be much lower than the solubility limit of this element at the irradiation temperature. However, experimental studies [42] have shown that, in operation, nickel can be part of copper-rich and/or manganese rich defects. Nickel effect has been extensively studied since the beginning of the 80s. This element has a profound, and so far not fully explained, pernicious impact on the irradiation-induced hardening of RPV steel (e.g. [19]). While precipitation and segregation were extensively studied, it is still unclear what the nature and the main mechanisms of the formation of matrix damage are. Nickel was clearly identified as playing an important role in the formation of the matrix damage in particular at high fluence and at low irradiation temperature [43]. But it is not yet completely clear how nickel affects the matrix damage.
Manganese{ TC "Manganese" \f C \l "5" }
Also manganese contents in RPV steels were expected to be lower than the solubility limit at the operation temperature. Some manganese has however been found in the copper-
p. 34 Introduction rich precipitates [42]. It was also illustrated that manganese delays the copper precipitation [42]. In addition, a thermodynamic approach reveals that nickel- and manganese-rich phases can be formed, containing only small amounts or even no copper (indicated as "late blooming phase" [19]). These phases are assumed to be promoted by high nickel and manganese contents, high fluences, low copper contents and low irradiation temperatures. The presence of these phases has been experimentally found in e.g. [42]. In a recent conference [44], it was suggested that such phases could not appear if no manganese is present, but the hardening caused by these defects would not be dependent on the manganese content. The embrittlement associated with the formation of "late blooming phases" may eventually equal or even exceed that produced by copper-rich precipitates at high Cu levels, as it is shown in Figure 25, given by Odette and Lucas [19]. However, it is still debated whether these are stable phases. It is also not established that they are really "late blooming" and thus not appearing at low irradiation doses.
Figure 25 The hardening increase predicted by a model for the copper-rich precipitate dominated microstructure in a high Cu/medium Ni steel, compared to the manganese and nickel rich precipitate dominated microstructure in a low Cu/high Ni steel, with the incubation fluence increased by a factor of 200 [19]. The irradiation dose is given in milli-dpa (mdpa).
Phosphorus{ TC "Phosphorus" \f C \l "5" }
The effect of phosphorus during thermal aging of ferritic steels is well known. It causes intergranular segregation [45]. The same occurs under irradiation [24], [46], [47]. Among others, [46] found that phosphorus segregation leads to an embrittlement mechanism, directly detected by Charpy testing, with a non-hardening nature, as no substantial indication of material degradation could be observed in tensile tests. The phosphorus coverage of grain boundaries in a neutron-irradiated weld material is significantly higher than in the unirradiated material [47]. Additionally, copper-rich precipitates were observed to be phosphorus enriched in steels with high phosphorus levels.
p. 35 Chapter 1
Experimental programs showed thus that, for concentrations higher than about 0.015 %, an irradiation-induced shift of the Charpy transition curve occurs. But, no clear effect on hardness and yield stress was reported. This segregation causes thus hardening-free embrittlement. To avoid this segregation, from the beginning of the 70s, the phosphorous concentration in RPV steels and their welds has been limited to a maximum value of 0.015 %, and nowadays even lower values are aimed at in most Western countries.
Nitrogen{ TC "Nitrogen" \f C \l "5" }
Several studies showed that nitrogen has a low influence on the irradiation sensitivity of RPV steels at temperatures higher than 250 °C. Indeed, the free nitrogen content seems to be around some tens of ppm (20-30 ppm) in silicon-killed steels (steels were silicon is added in order to form nitrides and to reduce the free nitrogen content) [48], which is much lower than the nitrogen solubility limit in iron, under service conditions.
Silicon{ TC "Silicon" \f C \l "5" }
Silicon is added to the steels to reduce the concentration of free nitrogen. Nevertheless, Si is sometimes found to be present in the Cu-rich precipitates [29], [49]. But, no clear influence on the hardening is found.
Tin{ TC "Tin" \f C \l "5" }
It was found that tin has a small contribution to the irradiation embrittlement of RPV steels [24]. Similarly to the binary Fe-P alloy, irradiation-induced intergranular segregation was observed in the binary Fe-Sn alloy. In both alloys, the yield stress and DBTT shift as a function of the concentration gave a non-linear shape, in contrast to all other alloys, where no segregation is found.
Microstructure{ TC "Microstructure" \f C \l "4" }
During the vessel manufacturing, the material undergoes several stress-relief heat treatments, which influence its microstructure. In principle, this microstructure (grain size, density of carbides, density of dislocations, …) does play a role in RPV steel irradiation
p. 36 Introduction response by setting the types and quantities of sinks for mobile point defects. If for example the grains have smaller sizes, more grain boundaries will be present, leading to a higher amount of sinks. Thereby, not only the formation of matrix damage decreases, but also copper diffusion rates are decreased [24]. However, the differences of behaviour have been found to be very small [19]. The microstructure has thus apparently no major effect on the hardening of RPV steels, notwithstanding the fact that it may cause important differences in the initial mechanical conditions of the steels.
Irradiation conditions{ TC "Irradiation conditions" \f C \l "4" }
Most of the light water reactors operate at temperatures ranging from about 270 to 330 °C and a pressure of ca 150 bar in PWRs and 70 bar in BWRs. Its core emits a neutron flux between 0.8 and 7 × 1011 n cm-2 s-1. Their lifetime is set at about 40 years of operation; this corresponds to a neutron fluence of ca 7 × 1019 n cm-2. However, if the irradiation conditions are changed, they will influence the mechanisms behind the irradiation-induced hardening and embrittlement.
Temperature{ TC "Temperature" \f C \l "5" }
The temperature has a strong influence on irradiation embrittlement of RPV steels. At higher irradiation temperatures, the level of damage is considered to be reduced, due to the increased mobility of the defects and to enhanced vacancy and self-interstitial recombination processes. The irradiation-induced defects will be annealed out from the steel, and therefore they will not contribute to the microstructural changes due to irradiation. A decrease in number density of defects is thus observed with increasing temperature [50], [51]. There is only a weak effect on the copper component, but a strong dependence of the unstable vacancy component of the damage [24].
Fluence{ TC "Fluence" \f C \l "5" }
It has been shown by many authors that the irradiation embrittlement increases with increasing neutron fluence. Until recently, it was believed that this hardening-induced embrittlement would saturate after a certain dose. However, recent studies have shown that it
p. 37 Chapter 1 may increase again after a saturating period. This effect has been referred to as "late blooming phase" [19] (see above for the influence of each element with dose).
Flux{ TC "Flux" \f C \l "5" }
Using material test reactors, such as BR2 (Belgian Reactor 2) in Mol (Belgium), the influence of the neutron irradiation on these steels after 10, 20 and even 40 years has been mimicked. To obtain the necessary neutron doses in only a few days, a higher flux is used. In this way, the behaviour of the material can be anticipated. Based on such tests, semi- empirical and physically-based embrittlement models have been proposed, but still very few take the influence of the dose rate (flux) into account [19], as the effect of this higher flux on the hardening and embrittlement is not fully understood. The influence of the flux may however be very important. Many authors already noticed experimentally that there is a change in the hardening results due to a difference in flux. Among others, Hawthorne and Hiser [52] have noticed a difference between a power reactor (the 250 MW, boiling-water Gundremmingen reactor, with a dose rate between 2.5 and 15 × 109 n cm-2 s-1) and the UBR test reactor. The material irradiated in the test reactor (accelerated irradiation conditions) exhibit less embrittlement than the vessel material at approximately the same fluence. The copper concentration of the material is about 0.15 wt%. However, Kussmaul et al. [53] found that the difference in dose rate only provides a small contribution to the difference in hardness for materials with about the same copper content. They observed a very high degradation in their material, but they claimed it to be typical for this material only. English et al. [54] noticed again that, in materials with the same concentration of copper, there is no evidence of fluence rate effects on the embrittlement for their material.
Flux differences are however not only observed between surveillance data and material test reactor data. Indeed, there are important differences in fluxes between BWRs and PWRs. Nevertheless, the same models are used for the prediction of the behaviour of both types of reactors. In addition, significant flux differences are present in one and the same reactor. As discussed before, the lead factor of the surveillance data is generally in the range of 1 to 3. This indicates that the flux of these surveillance capsules can be more than 3 times higher than the flux of the reactor material located at the position with the highest flux. Moreover, p. 38 Introduction material close to the core of the reactor will experience a flux which may be orders of magnitudes higher than the flux experienced by the material of for instance the closure head. Up to now, it is believed that the influence of the higher fluence (for the same irradiation time at places with a higher neutron flux) is much more importance than the effect of the flux difference. The flux influence is nevertheless not yet fully understood.
1.3.3. Influence of parameters on future generation reactor steels For the generation IV and fusion reactors, high Cr ferritic-martensitic steels are candidate structural materials. Most on the knowledge of the influence of the chemical composition, the microstructure and the irradiation on the behaviour of the second generation RPV steels conditions can be extended to the generation IV materials. The major differences are listed here
Chemical composition{ TC "Chemical composition" \f C \l "4" }
Two of the most promising structural materials, selected for further investigation, are the T91 and Eurofer 97 steels. Both steels have a Cr-content between 8 and 9 wt%, which is believed to be the best option against many effects, such as swelling, caused by extensive irradiation [55].
Table 6(a) The chemical composition (in wt %) of 2 steels and their corresponding ASTM standard. C N Si P S ASTM A213 0.08 - 0.12 0.030 - 0.070 0.20 - 0.50 ≤ 0.020 ≤ 0.010 T91 0.1 0.03 0.32 0.02 -- Eurofer 97 0.12 0.016 0.07 < 0.05 --
Table 6(b) The chemical composition (in wt %) of 2 steels and their corresponding ASTM standard (continue). V Cr Mn Ni Cu Mo ASTM A213 0.18 - 0.25 8.00 - 9.50 0.30 - 0.60 ≤ 0.40 -- 0.85 - 1.05 T91 0.24 8.32 0.43 0.24 -- 0.96 Eurofer 97 0.19 8.96 0.43 0.07 -- < 0.001
The chemical composition of both steels is listed in Table 6, as well as the ASTM standard corresponding the T91 steel (i.e. A213) [56]. Within this standard, the strength and
p. 39 Chapter 1 elongation level is comparable with the A533-B Class 1 steel, i.e. 585 MPa (ultimate tensile strength), 415 MPa (yield strength) and 20 % (total elongation).
The main difference in the composition of these steels compared with the ones used for the current nuclear reactor is the presence of chromium. Nevertheless, the copper, manganese and nickel contents are kept much lower, to reduce their influences (see above) and to keep the activation at reduced levels in the case of Eurofer 97. The solubility limits of chromium in pure iron are given in Table 7 at 300 and 600 °C.
Table 7 The solubility limit (in wt %) of chromium in α-iron at 300 °C and 600 °C, respectively. Temperature Cr 300 °C 7.7 [57] 600 °C 22.4 [57]
Chromium{ TC "Chromium" \f C \l "5" }
High chromium (9 – 12 wt%) steels are among the most promising candidate structural materials for the construction of important components in future nuclear options. This element is added, because it strongly reduces the swelling, present in steels irradiated to very high fluences and 9 wt% of Cr seems to provide the lowest embrittlement after irradiation. [58] gives a detailed review of the effect of Cr.
Irradiation conditions{ TC "Irradiation conditions" \f C \l "4" }
It is important to mention that the fluxes, to which these steels will be subjected, are much higher than the ones reached in most of the current reactors. The fluences that these steels are expected to receive are thus also considered to be orders of magnitude higher than those of the current RPV steels. The effect of such high neutron fluxes and fluences still needs close examination. Depending on the type of reactor, different temperatures will be used. However, they will all be well above those of the current reactors. Also the behaviour under these high operation temperatures is still being investigated.
p. 40 Introduction
1.4. Mechanistic correlations In this section, the mechanistic models proposed in the literature to predict the hardening and embrittlement in RPV steels are summarized and reviewed from a historical perspective.
First investigations{ TC "First investigations" \f C \l "3" }
Already in 1961, Cottrell [59] discussed the irradiation-induced embrittlement of pressure vessel steels. He illustrated that vacancies as well as self-interstitials, produced by knock-on collisions from fast neutrons, gather together due to thermal agitation like fine precipitates. He claimed that these clusters are causing the material to harden during irradiation following equation 1.
1 3 Δσ Y = A ⋅ (φt) (1)
In this equation Δσ Y is the increase in yield stress, A is a constant and φt is the neutron fluence, where φ is the neutron flux and t the time of irradiation. This first equation predicting the hardening is very empirical and is based on results with fluences lower than 1018 n cm-2. Moreover, it doesn't include any irradiation conditions (neutron-spectrum, temperature, dose rate, etc.) or material properties (composition, heat treatments).
In the seventies, the basics of the present know-how on irradiation hardening were established. It started in 1972, when Russell and Brown [60] presented a first model for iron- copper alloys. By this time, Potapovs and Hawthorne [61] had proven the role of copper as a significant contributor to the radiation-embrittlement sensitivity. At the same time, Fujii et al. [62] illustrated that the precipitation-hardening of copper-precipitates in an iron-copper alloy occurs by the mechanism explained by Orowan. This theory assumes that the dislocation bows out between the particles, which are finally left encircled with dislocation loops. Starting from the Orowan stress, Russell and Brown adjusted the formulae to spherical particles (with a mean planar radius, r ) of lower shear modulus (G ) than the matrix phase. They obtained equations 2 and 3, for the precipitation-hardening of annealed iron-copper
p. 41 Chapter 1 alloys. In this system the obstacles tend to attract dislocations, due to their lower shear modulus.
1 2 G ⋅b ⎡ E 2 ⎤ ⎛ E ⎞ τ = 0.8⋅ 1− 1 sin −1 ⎜ 1 ⎟ ≤ 50° (2) ⎢ 2 ⎥ ⎜ ⎟ L ⎣ E2 ⎦ ⎝ E2 ⎠ 3 4 G ⋅b ⎡ E 2 ⎤ ⎛ E ⎞ τ = 1− 1 sin −1 ⎜ 1 ⎟ ≥ 50° (3) ⎢ 2 ⎥ ⎜ ⎟ L ⎣ E2 ⎦ ⎝ E2 ⎠
Here the shear stress (τ ) is given as a function of the obstacle spacing in the slip plane ( L ) and of the energy of the dislocation line per unit length across an interface on the side of the precipitate ( E1 ) and the matrix ( E2 ), respectively. The shear modulus and the Burgers vector ( b ) are chosen constant for each material. E1 and E2 are related to each other as shown in equation 4.
∞ r R E1 ⋅ log log E r 1 = 0 + r (4) E2 ∞ R R E2 ⋅ log log r0 r0
Here R and r0 are respectively the outer and the inner cut-off radii used to calculate the
∞ ∞ energy of the dislocation ( r0 ≈ 2.5⋅b and R ≈ 1000⋅ r0 ). The parameters E1 and E2 refer to
∞ ∞ the energy per unit length of a dislocation in infinite media. The ratio E1 E2 = G1 G2 for a
∞ ∞ screw dislocation and E1 E2 = ()G1 ⋅(1−ν 2 ) (G2 ⋅(1−ν 1 )) for an edge dislocation. For a void,
∞ ∞ E1 E2 is equal to zero, and for a copper precipitate this ratio is 0.6.
In 1973, Igata et al. [63] were among the first to investigate the role of some alloying elements, such as nickel and copper, on irradiation hardening. In those times, the solute nitrogen content of the alloys was considerable. The hardening increase during irradiation was therefore mainly explained by the presence of solute nitrogen-complexes. They found that nickel is not able to suppress irradiation hardening, because there is no interaction between nickel and solute nitrogen atoms. For the iron-copper alloys, it was found that the complex defects are not suppressed but finely dispersed. These copper-nitrogen complexes
p. 42 Introduction have been proven to be strongly bounded, as the recovery temperature becomes higher than 400°C.
First mechanistic models{ TC "First mechanistic models" \f C \l "3" }
In the eighties, a better insight into the microstructural causes of irradiation hardening was obtained. Based on a comprehensive microstructural study of selected surveillance specimens, Fisher et al. [15] formulated a model for radiation hardening (henceforth Fisher's model). They showed that the hardening contribution due to the copper precipitates can be calculated using the equation proposed by Russell and Brown (equations 2 and 3) for copper precipitation during annealing. This model thus assumes the same mechanisms as for thermally aged alloys; the mechanisms are only accelerated by the irradiation. Using the equation of Burke (equation 5 [64]) and some existing data, Fisher et al. were able to express the time to peak strength ( t p , in years) as a function of the annealing temperature (Ta , in Kelvin) (equation 6).
E ln(t p )= + const (5) k ⋅Ta
In this equation, E is an effective activation energy for the process and k is the Boltzmann constant.
11000 log(t p )= −18.17 (6) Ta
Using this definition of t p , they found the following semi-empirical description of the copper contribution to the strength. The profile of the thermal ageing peak has a characteristic form which can be described mathematically by a logarithmic rise to a peak, followed by a slow logarithmic decline as overageing of precipitates occurs.
p. 43 Chapter 1
t < 0.05 ⋅ t p Δσ Cu = 0 (7) ⎛ t ⎞ 0.05t ≤ t ≤ t Δσ = 0.77 ⋅ log⎜ ⎟ ⋅ Δσ max (8) p p Cu ⎜ ⎟ Cu ⎝ 0.05 ⋅ t p ⎠ ⎛ 0.01⋅ t ⎞ t < t Δσ = −0.5 ⋅ log⎜ ⎟ ⋅ Δσ max (9) p Cu ⎜ ⎟ Cu ⎝ t p ⎠
max The maximum copper contribution to the hardening ( Δσ Cu ) has been expressed as a function of the volume fraction of copper in the steel ( f ), as given in equation 10.
max 1 2 Δσ Cu = 3600 ⋅ f − 60 (10)
Based on the calculations of strengthening due to copper precipitation during annealing, its contribution under irradiation can be determined. The difference due to irradiation is assumed to be fully controlled by an enhanced copper diffusion, as a higher concentration of vacancies is available. The diffusion coefficient for copper diffusion under irradiation ( Dirr ) may therefore be calculated from equation 11.
irr CV Dirr = a ⋅ Da (11) CV
Here Da is the appropriate diffusion coefficient at the irradiation temperature, in the
a absence of irradiation. The steady-state concentration of vacancies during annealing (CV )
irr and under irradiation (CV ) may be calculated using equation 12 and 13, respectively.
f a ⎧ EV ⎫ CV = exp⎨− ⎬ (12) ⎩ k ⋅Ta ⎭
irr KV CV = 2 (13) DV ⋅ kV
f In these equations, EV is the formation energy of a vacancy, KV is the production rate
2 of mobile monovacancies and DV is the appropriate vacancy diffusivity. The parameter kV is given by equation 14.
p. 44 Introduction
2 kV = ZV ⋅ ρ d (14)
Here, ρ d is the dislocation density in the steel and ZV ≈ 2 .
irr Under irradiation, the critical size will be reached at time t p , which can be calculated starting from the time to reach the peak hardness under annealing at the same temperature, t p , as given in equation 15.
irr Da CV t p = ⋅ t p = irr ⋅ t p (15) Dirr CV
irr Now t p can be replaced by t p in equations 7 to 9, to obtain the outline for the calculation of the strengthening from a dispersion of copper precipitates as a function of time, under irradiation.
The contribution to the hardening of the matrix damage clusters is described as a function of the fission dose (φt ), by equation 16.
1 2 Δσ MD (t) = A ⋅ [α(φt)] (16)
The parameter A depends on steel composition and irradiation temperature. The value of A is influenced by the free nitrogen content of the steel, as this element tends to stabilize point defect clusters (probably self-interstitial dislocation loops) in the vicinity of neutron- induced displacement cascades. In aluminium-killed steels, in which the free nitrogen is removed by the formation of aluminium nitride particles, fewer clusters are stabilized, a higher proportion of point defects are lost by diffusion to sinks, and the hardening contribution is reduced. The α parameter refers to the location in the reactor. Below the core, α varies from 2 to 5, while next to the core the range of α is from 0.5 to 1.5.
Fisher et al. assumed a linear superposition between the two hardening contributions.
Δσ tot = Δσ MD + Δσ Cu (17)
p. 45 Chapter 1
It is clear that in this first model, no effect of the dose rate is assumed, although a good agreement is found for steels irradiated with very low neutron fluxes varying from 1 × 107 to 1.5 × 109 n cm-2 s-1 [15]. Nevertheless, at these variations of fluxes only little influence is expected.
Influence of the flux{ TC "Influence of the flux" \f C \l "3" }
The first to investigate the influence of the dose rate on the hardening mechanisms have been Lucas and Odette [24]. They suggested that higher fluxes lead to a larger population of unstable vacancy clusters (Odette's model). While these clusters produce some hardening, they also act as sinks for mobile point defects, thereby decreasing copper diffusion rates; this increases the time to peak hardening. But the appearance of a higher fixed sink density (within the microstructure) would have a similar effect in delaying precipitation. The model Lucas and Odette propose is also based on the Russell-Brown hardening model, assuming consistency with simple irradiation-enhanced precipitate growth models. A threshold fluence has been inserted, resulting from a combination of the nucleation and the initial growth period needed for precipitates to reach a size capable of producing significant hardening. The saturation of the hardening in low copper alloys is said to be consistent with the rapid build up of small unstable vacancy clusters to steady-state number densities. They also took into account the influence of nickel on the matrix damage.
A few years later, Fisher and Buswell [65] changed the original Fisher's model, by adapting it to yield an interpretation of the PWR surveillance and MTR (material test reactor) accelerated data. The most obvious difficulty is the wide range of dose rates employed in the irradiations. The surveillance data are drawn from irradiations with fluence rates from 1010 to 1011 n cm-2 s-1, the MTR data from irradiations at fluence rates from 1012 to 1013 n cm-2 s-1. The original model was based on data with irradiation rates in the BWR reactor order, from ca 108 to 109 n cm-2 s-1. In this model, the contribution to yield stress from the matrix damage is still independent of the flux. The contribution of the copper precipitates, on the other hand, is considered to be dependent on the neutron flux. The appropriate parameter is the dose to peak strength. Three regions are readily identifiable.
p. 46 Introduction
1) At low dose rates (φ < 1010 n cm-2 s-1) the concentration of vacancies due to thermal annealing at the irradiation temperature is much higher than the concentration due to the irradiation itself. In this region, the time to peak hardening has a "thermal" value, which is independent of the dose rate. 2) For intermediate dose rates (1010 n cm-2 s-1 < φ < 1011 n cm-2 s-1) a transition region is postulated. 3) At high dose rates ( φ > 1011 n cm-2 s-1) the concentration of vacancies due to thermal annealing at the irradiation temperature is much lower than the concentration due to the irradiation itself. This implies that the time to peak is
inversely proportional to flux, or that DP becomes independent of the flux. They found that, for all dose rates, copper precipitates to peak effectiveness at doses lower than 2 × 1019 n cm-2. Therefore, this phenomenon will play a significant, if not overwhelming, role in the embrittlement of PWR steels. In the model, the effect of copper is arbitrarily "switched off" at concentrations below 0.1 wt%.
In the meantime, Williams et al. [66] implemented an empirical model to fit their own data (henceforth Williams' model). In their model, they distinguished between three material compositions, low nickel welds, high nickel welds and plate material. For the low nickel welds, the matrix damage is assumed to depend on the primary interaction function (dependent on the dose rate), an irradiation temperature dependence function and the long term annealing function (dependent on the irradiation time). An empirical expression has then been added to this matrix damage component to describe copper precipitation. This component depends on the effective Cu-concentration in the matrix
( Cueff ), which saturates at 0.2265 wt%, and on the irradiation dose. The Cueff -term introduces upper and lower limits to copper available in the matrix for precipitation. The upper limit is related to copper precipitated during welding or heat treatment prior to irradiation. The copper precipitation term as a whole is purely an ad hoc expression to enable simultaneous fitting of results from these welds, and it may not be applicable for other compositions. The damage in the high nickel welds cannot be modelled in quite the same way as the low nickel welds. In this case, there were insufficient data to establish a temperature dependence, and therefore they assumed that there is no effect of irradiation temperature on either matrix or precipitation damage. The copper precipitation appeared to be more
p. 47 Chapter 1 moderate and to depend on the copper level. The effective Cu-concentration used here, already saturates at 0.1647 wt%. For the low copper plates, again insufficient data were available to obtain a temperature dependence of the hardening. If it is assumed that the effect of neutron dose rate is simply to alter the kinetics of copper precipitation, the model can be used to predict the maximum effect of dose rate. For all three material groups, it is true that, when copper levels are low (< 0.15 wt%), there is no difference between low and high flux results. However, for higher copper levels, there is a marked effect at low doses (< 0.01 dpa), where the low flux gives a significantly higher shift than high flux irradiations. This effect is explained as an effect of flux on the precipitation damage rather than the matrix damage, matrix damage being considered relatively unaffected by dose rate. This is in contrary to what has been suggested by Lucas and Odette's model [24]. This may be interpreted to be an effect of precipitation proceeding at a rate which depends upon the vacancy supersaturation. The plateau of the precipitation shift is not affected by flux.
In 1993, Odette et al. [67] proposed some adjustments to Odette's model in order to take into account even better the effect of flux on irradiation hardening of pressure vessel steels. A minimum of three hardening features was proposed, including copper-rich precipitates (CRP), unstable matrix defects (UMD) and stable matrix features (SMD). The most plausible candidates for the unstable matrix defects are small vacancy, or perhaps self-interstitial clusters, quite possibly lightly complexed with solutes and formed in association with displacement cascades. Candidate stable matrix features include larger (i.e. nanovoids) and more highly complexed clusters and perhaps other irradiation induced (phosphide) or enhanced (carbo-nitride) phases. The hardening from these features increases roughly as the square root of exposure and becomes significant at high fluences. The effects of flux on these matrix features are not known. The radiation enhanced diffusion coefficient ( D *) of copper rich precipitates can be expressed as a function of the flux (cf the difference with equation 11).
D ∗ = K ⋅φ (18)
The radiation enhanced diffusion factor ( K ) depends on flux, temperature and microstructure. It increases with decreasing flux, decreasing fluence and increasing irradiation temperature. Although more unstable matrix defects are produced when p. 48 Introduction irradiating with higher flux, more recombinations occur as well and therefore the diffusion coefficient increases. On the other hand, the matrix damage itself also induces an increase in hardening. All this can be seen in Figure 26. In addition high flux delays the formation of stable features.
Figure 26 (left) A schematic illustration of the effect of flux on extrapolating the radiation enhanced diffusion factor ( K has been normalized to 1 at 1016 n m-2 s-1). (right) Hypothetical hardness increase due to unstable matrix defects as a function of fluence for various flux levels. (FIG. 1 from ref. [67]).
Figure 27 Hypothetical hardening as a function of fluence at low and high flux for high and low copper contents. Curves marked CRP correspond to hardening from copper-rich precipitates, SMD from stable matrix defects, and UMD from unstable matrix defects (FIG. 2 from ref. [67]).
p. 49 Chapter 1
The hypothetical hardening contributions from various features and the total hardening are shown in Figure 27.
Also in 1993, English et al. [68] established a comparison between the then known models (Fisher's and Williams'). Both models assume that the irradiation-induced increase of hardening is determined by two components, a copper precipitation term and a copper- independent matrix term. Fisher's model is adapted by giving the choice of allowing precipitate overageing to occur, or not. Under accelerated irradiation conditions, the evidence is that overageing of precipitates does not occur and that the copper contribution needs to be set at its peak value at all doses after being first developed. The equation employed for the matrix damage by Williams' model is found to be very similar to the effect of the matrix term by Fisher's model, except that Williams' model includes provisions for long term damage annealing effects.
Later, also Williams and Phythian compared two models (an updated William's model and the Russell-Brown model) [69]. By that time, Williams' model had been extended with a component related to phosphorus precipitation. The model is valid for high dose rate (ca. 6 × 10-9 dpa s-1) irradiations at 255 °C. This model is compared to the Russell and Brown model (equations 2 and 3). A fairly good agreement is found. STEM and SANS studies have provided a clear physical confirmation on many of the theoretically or empirically derived assumptions of Williams' model. Nevertheless, the Russell and Brown model was used to predict the further development of hardening. The effect of dose rate appears evident from the experimental results. While copper increases the total amount of hardening, nickel causes a delay in the time to achieve the maximum copper hardening. Nickel also results in the formation of smaller, higher volume fraction precipitates during irradiation, with higher manganese and nickel contents, higher elastic modulus and therefore lower strength. On the other hand, more matrix damage is observed in the high nickel weld.
Dohi et al. [70] irradiated commercial reactor pressure vessel steels having high and low copper contents, under different irradiation conditions with neutron flux levels of approximately 6 × 1014, 7 × 1015 and 8 × 1016 n m-2 s-1 (E > 1 MeV) at temperatures of about 50 °C. They have shown that the lowest neutron flux level tends to induce a larger increase in DBTT for both low Cu steels and high Cu steels in the lower neutron fluence range.
p. 50 Introduction
Recent updates{ TC "Recent updates" \f C \l "3" }
In 2007, Soneda et al. [49] published an important paper which includes microstructural analyses of Japanese surveillance materials using state-of-the-art experimental techniques. The embrittlement correlation method proposes a new approach to predict the microstructural changes in materials during irradiation using a set of rate equations. Detailed microstructural analyses are performed to verify and improve the correlation method. An important concern is the effect of neutron flux. The contribution of copper enriched clusters to embrittlement reaches a plateau, showing saturation of the contribution, but the time (or neutron fluence) required to reach the plateau is affected by the neutron flux (dose rate). In the flux levels of commercial reactors and their surveillance program conditions, lower flux irradiation of copper containing materials, with Cu content > 0.1 wt%, results in larger embrittlement, while no flux effect has been identified in low-copper materials. In these alloys, a mechanism, other than the clustering of supersaturated copper atom, is causing the formation of solute atom clusters with nickel, silicon and manganese but little or no copper. The copper atoms do not form copper enriched clusters in low-copper materials but they are still effective in the nucleation of solute atom clusters.
Kinetic Monte Carlo (KMC) simulation (Figure 28) shows that, in a high-flux region (region I), the intercascade pair recombination of point defects becomes dominant, resulting in the reduction of the number of vacancy jumps, which can be a measure of the diffusivity of copper atoms, and a suppression of the copper clustering. If the flux is sufficiently low (region II), point defects may diffuse to sinks such as dislocations or grain boundaries before they find other point defects produced in other cascades and thus no flux effect will exist. If the flux is further decreased (region III), the average vacancy concentration becomes comparable to the thermal equilibrium vacancy concentration at the temperature. Another type of flux effect, i.e. the contribution of thermal vacancies, will become effective. All this can be observed in Figure 28.
p. 51 Chapter 1
Figure 28 Dose rate effect on the number of vacancy jumps, using a KMC study by Soneda et al. [49].
A clear influence of dose rate is observed in Figure 29. The higher flux irradiations (green and blue curve (left); pink and green curve (right)) are located in region II, where the flux effect is weak. The lowest flux level (red curve (left); blue curve (right)) on the other hand is in region III, where a relatively strong effect of thermal vacancies is expected. The effect of a low flux irradiation on copper containing materials would therefore be to enhance the growth of copper enriched solute atom clusters as well as to increase their number density.
Figure 29 (left) Transition temperature shifts of high copper (0.24 wt%) RPV material irradiated at three different fluxes: i.e. ~ 1 × 109 n cm-2 s-1 in red, ~ 2 × 1010 n cm-2 s-1 in green and 7 × 1011 n cm-2 s-1 in blue (Figure 11 from ref. [49]). (right) Embrittlement predictions of relatively high copper material irradiated at three different fluxes (Figure 16 from ref. [49]).
p. 52 Introduction
The total amount of embrittlement is calculated using the square root of the sum of the squares of the contributors. In the other embrittlement correlation models, the total temperature shift is a simple sum of the copper enriched clusters and matrix damage contributions. The linear sum method can be a good approximation when the obstacle strengths of the two kinds of particles are very different and the population of the stronger particles is much less than that of the weaker particles. In general, however, the square root method is a more generic approximation. This method has the characteristic that the stronger contribution dominates the total shift. The contribution of the matrix damage to the embrittlement is considered to be proportional to the square root of the number density of the matrix damage features. This is a conventional way to model the contribution of matrix damage. And the contribution of the solute atom clusters to the embrittlement is calculated as the square root of the cluster volume fraction, which is modelled as the cluster number density multiplied by the average volume of the clusters.
Frequently used correlations{ TC "Frequently used correlations" \f C \l "3" }
By applying Charpy-V tests, semi-empirical embrittlement models have been proposed [19]. The measured variation of such tests is currently compared with six different empirical or semi empirical models: USNRC Regulatory Guide 1.99 Rev. 2 [71], NUREG/CR-6551 [72], ASTM E900-02 [73], NUREG 1874 [74], USNRC Regulatory Guide 1.99 Rev. 3 [75], and the so-called FIS formula [76]. These models have been proposed to predict the embrittlement of RPV materials as a function of accumulated fast neutron fluences. If surveillance data deviates from the proposed models, i.e. the results are outside the error range of the models, the safety of the reactor pressure vessel is questioned. The error range of the models corresponds to ± 2 times the standard deviation (includes 95 % of the cases). The reactor will be closed if strongly deviating points are observed. When the used models are not representative for the investigated material, this may however lead to premature or even to too late closedown. The models are thus constantly checked and updated if necessary. { TC "US NRC Regulatory Guide 1.99 Rev. 2 (May 1988)" \f C \l "4" }
p. 53 Chapter 1
US NRC Regulatory Guide 1.99 Rev. 2 (May 1988)
"Regulatory guides are issued to describe and make available to the public, methods acceptable to the nuclear regulatory commission staff of implementing specific parts of the commission's regulations, to delineate techniques used by the staff in evaluating specific problems or postulated accidents, or to provide guidance to applications." In the guide proposed in 1988, the adjusted reference temperature ( ART , in °F) for each material in the beltline is given by the following expression.
ART = RTNDT ,initial + ΔRTNDT + M (19)
RTNDT stands for the reference temperature for nil ductility transition and the initial value is the reference temperature for the unirradiated materials. The mean value of the adjustment in reference temperature caused by irradiation ( ΔRTNDT ) should be calculated as shown in equation 20.
(0.28−0.10⋅log(φt )) ΔRTNDT = CF ⋅φt (20)
Here, CF is the chemistry factor, a function of copper and nickel content. The value of this factor is provided in tables, for welds and for base metals (plates and forgings). Linear interpolation is permitted. The neutron fluence (φt , in 1019 n cm-2, E > 1 MeV) at any depth from the inner wetted surface ( x , in inches) in the vessel wall is determined starting from the calculated value of the neutron fluence at the inner surface of the vessel (φt surf ).
φt = φt surf ⋅ exp{− 0.24 ⋅ x} (21)
The margin M is the quantity that is to be added to obtain conservative, upper-bound values of ART for the calculations. M is determined using the standard deviation for the initial value of RTNDT and for ΔRTNDT , σ I and σ Δ , respectively. σ Δ is 28 °F for welds and
17 °F for base metals, as long as it does not exceed 0.50 times the value of ΔRTNDT .
2 2 M = 2 ⋅ σ I + σ Δ (22) { TC "US NRC NUREG/CR-6551 (November 1998)" \f C \l "4" }
p. 54 Introduction
US NRC NUREG/CR-6551 (November 1998)
The embrittlement correlation in Regulatory Guide 1.99 Rev. 2, used to predict the increased embrittlement over the life of the vessel was based on analysis of Charpy data available in 1984. Since then, a large body of additional Charpy surveillance data has become available, and the understanding of embrittlement mechanisms has advanced. In 1998, improved embrittlement correlations have been published by Eason et al. [72]. All of the models predict the transition temperature shift ( TTS , in °F) using a relationship of the following form.
TTS = SMD(Tirr , P,φt) + CRP(Ni,Cu,φt,tirr ) (23)
Here, SMD represents a stable matrix defect contribution to TTS , which is dependent on the irradiation temperature (Tirr , in °F), the phosphorous content ( P , in wt%) and the irradiation fluence (φt ). CRP is the copper-rich precipitate contribution to TTS , among others, dependent on the irradiation time ( tirr ). Cu and Ni stand for the weight percent copper and nickel, respectively.
The example for the model with no phosphorous term, no irradiation time term and a constant fluence power is given in equation 24.
(0.4132) ⎧2.207 ×10 4 ⎫ ⎛ φt ⎞ TTS = A ⋅ exp⎨ ⎬ ⋅ ⎜ ⎟ T + 460 ⎝1019 ⎠ ⎩ irr ⎭ (24) 0.682 1.381 ⎛ ⎧log()φt −18.27⎫⎞ + B ⋅ ()()Cu − 0.072 ⋅ 1 + 2.35 ⋅ Ni ⋅ ⎜0.5 + 0.5 ⋅ tanh⎨ ⎬⎟ ⎝ ⎩ 0.849 ⎭⎠
In this equation, the operating temperature Tirr is assumed to be 550 °F (~ 300 °C). The parameter A is equal to 1.07 × 10-8 for weld and to 1.04 × 10-8 for plate material, while the parameter B is 235 for weld and 192 for plate material.
p. 55 Chapter 1
ASTM E900-02 (2005){ TC "ASTM E900-02 (2005)" \f C \l "4" }
The model proposed by Eason et al. has been updated and published as the ASTM E900-02 model [73]. Here, the stable matrix damage is given by equation 25 and the copper- rich precipitation term by equation 26.
⎧ 20730 ⎫ 0.5076 SMD = A ⋅ exp⎨ ⎬ ⋅φt (25) ⎩Tirr + 460⎭
1.173 ⎛ ⎧log()φt −18.24⎫⎞ CRP = B ⋅ ()1 + 2.106 ⋅ Ni ⋅ f ()Cu ⋅ ⎜0.5 + 0.5 ⋅ tanh⎨ ⎬⎟ (26) ⎝ ⎩ 1.052 ⎭⎠
Here, A is equal to 6.70 × 10-18 and B is 234 for welds, 128 for forgings, 208 for combustion engineering plates and 156 for other plates. Tirr is again given in °F. f (Cu) and thus also the whole copper-rich term is zero when the copper content is lower than or equal to 0.072 % and in the other case, f ()Cu is given by (Cu − 0.072)0.577 . The standard error of the TTS is reported to be 22 °F (or ~ 12.2 °C)
US NRC NUREG-1874 (2007){ TC "US NRC NUREG-1874 (2007)" \f C \l "4" }
For several years the U.S. Nuclear Regulatory Committee has been developing an updated embrittlement correlation based on the analysis of a large database. In 2006, Eason et al. thus presented the following form of his model, which has been described in NUREG- 1874 [74]. The matrix damage term is given by equation 27.
2.471 MD = A ⋅ ()1 − 0.001718 ⋅Tirr ⋅ (1 + 6.130 ⋅ P ⋅ Mn ) φte (27)
The parameter A is now equal to 1.140 × 10-7, 1.561 × 10-7 and 1.417 × 10-7 for forgings, plates and welds, respectively. It should be noticed that the concentration of manganese ( Mn , in wt%) is now also taken into account. The effective fluence (φte , in n cm-2) depends on the neutron flux, as given in equations 28 and 29.
p. 56 Introduction
10 -2 -1 φte = φt for φ ≥ 4.3925 × 10 n cm s (28) ⎛ 4.3925 ×1010 ⎞ ⎜ ⎟ 10 -2 -1 φte = φt ⋅ ⎜ ⎟ for φ < 4.3925 × 10 n cm s (29) ⎝ φ ⎠
The copper-rich precipitation term is given by equation 30.
1.1 1.191 ⎛ Tirr ⎞ CRP = B ⋅ ()1 + 3.769 ⋅ Ni ⋅ ⎜ ⎟ ⋅ f ()(Cue , P ⋅ g Cue , Ni,φte ) (30) ⎝ 543.1⎠
The effective copper content (Cue , in wt%) is zero if Cu ≤ 0.072 % and equal to Cu if
Cu > 0.072 %. The maximum value of Cue is 0.37 if Ni < 0.5 %, 0.2435 if 0.5 % ≤ Ni ≤ 0.75 % and 0.301 if Ni > 0.75 %. Moreover, B is equal to 102.3 for forgings, 102.5 for plates in non-combustion engineering vessels, 135.2 for combustion engineering plates, 155 for welds and 128.2 for standard reference materials. The functions f ()Cue ,P and
g()Cue ,Ni,φte are given as follows.
⎧log(φt) + 1.139 ⋅ Cue − 0.4483 ⋅ Ni −18.12025⎫ g()Cue , Ni,φte = 0.5 + 0.5 ⋅ tanh⎨ ⎬ (31) ⎩ 0.6287 ⎭
f ()Cue , P = 0 for Cue ≤ 0.072 % (32) 0.6679 f ()(Cue , P = Cue − 0.072 ) for Cue > 0.072 % and P ≤ 0.008 % (33) 0.6679 f ()Cue , P = ()Cue − 0.072 + 1.359 ⋅ (P − 0.008) for Cue > 0.072 % and P > 0.008 % (34)
The standard error of the correlation depends on the product form (forging, plate or weld) and on the copper content, and ranges from 17.5 °F (or ~ 9.7 °C) to 26.3 °F (or ~ 14.6 °C). This model has been proposed for the Regulatory Guide 1.99 Rev. 3. { TC "USNRC Regulatory Guide 1.99 Rev. 3 (2007)" \f C \l "4" }
USNRC Regulatory Guide 1.99 Rev. 3 (2007)
The latest proposed Rev. 3 uses, in fact, a model developed by Erickson Kirk [75]. This model is based on a combination of physical understanding and empirical calibration using an extended updated surveillance database [77]. The proposed relationship for the increase of the 30 ft-lb (~ 41 J) transition temperature ( ΔT30 , in °F) is given in equation 35.
p. 57 Chapter 1
LOW HIGH ΔT30 = (1 − W )⋅ ΔT30 + W ⋅ ΔT30 (35)
The parameter W is zero for fluences ≤ 2 × 1019 n cm-2, equal to one for fluences above 4 × 1019 n cm-2 and equal to equation 36 for fluences in-between these two values.
1 ⎛ φt ⎞ W = ⋅ ⎜ − 2⎟ (36) 2 ⎝1×1019 ⎠
The transition temperature increase in the low fluence regime is given by a matrix damage contribution and a copper-rich precipitate component.
−14.64 −3.44 LOW ⎛ Tirr ⎞ ⎛ log(φ)⎞ ΔT30 = A ⋅ ()1 + 35 ⋅ P ⋅ ⎜ ⎟ ⋅ ⎜ ⎟ ⋅ φt ⎝ 550 ⎠ ⎝ 10.7 ⎠ (37) −1.75 ⎛ T ⎞ ⎛ ⎧ − φt ⎫⎞ + B ⋅ CF ⋅ irr ⋅ ⎜1 − exp ⎟ CRP ⎜ ⎟ ⎜ ⎨ 18 ⎬⎟ ⎝ 550 ⎠ ⎝ ⎩2.38 ×10 ⎭⎠
The parameter A is equal to 6.7 × 10-9 for weld, 8.1 × 10-9 for plate and 4.75 × 10-9 for forging materials. The parameter B is equal to 0.301 for weld and 0.233 for plate and forging materials. The chemistry factor of the copper-rich precipitate contribution is given in equation 38 and 39.
CFCRP = f ()Cu + 2500.3 ⋅ min[0.32, max[0,Cu − 0.048]⋅ Ni] (38) f (Cu) = −116.3 + 530.8 ⋅ Cu subject to 0 ≤ f (Cu) ≤ 185 (39)
The transition temperature increase in the high fluence regime is given by a matrix 19 -2 damage component ( ΔYS MD ) if the fluence is higher than 1 × 10 n cm , a copper-rich precipitate component ( ΔYSCRP ) if the copper content is higher than 0.03 % and a phosphorous-rich precipitate component ( ΔYS PRP ) if the phosphorous content is higher than 0.012 %. The parameter C is equal to 1.39 for welds, 1.18 for plates and 0.84 for forgings.
p. 58 Introduction
HIGH 2 2 ΔT30 = C ⋅ (ΔYSMD + ΔYSCRP + ΔYS PRP ) (40)
ΔYS MD = ⎛ ⎧ ⎫⎞ ⎜ ⎧ ⎫ ⎟ ⎪ ⎪ − 4003.7 ⎪⎪ ⎜585 ⋅ exp −1250 ⋅ exp ⎟ ⎜ ⎨ ⎨ ⎬⎬⎟ ⎪ ⎪ 5 ⎪⎪ ⎧ ⎛ φt ⎞⎫ (41) ⎜ 273.15 + ⋅ ()Tirr − 32 ⎟ ⋅ 1 − exp − 0.01⋅ −1 ⎪ ⎪ ⎪⎪ ⎨ ⎜ 19 ⎟⎬ ⎜ ⎩ ⎩ 9 ⎭⎭⎟ ⎩ ⎝1×10 ⎠⎭ ⎜ ⎛ ⎛ 5 ⎞⎞ ⎟ + ⎜3880 − 6.3 ⋅ 273.15 + ⋅ T − 32 ⎟ ⋅ Ni ⎜ ⎜ ⎜ ()irr ⎟⎟ ⎟ ⎝ ⎝ ⎝ 9 ⎠⎠ ⎠
ΔYSCRP = 215 ⋅ (1 − exp{}− 2.7 ⋅ (Cu − 0.03) ) (42) ⎛ ⎛ 5 ⎞⎞ ΔYS PRP = ⎜44470.5 − 70 ⋅ ⎜273.15 + ⋅ ()()Tirr − 32 ⎟⎟ ⋅ P − 0.012 (43) ⎝ ⎝ 9 ⎠⎠
The uncertainty of the correlation is expressed in terms of a margin term, which is zero in case of a probabilistic evaluation, which already takes into account sources of uncertainty for ΔT30 . In the case of a deterministic evaluation, the margin is given by equation 44.
M = min[2 ⋅σ Δ , ΔT30 ] (44)
The standard deviation of the temperature shift (σ Δ ) depends on the fluence and copper content. It is equal to 33 for fluences > 3 × 1019 n cm-2, and for fluences lower than or equal to this value, it is 19 if Cu ≤ 0.048 % and 25 if Cu > 0.048 %.
FIS formula{ TC " FIS formula" \f C \l "4" }
In Belgium, the FIS formula is used, which is much easier than the models explained above, but which was shown to be satisfactory for the case of the Belgian reactors. The formula is given in equation 45.
2 0.35 ΔRTNDT = 8 + (24 +1537 ⋅ (P − 0.008) + 238 ⋅ (Cu − 0.08) +191⋅ Cu ⋅ Ni )⋅φt (45)
Also here, the respective terms become zero if P is smaller than 0.008 % and if Cu is smaller than 0.08 %.
p. 59 Chapter 1
1.5. Conclusions The most important message of this chapter is that the vessels for the reactor walls, in all types of reactors, embrittle during irradiation. Although much is known about the microstructural defect formation in these defects, still many questions remain. How are copper precipitates formed, what elements participate in these precipitates and how do they evolve with further irradiation? Why does nickel precipitate in low-Cu alloys and what is the role of manganese in the matrix damage? How do the vacancy-solute configurations look like? What are the "late blooming phases"? And finally, how does each defect contribute to the hardening/embrittlement of the steel? It is the purpose of this thesis to clarify a few of these question marks.
The bulk of this work has been performed as part of the PERFECT project [78], partially founded by the European Commission. This project was an international joint effort aimed at developing multiscale modelling computational toolboxes, capable of simulating the behaviour of materials under irradiation at different time and length scales. The development of simulation tools requires a continuous feedback from experimental data. To achieve this objective, several European laboratories are closely collaborating, while exchanging data with American and Japanese laboratories currently pursuing similar approaches.
p. 60
Chapter 2 Materials and irradiation conditions
“A theory is something nobody believes, except the person who made it. An experiment is something everybody believes, except the person who made it.” Albert Einstein (American German 1879-1955)
It was introduced in chapter 1 that the hardening and embrittlement of reactor pressure vessel (RPV) steels is of great concern in the actual nuclear power plant life assessment. Fe- Cu binary alloys are often used to mimic the behaviour of such steels. Their study allows identifying the Cu-rich precipitates, which play an important role in the hardening of the steels. But, more recently, the influence of manganese and nickel in low-Cu RPV steels has been found to be important as well. In contrast with the existing models for high-Cu steels, which predict that the hardening saturates after a certain dose, Fe alloys containing nickel and manganese irradiated within this work showed a continuing increase of the hardening. In future nuclear reactors, the reactor pressure vessel steel will contain a certain amount of chromium, as this element is found to lead to many good properties, such as a reduction of the swelling during irradiation. The most accurate way to investigate the influence of these alloying elements in steels is by irradiating some well-defined model alloys and by comparing them with the behaviour of commercial steels. The definition of the full material matrix is done in the first section of this chapter. More details are given concerning the fabrication of the materials, their chemical composition, their microstructural and mechanical properties before irradiation and the specimens used for the analysis of the materials.
The influence of the different elements may however change with the irradiation dose. The materials are therefore irradiated up to different doses. But, also two different fluxes are applied to determine its influence on the hardening features. The irradiation conditions (including the description of the material test reactor used for the irradiation) are fully described in a second section of this chapter. At the end of this chapter, some conclusions are drawn.
p. 61 Chapter 2
Table of content Chapter 2 Materials and irradiation conditions ...... 61 2.1. Materials...... 63 REVE matrix...... 63 Fabrication ...... 63 Chemical composition...... 64 Specimen fabrication...... 66 Metallographic study...... 66 Mechanical properties ...... 68 MIRE-Cr matrix...... 69 Fabrication ...... 69 Chemical composition...... 70 Specimen fabrication...... 71 Metallographic study...... 71 Mechanical properties ...... 73
2.2. Irradiation...... 75 Belgian reactor 2...... 75 Applications ...... 76 CALLISTO ...... 76 REVE matrix irradiation...... 77 Encapsulation...... 77 Temperature control...... 78 Neutron energy spectra ...... 79 Flux and fluence...... 80 MIRE-Cr matrix irradiation ...... 81
2.3. Conclusions ...... 82
p. 62 Materials and irradiation conditions
2.1. Materials Within the PERFECT project, a matrix of materials examined (the so-called REVE matrix) was to be irradiated and defined, composed of six iron-based model alloys and an RPV steel (16MND5 or A533B type, as indicated in chapter 1). The purpose of this matrix was threefold. Firstly, it is to investigate the defects produced during neutron irradiation for structural materials for reactors of generation II type of power plants. Secondly, this matrix addressed the problem of the influence of different alloying elements, i.e. carbon, copper, manganese and nickel. Ternary and quaternary alloys were included for the study of correlated effects. And thirdly, the matrix made it possible to extract the correlation between the observed microstructural features and the hardening needed.
In addition to this REVE matrix, chromium-rich alloys and steels (the so-called MIRE- Cr matrix) have also been examined in the framework of this thesis, for investigations dealing with materials for future generations of reactors. As the Cr content is important for the behaviour of the material, binary Fe-Cr alloys were prepared with different Cr concentrations. These results are compared with two steels, selected for use in future reactors.
REVE matrix{ TC "REVE matrix" \f C \l "3" }
The main part of this thesis deals with Cu-containing iron alloys, used for the vessel of generation II reactors. Therefore, the first part of this section will concentrate on these materials.
Fabrication{ TC "Fabrication" \f C \l "4" }
Model of growing chemical complexity alloys were fabricated, starting from electrolytic iron, to investigate the influence of the presence of carbon, copper, manganese and nickel in neutron irradiated iron. For comparison, also a steel was added to the matrix, with the typical composition of French RPV steels. The alloys were prepared using argon-arc melting and zone refinement methods. Argon-arc melting is a melting procedure that heats charged material by means of an electric arc, in an argon atmosphere. Zone refining is a method of separation by purification in which
p. 63 Chapter 2 a molten zone traverses a long ingot of impure metal. The impurities concentrate in the molten region, which is moved to one end of the ingot, and removed at the end of the process. The resulting ingots were cold worked after austenising tempering. A final heat treatment for 1 h at 1075 K in argon atmosphere was performed to release the stresses an to get well recrystallized materials. This heat treatment was followed by a water quenching.
Chemical composition{ TC "Chemical composition" \f C \l "4" }
Table 8 list the nominal composition of the fabricated materials, in mass percentage (wt %). The analyses were performed by induced coupled plasma mass spectroscopy (ICP- MS) at EDF R&D (France) for the metallic elements, while C and N were measured using the combustion technique. The carbon concentration of all alloys is below the detection limit of these techniques (0.005 wt %). Based on the appearance of the Snoeck peak in internal friction measurements (Figure 30), it can be deduced that indeed the C content is much less than 20 atomic ppm for all model alloys, except for the Fe-C alloy. In the latter, the concentration of C should be at least 50 atomic ppm.
Table 8 The chemical composition of the as received materials, obtained by induced coupled plasma mass spectroscopy in wt %. Composition in wt % Material C N Si P S Mn Ni Cu Pure Fe < 0.005 < 0.001 < 0.005 < 0.005 < 0.005 0.010 < 0.005 < 0.005 Fe-C < 0.005 0.0021 0.006 0.007 < 0.005 0.015 < 0.005 0.015 Fe-0.1% Cu < 0.005 -- < 0.005 < 0.005 < 0.005 0.007 < 0.005 0.11 Fe-0.3% Cu < 0.005 -- 0.012 < 0.005 < 0.005 0.010 < 0.005 0.315 Fe-Mn-Ni < 0.005 < 0.001 < 0.005 0.005 < 0.005 1.09 0.75 < 0.005 Fe-Mn-Ni-Cu < 0.005 < 0.001 < 0.005 < 0.005 < 0.005 1.08 0.72 0.105 RPV steel 0.14 0.07 0.195 0.007 0.006 1.30 0.75 0.064
The compositions were also checked by atom probe tomography (APT) analysis at the University of Rouen (France) before irradiation, in the Fe-0.1% Cu, Fe-Mn-Ni, Fe-Mn-Ni-Cu model alloys and in the RPV steel [79]. The results for these analyses are in atomic percentage (at %) and summarized in Table 9 (Note that Table 8 was given in wt %).
p. 64 Materials and irradiation conditions
Figure 30 The internal friction measurements of the as-received pure iron, Fe-C, binary Fe-Cu alloys and the Fe-Mn-Ni alloy [80].
Table 9 The composition of the as received materials, obtained by atom probe tomography experiments in at%. Composition in at % Material C Si P Mn Ni Cu 0.0045 0.085 Fe-0.1% Cu ------± 0.001 ± 0.006 0.0045 1.12 0.73 Fe-Mn-Ni ------± 0.001 ± 0.02 ± 0.01 0.0034 0.98 0.57 0.068 Fe-Mn-Ni-Cu -- -- ± 0.0015 ± 0.02 ± 0.02 ± 0.006 0.048 0.48 0.008 1.07 0.6 0.05 RPV steel ± 0.01 ± 0.04 ± 0.006 ± 0.06 ± 0.05 ± 0.01
ICP-MS and APT measurements performed in the Fe-0.1% Cu and Fe-Mn-Ni alloys are in good agreement. In the Fe-Mn-Ni-Cu alloy, the APT measurements give however lower values than ICP-MS. The difference is most probably due to the non-homogeneous distribution of the alloying elements in the whole produced ingots, correlated with the very small APT sample volume (see chapter 3 for more information on APT). In the case of the RPV steel, the observed depletion in Mn (1.32 at% in ICP-MS) and C (0.65 at% in ICP-MS) is most certainly due to the presence of carbides, observed by transmission electron microscopy (TEM) [79]. Furthermore, the APT analyses were used to check the initial distribution of the solutes known to precipitate under irradiation (Cu, Mn, Ni and Si). The statistical χ2 test confirmed their homogeneous distribution before irradiation, at least in the samples checked by APT.
p. 65 Chapter 2
Specimen fabrication{ TC "Specimen fabrication" \f C \l "4" }
For each material and irradiation condition (five conditions + the as-received condition, for more details see the next section), specimens were fabricated as listed in Table 10. The tensile specimens were produced at EDF (France) and the rest at SCK•CEN. An illustration of the shape of the tensile specimens is given in Figure 31. In addition to these specimens, enough material to fabricate 12 transmission electron microscopy samples was prepared at CIEMAT (Spain), which was encapsulated in small 5 × 5 × 3 mm3 boxes.
Table 10 The type of specimens that were fabricated for investigation of the REVE materials. Amount Size Application 4 See Figure 31 Tensile tests - Small angle neutron scattering (non-destructive) 3 10 × 10 × 1 mm3 - Positron annihilation spectroscopy (non-destructive) - Hardness tests 20 φ (0.2 mm) × 20 mm Atom probe tomography 2 1.3 × 1.3 × 15 mm3 Internal friction
Figure 31 A schematic drawing of the tensile specimens [80].
Metallographic study{ TC "Metallographic study" \f C \l "4" }
The microstructure of the alloys before irradiation is shown in Figure 32. In addition, Table 11 gives the average grain size and the dislocation density determined for the individual alloys before irradiation. They were obtained by conventional metallography and TEM, respectively.
p. 66 Materials and irradiation conditions
Table 11 The average grain size and dislocation density for each as received model alloy. The grain sizes are estimated using conventional metallography, while TEM is used for the determination of the dislocation densities. Material Pure Fe Fe-C Fe-0.1% Cu Fe-0.3% Cu Fe-Mn-Ni Fe-Mn-Ni-Cu Average grain size 250 350 125 177 88 88 (µm) Dislocation density 7 ± 2 9 ± 1 9 ± 2 9 ± 1 3.2 ± 0.5 3.8 ± 0.4 (1013m-2)
Optical microscopy TEM Optical microscopy TEM
Pure Fe Fe-C
Fe-0.1% Cu Fe-0.3% Cu
Fe-Mn-Ni Fe-Mn-Ni-Cu Figure 32 Optical and transmission electron microscope observations of the as received model alloys [80].
The model alloys resulted to be essentially composed of ferritic grains having a size ranging from ca 90 to about 250 µm when going from the quaternary alloy (Fe-Mn-Ni-Cu) to pure Fe. While the grain size decreases slightly with increasing alloy complexity, the average initial dislocation density is very similar in all alloys, about 5 × 1013 m-2 (dislocation density can vary from about 1 × 1010 m-2 in a defect-free metal, to ca 1 × 1015 m-2 in a metal after work hardening).
p. 67 Chapter 2
Mechanical properties{ TC "Mechanical properties" \f C \l "4" }
The tensile tests and hardness measurements on the non-irradiated materials have been measured at room temperature. Figure 33 presents the results of the tensile tests for the materials considered in this experimental program. Both the yield strength (YS) and ultimate tensile strength (UTS) values are related to the hardening of the material. Therefore, Figure 34 visualizes both strengths as a function of the Vickers hardness. Both strengths exhibit in reasonable approximation direct proportionality with the corresponding Vickers hardness.
Figure 33 The engineering stress-strain curves of pure iron, Fe-C, Fe-0.1% Cu, Fe-0.3% Cu, Fe-Mn- Ni and the RPV steel for the non-irradiated specimens.
Figure 34 The yield and ultimate tensile strengths versus the Vickers hardness for the materials of the REVE project experiment before irradiation, tested at room temperature.
The correlation factor between the hardening and the YS and UTS is found to be respectively 3.26 and 3.19. As also seen in the figure, these values are very similar. Values of the ratio of the Vickers hardness to the YS and the UTS can be found in literature for steels [81]. The former ratio has been found to be 0.79 (here 0.307), while the latter ratio is given by 0.81 (here 0.313). The factors given by the literature are equivalently equal, compared with the values found here. However, a difference of about 2.5 is found. This is most probably due to the difference between model alloys and steels, by the presence of carbides.
p. 68 Materials and irradiation conditions
However, in the case of the Fe-Mn-Ni-Cu alloy, due to a shortage of material, no tensile tests could be performed on the as-received material. From the hardness data and the above shown relation between this hardness and both yield and ultimate tensile strength, it was possible to estimate, with good approximation, the corresponding strengths.
MIRE-Cr matrix{ TC "MIRE-Cr matrix" \f C \l "3" }
High-Cr iron alloy modelling steels that are candidates to be used for future generation reactors, have been investigated as well and compared with the results from the REVE matrix. The material was fabricated within the PhD-thesis of Milena Matijsevic [55].
Fabrication{ TC "Fabrication" \f C \l "4" }
Four Fe-Cr based model alloys were produced, namely Fe-2.5% Cr, Fe-5% Cr, Fe- 9% Cr and Fe-12% Cr. Pure iron has not been explicitly investigated, but the results obtained from the REVE matrix are used whenever it is needed for comparison. The model alloys were fabricated at the University of Ghent (Belgium), by furnace melting of industrial purity Fe and Cr. After casting, the obtained ingots were cold worked under protective atmosphere to fabricate plates of 9 mm thickness. These plates were then annealed for 3 hours at about 1320 K in high vacuum for austenisation and stabilization. The duration of the heat treatment was chosen in order to get rid of any possible precipitation or phase transformation that might have happened during hot rolling and also to allow a maximum degassing of the alloys. This treatment was then followed by air cooling to room temperature. The tempering procedure, following the normalizing treatment, is of critical importance for the high-Cr steels. It was found that tempering at ca 1000 K for 4 hours followed by air cooling was the best way to ensure a full martensitisation of the higher Cr model alloys.
In addition, two 9 wt% Cr ferritic-martensitic steels have been investigated, namely T91 and Eurofer 97. The former, a commercially available ferritic-martensitic steel, was provided by CEA (Saclay, France) in the framework of the SPIRE project [82] and delivered as plates of 25 mm thickness. The latter, the experimental European reduced activation ferritic- martensitic (RAFM) steel, was provided by FZK (Karlsruhe, Germany) within the EFDA task TTMS001 [83] and delivered in the form of a forged bar with a diameter of 100 mm.
p. 69 Chapter 2
Both materials were delivered in normalized and tempered conditions. For T91 the normalizing treatment consisted of heating the alloy up to about 1310 K for 1 hour, after which the material was air cooled to room temperature. This treatment produced a full martensitic structure. The tempering treatment for this materials consisted of heating the normalized steel up to ca 1000 K for 3 h 42 min, followed by air cooling to room temperature. On the other hand, the investigated samples of Eurofer 97 were treated for 1 h 51 min at about 1250 K, followed by air cooling, before a tempering treatment at ca 1010 K for 3 h 42 min [84].
Chemical composition{ TC "Chemical composition" \f C \l "4" }
After the heat treatments, the chemical composition of each model alloy and steel was measured using induced coupled plasma mass spectrometer (ICP-MS) and the combustion technique at OCAS (Zelzate, Belgium). The chemical compositions are listed in Table 12. For the model alloys, the amount of impurities does not exceed 300 wt ppm.
Table 12(a) The chemical composition of the as received materials, obtained by induced coupled plasma mass spectroscopy in wt%. Composition in wt % Material C N O Al Si P S Fe-2.5% Cr 0.01 0.012 0.04 0.003 0.02 0.01 0.002 Fe-5% Cr 0.02 0.013 0.07 0.003 0.04 0.01 0.006 Fe-9% Cr 0.02 0.015 0.07 0.007 0.09 0.01 0.001 Fe-12% Cr 0.03 0.024 0.03 0.003 0.11 0.05 0.006 T91 0.10 0.030 -- -- 0.32 0.02 -- Eurofer 97 0.12 0.016 -- -- 0.07 < 0.005 --
Table 12(b) The chemical composition of the as received materials, obtained by induced coupled plasma mass spectroscopy in wt% (continue). Composition in wt % Material Ti V Cr Mn Ni Mo Ta W Fe-2.5% Cr 0.004 0.001 2.4 0.01 0.04 ------Fe-5% Cr 0.003 0.001 4.6 0.02 0.06 ------Fe-9% Cr 0.003 0.002 8.4 0.03 0.07 ------Fe-12% Cr 0.004 0.002 11.6 0.03 0.09 ------T91 -- 0.24 8.3 0.43 0.24 0.96 -- < 0.01 Eurofer 97 -- 0.19 9.0 0.43 0.07 < 0.001 0.13 1.1
p. 70 Materials and irradiation conditions
Specimen fabrication{ TC "Specimen fabrication" \f C \l "4" }
The amount, size and shape of the specimens loaded in the MIRE-Cr experiment was done in such a way that all fundamental properties of the material can be obtained. Table 13 illustrates the test matrix, elaborated to fulfil this task. Additionally, mini Charpy-V and compression specimens were made for the characterization of the as-received material. In total, within MIRE-Cr project, 777 specimens were fabricated, among which 480 specimens were irradiated. In this work, only the specimens irradiated to the lowest dose were analyzed.
Table 13 The type of specimens that were fabricated for investigation of the MIRE-Cr materials. Amount Size Application 6 See Figure 35 Tensile tests 3 5 × 5 × 1 mm3 Positron annihilation spectroscopy - Small punch tests 20 - TEM analysis
Figure 35 The geometry and size of tensile specimens (in mm) [55].
Metallographic study{ TC "Metallographic study" \f C \l "4" }
The metallographic examination of all as received materials was carried out. The results of optical microscope and TEM observations are shown in Figure 36. The microstructure observed by TEM is illustrated by bright field images. In addition, Table 14 summarizes the average grain size and dislocation density, estimated by optical microscopy and TEM, respectively. The density of dislocations is shown to be similar for all materials.
p. 71 Chapter 2
Optical microscopy TEM Optical microscopy TEM
Fe-2.5% Cr Fe-5% Cr
Fe-9% Cr Fe-12% Cr
T91 Eurofer 97 Figure 36 Optical and transmission electron microscope observations of the as received model alloys [55].
Table 14 The average grain size and dislocation density for each as received model alloy and steel. The grain sizes are estimated using conventional metallography, while TEM is used for the determination of the dislocation densities. Material Fe-2.5% Cr Fe-5% Cr Fe-9% Cr Fe-12% Cr T91 Eurofer 97 Average grain size 50 35 20 15 37 14 (µm) Dislocation density 1.2 5.8 6.3 5.5 5 8 (1013 m-2)
The Fe-Cr model alloys exhibit a changing microstructure with increasing Cr content. Grain size decreases with Cr concentration and it is determined to vary from 50 to 20 µm for model alloys. With the increase of Cr content, the microstructure varies from ferritic to ferritic-bainitic. TEM bright field images of Fe-2.5% Cr and Fe-5% Cr alloys show massive amount of ferrite grains with randomly oriented grain boundaries that are the signature of fast cooling, which prevents the formation of equiaxed ferrite. Higher Cr alloys with 9 % and
p. 72 Materials and irradiation conditions
12 % of Cr have very small sub-grains, of the order of 1 µm. Their microstructure consists of bainitic ferrite, which is obtained by rapid cooling. Furthermore, it can be seen that, with increasing Cr content, the model alloys have a strongly pronounced cellular dislocation structure, with variations in cell sizes and shapes. Therefore the microstructure of high Cr alloys is very similar to the ferritic-martensitic steels, as the grains resemble martensitic laths. The microstructure of the T91 and Eurofer 97 steels is tempered ferritic-martensitic, with high dislocation density sub-boundaries in the matrix. There are no significant differences in the martensitic lath structure and distribution of carbides between these two steels. The carbides are of type M23C6 and their sizes vary from about 0.14 to 0.6 µm. The sub-boundaries are stabilized by the precipitation of carbides, but the carbides are also found at the prior austenite grain boundaries. The prior austenitic grain size is 14µm for Eurofer 97 and 37µm for T91, and the martensite laths have a size of 1µm. The grain size is at this stage the main difference between these two steels, which is probably due to the presence of Ni in T91, which increases the initial austenitic grain size. A higher tantalum concentration in Eurofer 97 can also account for the smaller prior-austenitic grain size in the Eurofer 97 steel.
Mechanical properties{ TC "Mechanical properties" \f C \l "4" }
Tensile tests and hardness measurements have been performed at room temperature. Engineering stress-strain curves are presented in Figure 37.
Figure 37 The engineering stress-strain curves for the non-irradiated specimens [55].
p. 73 Chapter 2
The hardness measurements have been done according to the requirements of ASTM E384. Measurements were done in all directions and average values are taken. In Figure 38, the yield strength (YS), ultimate tensile strength (ULT) and hardening results are plotted as a function of chromium concentration. In the model alloys, a linear increase can be found for all three properties with increasing chromium content, while the steels exhibit higher values.
Figure 38 The tensile property (left) and hardness (right) evolution as a function of chromium content [55].
p. 74 Materials and irradiation conditions
2.2. Irradiation Samples from each material were neutron irradiated in the CALLISTO loop of the BR2 test reactor at SCK•CEN (Mol, Belgium). During irradiation, the temperature and the pressure were maintained constant at about 575 K (~ 300 °C) and 15 MPa, respectively. These irradiation conditions mimic the situation encountered in a pressurized water reactor. Using the higher flux of the test reactor, irradiation doses up to 0.2 displacements per atom (dpa) are reached within a few weeks of irradiation. This dose corresponds to about 80 years of operation at the highest flux of pressurized water reactors. Future generation reactors are supposed to have a much higher irradiation flux, leading to much higher doses at the planned end-of-life of the reactors. Obtaining comparable doses in the current test reactors takes a very long time and is very expensive. As a first step, it is any way useful to investigate the influence of the material composition in the dose range for which already a lot of data on other steels are available. Comparable irradiation doses were thus investigated to check the differences in effect of material composition.
Belgian reactor 2{ TC " Belgian reactor 2" \f C \l "3" }
The Belgian reactor 2 (BR2) is a high flux material test reactor. The reactor has been designed in 1957, became critical in 1963 and has been refurbished in 1980 and 1996. Its nuclear power is nominally 125 MW. BR2 differs from comparable material test reactors by its unique core geometry. The core is composed of hexagonal beryllium blocks with channels through their centres. These channels form a twisted hyperboloidal bundle and hence are close together at the midplane but more apart at the upper and lower ends, where the channels penetrate through the covers of the reactor pressure vessel. With this array, a high fluence density is achieved in the middle part of the vessel (reactor core) while leaving enough space at the extremities for easy access to the channel openings [85]. The core geometry of the BR2 reactor is illustrated in Figure 39, where a schematic overview is given, as well as a top view of the reactor.
p. 75 Chapter 2
Figure 39 (left) A schematic general view of the BR2 reactor and (right) a top view of the reactor [9].
Applications{ TC "Applications" \f C \l "4" }
Thanks to its high neutron flux and large amount of irradiation spaces, BR2 plays a prominent role in the research of the behaviour of materials and fuel under irradiation. These investigations are performed within international collaborations for both the current NPPs, as well as for future systems, such as generation IV and fusion reactors.
BR2 also produces radioisotopes, for instance for diagnose and therapy applications in the nuclear medicine, for controlling of welds in the industry, as mark in the agriculture and for fundamental research. In addition to the above mentioned application, BR2 performs commercial irradiation for the production of semiconductors for the microelectronics, such as the neutron doping of silicon. The thereby doped silicon has a very pure quality.
CALLISTO{ TC "CALLISTO" \f C \l "4" }
CALLISTO stands for capability for light water irradiation in steady state and transient operation [86]. The CALLISTO rig is an experimental loop of the PWR type, which is nearly unique in Europe with real circumstances, such as high pressure, high temperature, realistic thermo hydraulics and realistic chemistry of the water. With this loop, it is possible to study the behaviour of commercial PWR-RPV material and fuel.
p. 76 Materials and irradiation conditions
CALLISTO consists of three experimental rigs, in-pile sections (IPS) 1 to 3, which are installed in three reactor channels to meet various irradiation conditions. They are connected to a common pressurized loop, which can deliver a wide range of pressure and temperature working regimes. The cross-section of each IPS is illustrated in Figure 40. In each IPS, 9 rods, each about 1 m long, are present, which can be filled with test materials or fuel.
Figure 40 The cross section of the CALLISTO fuel basket [9].
REVE matrix irradiation{ TC "REVE matrix irradiation" \f C \l "3" }
Samples from the REVE matrix were neutron irradiated in the CALLISTO loop at five different irradiation conditions. The temperature and the pressure were maintained constant during irradiation respectively between 570 and 575 K and at 15 MPa, thereby mimicking the conditions encountered in a reactor.
Encapsulation{ TC "Encapsulation" \f C \l "4" }
The prepared specimens were inserted at SCK•CEN in ad-hoc fabricated 3 mm-thick specimen-holders and then adequately encapsulated in He-tight stainless steel capsules. In each irradiation group, consisting of then capsules, 4 dosimeters (Al-1% Ag for the thermal spectrum, Al-1% Co for the epithermal spectrum and Fe and Ni for the fast spectrum) were inserted in selected positions to asses the spatial variation of the flux within. The photographs in Figure 41 show the reactor basket, as it was used for the REVE irradiation.
p. 77 Chapter 2
Figure 41 (upper) Photograph of the BR2 rig including the capsules of the REVE experiments. (lower) Zoom of the capsules irradiated at lower flux [80].
The irradiation was performed in water, but the specimens were not in contact with it, to avoid corrosion. The materials were thus wrapped tightly in steel capsules to avoid this contact. The capsules were also designed to ensure a high thermal conductivity and proper heat removal, thereby limiting the effects of γ heating.
Temperature control{ TC "Temperature control" \f C \l "4" }
The whole arrangement was carefully designed to guarantee that the temperature in all specimens remained constant. In order to check this, finite element thermo hydraulic calculations were performed using the SYTUS code, which includes the effect of gamma heating. Conservative assumptions were made, such as loose contact between specimens and capsule walls and a constant water temperature of 300 °C (573 K). The actual temperature was however expected to be in-between 290 and 295 °C (563-568 K). Figure 42 illustrates that the temperature exceeds nowhere 310 °C, while the temperature distribution is rather uniform. The temperature was thus expected to be at most a little more than 300 °C everywhere.
Indeed, the average temperature measured by the numerous thermocouples (more than 14 per capsule) was (300 ± 5) °C.
p. 78 Materials and irradiation conditions
Figure 42 The temperature distribution according to finite element calculations in the most critical region of the specimen-holder, containing the REVE specimens [80]. The calculations have been performed using the SYTUS code, with conservative hypotheses and including the gamma heating.
Neutron energy spectra{ TC "Neutron energy spectra" \f C \l "4" }
The neutron energy spectra were calculated by a Monte Carlo n-particle (MCNP) code [87]. This calculation was done to have the correct input for radiation damage models, mimicking the behaviour of the investigated matrix. Indeed, within the PERFECT project, modelling efforts were undertaken to simulate the results coming from the experimental testing. The spectrum calculations were done for both positions occupied by the specimens in the BR2 reactor (i.e. midplane/high flux and top level/low flux). As a first approximation, the spectra were assumed to be constant in the whole volume containing all capsules of a certain group. Figure 43 presents the results of the spectra, obtained in this approximation.
Figure 43 The results of the MCNP calculations of the BR2 neutron energy spectra in the two positions (midplane/high flux and top level/low flux) of relevance for the REVE irradiation.
p. 79 Chapter 2
Flux and fluence{ TC "Flux and fluence" \f C \l "4" }
All materials from the REVE matrix were neutron irradiated in the CALLISTO loop to four different doses, up to a damage of about 0.2 displacements per atom (dpa). It is worth mentioning that at the highest flux of pressurised water reactors, an irradiation dose of about 0.1 dpa corresponds to the displacement dose of about 40 years of operation and therefore to the planned lifetime of most western NPPs. Moreover, an additional irradiation was performed at lower flux, to determine the flux effect on the irradiation-induced damage. To irradiate these samples, the top part of the reactor was used, to guarantee an as large as possible difference with respect to the value of the flux at the midplane. However, the top level has an axial flux gradient. In order to minimize the effect of this gradient and to have a uniform fluence in all specimens, the capsules were 180°-rotated after half of the irradiation time.
The reached neutron fluences and fluxes were determined via the analysis of the multiple flux monitors that were inserted in each capsule. The dosimeters were placed in a stainless steel tube. The fast spectrum is detected by Fe and Ni dosimeters, measuring the activity of 54Mn, 58Co and 93mNb. These elements are formed by the following reactions. Small corrections due to the burn up of 58Co had to be applied on the Ni dosimeters.
54 1 54 1 26 Fe+ 0 n→ 25 Mn+1 p (46) 58 1 58 1 28 Ni+ 0 n→ 27 Co+1 p (47) 93 1 93m 1 41 Nb+ 0 n→ 41 Nb+ 0 n' (48)
For the thermal spectrum an Al-1% Ag dosimeter was used, while the epithermal spectrum was detected by an Al-1% Co dosimeter. In these cases, the fluxes are derived from the following reactions.
59 1 60 27 Co+ 0 n→ 27 Co + γ (49) 109 1 110 47 Ag+ 0 n→ 47 Ag + γ (50)
Table 15 summarizes the full set of reached irradiation fluences, their corresponding dose and their average flux during irradiation. The results for the thermal neutrons are given as well as for the neutrons having an energy higher than 1 MeV. The dose in dpa was
p. 80 Materials and irradiation conditions obtained by dividing the fluence of the high energy neutrons by the well-known conversion fraction (cf 6.67 × 1020 n cm-2 dpa-1) valid for steels.
Table 15 The determined neutron flux and fluence of the materials after irradiation. 13 -2 -1 19 -2 Irradiation Flux (10 n cm s ) Fluence (10 n cm ) Dose
time (days) n-thermal En > 1 MeV n-thermal En > 1 MeV (dpa) 2 9.4 ± 0.5 9.0 ± 0.7 1.5 ± 0.7 1.8 ± 0.1 0.026 4 9.3 ± 0.6 9.5 ± 0.5 3.0 ± 0.5 3.5 ± 0.3 0.052 8 9.5 ± 0.5 8.6 ± 0.5 6.9 ± 0.5 6.9 ± 0.5 0.10 16 9.6 ± 0.5 9.5 ± 0.5 12.5 ± 1.1 13.1 ± 1.1 0.20 175 0.15 ± 0.05 0.16 ± 0.06 2.4 ± 0.5 2.1 ± 0.5 0.032
It should be noted that the neutron flux of the samples irradiated at high flux (~ 1 × 1014 n cm-2 s-1) is three orders of magnitude higher than the typical flux seen by the pressure vessel of a pressurized water reactor (i.e. 1 × 1011 n cm-2 s-1), while the low flux (~ 1 × 1012 n cm-2 s-1) condition still show one order of magnitude difference. The examined fluxes have thus between them two orders of magnitude difference, to investigate the influence of the irradiation flux.
MIRE-Cr matrix irradiation{ TC "MIRE-Cr matrix irradiation" \f C \l "3" }
The irradiation of the MIRE-Cr matrix underwent analogue conditions as explained for the REVE matrix. The material is irradiated to three different doses, namely 0.06, 0.6 and 1.5 dpa at a neutron flux of about 7.5 × 1013 n cm-2 s-1. The irradiation conditions are given with ample details in [55]. For comparison with the results of the REVE matrix, only the material irradiated up to 0.06 dpa is investigated in this work.
p. 81 Chapter 2
2.3. Conclusions Different model alloys have been investigated for better understanding of the influence of the alloying elements, such as carbon, copper, manganese and nickel. The fundamental effect of chromium addition is investigated on the behaviour of binary Fe-Cr alloys. Next to these model alloys, commercial steels were added for comparison. In this chapter, properties of these materials were given, such as their chemical composition and their as-received microstructural and mechanical properties.
Different irradiation conditions have been considered to examine the influence for instance of the neutron fluence and flux. The irradiation conditions used are adapted to mimic as much as possible the environmental conditions of a commercial generation II pressurized water reactor (in the CALLISTO loop of the BR2 reactor). The materials of the two investigated matrices were irradiated to the same conditions, under comparable neutron fluxes and to similar doses. This is done, in order to be able to compare their results, and to investigate the influence of their composition more closely.
p. 82
Chapter 3 Techniques
“You have your way. I have my way. As for the right way, the correct way, and the only way, it does not exist.” Friedrich Nietzsche (Germany 1844-1900)
In chapter 1, the irradiation-induced mechanisms causing hardening and embrittlement in RPV steels were introduced. These mechanisms were classified within three groups, i.e. the irradiation-induced precipitates, the so-called matrix damage, including nanovoids and self-interstitial clusters, and the grain boundary segregation. All clusters (including the precipitates) formed under irradiation at the temperatures and neutron doses of interest are generally ≤ 2 nm in diameter. Only self-interstitial loops are sometimes observed to be bigger in model alloys. Therefore, only some accurate experimental techniques for microstructural characterization are sensitive to these defects. In addition, they should be adapted for the examination of irradiated materials. The advantages and disadvantages of different techniques used for this purpose are presented in the first section of this chapter.
This thesis focuses on the use of the positron annihilation spectroscopy technique. Therefore, this technique is described in detail in a second section of the chapter. The improvements necessary to measure activated specimen is also detailed.
In addition, atom probe tomography experiments have been performed within this thesis. And within the European PERFECT project, also tensile tests, as well as small angle neutron scattering and transmission electron microscopy examinations were executed. All these techniques are necessary to obtain a complete picture of the irradiation-induced defects, and their effect on the hardening. Therefore, all used techniques are shortly introduced in the third section of this chapter.
A short conclusion on the different techniques ends this chapter.
p. 83 Chapter 3
Table of content Chapter 3 Techniques...... 83 3.1. Introduction ...... 85
3.2. Positron annihilation spectroscopy...... 87 3.2.1. Theory of the positron annihilation...... 87 Principle ...... 87 Positron annihilation sites ...... 88 Positron sources ...... 91 3.2.2. Positron annihilation lifetime spectroscopy...... 92 Positron lifetime experiment ...... 92 Experimental technique...... 92 Positron lifetime measurements ...... 93 Working procedure...... 93 Analysis...... 94 3.2.3. Coincidence Doppler broadening...... 97 Doppler broadening experiment...... 97 DB versus CDB...... 98 Experimental technique...... 98 Coincidence Doppler broadening measurements ...... 99 Working procedure...... 99 Analysis...... 99
3.3. Atom probe tomography ...... 103 APT experiment ...... 103 Field ion microscope ...... 103 Atom probe microanalysis...... 104 Position sensitive atom probe...... 105 Experimental technique...... 106 Atom probe measurements...... 107 Measurement ...... 107 Calibration...... 108 Results...... 109
3.4. Transmission electron microscopy...... 110 TEM technique...... 110 Experimental technique...... 111 Measurements ...... 112
3.5. Small angle neutron scattering ...... 113 SANS experiment ...... 113 Experimental technique...... 114 SANS measurements...... 114
3.6. Tensile tests...... 117 Theory...... 117 Experimental setup...... 117 Measurements ...... 117
3.7. Conclusions ...... 118
p. 84 Techniques
3.1. Introduction The central feature of the irradiation-induced microstructure in irradiated RPV steels is that the clusters formed under irradiation at the temperatures and neutron doses of interest are generally very small. Thus, advanced techniques, capable of detecting such small features, must be employed. Several techniques have emerged as being sufficiently mature to be reliably applied to characterize the irradiation-induced microstructural changes in commercial RPV steels. The main features of these techniques, used to identify the defects causing the hardening in irradiated samples, are summarized in Table 16 and Table 17 [23], [88]. The specifications given in the tables are for the general use of the techniques. In specific cases, when special care is taken to optimize the techniques for the observation of the irradiation- induced nanofeatures, they can offer a better resolution.
Table 16 The resolution and the analyzed volumes of different techniques. Technique Resolution Analyzed volume Transmission electron microscopy - ~ 50 nm thick ≥ 2 nm (TEM) - Area depends on foil quality Scanning TEM (STEM) Chemical information Idem TEM High resolution TEM (HRTEM) Atomic scale Idem TEM Positron annihilation - ~ 0.5 mm positron penetration Atomic scale spectroscopy (PAS) - ~ 5 mm area diameter Small angle neutron scattering - ~ 2 mm thick 0.5 – 50 nm (SANS) - ~ 8 mm beam diameter Muon spin resonance (µSR) Vacancies Little restrictions on sample size - Surface layer: 1 - 3 µm thick Ion channelling (IC) Concentration > 10-3 - 1 - 5 nm beam diameter Internal friction (IF) Concentration > 10-6 ~ 1.3 × 1.3 × 15 mm3 (or bigger) Mössbauer spectroscopy (MS) Atomic environment Little restrictions on sample size Field ion microscopy/Atom probe Atomic scale ~ 10 × 10 × 200 nm3 tomography (FIM/APT)
It is apparent from Table 16 and Table 17 that no single technique can provide all the information required to characterize the irradiation-induced microstructure. Also Figure 44 illustrates that the combination of different techniques is necessary to obtain the full picture of defects of all sizes and concentrations [89]. In addition, the interpretation of the information given by each technique needs proper attention and therefore applying several techniques to the same specimens appears to have synergical benefits.
p. 85 Chapter 3
Table 17 The possibility to observe the matrix damage and the precipitates by each technique and its specific limitations. Technique Matrix damage Precipitates Limitations TEM ≥ 2 nm No (when coherent) Specimen thickness Approximated concentrations of STEM No Complex interpretation alloying elements HREM Yes ? If lattice mismatches exist Complex interpretation - Positron affinitive clusters - Bulk average PAS Vacancies (< 50) (e.g. Cu precipitates in Fe) - Complex interpretation - If clusters contain vacancies - Complex interpretation - Cluster size SANS Yes - Bulk average - Indirect cluster composition - Low spatial resolution µSR Yes Yes Only model alloys IC Small clusters Small clusters Bulk average IF Small clusters Small clusters Only selected defects Solute-defect - Only specific systems MS No complexes - Complex interpretation FIM/APT Yes Cluster size and composition Limited volume
Figure 44 The observable defect sizes (left) and concentrations (right) as functions of the specimen depth for PAS, scanning tunnelling microscopy (STM), atom probe field-ion microscopy (AFM), TEM, optical microscopy (OM), X-ray scattering and neutron scattering (nS) [89]. The AFM is a surface detection method, while APT is able to analyze much bigger specimens.
In the following sections, special attention is given to the nowadays widely used techniques, namely PAS, APT, TEM and SANS. This thesis focuses on the use of the PAS technique. Therefore, this technique is described in detail in this chapter. But, besides the positron measurements, other measurements were performed by colleagues in Europe and all over the world, on the same set of specimens. This was done with the intention to form a complete picture on the defects, produced by irradiation in the materials, and their effect on the mechanical properties.
p. 86 Techniques
3.2. Positron annihilation spectroscopy One of the methods that give valuable information for the study of defect formation under neutron irradiation and their thermal stability is positron annihilation spectroscopy (PAS) [50], [90]-[92]. As vacancies are the diffusion vehicles in metals, they play a determining role in the formation and evolution of precipitates and matrix damage. PAS is found to be an excellent experimental technique to identify the evolution of these vacancy types of defects, as well as of selected solutes, due to its self-seeking and self-selective nature [50], [91], [93], [94]. Typical examples of positron annihilation sites are vacancy-type of clusters and positron affinitive ultra-fine precipitates.
Various measurement techniques are used in the field of positron annihilation, such as the positron lifetime, the Doppler broadening and the angular correlation measurements. A detailed description of each technique can be found in [93]. Positron annihilation lifetime spectroscopy (PALS) and coincidence Doppler broadening (CDB) spectroscopy, both available in the hot cell laboratory of SCK•CEN, are used in a complementary way. While PALS measurements give information on the electronic density of the material at the place of the positron annihilation, CDB spectroscopy allows the measurement of the momentum distribution of the electron-positron annihilation pair (especially inner shell electrons), giving information on the chemical environment of the positron annihilation site.
3.2.1. Theory of the positron annihilation A general introduction and short history of the positron is given in appendix A. In this section, the behaviour of the positron in metals, the different annihilation sites and the possible positron sources are discussed.
Principle{ TC "Principle" \f C \l "4" }
As it will be explained further on in this section, different positron sources are available. For the explanation of the theory behind the positron annihilation experiment, as illustrated in Figure 45, a sodium-22 (22Na) source is used, as this is also the source applied in the
p. 87 Chapter 3 experiments done within this work. The main advantage of sodium-22 is that within a few picoseconds after the positron is released, a γ-ray is emitted with an energy of 1 274 keV. This γ-ray is detected and used as the birth of the positron.
Figure 45 The schematic view of the positron annihilation experiment, with the different steps in the positron life: 0. Positron birth; 1. Implantation; 2. Thermalization; 3. Diffusion; 4. Trapping; 5. Positron annihilation.
After its thermalization (with a total crossed material length of ~ 100 µm, in a matter of a few ps), the injected positron will diffuse in the matrix, i.e. typically 100 nm in metals. This diffusion process determines the "self-seeking" nature of the positron [50]. During this diffusion, the positron can be trapped by the defects. This is the so-called "self-selective" nature of the positron. At this defect, the positron will stay until it annihilates with an electron nearby. During annihilation, the electron-positron pair will disappear by emitting two anti-collinear γ-rays with an energy of 511 keV. The lifetime of the positron can thus be measured as the time delay between the birth and the annihilation gammas.
Positron annihilation sites{ TC "Positron annihilation sites" \f C \l "4" }
The PAS technique in general is found to give valuable information on the irradiation- induced defects for the following reasons [50]. In this technique, the positron can be regarded as a probe. As antiparticle of the electron, the positron has a positive charge. Therefore, it can be trapped by sites with a negative charge, such as vacancies, vacancy clusters, interfaces, second phase particles, dislocations, etc [95], [96]. These sites have in most cases a different electron density than the bulk material. The positron annihilation characteristics in the neighbourhood of these defects are thus different when compared to defect-free materials.
Figure 46 illustrates the positron density at vacancy-type defects. The calculations are carried out employing the so-called atomic superposition (ATSUP) model [97], which has p. 88 Techniques been implemented in a code developed at Charles University in Prague (Czech Republic). The imaging has been done with the Amira program [98].
Figure 46 The positron density in a perfect iron crystal (left), at a monovacancy in an iron crystal (middle) and at a vacancy cluster (V15) in an iron crystal (right).
Trapping can be understood as the process of transition from the delocalized state of the positron to a more localized one. The tendency of such trapping can be easily understood. A thermalized positron in a metal is strongly repelled by the positive ions, due to its positive charge. This is visualized in the left-side image of Figure 46. The positron density has thus the same periodicity as the crystal structure. In the case a potential well is present, the positron can relax therein, decreasing its energy. Examples of attractive centres for positrons are vacancies, voids and dislocations, as these places have a decreased repulsion between the positron and ion cores. Figure 46 also shows that the trapping probability will increase with growing vacancy cluster size. Nevertheless, the potential well of a single vacancy is already large enough to trap the positron.
Moreover, due to the difference in the positron affinity of the different atomic species, positrons can annihilate with a higher probability in precipitates as compared to the bulk material [94]. The positron affinities for many elemental metals, calculated by Puska et al. [99], are given in Table 18.
Table 18 Calculated positron affinities (eV). Li Be C
-7.36 -3.14 -2.50 Na Mg Al Si
-7.12 -6.18 -4.41 -6.95 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ge
-7.05 -6.40 -5.10 -4.06 -3.44 -2.62 -3.72 -3.84 -4.18 -4.46 -4.81 -5.24 -6.69 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd Sn
-6.98 -6.41 -5.31 -3.98 -2.93 -1.92 -1.67 -1.92 -3.10 -5.04 -5.36 -5.78 -7.60 Cs Ba Lu Hf Ta W Re Os Ir Pt Au Pb
-6.94 -6.13 -4.90 -3.70 -2.63 -1.31 -0.97 -0.89 -1.53 -3.63 -4.59 -5.56
p. 89 Chapter 3
The positron affinity of Cu-rich precipitates, for instance, is higher than the affinity of the Fe-matrix [99]. It should be mentioned that these affinities are given for the most stable structure of each element, i.e. fcc for Cu and bcc for Fe. The small copper-rich precipitates in the irradiated samples are however of bcc structure. Brauer et al. calculated the positron affinity in both the bcc and fcc copper and found values which are very close to each other [100]. Nevertheless, the potential well of one copper atom in an iron matrix (about 1 eV) is too small and narrow to trap a positron. In a precipitate, however, the well becomes wider and the positron can be trapped.
In Figure 47, it is illustrated that the positrons are likely to be located at the edge of copper atoms, while the positron would be trapped in the middle of a vacancy. Nevertheless, if both vacancies and copper atoms are present, the positron density at the vacancies is much higher, compared to the one at the copper atoms. But, if a cluster consists of vacancies and copper atoms at the same time, the probability of trapping will be a little higher compared to the vacancies surrounded by iron atoms only.
Figure 47 (left) The positron density at a copper atom in an iron crystal. (middle) The comparison between the positron density at a monovacancy and a copper atom in an iron crystal. (right) The comparison between the positron density at a vacancy-copper atom pair and a monovacancy in an iron crystal. The copper atoms are represented by a small blue sphere, while the vacancies are given by a little bigger yellow sphere. The results obtained are calculated with the ATSUP program [97] and visualized by the Amira program [98].
The power of PAS lies in its "self-seeking" and non-destructive nature, which gives the possibility to find very small defects (> 0.1 nm) even at very low concentrations (starting from 1 ppm). Positrons are used in many different fields of materials science, for instance to characterize building materials (e.g. cement [101], polymers [102]-[104]), semiconductor- based systems for the information technology [105], as well as nuclear materials [50], [90], [91].
p. 90 Techniques
Positron sources{ TC "Positron sources" \f C \l "4" }
The easiest way to inject positrons in materials is with the use of radioactive isotopes, emitting positrons. Typical examples are 22Na, 58Co and 64Cu. As mentioned before, in this work the 22Na source is used. Besides the additional photon emission of 1 274 keV (indicating the birth of the positron), this source has a half life of about 2.6 years, which is long enough to avoid quick changes in the source activity and short enough to ensure a high activity with only a small source. The sodium is commercially available in the form of a NaCl-solution. The NaCl-solution is deposited on a foil and dried. Mostly used are kapton or Mylar foils. At SCK•CEN, the kapton foil is preferred, as it has only 1 contribution to the positron lifetime spectrum of about 382 ps. The source was made by evaporating 22NaCl onto a standard kapton foil (7 µm thickness), which was then sealed with another foil. Due to the β-decay, the source emits positrons with a broad energy distribution extending from zero up to 545 keV, as illustrated in Figure 48. As a result, the positrons are implanted in the sample from the surface to the bulk, with an average penetration depth of 100 µm in iron, where they annihilate with an electron into two anti-collinear 511 keV photons.
Figure 48 The positron energy spectrum emitted by a 22Na source and after moderation to obtain a mono-energetic positron beam [106].
Nowadays, also mono-energetic positron beams are used. Within this beam the energy of the positrons can be selected in a certain range. In this way, it is possible to perform a depth dependent examination of materials. However, the energy of such positrons is rather low compared to those of the positrons emitted by the sodium source and also the concentration of positrons (the activity) is much lower. Figure 48 gives an example of a mono-energetic positron spectrum. The major difficulty of a positron beam is to obtain the exact birth time of the positron.
p. 91 Chapter 3
3.2.2. Positron annihilation lifetime spectroscopy PALS measurements give information on the electronic density of the material at the place of the positron annihilation.
Positron lifetime experiment{ TC "Positron lifetime experiment" \f C \l "4" }
The actual lifetime of the positron is measured via this technique. Therefore, the difference in occurrence in time is taken of the birth gamma, detected by the start detector, and the two, coincident annihilation gammas, detected by the two stop detectors. This is schematically illustrated in Figure 45 and has been discussed before.
Experimental technique{ TC "Experimental technique" \f C \l "4" }
Although there are still difficulties in measuring radioactive specimens, PALS has been extensively used to characterize this type of materials, thanks to technical improvement, such as the ones recently proposed by our laboratory at SCK•CEN [107], [108] (see also appendix B).
Figure 49 The positron lifetime setup as it is installed in the hot cell laboratory of SCK•CEN.
Measurements of radioactive materials by means of PALS have been a concern for the last few decades. The difficulty concerning precise measurements of active material is the overlap of the γ-rays of 60Co and 54Mn that are produced by the activation of steels under neutron irradiation, with the γ-rays coming from the most practical positron source, namely 22Na. Indeed, as seen in Figure 50, the two successive photons with energy of 1 173.2 and 1 332.5 keV from 60Co cover the energy range of the nucleus gamma ( 22 Ne* → 22 Ne ) of
p. 92 Techniques
1 274 keV, corresponding to positron birth-gamma and can faultily trigger the start of the positron lifetime setup.
Figure 50 Gamma-ray energy spectra of non- radioactive and radioactive specimens measured with a BaF2 detector. The peaks represent different gamma-emitters: 1. Annihilation-gamma's at 511.0 keV; 2. 54Mn-gamma's at 834.8 keV; 3. Lower energy 60Co-gamma's at 1173.2 keV; 4. 22Na-source gamma's at 1274.6 keV; 5. Higher energy 60Co-gamma's at 1332.5 keV.
Back in 1996, Van Hoorebeke and co-workers [109] proposed at SCK•CEN the triple detector coincidence positron lifetime setup to overcome this problem. Since then, this approach has been used all over the world. Recently, the Van Hoorebeke original setup has been upgraded by using a digital oscilloscope [110].
The technical details can be found in appendix B. Here, it is noticed that the setup was optimized to analyze active samples. Lead shields were for instance placed between the different detectors, to reduce the Compton scattering, which is higher for active samples. The detectors have been updated to obtain a better time resolution. And the digital oscilloscope is capable of storing all signals, from which the user can subsequently filter the ones with no pileup and within the right energy range. This selection leads to further improvement of resolution function and signal-to-noise ratio of the positron lifetime set-up.
Positron lifetime measurements{ TC "Positron lifetime measurements" \f C \l "4" }
All specimens (non- and irradiated) are first surface polished to a mirror finish and then chemically etched using a (HF + H2O2 + H2O)-solution to remove the deformed surface layer. This is needed to be done before any positron measurement could be performed.
Working procedure{ TC "Working procedure" \f C \l "5" }
To perform positron lifetime measurements, a strict procedure is followed. A positron source, usually 22Na wrapped in a kapton foil, with a typical activity of 2 MBq, is sandwiched
p. 93 Chapter 3 between two specimens having the same characteristics (same material and same history) of maximal size of (10 × 10 × 1) mm3. The two specimens and the source are brought tightly together in a specimen holder. This operation is performed in either the hot cell or a fume hood depending on the activity of the specimen. After the mounting of the specimens and the source in the specimen holder, the latter is encapsulated in a lead container to be transported to the positron annihilation instrument.
In agreement with the radioprotection rules at the instrument surroundings, the radioactive specimens within the specimen holder are quickly and easily pulled out from the lead container and positioned in the measurement cell between the three BaF2 detectors working in coincidence mode (Figure 149 in appendix B). This is done automatically with a pneumatic loading system. After the optimization of the detector distances (depending on the radioactivity of the samples) the data acquisition can start. Due to the consequent long detector distances, the acquisition of statistically relevant number of counts, namely at least one million, requires measurements up to one month, for each of the high dose irradiated samples. All measurements were performed at room temperature.
Analysis{ TC "Analysis" \f C \l "5" }
The positron lifetime spectrum N(t) in time t obtained during the measurements is given by equation 51, which relates the intensities I i and the average positron lifetimes τ i , associated with the positron annihilation site of type i . It should be mentioned that the different positron lifetimes do interfere; the value of τ n does not only depend on the positron annihilation site n , but also from the intensities and the lifetimes of the other sites. In this equation, the effect of k different kinds of positron annihilation sites (defects) is superposed.
k +1 I i ⎛ t ⎞ N()t = ∑ ⋅ exp⎜− ⎟ (51) i=1 τ i ⎝ τ i ⎠
The positron lifetime spectra consist thus of exponential decays convoluted by a resolution function. The decomposition of the different components is very difficult. The program mostly used in the literature, for this decomposition, is PATFIT [111], [112], but in
p. 94 Techniques this work the LT program, written by Kansy [113], is used. In fact, it has been shown that PATFIT gives a better result, if the full width at half of the maximum ( FWHM ) of the resolution function is known exactly [114]. But as soon as there is a small deviation of the FWHM from the given one, the positron lifetime of the different components will deviate systematically. In the LT program, the FWHM can be fitted as well, as it can be taken as a constant. The fitting can be done by a single Gaussian, by several Gaussians or by a single Gaussian adjusted with two exponential decay functions. If the FWHM is fitted, the fit's variance will be much better. Both programs fit the spectra by the least squares criterion. So, as the two programs are based on the same theory, they give the same results, if the input values and the shape of the resolution curve are the same. But even in this case, the LT program has advantages, i.e. it is much easier to use. All results are given automatically, in terms of tables of data as well as in a graphical form. In addition, when many measurements have to be done, the LT program saves a lot of time.
In this work, the resolution function is represented by the sum of three Gaussians, as expressed in equation 52.
R = f 0 ⋅G(t; FWHM 0 , Δ 0 ) + f1 ⋅G(t; FWHM 1 , Δ1 ) + f 2 ⋅G(t; FWHM 2 , Δ 2 ) (52)
Here, G(t; FWHM, Δ) is a Gaussian in function of time t , centred round Δ , with a certain FWHM and f is the fraction of the respective term, for which it is known that the total resolution functions needs to have its maximum equal to one. In the LT program, Δ 0 is set to zero. Figure 51 shows an example of such a composed resolution curve.
Using the previously described setup and source, the total time resolution of the setup is constantly checked to be about 200 ps (for more details, see appendix B), while the source contribution is set to 15 %, with a single positron lifetime of 393 ps.
p. 95 Chapter 3
Figure 51 The resolution curve of a PALS measurement of pure iron, decomposed into three Gaussian functions.
The average error to be associated with the values is about ± 0.009 for the intensity and ± 3.5 ps for the positron lifetime. A typical example of a positron lifetime spectrum for pure unirradiated iron is given in Figure 52. The left side of the spectrum indicates the resolution function, while the right side of the spectrum shows an increase caused by the positron lifetime contributions of both the pure defect-free iron (component 1) and the source contribution (component 2).
Figure 52 A typical example of a positron lifetime spectrum (the yield is given in logarithmic scale), decomposed into one positron lifetime component and one source contribution component. Both the resolution function and the background are first subtracted for the calculations and then added to both components and the total curve.
It is known that the positron lifetime increases with increasing amount of vacancies in defects, as a low amount of electrons is available with increasing vacancy cluster size. When the spectrum is deconvoluted into two components (next to the source component), the second component will contain the information on the defects. A higher amount of defects will increase the intensity of this component. Therefore, using the positron lifetime results, the amount and size of vacancy-type defects can be determined. Alloying elements such as copper has a lifetime very similar to the one of the iron matrix. This lifetime does almost not change with growing size of copper-rich clusters. It is thus difficult to obtain the size and density of such clusters using the positron lifetime setup.
p. 96 Techniques
3.2.3. Coincidence Doppler broadening CDB spectroscopy allows measuring the momentum distribution of the electron- positron annihilation pair, giving information on the chemical environment of the positron annihilation site.
Doppler broadening experiment{ TC "Doppler broadening experiment" \f C \l "4" }
If a reference system of coordinates is chosen in which the centre of mass of the electron-positron pair is at rest, the two annihilation photons are emitted in anti-collinear directions (i.e. the angle between the directions is 180°) with an energy of 511 keV. But, in the laboratory system, the centre of mass is not at rest. The momentum of the annihilating electron-positron pair is transmitted to the annihilation quanta. The longitudinal component p L of this momentum along the direction of the γ-ray emission produces a
Doppler shift ΔE = p L ⋅ c 2 on the energy of the annihilation radiation ( c is the speed of light). This shift results in a broadening of the annihilation peak at 511 keV ( = m ⋅ c 2 , with m the mass of an electron), which is easily observed in an accurate energy measurement of the photons (see Figure 53).
Figure 53 A schematic illustration of the DB experiment. If the electron- positron pair moves towards the detector, a higher photon energy (Edet1) will be emitted towards this detector. A lower photon energy will be observed, if the pair moves away from the detector.
The momentum of the electron-positron pair is mainly ascribed to the momentum of the electron. Indeed, the positron is thermalized before the annihilation, thereby losing its energy. The electron, on the other hand, possesses a kinetic energy of at least a few eV. The shift observed by the Doppler broadening (DB) setup corresponds thus to the kinetic energy of the electrons with which the positron annihilate. Therefore, the DB technique provides information on specific electrons of the atoms in the material.
p. 97 Chapter 3
DB versus CDB{ TC "DB versus CDB" \f C \l "4" }
In the coincidence Doppler broadening setup, the two annihilation gammas are collected in coincidence. Only when the sum of the energies of the two gammas detected in coincidence is equal to 1022 keV (two times 511 keV), the signals are accepted. This drastically reduces the background of the system, as shown in Figure 54.
Figure 54 The spectrum measured by a coincidence Doppler broadening setup compared to the one of a conventional Doppler broadening setup [116].
Experimental technique{ TC "Experimental technique" \f C \l "4" }
For the coincidence Doppler broadening spectrometry, Van Petegem et al. [115], [116] at the University of Ghent have developed a fairly precise and stable setup. At SCK•CEN, lately, a similar system has been constructed, calibrated and tested. The newly installed CDB spectroscope (Figure 55) is described with ample details by Verheyen et al. [117]. It is used with a very high reliability for the measurement of highly radioactive materials [118].
Figure 55 (left) The coincidence Doppler broadening setup as it is installed in the hot cell laboratory of SCK•CEN. (right) The liquid nitrogen dewals of the two HPGe detectors.
p. 98 Techniques
The technical details for this setup can be found in appendix C. To prevent pileup, due to the activity of the samples, the detectors are movable to larger distances from the sample (up to 1.5 m). For all measurements the death time of the detectors is kept below 10 %. This corresponds to a count rate of each detector of about 10 000 counts per second. The count rate of the two detectors in coincidence is about 300 counts per second. { TC "Coincidence Doppler broadening measurements" \f C \l "4" }
Coincidence Doppler broadening measurements
Again, all specimens are first surface polished and then chemically etched, to obtain reliable results.
Working procedure{ TC "Working procedure" \f C \l "5" }
The specimen preparation for CDB and the loading of the samples in the setup happen in a similar way as explained for the positron lifetime measurements. Also with this technique, all measurements were performed at room temperature using a 22Na positron source of 2 MBq strength, wrapped in a kapton foil.
Analysis{ TC "Analysis" \f C \l "5" }
Analysis of the spectra is done with Matlab. In the lower left side of Figure 56, an example of a typical two-dimensional energy spectrum is shown. The elliptical region corresponds to events where the photons have a total energy of 1022 keV and each photon has an energy close to 511 keV. The horizontal and vertical bands represent the coincidence of an annihilation photon with a background photon. It should be avoided that these bad coincidences occur in the one-dimensional spectrum.
The analyses of the results are made based on the selection of a channel across the coincidence region of the 2-D spectra obtained from the measurements. The events for which
2 2 2 ⋅ m ⋅ c − δ ≤ E1 + E2 ≤ 2 ⋅ m ⋅ c + δ , are included in the one-dimensional spectrum. In this equation, E1 and E2 are the energies of the photons observed by the two detectors, and δ is the width of the window. In standard conditions, δ is taken equal to 1 keV.
p. 99 Chapter 3
Figure 56 The Matlab program which converts the two-dimensional energy spectrum (left) into a one- dimensional spectrum (right).
A CDB curve is logically symmetric around the peak value of 511 keV. Indeed, electron-positron pairs, with a certain momentum, annihilate in all directions (i.e. towards both of the detectors) with the same probability. Therefore, the CDB curves are often only plotted starting from an energy of 511 keV or starting from zero momentum. The resulting 1-D spectrum from each sample is then normalized to the one of unirradiated defect-free pure Fe. The thereby obtained CDB ratio curves allow a clear description of the shape of the momentum distribution. Examples of such curves are given in Figure 57 for pure elements (such as copper and nickel) normalized to pure defect-free iron.
Figure 57 The CDB spectra of some elements normalized to the spectrum of pure, defect-free iron as function of the momentum (PL) of the electron-positron pair, as found by Nagai et al. [119].
The momentum distribution of an annihilating electron-positron pair ρ 2γ can be written as a function of the momentum p , as shown in equation 53. p. 100 Techniques
2 ρ p = γ ⋅ exp − i ⋅ p ⋅ r ⋅ψ r ⋅ψ r ⋅dr (53) 2γ ()∑ j ∫ { }−, j ()+ () ε j ≤ε F
Here, γ j is the enhancement factor and ψ − (r) and ψ + (r) are the wave function of the electron and positron, respectively. The many-body interaction between the electrons and the positron is simplified by the use of the enhancement factor, which corresponds to the correlation between the different wave functions.
Separation procedures of the different components have been developed, but their reliability is always limited. Therefore, Doppler broadening spectra are commonly characterized by an S parameter (line-shape parameter) and a W parameter (wing parameter). These two parameters, illustrated in Figure 58, are extracted from each spectrum, by integrating the curve in the central and peripheral intervals. The choice of the precise intervals is to some extent arbitrary. In this work, S and W are defined respectively as the -3 -3 ratio of low-momentum (|c ⋅ p L |< 2.5 × 10 mc) and high-momentum (15 × 10 mc < | c ⋅ p L | < 25 × 10-3 mc) regions in the CDB spectrum, normalized to the total region.
Figure 58 The definition of the S and W parameter in the CDB spectrum.
Since the total curves are normalized, the S and W parameters will be necessarily correlated. Nevertheless, either parameter carries different information. The valence electrons can only give rise to a small difference in the energy of the annihilation γ-rays, while the inner shell electrons can lead to energy changes of any magnitude. The former will thus mainly contribute to the peak of the CDB curves, and will therefore be observed by the S parameter, which therefore carries mainly information about the open-space defects (e.g. vacancies). The latter, on the other hand, will contribute to the wide momentum region.
p. 101 Chapter 3
Therefore, the W parameter qualifies these electrons. Therefore, the changes in the γ- energies due to the inner shell electrons will carry specific information on the corresponding chemical species. It should be mentioned that S is also affected by the inner shell electrons, and W will change with the presence of vacancies. These effects are however secondary.
In the following, the low- and high-momentum parameters are given, as a ratio to the values found for pure iron. For the non-irradiated specimens these values will thus be close to 1. The error bars can be determined by the amount of counts used for the measurements. The average error to be associated with the pre-defined ratio values is ± 0.000874 for S and ± 0.00185 for W .
The resolution function can be described fairly well by a Gaussian function, with a full
2 2 width at half of the maximum ( FWHM ) equal to FWHM 1 + FWHM 2 , with FWHM 1 and
FWHM 2 the resolution of the respective detector at 511 keV. But, the two annihilation photons have Doppler shifts which are equal but of opposite sign. This results in an improvement of the effective resolution to FWHM 2 . The overall energy resolution of the setup used for this work is ~ 1.07 keV FWHM , which corresponds to the momentum resolution of ~ 4.2 × 10-3 mc FWHM .
p. 102 Techniques
3.3. Atom probe tomography Within this thesis some atom probe tomography (APT) experiments were performed in addition to the positron annihilation measurements. For this purpose, I went to the University of Rouen (France) to master the technique and to do some first experiments and to the Tohoku University (Japan) to apply the technique to some post-irradiation annealing experiments. In addition, APT experiments have been performed on the same set of specimens (the REVE matrix) as discussed in this thesis, by colleagues from the University of Rouen. In chapter 5, the results of the different techniques are put together to find the effect of the defects observed by the different techniques on the hardening mechanisms under irradiation. Here, the APT technique is briefly described.
APT experiment{ TC "APT experiment" \f C \l "4" }
APT is an evolution from the field-ion microscope developed by Müller et al. [120]. During its many years of existence, a great deal of improvements has been done, starting from the original technique, to come to the current form of the three-dimensional atom probe microscopy.
Field ion microscope{ TC "Field ion microscope" \f C \l "5" }
The field ion microscope (FIM) is a type of microscope that can be used to image the arrangement of atoms at the surface of a sharp metal tip. The preparation of such is tip is discussed in appendix D. It was the first technique by which individual atoms could be spatially resolved. The technique was pioneered by Erwin Müller, in 1951 [121]. Gas atoms adsorbed on the tip are ionized by the strong electric field in the vicinity of the tip ("field ionization"). As these ions become positively charged, they are repelled from the tip, in a direction roughly perpendicular to the surface. This "point projection" effect causes a natural magnification of the image on the detector, which is placed so as to collect the repelled ions. The FIM tip is cooled below 100 K, to control the voltage at which the ions are repelled.
p. 103 Chapter 3
Figure 59 The FIM image formation process [7].
Unlike conventional microscopes, where the spatial resolution is limited by the wavelength of the particles which are used for imaging, the FIM is a projection type microscope with atomic resolution and an approximate magnification of a few million times. If the electric field is increased, the upper layer of the tip is evaporated, and a second FIM image can be taken. Consequently, a 3-D image can be obtained.
Atom probe microanalysis{ TC "Atom probe microanalysis" \f C \l "5" }
The FIM, on its own, cannot identify the chemical identity of the atoms. The atom probe FIM (APFIM; designed in 1967 by Erwin Müller [120]) makes one-dimensional compositional maps by combining time-of-flight mass spectroscopy and the FIM. A region of the tip's surface is selected from the FIM image and placed over a probe hole, by moving the tip. The atoms at the apex of the tip are then ionized, either by a positive pulse voltage or a laser. These ions are repelled from the tip electrostatically and those passing through the probe hole are identified.
Figure 60 The APFIM image formation process [122]. A combination of a FIM and a time-of- flight mass spectrometer of a single ion sensitivity.
p. 104 Techniques
Position sensitive atom probe{ TC "Position sensitive atom probe" \f C \l "5" }
In 1986, Mike Miller developed a technique which uses a position-sensitive detector to deduce the lateral location of the atoms [123]. Almost all the species reaching the detector are analyzed and the in-depth investigation of the sample is provided by the layer-by-layer evaporation of the specimen. This allows 3-D reconstructions to be generated [124]. Since its development, there have been many refinements to increase the field of view, mass and position resolution and data acquisition of the instrument.
Figure 61 The atom probe tomography image formation process, with a position sensitive detector [125].
The two first prototypes were designed successively at the University of Oxford [126] and Rouen [127]. One advantage of the three-dimensional atom probe (3DAP), compared to for instance high resolution electron microscopy, is the 3-D imaging capabilities at the atomic scale. This is the only nanoanalytical microprobe able to provide 3-D atomic-scale images. It makes it possible to give the spatial distribution of chemical species in the small volume (10 × 10 × 100 nm3) that is analyzed.
Three-dimensional atom probe microscopy is a unique method to map out the alloying elements in three-dimensional space with near-atomic resolution. This technique is for instance known to be a very efficient tool for the chemical analyses of solute-enriched clusters in irradiated RPV steels [128]. The atom probe is a particularly powerful tool for the characterization of irradiated materials, due to its high spatial resolution, light element sensitivity and ability to quantify the
p. 105 Chapter 3 composition of ultrafine (< 5 nm) precipitates [129]. The atom probe technique has provided valuable information about ultrafine precipitates, solute clustering and segregation to lath and grain boundaries. The size, shape and number density of these ultrafine features are obtained from high magnification images in the field ion microscope. The composition of these features and the matrix has been obtained by 3DAP.
Experimental technique{ TC "Experimental technique" \f C \l "4" }
At the University of Rouen (France), there are currently three experimental setups, i.e. the tomographic atom probe (TAP), the energy compensated optical TAP (ECOTAP) and the wide angle TAP (WATAP). For both TAP and ECOTAP, the detector is positioned at about 40 cm of the experimental tip. Therefore, in these techniques only a limited solid angle can be measured. The new setup (WATAP) uses a distance of 5 cm, which increases the solid angle drastically. By atom probe, the atomic species are identified by a mass spectrometer. The atoms are emitted with fixed speed to the detector, and the time of flight (i.e. the time needed to reach the detector) is measured. Using the speed and the time of flight, the mass of the atom can be determined. In the TAP and WATAP setup, the speed of the atoms is determined depending on the peak voltage at the tip. This voltage may change little, leading to broader mass peaks in the mass spectrometer. To avoid this, in ECOTAP a magnetic field is applied to remove atoms with different speed. For this purpose, a certain distance between the tip and the detector is necessary, and therefore the advantages of the ECOTAP and the WATAP are not yet reconcilable. To reduce the energy spread of the emitted ions, the setup was provided with an energy compensating device (a reflectron lens). Furthermore, to avoid the preferential evaporation of copper, the experiments were carried out at a cryogenic temperature of 50 K and with an electrical pulse fraction of 20 % of the standing voltage. All the experiments were performed with a pulse rate limited to 0.03 atoms per pulse to reduce the risk of failure of the needle- shape sample. More details about the treatment of the data and how to get the essential information out of them can be found in [130].
At the Tohoku University (Japan), three-dimensional atom probe analyses are carried out with a local electrode atom probe (LEAP) by IMAGO Scientific Instruments [131]. LEAP analyses are performed at a pulse fraction of 20 %, with a pulse repetition rate of p. 106 Techniques
200 kHz, a DC voltage usually in a range from 5 to 11 kV and a specimen temperature of 50 K. The LEAP enables much larger volumes to be analyzed than was previously possible, hence the statistics for the analysis are greatly improved.
Atom probe measurements{ TC "Atom probe measurements" \f C \l "4" }
The emission of atoms toward the detector is only possible in case a very sharp needle (< 50 nm tip radius) is available. Therefore, the accuracy of the measurement will depend strongly on the state of the tip of the sample. The preparation of an adequate tip is discussed in appendix D. The same procedure is used for the active samples as for the non-irradiated ones.
Measurement{ TC "Measurement" \f C \l "5" }
The sharpness of all prepared tips is checked by an electron microscope, after which they are immediately installed in the storage room of the atom probe setup. This chamber has a temperature of about 80 K and a very low pressure to avoid oxidation of the tip. The specimens remain at least 24 h in this chamber to get well acclimatized to this temperature and pressure. Afterwards, the sample can be taken to the analysis chamber. During analysis, an inert gas is introduced in the chamber. In most laboratories, argon or neon is applied. While the setup of the Tohoku University uses a laser for the emission of the atoms, in most of the setups used in Rouen, the atoms of the tip are emitted using an adequate voltage.
An average voltage V0 is directly applied to the tip and an additional peak voltage VP is transferred to the tip by the inert gas. Usually, the peak voltage is about 20 % of the average voltage (VP ≈ 20%⋅V0 ). The peak voltage determines the moment of the emission of the atoms.
During the analysis, first a field ion microscopy (FIM) image is obtained. To obtain this image, the temperature is fixed to 70 K. At this point already, badly made tips can be eliminated and the needles are positioned to obtain the highest count rate. At the edge of a crystal plane, the intensity of emitted atoms is the highest. So, using the FIM image, an area can be chosen with high number of crystal plane edges and therefore also higher atom emission rate.
p. 107 Chapter 3
Once the tip is correctly positioned, the temperature is decreased to about 50 K. This low temperature makes the material more brittle (leading to a higher probability of fractures of the tip), but is necessary to have a homogeneous emission of different alloying elements. In Figure 62, it is illustrated that for instance copper atoms may evaporate already at the average voltage, if the temperature is chosen too high. These atoms will then have another speed compared to those emitted during the peak voltage and also the time of flight will be wrongly estimated, leading to a loss of these atoms in the final atom probe image. However, if the temperature is chosen too low, some atomic species will not be emitted at the chosen peak voltage.
Figure 62 Illustration of the loss of atoms at too high temperatures. If the temperature is higher than the cross of the average voltage and the energy-temperature line of a certain atomic specie, its atoms will be emitted without the necessity of the peak voltage. However, if the temperature is chosen too low, the peak voltage will not be enough for emitting all species.
A typical measurement runs for a few hours. It is stopped by the breaking of the point, or in case the peak voltage needed for evaporation of the atoms becomes too high (due to the broadening of the tip).
Calibration{ TC "Calibration" \f C \l "5" }
Although during the measurement, the flight length is adapted to obtain for the highest peak (the iron peak) an exact value of 28 in the mass spectrum, it is advised to recalibrate the spectrum after the measurement. The new flight length ( L2 ) is calculated using the old one
( L1 ) and the current value of the highest peak in the mass spectrum ( x ), using the following equation.
x L = ⋅ L (54) 2 28 1
p. 108 Techniques
Results{ TC "Results" \f C \l "5" }
After the calibration, the detected atoms are appointed and they are plotted in a three- dimensional atomic map. A typical example of such a map is given in Figure 63, where every atomic specie is shown by another colour.
Figure 63 A typical example of an APT three-dimensional map in a Russian nuclear vessel steel [132]. The different atomic species are illustrated by different colours.
It is obvious that by the use of this technique, solute clusters, produced during irradiation, can be identified.
After each atom probe experiment, the data were always treated in the same way. First, an algorithm to identify clusters was applied to the volume [133]. This tool allows identifying small clusters, which are not directly visible in the 3-D reconstruction. The principle is the following. A sphere with a fixed radius (0.8 nm contains about 100 detected atoms) is placed around each atom. If the concentration of an element inside this sphere is higher than a fixed concentration threshold (e.g. 4 at%), the atom is considered to be in a cluster. This method and the proposed parameters allow detection of clusters containing at least five detected alloying atoms. Taking into account the detection efficiency of ca 0.5, these clusters thus have at least ten alloying atoms. The identified clusters are characterized in terms of size (radius or number of detected atoms in the cluster), chemical composition and number density. The matrix composition is then the composition of all volume without clusters. If any cluster is identified, the matrix composition is assimilated to the composition of the analyzed volume. In this case, statistical χ2 test of the spatial distribution of solute atoms is done, in order to determine if copper is still homogeneously distributed.
p. 109 Chapter 3
3.4. Transmission electron microscopy Transmission electron microscopy (TEM) experiments have been performed on the same set of specimens (the REVE matrix), as studied by PAS in this thesis. Both irradiated and non-irradiated samples have been investigated in a similar way. In chapter 5, the results of the different techniques are put together to build a complete picture of the microstructural changes and their effects on the hardening mechanisms under irradiation. Here, the TEM technique is briefly explained.
TEM technique{ TC "TEM technique" \f C \l "4" }
In transmission electron microscopy, a beam of electrons is transmitted through an ultra thin specimen. An image is formed from the interaction of the electron transmitted through the specimen, which is magnified and focused onto an imaging device.
A beam of electrons is generally generated by heating a tungsten or LaB6 filament source that has the shape of a sharp tip. In the newer generation of microscopes, however, the electrons are extracted from the sharp tip using a high voltage. The electrons are accelerated by the voltage varying from 100 kV to more than 1000 kV, depending on the microscope. A combination of magnetic lenses then focuses the electron beam on the sample. After the interaction with the specimen, the transmitted electrons pass through a second combination of lenses which magnify the image. Finally, the electrons fall on a fluorescent screen where an enlarged image of the sample is obtained. Alternatively, detection materials are photographic films, a digital CCD-camera (for the permanent storage of the image) or a camera for direct projection of the image on a TV screen. To avoid undesirable interaction with gas molecules, the electron microscope operates under ultra high vacuum conditions.
The TEM is capable of imaging at a significantly higher resolution than light microscopes, owing to the small wavelength of the electrons. This enables the instrument to be able to examine fine details, up to tens of thousands times smaller than the smallest resolvable object in a light microscope.
p. 110 Techniques
Figure 64 The TEM setup [134].
The crystallographic structure of a sample at an atom scale can be investigated by high resolution TEM (HRTEM). Because of its high resolution, this tool is invaluable to study nanoscale properties of crystalline materials. At present, the highest resolution obtained is about 0.08 nm. This is more than 10 times smaller, compared to the resolution of the conventional TEMs, i.e. about 2 nm. But, one of the difficulties with the HRTEM is that image formation relies on phase- contrast. In phase-contrast imaging, contrast is not necessarily intuitively interpretable as the image is influenced by strong aberrations of the image lenses in the microscope. In addition, an ideal specimen for TEM should be thin, bulk material representative, clean, stable, flat with parallel sides, easily handled, conductive, free of surface segregation and self-supporting. All these requirements cannot always be fulfilled and the fulfilment is even more difficult for the samples for the HRTEM. The area investigated by HRTEM is about 104 times smaller than the one in the conventional TEM, and the thickness of a specimen suitable for TEM is limited to about 200 nm for conventional work and to 50 nm for high resolution observations.
Experimental technique{ TC "Experimental technique" \f C \l "4" }
In the specific case of interest here, the microstructure of the materials was examined by TEM with a JEOL microscope, model JEM-2010 operating at 200 keV, at CIEMAT laboratories (Spain). This microscope is able to detect clusters of point defects (vacancies or self-interstitials), with sizes over 1.5 nm. It is worth to point out that information from the
p. 111 Chapter 3 self-interstitial component of the damage can be obtained. This is not detected with other microstructural characterization techniques in such a direct way. A full description of the methodology employed is described in [135].
Measurements{ TC "Measurements" \f C \l "4" }
Diffraction contrast methods were employed for imaging defect microstructure, according to methodologies described for instance in [136], [137]. From TEM images (e.g. Figure 65), quantitative information was obtained about the density and size of the observed defects (e.g. Figure 66). Defects were counted on TEM images recorded under reflections type g = (1,1,0), where the best contrast was obtained. The presence of voids was studied by means of a through-focal series recorded with the foil tilted away from the Bragg condition for all reflections [136], [137]. The trend of microstructure evolution has been studied in terms of defect density and defect size distribution.
Figure 65 A typical example of a TEM micrograph showing the defect structure in an irradiated alloy [135].
Figure 66 A typical example of a defect size distribution in an irradiated alloy [79].
p. 112 Techniques
3.5. Small angle neutron scattering Also small angle neutron scattering (SANS) experiments have been performed on the same set of specimens (the REVE matrix) and compared with the results from the other techniques in chapter 5.
SANS experiment{ TC "SANS experiment" \f C \l "4" }
The term "neutron scattering" encompasses all scientific techniques whereby the deflection of a neutron beam is used as a scientific probe. Neutrons interact with atomic nuclei and magnetic fields from unpaired electrons, making a useful probe of both structure and magnetic order. As the neutron is an electrically neutral particle, it penetrates deeply in the sample, thereby being suitable to probe the bulk material. Consequently, it enables the use of a wide range of sample environments that are difficult to use with for example X-ray sources, with which scattering experiments are traditionally performed. On the other hand, small angle scattering is a scattering technique based on a small deflection (0.1 – 10°) of the particle beam, away from the straight trajectory after it interacts with structures that are much larger than the wavelength of the radiation. Small angle scattering techniques can give information about the size, shape and orientation of nanostructures in a sample. Small angle neutron scattering is an elastic scattering technique. The neutrons do not excite the nuclei or electronic magnetic fields, with which they interact. SANS is therefore a non-destructive technique.
During a SANS experiment, a beam of neutrons is directed onto the sample. The neutrons are elastically scattered by changes of refractive index on nanometre scale features inside the sample. In zero order dynamical theory of diffraction, the refractive index is directly related to the scattering length density and is a measure of the strength of the interaction of a neutron wave with a given nucleus.
p. 113 Chapter 3
Figure 67 The SANS setup [138].
SANS is capable of characterizing the size distribution of nanometre sized defect-solute clusters in ferritic alloys. This is done by measuring the scattering cross section in a saturation magnetic field applied to the sample, separating nuclear and magnetic contributions from the anisotropy introduced by the magnetic field, subtracting the scattering cross section for a defect-free control sample and calculating the size distribution by solving an inverse problem.
Experimental technique{ TC "Experimental technique" \f C \l "4" }
The SANS experiments on the REVE matrix have been performed at two different experimental facilities. Part of the experiments was carried out at the SANS instrument of the SINQ facility of PSI, Villigen (Switzerland) [139] at a wavelength of 0.5 nm with a sample- detector distance of 2 m. The range of the magnitude of the scattering vector ( Q ) from 0.3 nm-1 to 2.7 nm-1 was covered. The other part of the SANS measurements was carried out at the PAXE instrument of the Orphee research reactor at LLB Saclay (France) [140] at a 2 wavelength of 0.6 nm. The SANS intensity was measured with a 2-D 64 × 64 cm BF3- detector. In these experiments, the Q -vector covers a range from 0.16 nm-1 to 1.6 nm-1. The samples are placed in a saturation magnetic field. The data analysis was performed by FZD (Germany).
SANS measurements{ TC "SANS measurements" \f C \l "4" }
The measuring procedure and analysis are described in detail in [35]. SANS measurements deliver information on the reciprocal space, and therefore a certain morphology and composition of the scatterers need to be assumed, in order to calculate their size distribution. In this work, a dilute two-phase matrix is assumed for the microstructure of p. 114 Techniques the analyzed specimens. The inclusions are considered to be homogeneous non-magnetic spherical scatterers randomly dispersed in a pure Fe matrix. For a number of N scatterers with radius R and volume V in the probed volume V p , the coherent scattering cross section
()dΣ dΩ C can be expressed as in equation 55.
2 ⎛ dΣ ⎞ N 2 2 9 ⋅ (sin(Q ⋅ R)()− Q ⋅ R ⋅ cos Q ⋅ R ) ⎜ ⎟ ()Q = ⋅ Δη ⋅V ()R ⋅ 6 (55) ⎝ dΩ ⎠ C V p ()Q ⋅ R
Magnetic and nuclear scattering are not distinguished in equation 55. The scattering contrast ( Δη 2 ) is given by equation 56.
2 2 Δηi = [(n ⋅ b i )scatterer − (n ⋅ b i )matrix ] (56)
Here, i is M for magnetic scattering and N for nuclear scattering, while b denotes the average scattering length. In the case of non-magnetic scatterers, b M ,scatterer is equal to zero.
This assumption (b M ,scatterer = 0 ) will represent the lower bound of the real size distributions, in case of non-zero magnetic scatterers. This is for instance the case, if the scatterers contain a significant amount of iron atoms, bearing a magnetic moment. The indirect transformation method [141], which is based on a description of the size distribution according to equations 55 and 56, is applied in order to derive the size distribution of scatterers without assuming a certain type of distribution. For each material the unirradiated control is subtracted from the results of the irradiated specimens after performing the transformation.
The A -ratios, originally defined as the ratio of the scattering cross-sections (dΣ dΩ ) perpendicular and parallel to the magnetic field direction, can be calculated according to [142]. Here, A =1 + M N , where M and N denote the magnetic and nuclear contributions to the total intensity integrated in the size space. In general, the complete cluster composition cannot be deduced from the A -ratio. Conversely, the A -ratio can be estimated according to equation 57 [143], if the composition is known.
p. 115 Chapter 3
2 ⎛ 6.0 ⋅ (nFe − 1) + 1.0 ⋅ n Ni ⎞ A =1 + ⎜ ⎟ (57) ⎝ 9.45 ⋅ ()nFe −1 + 10.3 ⋅ n Ni + 7.72 ⋅ nCu − 3.75 ⋅ nMn ⎠
In the case of vacancy clusters in pure iron, the measured A -ratios should be equal to 1.4. Pure copper precipitates have an A -ratio equal to about 13. Mn-atoms are the only ones which exhibit a negative nuclear scattering length, and therefore they are capable of reducing the A -ratio to lower values.
The lower detection limit is about 0.5 nm in cluster radius (this corresponds to about 50 atoms). An advantage is the averaging capability resulting from a probed volume of some 10 mm3 and from a number of scattering events of the order of 106. In addition, some integrated information on the average cluster composition is given by the ratio of magnetic and nuclear scattering.
A typical example of a coherent SANS cross section is given in Figure 68. The correlated size distribution of the observed defects is illustrated in Figure 69.
Figure 68 The total coherent SANS cross section for an irradiated Fe (full symbols) and for the unirradiated reference (open symbols) [35].
Figure 69 The size distribution of the defects observed by the SANS results shown in Figure 68 [35].
p. 116 Techniques
3.6. Tensile tests In order to correlate the observed nano- and microstructure with the mechanical property changes, produced by irradiation, tensile tests have been performed.
Theory{ TC "Theory" \f C \l "4" }
A tensile test is a fundamental mechanical test in which a carefully prepared specimen is uniaxially loaded in a controlled manner. The applied load and the elongation of the specimen over some distance are measured. Tensile tests are used to determine the modulus of elasticity, yield strength (elastic limit), elongation, reduction in area, ultimate tensile strength and other mechanical properties [144].
Experimental setup{ TC "Experimental setup" \f C \l "4" }
The tensile tests were performed using an electro-mechanical test frame (INSTRON 8500, model 1362), equipped with a 10 kN load cell.
Measurements{ TC "Measurements" \f C \l "4" }
The specimens had a gauge length of 15 mm with a cross section of (3 × 3) mm2. The heads of the specimen had a thickness of 8 mm and the total length was 26 mm (see Figure 31). Most of the measurements were performed at room temperature, with a strain rate of about 2 × 10-4 s-1 (the machine head displacement was fixed to 0.1 mm min-1). Starting from the engineering stress-strain curves, the yield strength was obtained. The increase of yield strength in the irradiated material is calculated compared to the non- irradiated state of the same material. The average error bar to be associated with the data is ± 6 % of the yield strength value, i.e. the average error for the setup in steels. This error thus varies between ± 5 MPa for the non-irradiated pure iron and ± 35 MPa for the steel irradiated to the highest dose.
p. 117 Chapter 3
3.7. Conclusions In this chapter, the different experimental techniques, applied to characterize the neutron irradiated materials investigated in this PhD work, have been presented. As positron annihilation spectroscopy represents the bulk of this work, this technique has been explained with ample details in a first section. The other techniques have been more succinctly summarized.
It is clear that all of the discussed techniques are able to characterize some of the formed defects under irradiation, but none of them can provide information on all the existing defects. Positron annihilation spectroscopy is able to detect vacancy-type defects, starting from only monovacancies and in addition, this technique can deduce some of the alloying elements in the neighbourhood of the positron annihilation sites. The correct number of alloying elements is however difficult to estimate. Atom probe tomography results in a complete three-dimensional image of the solute atoms. On the other hand, the presence of vacancies cannot be observed and due to the low analyse volumes, the errors of size and number density may be important. Small angle neutron scattering detects the same defects as PAS and APT, observing both solute atoms and vacancies. Small defects are however not observed, due to its higher detection limit (compared to PAS and APT). Transmission electron microscopy cannot detect the above mentioned defects. Nevertheless, self-interstitial atoms are observed, which are not detected by any other technique.
The combination of the different techniques will thus lead to a better understanding of the correlation between the microstructural changes and the mechanical behaviour of the neutron irradiated materials to which this thesis is devoted.
p. 118
Chapter 4 Positron annihilation spectroscopy results
“The most exciting phrase to hear in science, the one that heralds the most discoveries is not "Eureka!" (I found it!) but "That's funny".” Isaac Asimov (Russian American 1920-1992)
As indicated in the previous chapters, positron annihilation spectroscopy is a very effective tool for analyzing irradiation-induced defects. It is able to detect vacancy-type defects and is sensitive to the chemical composition of the positron annihilation site. In combination with hardening results of the same materials, it is even possible to determine, in an indirect way, some of the defects inducing hardening, which are not visible by PAS.
In the first section of this chapter, a summary is made of the type of defects visible by positrons. Second and third sections then give the results of the REVE matrix for the positron lifetime experiments and the coincidence Doppler broadening measurements, respectively. The results are discussed, in combination with results obtained by tensile tests on the same materials, in section 4. Section 5 discusses then the influence of different irradiation fluxes on the positron annihilation results. Fe-Cr alloys, investigated in the framework of studies of materials for future energy reactors, have also been analyzed with the positron experiments and the results are discussed in section 6. The final section gives shortly the conclusion of this chapter.
p. 119 Chapter 4
Table of content Chapter 4 Positron annihilation spectroscopy results...... 119 4.1. Positron affinitive sites in steels ...... 121
4.2. Positron lifetime results...... 123 4.2.1. Pure iron and the binary Fe-C alloy ...... 123 4.2.2. Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper...... 126 4.2.3. Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy ...... 127 4.2.4. Low-Cu RPV steel...... 129
4.3. CDB results...... 131 4.3.1. Pure iron and the binary Fe-C alloy ...... 131 4.3.2. Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper...... 133 4.3.3. Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy ...... 135 4.3.4. Low-Cu RPV steel...... 138
4.4. Discussion...... 140 4.4.1. Binding energies of the investigated elements with Vs and SIAs...... 140 4.4.2. Hardening of the alloys ...... 143 4.4.3. Discussion of the PAS results...... 144 Pure iron and the binary Fe-C alloy ...... 144 Binary Fe-Cu alloys...... 146 Alloys containing manganese and nickel ...... 148 Low-Cu RPV steel...... 151 4.4.4. Influence of the defects observed by PAS on the hardening of steels...... 151
4.5. Flux effect...... 155
4.6. Fe-Cr alloys...... 158
4.7. Conclusions ...... 164
p. 120 Positron annihilation spectroscopy results
4.1. Positron affinitive sites in steels It has been explained in section 3.2.1., that the positron affinity to the detected defects is related to the electron density surrounding them. Positrons are very sensitive to vacancy-type defects, but much less to self-interstitial clusters and loops. On the other hand, alloying elements have different positron affinity, compared to the iron matrix [99] and thus influence the positron response to the defects. It is reported that the affinity of positrons to iron is -3.84 eV. Copper and nickel have a higher positron affinity (-4.81 eV and -4.46 eV, respectively), while carbon and manganese have a lower affinity (-2.50 eV and -3.72 eV, respectively). Therefore, defects containing copper and/or nickel trap the positrons more easily, while the opposite occurs for defects containing carbon and manganese.
As mentioned in section 3.2.3., the low momentum part of the coincidence Doppler broadening (CDB) results, or S parameter, is especially due to positrons annihilating with valence electrons of atoms near the positron annihilation site. Therefore, this part of the spectrum contains information about the vacancy-type defects present in the material. The high momentum part, or W parameter, on the other hand, is affected by the inner shell electrons of the atoms. This parameter can thus give some information on the chemical species near the positron annihilation sites. The CDB spectra for all elements, that compose the materials studied in this work, can be found in the literature, e.g. [119] and [145]. It is for instance known that copper and nickel induce a similar effect. They both yield to an elevated W parameter, although this effect is higher for copper than it is for nickel. PAS is thus an excellent technique to identify defects containing one or the other of these two elements. Nevertheless, it is difficult, if not impossible, to distinguish between them, when they are simultaneously present.
The positron lifetime results (section 3.2.2.) can provide information on the number density of vacancy clusters and the average amount of vacancies per cluster, if the trapping and detrapping rates are rigorously known. Pure defect-free iron has only one positron lifetime component, equal to 107 ps. When defects appear, more positron lifetime components can be deconvoluted. Generally, the spectrum is resolved into two components. The first one is assigned to the positron annihilation with the iron matrix, while the second one reflects the presence of other positron annihilation sites, such as irradiation-induced
p. 121 Chapter 4 defects. For vacancy-type defects, the positron lifetime value of the latter component increases with the number of single vacancies that form a cluster, up to a size at which the cluster can be defined as a void [146]. When the voids contains 30 vacancies, the lifetime starts to saturate (see Figure 164 in appendix F) The intensity of the second component depends on the amount of defects contributing to the process of positron annihilation. The positron lifetimes for pure defect-free copper and nickel, found by Puska and Nieminen [94], 106 ps and 96 ps, respectively, are very close to the one for pure defect-free iron (101 ps in [94]). Vacancy-free copper and nickel precipitates will thus contribute to the first component (or the bulk component) rather than to the second component. Therefore, only the precipitates and solute atoms associated with vacancies can be seen within the second PALS component.
p. 122 Positron annihilation spectroscopy results
4.2. Positron lifetime results In this section, the positron annihilation lifetime spectroscopy (PALS) results are given for all the materials investigated. The average error bar to be associated with the reported values is low for all materials except for the RPV steel (see later). For all model alloys, the errors are about ± 0.9 % for the intensity and about ± 3.5 ps for the positron lifetime. Computer simulations performed by Kuriplach et al. [146] found specific positron lifetimes for clusters with one, two and more vacancies. Some of these simulation results are given in the figures showing the different positron lifetime components. The positron lifetime results for the non-irradiated materials are found to have only one positron lifetime component, very close to the one of pure iron. For clarity, these values are not given in the figures showing the PALS results.
4.2.1. Pure iron and the binary Fe-C alloy Before the results can be used, their accuracy needs to be checked. The stability of the resolution function and the source contribution is controlled during the analysis. Figure 70 illustrates the spectra for the pure Fe and the binary Fe-C alloy, from which the random contribution (background) has been subtracted. The net spectra have then been normalized to the same total number of counts.
Pure Fe Fe-C
Figure 70 The positron lifetime spectra for pure iron (left) and for the binary Fe-C alloy (right). The random contribution has been subtracted and the net spectra have been normalized to the same total number of counts.
p. 123 Chapter 4
A two-component analysis is then performed by the LT program for all these spectra. The results are given in Figure 71, as functions of the irradiation dose. For the irradiation to 0.05 dpa, no pure iron specimen was inserted in the reactor, and therefore no results could be obtained for pure iron at this irradiation condition. The positron lifetime results of non-irradiated material cannot be decomposed into two components; there is only one bulk component. It is found that they are all very close to the value of defect-free pure iron, i.e. about 107 ps. For the non-irradiated iron, a value of 115 ps is obtained, while the Fe-C alloy has a value of 125 ps. This slight increase is most probably due to the presence of some dislocations, prior to irradiation.
Figure 71 The positron lifetime results of pure iron and the binary Fe-C alloy are given as functions of the irradiation dose. The results are divided into two positron lifetime components (τ1 and τ2) and their average is given as well (τm). I2 is the intensity of
τ2 (I1 (τ 1 )()+ I 2 τ 2 =1 ). In the figure, the theoretical values of positron lifetime in vacancy clusters (V, V2, V4 and V10) obtained by Kuriplach et al. [146] are also reported.
When vacancy clusters are produced under irradiation, a second PALS component, related to the defects, appears. In the figure, it is clearly seen that there are only a few (low intensity compared to the other alloys) vacancy clusters created in pure iron, after irradiation up to 0.2 dpa, but these clusters are found to be relatively big (the positron lifetime suggests more than 10 vacancies per cluster in average). These vacancy clusters appear to grow steadily in pure iron during irradiation (increase of the second component's positron lifetime). At early stages of irradiation, the intensity of the second PALS component remains constant. It seems thus that no important amount of new clusters is formed, and the supply of new vacancies, produced at this stage of irradiation, p. 124 Positron annihilation spectroscopy results joins the previously formed clusters. This leads to the growth of the clusters. As the number density of the second PALS component decreases considerably at higher irradiation doses, this growth, observed by the second component's positron lifetime, is then mainly caused by agglomeration of smaller defects. Nevertheless, as the specific trapping rate is dependent on the size of the clusters (see appendix F), the intensity can give lower values while the number density of defects does not decrease. The mean positron lifetime, on the other hand, saturates at high irradiation doses. This indicates that most of the newly produced vacancies disappear at sinks, although some single vacancies (most probably stabilized by the present dislocations), that are located too far from the sinks to disappear, are present in the matrix as well. In these vacancies, the positron has a much smaller positron lifetime than the one in the clusters and therefore they will be found as a part of the first PALS component. Indeed, an increase of this first component's positron lifetime is observed.
For the Fe-C alloy, the same observations can be made; the intensity of the second component gradually decreases, the positron lifetime of the second component increases, while the mean positron lifetime saturates and the positron lifetime of the first component increases at higher irradiation doses. Nevertheless, it is clear that the addition of carbon hampers the vacancy-clusters growth, while the size of the clusters even seems to saturate at higher doses. At the same time, more single vacancies (most probably stabilized by the present dislocations) are observed in the matrix at the highest dose, inducing a higher positron lifetime of the first component, compared to the results of the pure iron alloy. This leads to a small decrease in the intensity of the second component. It should, however, be mentioned that in case the defects contain carbon atoms, the annihilation probability of positrons in the bulk material will be higher compared to the results with the same amount of defects in pure iron. This effect may partly be responsible for the lower second component intensity and positron lifetime of the second component. Also an enhanced recombination of the vacancies with C-immobilized SIA clusters could lead to the same results.
p. 125 Chapter 4
4.2.2. Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper The resolution function and source contribution are also controlled for the binary Fe-Cu alloys. Figure 72 shows the spectra for these alloys.
Fe-0.1% Cu Fe-0.3% Cu
Figure 72 The positron lifetime spectra for the Fe-0.1% Cu alloy (left) and the Fe-0.3% Cu alloy (right). The random contribution has been subtracted and the net spectra have been normalized to the same total number of counts.
Figure 73 The positron lifetime results of the binary Fe-Cu alloys are given as functions of the irradiation dose. The results are divided into two positron lifetime components (τ1 and τ2) and their average is given as well (τm). I2 is the intensity of τ2
( I1 (τ 1 )()+ I 2 τ 2 =1 ). In the figure, the theoretical values of positron lifetime in vacancy clusters (V, V2, V4 and V10) obtained by Kuriplach et al. [146] are also reported.
The results of the two-component analysis of all these spectra are given in Figure 73, as functions of the irradiation dose. The positron lifetime of both non-irradiated materials have
p. 126 Positron annihilation spectroscopy results again only one component of about 125 ps, due to the presence of some dislocations, prior to irradiation.
As copper has a higher positron affinity than iron, the opposite feature is observed in these alloys than in the Fe-C alloy. Copper close to the vacancy clusters will increase their visibility. Therefore, fewer positrons will annihilate in the bulk compared to a pure iron alloy with the same amount of defects.
The presence of copper increases the intensity of the second component in the binary Fe-Cu alloys compared to the pure iron and the Fe-C alloy, i.e. the number of detected vacancy clusters is higher. However, the vacancy clusters will remain smaller in terms of amount of vacancies, when copper is added, similarly to what has been observed by the addition of carbon in iron. Moreover, the positron lifetime of the first component stays unchanged. Most of the vacancies produced during the irradiation will thus join previously formed clusters. This high first component may also be slightly caused by the presence of copper-rich precipitates free from vacancies. Only a few vacancies disappear at sinks, as the mean positron lifetime does not saturate in the same way as observed in all other alloys. In contrast to what is seen in the pure iron, the intensity of the second component does not increase. The number density of defects experiences thus no drastic changes.
For the alloy with 0.3 % of copper, the amount of vacancies per cluster is substantially lower compared to the alloy containing 0.1 % of copper. A slight increase in number density of the defects is observed in the intensity of the second component at early irradiation.
4.2.3. Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy The resolution function and source contribution are controlled for the model alloys containing manganese and nickel, as well. In Figure 74, their spectra are given.
The results of the two-component analysis of all these spectra are given in Figure 75, as functions of the irradiation dose. The positron lifetime of the non-irradiated materials is about 124 ps for the Fe-Mn-Ni alloy and about 112 ps for the Fe-Mn-Ni-Cu alloy.
p. 127 Chapter 4
Fe-Mn-Ni Fe-Mn-Ni-Cu
Figure 74 The positron lifetime spectra for the Fe-Mn-Ni alloy (left) and the Fe-Mn-Ni-Cu alloy (right). The random contribution has been subtracted and the net spectra have been normalized to the same total number of counts.
Figure 75 The positron lifetime results of the Fe-Mn-Ni and Fe- Mn-Ni-Cu alloy are given as functions of the irradiation dose. The results are divided into two positron lifetime components (τ1 and τ2) and their average is given as well (τm). I2 is the intensity of
τ2 (I1 (τ 1 )()+ I 2 τ 2 =1 ). In the figure, the theoretical values of positron lifetime in vacancy clusters (V, V2, V4 and V10) obtained by Kuriplach et al. [146] are also reported.
Like copper, nickel will increase the visibility of the defects, while manganese will decrease their affinity to positrons, the same way as observed in the Fe-C alloy. For the alloys containing manganese and nickel, no important clustering of vacancies occurs. It can be seen by the low τ 2 values that the observed vacancy clusters are and remain very small. The intensity of the second component is, however, spectacularly high to more than 90 %. This means that almost all positrons annihilate near defects and almost none of them annihilate in the bulk material. The vacancies are thus uniformly distributed in the
p. 128 Positron annihilation spectroscopy results matrix, most probably combined with some alloying elements, which stabilize the defects and prevent them from agglomerating.
The addition of copper causes a less pronounced intensity increase as in the ternary Fe- Mn-Ni alloy, while the clusters contain even less vacancies. Therefore, the vacancies appear to be even more dispersed in the material, combined with some foreign atoms. At the same time, the positrons are able to annihilate with precipitates consisting of vacancy-free copper and/or nickel. This leads to an increase of the intensity of the first component, and thus also a decrease of the intensity of the second component (as the sum of the two intensities should be equal to 100 %).
4.2.4. Low-Cu RPV steel The resolution function and source contribution are controlled for the low-Cu RPV steel, irradiated to doses up to 0.05 dpa. Figure 76 illustrates the spectra for the steel. It is clear that, in the steel samples irradiated to doses higher than 0.05 dpa, not enough statistics could be obtained, due to their high activity. Indeed, to avoid pileup in the detectors, the distance of the detectors to the sample has to increase drastically with these highly activated samples. This causes an enormous decrease in the number of signals with triple coincidence. Much longer measuring times are thus necessary to obtain good statistics. For the two samples with the higher activity, the measurement was stopped after about 1 month for reasons of time and storage management. Nevertheless, an estimation of the values could be obtained, fixing components such as the source contribution and the resolution function, to what was found for previous measurements. The results seem in agreement with those at lower doses.
Figure 76 The positron lifetime spectra for the low-Cu RPV steel. The random contribution has been subtracted and the net spectra have been normalized to the same total number of counts.
p. 129 Chapter 4
The results of the two-component analysis of all these spectra are given in Figure 77, as functions of the irradiation dose. The positron lifetime of the non-irradiated steel is about 112 ps. This is very close to the positron lifetime of bulk iron, i.e. 107 ps. The average error bar to be associated with the values for the two samples irradiated at doses higher than 0.05 dpa is about ± 3.9 % for the intensity, ± 4.7 ps for the mean positron lifetime, ± 40 ps for the first component's positron lifetime and ± 5.0 ps for the second component's positron lifetime.
Figure 77 The positron lifetime results of the low-Cu RPV steel are given as functions of the irradiation dose. The results are divided into two positron lifetime components (τ1 and τ2) and their average is given as well (τm). I2 is the intensity of τ2
( I1 (τ 1 )()+ I 2 τ 2 =1 ). In the figure, the theoretical values of positron lifetime in vacancy clusters (V, V2, V4 and V10) obtained by Kuriplach et al. [146] are also reported.
The results of the low-Cu steel resemble closely the results of the alloys containing nickel and manganese; the positron lifetime of the second component is very small and its intensity grows up to very high values. Indeed, the positron lifetime of the second component of the steel is almost the same as the one of the Fe-Mn-Ni alloy, while its intensity is a little lower. The mean positron lifetime of the steel is between those of the two model alloys (Fe- Mn-Ni and Fe-Mn-Ni-Cu).
p. 130 Positron annihilation spectroscopy results
4.3. CDB results This section gives the results of coincidence Doppler broadening (CDB) for all alloys. The numbers shown correspond to the ratio of the values obtained from the measurement of the investigated alloys to the one of non-irradiated pure iron. In case enough statistics are present, the error on the S and W parameter can be approximated by the ratio of the number of counts participating in the area of the parameter to the total number of counts in the spectrum. The error bar to be associated with the reported values is thus ± 0.000874 for S and ± 0.00185 for W .
4.3.1. Pure iron and the binary Fe-C alloy The spectra of the irradiated iron and Fe-C alloys, normalized to the one of pure, defect- free iron, are shown in Figure 78. When vacancies appear, the low momentum range of the CDB curve show an increase, while the high momentum part decreases. This is visible for both pure iron and the Fe-C alloy.
Pure Fe Fe-C
Figure 78 The coincidence Doppler broadening spectra for the pure iron (left) and the Fe-C alloy (right). The net spectra have been normalized to the spectrum of pure, defect-free iron.
The S and W parameters have been calculated for each spectrum in regions between -2.5 and 2.5 mc for S and between -25 and -15 mc, as well as between 15 and 25 mc, for W . These values, normalized to the ones of pure, defect-free iron, are given in Figure 79 for the irradiated iron and Fe-C alloys. The values for the non-irradiated materials are close to 1, as these materials do not contain any defects or positron affinitive places before irradiation.
p. 131 Chapter 4
Figure 79 The S (left) and W parameter (right) calculated from the coincidence Doppler broadening spectra for the pure iron and the Fe-C alloy. The parameter values have been normalized to those of pure, defect-free iron.
During irradiation more vacancies are formed, thus the S parameter increases. At the same time fewer positrons are able to annihilate with inner-shell electrons (as they annihilate with outer-shell electrons at vacancies), and the W parameter decreases. The irradiated pure iron, in Figure 79, has thus a positive S parameter variation and a negative W parameter variation. The saturation-like behaviour which has been observed in the mean positron lifetime of the PALS results reappears in the behaviour of the S parameter with dose. Also the W parameter shows a saturation-like behaviour.
If some carbon is added, a lower S value is observed compared to the one in pure iron, while W remains almost the same. The defects where the positrons annihilate thus have the same chemical environment in both alloys, but the presence of carbon seems to reduce the number of vacancies in the observed vacancy-type defect clusters. However, also the reduced visibility due to the presence of carbon could play a role in reducing the S values. A sudden decrease in number density of defects, observed by the decrease of intensity of the second PALS component, may be the reason for the fact that the S and W parameters drop a little to their defect-free state at 0.05 dpa. Indeed, the low density and the presence of carbon make the defects much less visible to the positrons. They will annihilate with much more probability in the matrix. At higher doses, the clusters have grown considerably, which leads to an increase of their detectability.
p. 132 Positron annihilation spectroscopy results
4.3.2. Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper The spectra of the irradiated binary Fe-Cu alloys, normalized to the one of pure, defect- free iron, are shown in Figure 80. It is clear that, for all irradiation doses, the copper-specific peak is present. Therefore, it is possible to conclude that copper is located at the positron annihilation sites.
Fe-0.1% Cu Fe-0.3% Cu
Figure 80 The coincidence Doppler broadening spectra for the Fe-0.1% Cu alloy (left) and the Fe-0.3% Cu alloy (right). The net spectra have been normalized to the spectrum of pure, defect-free iron.
Figure 81 The S (left) and W parameter (right) calculated from the coincidence Doppler broadening spectra for the binary Fe-Cu alloys. The parameter values have been normalized to those of pure, defect-free iron.
The S and W parameters have been calculated for each spectrum, normalized to the ones of pure iron and shown in Figure 81 for the irradiated binary Fe-Cu alloys. Also in these alloys, the values for the non-irradiated materials are all close to 1. The copper atoms, homogenously distributed in the matrix, have only a very small positron affinity compared to
p. 133 Chapter 4 the one of vacancies. In addition, the copper is present in very low concentrations. No copper peak is thus found in the binary Fe-Cu alloys before irradiation.
The binary iron-copper alloys show on the one side an increase of W with increasing Cu content (a less negative variation compared to pure iron), as it can be observed in Figure 81. This indicates the presence of Cu-rich precipitates at the positron annihilation sites. This was already observed before in [118] and [147]. The alloy with more copper contains more precipitates and has thus a higher W value. At the same time, a decrease of W (and an increase of S ) during irradiation, indicates that the amount of vacancies near the positron annihilation sites is increasing for both alloys. Interesting to mention is that the W value does not saturate with the dose. The newly produced vacancies (during further irradiation) will thus be located at the pre-existing Cu-rich precipitates, and therefore the composition of the precipitates will continue to change during irradiation. At this stage, it is not yet clear if the results come from the simultaneous presence of copper-free vacancy cluster and vacancy-free copper clusters or from the presence of copper- vacancy co-clusters. Later on in this thesis, it is however shown that an average copper fraction close to 100 % is found at the positron annihilation sites for some irradiation conditions (see Figure 105 in chapter 5). Together with the high amount of vacancies found here, it is concluded that the copper and the vacancies should be present at the same positron annihilation site. The behaviour of S is more complicated to rationalize. Figure 81 shows that, for the alloy with 0.1% of copper, the S parameter starts at a high value. Thus more positrons annihilate near vacancies at this stage of irradiation, in this alloy. On the one side, the S parameter of the pure iron and Fe-C is lower, due to the lack of the more positron affinitive Cu-V complexes. On the other side, the S parameter of the alloy with 0.3% Cu is lower, due to the existence of vacancy-free Cu-precipitates, where part of the positrons annihilates. During further irradiation, these Cu-precipitates with no vacancies will capture some vacancies as well, in such a way that the S parameter of this alloy will come closer to the S value of the alloy with less copper. Indeed, S increases substantially in the Fe-0.3% Cu alloy.
The above argumentation can be easily illustrated in a S −W diagram, such as in Figure 82. It can be seen that the alloy with 0.1 % of copper exhibits a different behaviour, which indicates that the relative amount of vacancies near the positron annihilation sites
p. 134 Positron annihilation spectroscopy results compared to the low irradiation dose will increase faster in this alloy than in the other ones. Indeed, the copper precipitates will attract more vacancies, compared to pure iron, while there are less precipitates to compete with each other for the available vacancies, compared to the alloy containing 0.3 % of copper. In the latter alloy, more competition between vacancy- containing and vacancy-free copper clusters occur.
Figure 82 The high momentum part of the CDB results ( W parameter) is shown as a function of the low momentum part ( S parameter) for pure iron and pure copper and for the Fe- C, Fe-0.1% Cu and Fe-0.3% Cu alloys.
It is interesting to mention that the points of the Fe-C alloy are on the same line as those of the pure iron in the S − W diagram of Figure 82, implying the same type of defects. Although the W parameter of the CDB measurement in the Fe-0.1% Cu alloy decreases up to the value of pure iron at the highest irradiation dose, it is still obvious that copper is present at the positron annihilation sites. Indeed, even for these irradiation conditions, a copper-specific peak is observed in the CDB spectra. In addition, the S −W diagram illustrates that the W value for copper-free defects with corresponding S value is even much lower.
4.3.3. Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy The spectra of the model alloys containing manganese and nickel, normalized to the one of pure, defect-free iron are shown in Figure 83. In the Fe-Mn-Ni alloy, a small nickel- specific peak is visible, especially at the higher irradiation doses. The Fe-Mn-Ni-Cu alloy exhibit a clear peak, but it is impossible to determine if the peak is originating from the
p. 135 Chapter 4 presence of copper, nickel or both elements at the positron annihilation sites, as the peak for pure nickel looks very much like the one of pure copper (mainly lower in height).
Fe-Mn-Ni Fe-Mn-Ni-Cu
Figure 83 The coincidence Doppler broadening spectra for the Fe-Mn-Ni alloy (left) and the Fe-Mn-Ni-Cu alloy (right). The net spectra have been normalized to the spectrum of pure, defect-free iron.
The S and W parameters have been calculated for each spectrum, normalized to the ones of pure iron and shown in Figure 84 for the irradiated model alloys containing manganese and nickel. Also in these alloys, the values for the non-irradiated materials are all close to 1.
Figure 84 The S (left) and W parameter (right) calculated from the coincidence Doppler broadening spectra for the model alloys containing manganese and nickel, as well as for the low-Cu RPV steel. The parameter values have been normalized to those of pure, defect-free iron.
p. 136 Positron annihilation spectroscopy results
In the alloys containing manganese and nickel, W experiences only a modest decrease with irradiation dose, while S remains very small. This effect can be interpreted as a sign that the vacancy clusters remain very small, much smaller than in pure iron. This was already observed by the PALS results. In contrast with the results of the binary Fe-Cu alloys, W saturates again, at higher irradiation doses for the alloys containing nickel and manganese. This indicates that the chemical environment of the positron annihilation sites does not change anymore at higher doses, and therefore it can be assumed that the amount of vacancies in the defects remain approximately constant.
The addition of copper to the Fe-Mn-Ni alloy leads, as expected, to an enormous increase of the W value. It is however hard to distinguish if the increase of the high momentum range in this alloy is originating from copper, nickel or both elements. This huge increase in W contributes to a further decrease of S , as a result of the equilibrium between the two parameters. The little decrease in W observed in the Fe-Mn-Ni-Cu sample can be due to the low amount of vacancies in the clusters. If only one vacancy is present in the clusters, the probability that the positron annihilates with an inner shell electron is much higher, compared to the case where the positron is trapped in a defect with more vacancies.
Figure 85 represents a S − W diagram for the alloys containing manganese and nickel.
Figure 85 The high momentum part of the CDB results ( W parameter) is shown as a function of the low momentum part ( S parameter) for pure iron, copper and nickel, for the Fe-0.1% Cu, Fe-Mn-Ni and Fe- Mn-Ni-Cu alloys and for the steel.
p. 137 Chapter 4
It can be observed that for the Fe-Mn-Ni alloy, at the start of the irradiation, the W parameter is lower than expected for pure vacancy defects (as observed in pure iron). As manganese is the only element present in the investigated alloys leading to a decrease of W , it is clear that manganese will be bound to the vacancies at this stage of irradiation. Further irradiating leads however to a decrease of this deviation from the pure vacancy type of defects, and even a crossing is observed of the Fe-Mn-Ni line with the pure Fe line. One may thus conclude that the influence of nickel becomes more pronounced at higher irradiation doses. A similar trend is already observed in the nickel-specific peak of the ratio curves (Figure 83), which seems to be more apparent at the higher doses. For the Fe-Mn-Ni-Cu alloy, a similar trend is observed, starting although from a higher W value, caused by the presence of the copper.
4.3.4. Low-Cu RPV steel The spectra of the low-Cu RPV steel, normalized to the one of pure, defect-free iron are shown in Figure 86. In these spectra a small peak is present, comparable to the one found in the Fe-Mn-Ni alloy. Nevertheless, it is not possible to determine if the peak is specific for the copper or the nickel.
Figure 86 The coincidence Doppler broadening spectra for the low-Cu RPV steel. The net spectra have been normalized to the spectrum of pure, defect-free iron.
The S and W parameters, calculated for each spectrum of the steel and normalized to the ones of pure iron, are already given in Figure 84 and Figure 85. Also in the steel, the values for the non-irradiated material are close to 1.
p. 138 Positron annihilation spectroscopy results
Similar considerations can be made for the RPV steel, as it has been done for the alloys containing nickel and manganese. This steel contains the same amount of nickel as the model alloys, but it has a very low concentration of copper. As a result of this, the effect of nickel is the most explicit. The discrepancies for S and W remain somewhat smaller than expected. This must be interpreted in terms of fewer or smaller vacancy clusters, caused by the presence of other chemical species.
p. 139 Chapter 4
4.4. Discussion In order to be able to discuss the types of defects detected by PAS, it is necessary to have an idea about the binding energies of all the elements playing a role in their formation, i.e. all alloying elements and the vacancies (Vs) and self-interstitial atoms (SIAs) produced by irradiation. The observed defects in the model alloys will then be discussed with respect to their contribution to the hardening. In a final section, the mean contributions to the hardening of a steel are discussed, based on the above described positron results.
4.4.1. Binding energies of the investigated elements with Vs and SIAs For the understanding of the above results, it is necessary to take into account what is known concerning the binding energies of the investigated atomic species with vacancies and self-interstitials, as well as with each other. These energies will play a significant role in the microstructural evolution produced under irradiation, which results in the changes observed in the PAS and tensile test results. For the solute-solute (Table 19) and vacancy-solute interactions (Table 20), the outcome of [148] has been used. Vincent et al. [149] give the self-interstitial interaction with solute atoms in α-Fe (Table 21). The interaction of an interstitial carbon atom with intrinsic point defects in α-Fe has been studied in [150] (Table 22). All calculations have been performed using the Vienna ab initio simulation package (VASP) [151]-[154] and the ultrasoft pseudopotential (USPP) approximation [155]. They are therefore consistently comparable. In all these calculations of binding energies, negative values indicate repulsion and positive values attraction.
Table 19 The solute-solute binding energies (Eb in eV) in first (1nn) and second (2nn) nearest neighbour calculated by ab initio calculations with 128 atom supercells and 27 k points and used to determine the pair interaction [148]. For the manganese, the state is antiferro-magnetic. Copper Nickel Manganese
Eb(Cu-X 1nn) 0.14 0.04 0.04 Eb(Cu-X 2nn) 0.03 -0.01 -0.07 Eb(Ni-X 1nn) -0.07 -0.06 Eb(Ni-X 2nn) -0.02 -0.11 Eb(Mn-X 1nn) -0.28 Eb(Mn-X 2nn) -0.15 p. 140 Positron annihilation spectroscopy results
Table 20 The vacancy-solute binding energies (Eb in eV) in first (1nn) and second (2nn) nearest neighbour, the vacancy formation energy (Efor in eV) in an α-iron matrix and the cohesive energies (Ecoh in eV) for the bcc structures, calculated by ab initio calculations with 128 atom supercells and 27 k points and used to determine the pair interaction [148]. For the manganese, the state is antiferro-magnetic. Some of the calculations (*) are performed using the PAW method (see text for more information) [156]. Copper Nickel Manganese Vacancy Iron
Eb(V-X 1nn) 0.17 0.03 (0.12*) 0.12 (0.21*) 0.14 (0.16*) Eb(V-X 2nn) 0.19 0.18 (0.20*) 0.07 (0.14*) 0.28 (0.23*) Eb,lit(V-X) 0.11 0.21 0.15 Eb,exp(V-X) 0.14 0.22 Fe Efor(V ) 2.02 Fe Efor,lit(V ) 1.53 - 2 Ecoh(X) -3.49 -4.34 -2.92 -4.28
Table 21 The SIA-solute binding energies (Eb in eV) obtained by ab initio calculations with 54- and 128-atom supercells and 27 k points and used to determine the pair interaction [149]. There are two different relative positions for the solute atom in first nearest neighbour; one in tension (Tens) and one in compression (Comp). In a third possibility, the solute atom takes part of the mixed dumbbell (see [149] for more information). For the manganese, the antiferro-magnetic (af) or ferro-magnetic (f) states are indicated. Some of the calculations (*) are performed using the PAW method (see text for more information) [156]. Copper Nickel Manganese Supercell size (atoms) 54 128 54 128 54 128 1nnTens_<110> 0.06 0.07 -0.14 -0.13 -0.36 f -0.36 f 1nnComp_<110> -0.03 -0.01 -0.06 -0.06 0.09 af 0.10 af mixed_<110> -0.53 -0.46 -0.36 -0.36 0.36 af 0.37 af (-0.16*) (0.57*)
Table 22 The Vacancy-interstitial impurity binding energies (Eb(V-X) in eV) and <110>- dumbbell binding energies (Eb(SIA-X) in eV) with impurities situated in three different interstitial positions [150]. The calculations were carried out using 54-atom supercells and 125 k points and 128-atom supercells and 27 k points. Carbon Supercell size (atoms) 54 128
Eb(V-X 1nn) 0.44 0.47 Eb(V-X 2nn) -0.09 -0.01 Eb,lit(V-X) 0.41 – 0.48 Eb,exp(V-X) 0.41 Eb,1(SIA-X) -0.39 -0.19 Eb,2(SIA-X) -0.58 -0.31 Eb,3(SIA-X) -0.32 -0.09
More recently, the projector augmented wave (PAW) approximation [157] has been compared to the USPP method and the results obtained with the PAW method are expected to
p. 141 Chapter 4 be more reliable. Some preliminary PAW results have been provided by Olsson [156] and are given in Table 20 and Table 21.
A dumbbell (a term used in Table 22) is a configuration of SIAs. Contrary to what one might intuitively expect, most self-interstitials in metals with a known structure have a split structure, in which two atoms share the same lattice site. Typically, the centre of mass of the two atoms is at the lattice site, and they are displaced symmetrically from it along one of the principal lattice directions. In bcc Fe, the ground state interstitial structure is a [110] split interstitial. This is illustrated in Figure 87.
Figure 87 The structure of a dumbbell in bcc iron [7].
From Table 20, it can be seen that the elements investigated in this work (Cu, Ni and Mn) tend to be bound to vacancies in Fe, in both first and second nearest neighbour position. Thus, all these elements are likely to accompany a vacancy in its motion. It is not clear whether this accompaniment will follow the dragging procedure or the exchange and release method. This remains true for nickel and manganese according to the PAW results. As the binding energy between two solute atoms, aside from copper, is negative (see Table 19), only copper-rich precipitates will be easily formed. In addition, atomistic studies show that vacancy clusters are preferentially associated with Cu atoms [158]. This is in agreement with the interpretation of previous PAS experiments [50], as well as ours, as it will be discussed later on in this work. The interaction of the elements with self-interstitial atoms (SIAs) is different (Table 21). Nickel will not be bound to an SIA in any case, while copper will be bound very weakly, as first nearest neighbour, but only in one specific configuration. These copper-SIA bindings will tend to dissociate immediately, as shown in [149]. Manganese, on the other hand, has a very strong binding energy with the SIA in a mixed dumbbell configuration. This value is
p. 142 Positron annihilation spectroscopy results even higher according to the PAW method. Thus, in presence of manganese, Fe-Mn mixed- dumbbells are likely to be formed and they are able to migrate in all three dimensions [149], providing a means to transport Mn atoms to sinks for SIAs (for example to SIA clusters, as well as dislocations and grain boundaries). Finally, the interstitial carbon atom binds vacancies very strongly, while single SIAs seem not to be bound at all (Table 22). A more recent investigation [159] suggests, however, that the dumbbell is weakly attracted by a carbon atom (binding energy up to about 0.19 eV), when located at a mutual distance of more than one lattice parameter. Furthermore, recent atomistic simulations suggest that a single C atom may trap a SIA cluster with a binding energy between 0.5 and 1 eV [36].
4.4.2. Hardening of the alloys Although these results will be discussed in detail further on in this thesis (chapter 6), some results are already given here, in order to be able to discuss the defects observed by the positrons in relation to their effect on the hardening. The tensile properties of the materials, before and after irradiation, were measured. In Figure 88, the data for the change in yield strength ( Δσ ), as a function of the square root of the dose, expressed in mdpa, is plotted.
Figure 88 The variation of the shift in yield stress as function of the dose square root (expressed in mdpa).
Within all uncertainties and considering the limited statistics, two separated trends seem clear. In pure Fe, Fe-C and Fe-Cu alloys, there is a saturation of radiation-induced hardening, visible already at very low dose, while in the case of the materials containing Ni and Mn, the
p. 143 Chapter 4 dependence on the square root of the dose is rather linear. In the latter alloys, the hardening does not saturate up to the highest investigated dose.
4.4.3. Discussion of the PAS results Once it is known which defects can be observed by the investigating technique, it is possible to discuss the results in a proper way.
As both the mean positron lifetime and the S parameter are giving information on the amount of vacancies in the material, it is possible to compare these parameters. For the materials studied here, their dependency seems close to linear, although this is not rigorously correct. In the plots showing their relation (Figure 89-Figure 92), the same trend line is used for all alloys.
Pure iron and the binary Fe-C alloy{ TC "Pure iron and the binary Fe-C alloy" \f C \l "4" }
The results of the positron lifetime as functions of the S parameter for the pure iron and the binary Fe-C alloy can be observed in Figure 89.
Figure 89 The positron lifetime results for the pure iron and the Fe-C alloy are given as functions of the low momentum part of the CDB results ( S parameter). A linear correlation is found for the mean positron lifetime as a function of the S value.
Under neutron irradiation, damage is produced by displacement cascades. Not only single vacancies and SIAs are produced in a displacement cascade, but also some small vacancy clusters and a few sizeable SIA clusters [20], [21]. In pure iron, these small defects are free to move according to their diffusion properties, until they annihilate with each other
p. 144 Positron annihilation spectroscopy results or at sinks or accumulate in bigger loops and voids. All these defects can cause irradiation hardening, because dislocations can be pinned by them. However, PAS is only sensitive to the vacancy clusters and their chemical environment. In pure iron, vacancies are surrounded by iron atoms only. Vacancy clusters in Fe are formed already at early irradiation, as a second component appears in the PALS spectrum. The clusters grow with further irradiation, as S increases, W decreases and the positron lifetime of the second PALS component increases substantially. The growth happens both by the supply of new vacancies and the agglomeration of smaller clusters.
The Fe-C alloy studied in this work contains a non-negligible amount of carbon impurities, with which both vacancy- and self-interstitial-type defects will interact. The PAS results however indicate only slight differences from pure iron. The similar W parameter suggests that the chemical environment at the positron annihilation sites is the same in Fe and Fe-C. However, if C was associated with vacancies, the technique would not be sensitive to it, due to its low affinity to positrons. The slightly higher values of W , compared to those of pure iron, may be due to the presence of a small quantity of copper (see Table 8) or simply to the smaller values of the S value. The lower value of S (Figure 79), as well as the lower intensity in the second PALS component (Figure 71) in the Fe-C alloy compared to pure iron may be caused by a somewhat enhanced recombination of vacancies with SIAs and a hindered growth of vacancy clusters. Indeed, as vacancies are relatively strongly trapped by carbon atoms, their effective diffusivity will be reduced (a well-known effect of C on vacancies, see e.g. [160]). So, they will have more opportunities to annihilate with single SIAs, before they could form clusters. In addition, the carbon atoms stop the SIA clusters, whereby the mobile vacancies can recombine with them. This could be the reason why fewer vacancies are observed in this alloy, in comparison to pure iron.
Since the vacancy cluster population in Fe-C and in pure Fe is essentially the same (the differences are very small), the irradiation hardening increase in these materials is most probably caused by a difference in the population of SIA clusters. Also the fact that the hardening increase at higher irradiation doses is more explicit for the alloy containing carbon impurities, indicate that the vacancy-clusters play only a minor role in the hardening, as the ones found in pure iron were observed to be bigger.
p. 145 Chapter 4
SIA clusters cannot directly be observed by PAS. However, when dislocation loops (SIA loops) are formed, vacancies may be trapped by them. The vacancy-dislocation combination has a positron lifetime of about 160 ps. These defects will be observed within the first positron lifetime component. This could be the cause of the high first component positron lifetime in both alloys. A higher density of SIA clusters will thus correspond to an increased number of pinning points for the dislocations and thus more hardening will appear. This is the case for the Fe-C alloy, as it was already suggested earlier that the carbon atom and a single dumbbell are attracted. The carbon atoms will provide some additional nucleation sites for SIA clusters that, being trapped, cannot disappear at sinks, thereby increasing the SIA density compared to in pure Fe. In addition, due to the trapping effect of C, the growth of loops by coalescence of SIA clusters will be hindered, thereby keeping their density higher, while their size remains smaller.
Binary Fe-Cu alloys{ TC "Binary Fe-Cu alloys" \f C \l "4" }
The results for the binary Fe-Cu alloys found with the positron lifetime technique are shown in Figure 90, as functions of the S parameter.
Figure 90 The positron lifetime results for the binary Fe-Cu alloy are given as functions of the low momentum part of the CDB results ( S parameter). A linear correlation is found for the mean positron lifetime as a function of the S value.
The addition of copper to iron hardens the material drastically. Based not only on our results, but also on the abundant literature on the matter, we know that this hardening is due to the appearance of Cu-rich precipitates. Nagai et al. [50] have suggested that copper atoms are dragged by migrating vacancies to form copper-vacancy complexes. Recently, this dragging p. 146 Positron annihilation spectroscopy results of copper was also shown by atomistic simulations [161], [162]. This is a consequence of the relatively high binding energy between a copper atom and a single vacancy, up to the second nearest neighbour distance. This not only provides a mechanism for the two species to migrate together, but is also the driving force for the easy nucleation and growth of the copper-vacancy complexes. These will further evolve into Cu precipitates with a number of associated vacancies. Our results confirm this point of view. As a large fraction of the positrons annihilate at these vacancy-rich precipitates, and therefore near copper atoms, the W values are significantly higher as compared to pure iron. At the same time, positrons interact with the vacancies in these precipitates and therefore also the S value is higher. The copper atoms will reduce the mobility of the vacancies by trapping them in complexes, leading to more clusters, containing fewer vacancies. This is observed by the higher intensity and reduced positron lifetime of the second PALS component for the Fe-Cu alloys compared to the pure iron. The very high positron lifetime of the second PALS component for the Fe-0.1% Cu alloy implies a high vacancy-to-copper ratio in the defects.
If more copper is present, as in the Fe-0.3% Cu alloy, even more vacancies become visible to PAS, due to the attraction of positrons towards copper-vacancy complexes. This is seen in the increase of the intensity of the second PALS component. But, in parallel the S parameter is found to decrease. This is easily explained considering that the same amount of vacancies are created during irradiation at the same dose in both Fe-Cu alloys (the presence of small quantities of Cu is known not to influence the number of produced Frenkel pairs [163]), while more copper atoms are available in the matrix. So, more precipitates will be formed and the vacancies will be distributed among them. Therefore, in each of them, the vacancy- to-copper ratio will be lower. And thus, proportionally more inner shell electrons are used for positron annihilation, and less valence electrons. This is the origin of the S decrease, accompanied by an important increase of W , while the decrease of the positron lifetime of the second PALS component is due to the lowering of the vacancy-to-copper ratio, i.e. the lowering of the average number of vacancies in the clusters associated with the copper precipitates.
In both binary Fe-Cu alloys, a small decrease of the hardening is observed at the highest irradiation dose. This decrease is very small and may be within the error bar for the
p. 147 Chapter 4 hardening. However, it is remarkable that a comparable behaviour is found for the two alloys. This was however not expected, as no decrease of the hardening was found before. It is found in literature that copper plays a role on the hardening in the very early stage of irradiation, but saturates quite rapidly [22], [146]. More detailed investigations should thus be performed to determine the origin of this decrease. In this work, this has been done using the PAS results. It is clear that for both irradiation doses (0.1 and 0.2 dpa), the copper-specific peak is still present (Figure 80). Therefore, it is possible to conclude that copper is still located at the positron annihilation sites, and that the precipitates are not dissolved. A marked change of the mean positron lifetime is also observed (see Figure 73). More vacancies are thus observed by the PAS techniques at the highest irradiation dose compared to the lower ones. As vacancies are preferentially localized in the copper-rich precipitates (see [148], [164]), it can be assumed that these precipitates will grow in amount of vacancies with augmenting dose, inducing an enormous decrease of W (positrons annihilate with valence electrons of the copper atoms), and an increase of S and the positron lifetime of the second PALS component. The amount of precipitates stays approximately constant, as the intensity of the second PALS component does not change for neither of the alloys. This change of the microstructural composition of the precipitates may be the cause of differences in the hardening, observed by the tensile tests. Indeed, the changing amount of vacancies may lead to a changing strength of the precipitates. Depending on the structure of the precipitate, the defects may become stronger or softer. When the precipitates consist of a void core, surrounded by copper atoms (i.e. the most stable form), more vacancies will lead to a bigger void, and the defect will become stronger, in terms of blocking the dislocation motion. If, however, the precipitate is not yet in its stable form and consist of a mixture of vacancies, copper atoms and even iron atoms, more vacancies will lead to an even more dilute defect, which will not necessarily be stronger. If the defects become softer, the total hardening of the sample will decrease.
To obtain more insight into the nature of the defects in binary iron-copper alloys, a post- irradiation annealing experiment has been performed, discussed in appendix E. It is found to be a good method to investigate the stability of the defects produced by irradiation. However, some of the obtained results require further investigation to be fully understood. { TC "Alloys containing manganese and nickel" \f C \l "4" }
p. 148 Positron annihilation spectroscopy results
Alloys containing manganese and nickel
Figure 91 illustrates the results of the positron lifetime technique as functions of the S parameter for the Fe-Mn-Ni and the Fe-Mn-Ni-Cu alloy.
Figure 91 The positron lifetime results for the model alloys containing manganese and nickel are given as functions of the low momentum part of the CDB results ( S parameter). A linear correlation is found for the mean positron lifetime as a function of the S value.
For the alloys containing manganese and nickel a second irradiation-hardening mechanism is proposed, which is independent of the mechanism related to copper. However, as mentioned before, manganese has only indirect effects on the PAS results; the positrons will rather be trapped by defects containing nickel or copper. Vacancy-Mn complexes can trap positrons, but with a lower probability than vacancy-Cu or vacancy-Ni complexes of the same size. Information on this second hardening mechanism can therefore only be obtained in an indirect way. Here, the hints coming from computer-modelling become very useful.
All three elements (Cu, Mn and Ni) have a binding energy with vacancies of the same order of magnitude. Therefore, migrating vacancies will all end up being bound to atoms of all three elements. It has been mentioned before that the binding energy between two solute atoms, different from copper, is negative, so only copper clusters will be easily formed (if Cu is present), and some vacancies will be bound to them. In addition, of all three elements, copper is the only element with a very low solubility limit in iron. The remaining vacancies (again produced in the same amount as in the other materials) will be dispersed in the matrix, bound to unclustered solute atoms, thereby being hindered from forming clusters of appreciable size. For the Fe-Mn-Ni alloy, it is even found in Figure 85 that manganese plays a more dominant role at early irradiation (as W is lower than expected for the given S value)
p. 149 Chapter 4 and its effect decreases with further irradiation. A relatively large amount of the manganese will thus be bound with the vacancies already at very early irradiation, while the interaction of the vacancies with nickel is increasing with dose. The interaction of all investigated elements with the produced vacancies is believed to be the reason why, in both the Fe-Mn-Ni and the Fe-Mn-Ni-Cu alloy, very small values of the S parameter and the positron lifetime of the second PALS component are observed, compared to the alloys containing no manganese and nickel. Since this implies that there are a large amount of very small vacancy-type defects, almost uniformly distributed in the matrix, where the positron can be trapped, the intensity of the second PALS component augments above 90 %. Thus, almost no positrons annihilate in the matrix. The fact that the alloy with no copper has a W value comparable with that of the Fe- 0.1% Cu alloy can be understood in a satisfactory way. Although the W increase due to nickel is lower than that due to copper, the nickel concentration is higher and the clusters contain fewer vacancies (low S ), which leads to these comparable values.
The additional presence of copper in the Fe-Mn-Ni-Cu alloy causes the vacancies to be dispersed even more. Di-vacancy clusters are reduced to just single vacancies. Therefore, the S parameter and the positron lifetime of the second PALS component decrease even more. But, again, more positrons annihilate with the inner shell electrons of copper and nickel, leading to a significant increase of the W parameter, which is even higher than the one caused by the highest copper concentration in the binary Fe-Cu alloys, especially at high irradiation doses. The small decrease in the intensity of the second PALS component compared to the Fe- Mn-Ni alloy can be explained by noticing that the first PALS component increases in this alloy. Therefore, it can be assumed that some positrons annihilate near copper or nickel atoms free from vacancies, as these defects will have a positron lifetime comparable to the one of the bulk material. This would be an additional explanation for the extreme increase of the W value. At the same time, the dispersion of vacancies in the matrix, bound by manganese and nickel atoms, reduces the number of vacancies bound to the copper atoms, thereby retarding the irradiation-induced precipitation of copper via vacancy dragging.
p. 150 Positron annihilation spectroscopy results
Low-Cu RPV steel{ TC "Low-Cu RPV steel" \f C \l "4" }
Figure 92 shows the correlation between the positron lifetime results and the S values for the RPV steel.
Figure 92 The positron lifetime results for the RPV steel are given as functions of the low momentum part of the CDB results ( S parameter). A linear correlation is found for the mean positron lifetime as a function of the S value.
The interpretation of the PAS data made for the model alloys containing manganese and nickel is also largely valid for the RPV steel. This steel contains the same amount of nickel as the model alloy and a very low concentration of copper. As a result, the specific effect of nickel is here more explicit. Small fluctuations, as compared to the model alloys, may be due to the more complex chemical composition. It should be mentioned as well that for the result of both the tensile tests and the PAS measurements, the low-Cu steel resembles most the Fe- Mn-Ni alloy. This emphasizes that manganese and nickel must play an important role in the hardening and embrittlement of these low-Cu steels.
4.4.4. Influence of the defects observed by PAS on the hardening of steels Clearly, the above explanations, based on the presence of uniformly distributed mono- and di-vacancy defects cannot explain the additional irradiation hardening seen in the tensile tests for the alloys containing manganese and nickel. The dislocations will move through these defects without major problems. So, the existence of an additional hardening feature should be invoked, which must be different from the copper precipitate hardening and also not related to the vacancy-type defects.
p. 151 Chapter 4
As stated before, manganese is strongly bound to self-interstitials. Therefore, it can be speculated that manganese decorates the SIA loops and, by lowering their energy, it reduces drastically the mobility of the loops. Similar to what has been postulated to happen in Fe-C, but in a more pronounced way, this will lead to the formation of a larger density of smaller loops, as compared to alloys free from Mn. These immobile, manganese-decorated SIA loops may interact with the mobile vacancy-solute combinations. When such a vacancy-solute combination meets a loop, the vacancy can recombine with a SIA from the loop, while the dragged solute (i.e. manganese, nickel or copper) would stay and also decorate the loop. Nickel and copper may therefore also end up stabilizing these small, virtually immobile loops, however the probability that copper decorates those loops will be much lower, as most of the copper is already trapped by the copper-rich precipitates. This phenomenon of manganese- decorated SIA loops is invisible to PAS, but it would be able to cause the additional hardening. Another possibility could be that vacancy-manganese and/or vacancy-nickel pairs, in spite of the mutual repulsion between single Mn and Ni atoms, succeed in transporting these solutes, until they agglomerate (in the same way as seen for the vacancy-copper combination) eventually forming Mn and Ni precipitates. This is supposing that a Mn- and Ni-rich phase accompanied by vacancies can be stable, or meta-stable, in bcc Fe. Due to the low intermetallic binding energy, the nucleation of these features will occur at a much lower rate than Cu precipitation and therefore they would only become visible after higher irradiation doses.
Since, over the whole dose-range, no vacancy clusters of more than a few vacancies are observed in the manganese and nickel containing alloys, the PAS results suggests that the clustering of manganese and nickel, caused by the dragging-effect of vacancies, must be very limited. Nevertheless, such clusters have been observed by other techniques. And in the literature, their occurrence has been referred to as the formation of "late blooming phases" [19]. The explanation of manganese-decorated SIA loops (later becoming enriched also in Ni and Cu), on the other hand, is still valid and therefore the most probable in our opinion.
Whichever its nature and origin, it has been observed that this second hardening component, caused by the presence of manganese, becomes predominant at higher doses [165].
p. 152 Positron annihilation spectroscopy results
The hardening features observed by the positron techniques can be summarized in a W − S − Δσ diagram, such as shown in Figure 93 for 0.1 and 0.2 dpa.
0.1 dpa 0.2 dpa
Figure 93 The hardening results for all materials, irradiated respectively to 0.1 dpa (left) and 0.2 dpa (right), are plotted as functions of the S and W parameter. Two different groups are visualized. The first one contains the Cu-rich alloys, while the second one consists of the alloys without copper.
At the lower dose of 0.1 dpa, most of the hardening is still due to copper precipitation. This can be observed in Figure 93, where the alloys are separated into Cu-rich and Cu-free alloys in the W − S − Δσ space. The former group reveals a high irradiation-induced hardening, while this hardening is relatively low for the latter one. The alloys containing copper, characterized by their high W value, all show a marked hardening. Due to the presence of a large amount of vacancies in the copper-rich cluster of the Fe-0.1% Cu alloy (indicated by a high S value), W decreases remarkably. Nevertheless, the hardening due to copper-precipitates is still important. Starting from 0.2 dpa, the hardening caused by the presence of manganese and nickel becomes comparable to the one caused by the presence of copper.
On the other hand, it is clear that the size of the vacancy clusters has a much less pronounced influence on the yield strength increase. Indeed, both groups of materials (with and without copper), irradiated up to 0.1 dpa, are scattered over the whole S range. In fact, in the Cu-rich materials the vacancy cluster effect on hardening, if any, is totally hidden by the Cu precipitates, as they are always associated with these precipitates. So, the hardening features should be better defined as copper-vacancy complexes. In Cu-free materials no correlation can be found between S and the hardening. Therefore, it seems to be likely that
p. 153 Chapter 4 not the vacancy-type of defects determines the irradiation-induced matrix damage hardening, but, instead, the self-interstitial-type defects play the major part in it. These speculations need of course to be, and can be, confirmed by looking at the results of other microstructural characterization techniques applied to the same materials. However, the PAS evidence, combined with a few computer-modelling results, is already sufficient to make this scenario highly plausible.
p. 154 Positron annihilation spectroscopy results
4.5. Flux effect As discussed in chapter 1, almost no differences have been found in the hardening and embrittlement results for the flux differences investigated in this work (i.e. ca 1 × 1012 n cm-2 s-1 and ca 1 × 1014 n cm-2 s-1) at the examined dose (ca 2 × 1019 n cm-2). This was explained by the fact that the amount of thermal vacancies are negligible compared to the vacancies created during irradiation and at the same dose, the same amount of vacancies are produced. The behaviour of the vacancies is thus expected to be the same at the two irradiation fluxes for the same dose. Nevertheless, microstructural differences between low and high flux have been found at these fluxes. Indeed, differences are visible in the PAS results, as can be observed in the following figures.
Figure 94 The average positron lifetime results for all materials are given for irradiation at low and high flux.
The average positron lifetimes (Figure 94) are shown to be higher for the samples irradiated at the higher flux for most specimens. This is expected, as at lower flux the vacancies in small clusters have more chances of being emitted before new vacancies come to further stabilize the clusters. The vacancies have thus more time to diffuse through the matrix, leading to more annihilation with self-interstitials and more disappearance at sinks. In the Fe- 0.3% Cu alloy and the steel, these vacancies will not disappear, but rather be trapped by alloying element clusters present in the matrix. At the same time, sufficiently large clusters will further grow at the expense of smaller ones in the materials irradiated at the lower flux. It is thus expected that the vacancy clusters
p. 155 Chapter 4 are bigger at lower flux, and less in amount. This is indeed found in Figure 95 for all materials, except for the alloy containing 0.3 % of copper, where the intensity of the second PALS component is found to be smaller at the high flux. This is however compensated by a higher first positron lifetime component, which indicates the presence of many small defects.
Figure 95 The two component positron lifetime results for all materials are given for irradiation at low and high flux. In the figure, the theoretical values of positron lifetime in vacancy clusters obtained by Kuriplach et al. [146] are also reported.
low flux high flux
Figure 96 The coincidence Doppler broadening spectra for all materials are given for irradiation at low (left) and high (right) flux. The net spectra have been normalized to the spectrum of pure, defect-free iron.
p. 156 Positron annihilation spectroscopy results
It should however be mentioned that the positron lifetime of the first PALS component increases drastically in the binary Fe-Cu alloys. This indicates that some of the positrons annihilate near vacancy-free copper atoms or clusters or copper atoms/clusters containing only one vacancy. Indeed, the copper-specific peak is much more pronounced at higher flux, as visible in Figure 96.
Figure 96 also shows that for all other alloys much less vacancies are visible at the lower flux. At this flux, almost no vacancy clusters are visible (due to their very low number density) in the manganese and nickel containing alloys (including the steel) and for the pure iron alloy. In the alloy containing carbon, the vacancy clusters are probably stabilized by the interstitial carbon atoms and these clusters can continue growing, leading to much bigger clusters compared to the pure iron. In all Cu-containing alloys, the copper-specific peak is visible, while only in the binary Fe-Cu alloys these copper-rich clusters contain a great amount of vacancies. The fact that they are surrounded with copper atoms leads to a much higher visibility of the vacancies.
p. 157 Chapter 4
4.6. Fe-Cr alloys The accuracy of the PALS results is checked by Figure 97 for all the Fe-Cr alloys, for the as received and the irradiated specimens. The stability of the resolution function and the source contribution is controlled by plotting the different spectra from which the random contribution has been subtracted and the net spectra have been normalized to the same total number of counts. Both parameters are stable for the investigated alloys.
as-received irradiated
Figure 97 The positron lifetime spectra for the as-received (left) and the irradiated (right) Cr- rich alloys. The random contribution has been subtracted and the net spectra have been normalized to the same total number of counts.
It is clear from Figure 97 that the resolution function of the as-received materials is larger than the one of the irradiated measurements. This is caused by the fact that the non- irradiated measurements were performed with only two detectors, to reduce the measuring time. Already in the spectra, it is however observed that the as-received model alloys are not defect-free. Indeed, with the analysis of the spectra, in all binary Fe-Cr alloys, defects with a positron lifetime of about 260 ps are found. This positron lifetime corresponds to defects with an average size of about 5 vacancies. The intensity of this component is however found to be very small, 20 ± 5 %. It is believed that they are caused by the cutting of the materials. More investigations are needed to see how they behave after annealing. Nevertheless, as it will be shown later on, these defects are not any more observed in the irradiated samples. These defects are also visible in the CDB spectra of the as-received model alloys. These spectra, as well as the spectra obtained from all irradiated materials are shown in Figure 98, normalized to the one of pure, defect-free iron. p. 158 Positron annihilation spectroscopy results
as-received irradiated
Figure 98 The coincidence Doppler broadening spectra for the as-received (left) and the irradiated (right) Cr-rich alloys. The net spectra have been normalized to the spectrum of pure, defect-free iron.
Notwithstanding the fact that the statistics are not very high for the PALS measurements of the irradiated samples (Figure 97), a reasonable decomposition is obtained. The results for the two component analysis are given in Figure 99.
Figure 99 The positron lifetime results of the irradiated chromium rich alloys are given as functions of the chromium concentration. The results are divided into two positron lifetime components (τ1 and τ2) and their average is given as well (τm). I2 is the intensity of τ2
( I1 (τ 1 )()+ I 2 τ 2 = 1 ). In the figure, the theoretical values of positron lifetime in vacancy clusters obtained by Kuriplach et al. [146] are also reported, as well as the results for the 0.1 dpa irradiated iron.
The found second component is very low, about 160 ps. The results from Kuriplach et al. for pure iron [146] indicate that this corresponds to the positron lifetime of a monovacancy,
p. 159 Chapter 4 while other authors (see for more details chapter 5) expect that this is even below the positron lifetime of a pure monovacancy. This low value could be the effect of chromium near the positron annihilation site. The mean positron lifetime increases with increasing chromium content, as a result of an increasing intensity of the second component. More defects are thus observed in the alloy with a higher chromium concentration.
For the pure iron, irradiated to a comparable dose, defects were found with a similar intensity of the second PALS component, but the defects had a much longer positron lifetime. Indeed, it was even found that the defects grow during irradiation. This could not yet have occurred in the Cr-rich materials, as the clusters still have only one vacancy.
The two steels (T91 and Eurofer 91) show very comparable results to those of the model alloys. Only a higher value for the first positron lifetime component is found. This is most probably due to the presence of other alloying elements, which may attract positron and annihilate them with a higher positron lifetime then present in pure iron.
The results coming from the CDB measurements are summarized in Figure 100, by the parameters S and W .
A maximum is observed in the S parameter simultaneously with a minimum in the W value. This return to a state with apparent fewer defects is in contradiction with the findings from the PALS results. Indeed, chromium near the positron annihilation sites will have the same effect as vacancies, i.e. an increase in S and a decrease in W . This is illustrated in Figure 101 [119]. However, the changes in the PALS results are very small at the highest irradiation doses.
A possible explanation is the fact that the positron affinity is lower at chromium-rich defects compared to the pure iron, as mentioned in chapter 3. This should however also have been observed by a decrease of the intensity of the second PALS component.
p. 160 Positron annihilation spectroscopy results
Figure 100 The S (upper) and W parameter (lower) calculated from the coincidence Doppler broadening spectra for the irradiated Cr-rich alloys. The parameter values have been normalized to those of pure, defect-free iron.
Figure 101 The CDB spectra of some elements (such as Cr) normalized to the spectrum of pure, defect-free iron, as it is found by Nagai et al. [119].
p. 161 Chapter 4
This return to the defect-free state is also visible in the W − S diagram (Figure 102).
Figure 102 The high momentum part of the CDB results (W parameter) is shown in function of the low momentum part ( S parameter) for the irradiated iron and the irradiated Fe-Cr alloys.
The small difference in trend between the irradiated pure iron and the Fe-Cr alloys is due to the nature of the defects. It was found that the pure iron grows defects with increasing size under irradiation. The trend line shows thus an increase in size. For the Fe-Cr alloys, on the other hand, the size remains the same, but the density of the defects increase with increasing chromium content. Also in the CDB measurements, the results of the steels are very comparable to the results of the model alloys.
Figure 103 The positron lifetime results for the pure iron and the Fe-C alloy as functions of the low momentum part of the CDB results ( S parameter). A linear correlation is given for the mean positron lifetime in function of the S value.
p. 162 Positron annihilation spectroscopy results
The results of the PALS technique are plotted as function of the S parameter, in Figure 103.
Again, the average positron lifetime shows a linear dependency on the S parameter. The result for the alloy with about 8.5 wt% chromium is located a little below the trend line ( S ≈1.06 ), while the result for the alloy with about 12 wt% of chromium situates a little above the line ( S ≈1.04 ). The result of the irradiated iron seems to deviate more from the trend line ( S ≈1.08 ). This may be caused by the different nature of the defects.
It may thus be concluded that the binary Fe-Cr alloys show a reduced mean positron lifetime component, compared to the pure iron, irradiated at a comparable neutron dose. This could be caused by the interaction of chromium with self-interstitials. It has been discussed, by e.g. Malerba et al. [58], that self-interstitials in different configurations interact rather strongly with Cr atoms. On the contrary, the interaction energy between Cr atoms and vacancies in an iron matrix is negligible. The chromium in the alloys will thus slow down the small SIA clusters, leading to more recombination of vacancies with self-interstitials and thereby reducing the amount of vacancies in the alloys. This could explain the lower mean positron lifetime in these alloys compared to the one of irradiated pure iron. Nevertheless, it does not explain why the vacancies seem not to cluster in these alloys. However, as the probability of forming voids is dependent on the square of the vacancy concentration, a reduction in amount of vacancies will strongly reduce the chance of void formation.
p. 163 Chapter 4
4.7. Conclusions In this chapter, the results obtained by the positron setups have been given and discussed. Positron annihilation spectroscopy, both positron lifetime and coincidence Doppler broadening, are powerful techniques to analyze Cu-rich precipitates and all kinds of defects containing vacancies. SCK•CEN has facilities which allow active specimens to be analyzed with a high accuracy. The positron lifetime results depend on the size and the volume fraction of vacancy clusters, and therefore PALS can extract information on the mean size of the defects. On the other hand, CDB can give information on the chemical environment of the positron annihilation sites, due to the high affinity of positrons to some alloying elements. By means of the combination of these two techniques, the growth of precipitates, the formation (or not) of vacancy clusters and their association (or not) with clustered and unclustered alloying elements can be traced. In pure iron, both vacancy and SIA clusters are produced during irradiation. Carbon stabilizes small SIA clusters, which leads to a slightly increased recombination of the vacancies with SIAs. The stabilization of the SIA clusters will also lead to an increase in number density of such clusters, causing an increase in the hardening. Copper, accompanying by vacancies, precipitates at very early irradiation, inducing a hardening which saturates with dose. If a higher amount of copper is available, more precipitates are formed, and more hardening will be observed. Manganese will again stabilize small SIA clusters. At these practically immobile clusters, other alloying elements can be added by the annihilation of their dragging vacancy. The effect of these stabilized clusters will become predominant at higher irradiation doses. This may be the origin of the observed manganese and nickel containing precipitates at high irradiation dose. Also chromium stabilizes the SIA clusters. The chromium content in the alloys is much higher than the concentration of the other investigated alloying elements. Much more stabilized clusters will thus occur, leading to a significant amount of recombination of the vacancies. Much less vacancies thus remain in the matrix. At high irradiation doses, chromium can thus reduce the swelling. The influence of the flux is found to be minor. Nevertheless, a trend of increasing vacancy size and decreasing number density is found with decreasing irradiation flux.
p. 164
Chapter 5 Quantification of the results
“If I cannot overwhelm with my quality, I will overwhelm with my quantity.” Emile Zola (France 1840-1902)
The results presented and discussed in the previous chapter are qualitatively correct, but very difficult to be understood for non-experts. In addition, it is not possible to compare them with the results of any other technique. It is thus necessary to make them quantitative. This is however a very difficult issue for positron annihilation results. Only very few attempts have been made in the past.
In the first section of this chapter, two different attempts are applied to the results of the previous chapter and discussed in detail. The estimated defect size and density, obtained by both attempts, are then compared to the results obtained by other techniques (transmission electron microscopy, atom probe tomography and small angle neutron scattering) for the same material compositions. The limitation and strengths of each technique is taken into account, as discussed in the second section. The influence of different neutron fluxes on the results of the techniques is shortly discussed in section 3, while section 4 focuses on the behaviour of chromium-rich materials. All the results are summarized in the last section.
p. 165 Chapter 5
Table of content Chapter 5 Quantification of the results...... 165 5.1. Quantitative results...... 167 5.1.1. First attempt...... 168 Pure iron and the binary Fe-C alloy ...... 168 Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper...... 170 Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy ...... 172 Low-Cu RPV steel ...... 174 5.1.2. Second attempt...... 175 Fitting of the parameters ...... 176 Pure iron and the binary Fe-C alloy ...... 178 Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper...... 179 Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy ...... 180 Low-Cu RPV steel ...... 182
5.2. Combination with other techniques...... 184 5.2.1. Limitations of the different techniques ...... 184 Transmission electron microscopy (TEM)...... 184 Atom probe tomography (APT) ...... 185 Small angle neutron scattering (SANS) ...... 186 Positron annihilation spectroscopy (PAS)...... 187 5.2.2. Results ...... 188 TEM versus the other techniques...... 191 SANS versus APT and PAS...... 191 APT versus PAS...... 192 Comparison of the two PAS calculations...... 193
5.3. Flux effect ...... 194
5.4. Fe-Cr alloys...... 197
5.5. Conclusions ...... 200
p. 166 Quantification of the results
5.1. Quantitative results For comparison with other techniques, quantitative calculations must be performed from the obtained PAS data. These calculations are used to deduce the size and density of the vacancy-type defects produced in each of the neutron irradiated materials. It is worth mentioning at this point that, although the positron lifetime results obtained show rather high reproducibility and low uncertainties (i.e. less than 5 ps), the estimated sizes and densities deduced from them are to be considered in conjunction with the assumptions and the models used.
In order to obtain the quantitative results from the positron annihilation analysis, it is necessary to solve the following differential equations.
k k dnB ⎛ ⎞ = −⎜λB + ∑κ i ⎟⋅nB + ∑δ i ⋅ nDi (58) dt ⎝ i=1 ⎠ i=1 dn Di = κ ⋅ n − ()λ + δ ⋅ n (59) dt i B Di i Di
In these equations, the quantities n (t) and n (t) are the densities of the positrons in B Di respectively the bulk and the defect state at time t , while κ is the trapping rate and δ is the detrapping rate. The indices B and Di denote the free (bulk) and the trapped (defect) state, respectively. For these calculations, the positron lifetime of a defect should be correlated with its size, i.e. the number of vacancies it contains. The solutions proposed in the literature have been summarized in appendix F. The determination of the average size of the defects is here not only obtained for pure iron, but also for the other alloys. Figure 164 gives the general trend line of the positron lifetime as a function of the defect size in pure iron. In appendix F, it is shown that only the lifetime of the defects in the binary Fe-Cu alloys do not follow this trend. For these alloys, Figure 166 gives the three-dimensional trend to follow.
p. 167 Chapter 5
5.1.1. First attempt In the differential equations 58 and 59, two trapping states are needed for irradiated alloys. Three components are thus present, i.e. the bulk component and the two trapping states. However, only a two-component analysis of the experimental results could be performed. In order to solve this problem, Vehanen et al. [166] proposed that the experimentally observed second PALS component corresponds to the component of the defect clusters only. The experimentally observed first component, on the other hand, is supposed to contain both the contribution of the bulk and the one of traps with a rather small positron lifetime. This is illustrated by the following equations.
I 3,theor = I 2,exp (60)
τ 3,theor = τ 2,exp (61)
I1,theor + I 2,theor = I1,exp (62)
τ 1,theor ⋅ I1,theor +τ 2,theor ⋅ I 2,theor = τ 1,exp ⋅ I1,exp (63)
Vehanen et al. assumed the small positron lifetime traps to have a positron lifetime
(τ 2,theor ) of 175 ps for pure monovacancies and 160 ps for vacancies combined with a carbon. In appendix F, however, it is discussed that it is better to use 160 ps in all cases. Indeed, even in the pure iron alloy, the vacancies can be localized by a dislocation, reducing the positron lifetime at the defect. Using the above given assumption, the differential equations 58 and 59 can be solved and the average defect density can be obtained (see appendix F).
Pure iron and the binary Fe-C alloy{ TC "Pure iron and the binary Fe-C alloy" \f C \l "4" }
Using the obtained positron lifetime results, the average size of the clusters and the number density of both the clusters (red curve) and the short positron lifetime traps (blue curves) are reported in Figure 104, as functions of the irradiation dose, for pure iron and the Fe-C alloy, as estimated following the methodology mentioned above.
For pure iron, it is observed that the size of the clusters increases gradually with the irradiation dose, while the number density of the clusters decreases. The clusters thus grow by agglomeration of single vacancies or smaller clusters. With increasing irradiation dose, the newly produced vacancies will be distributed between the clusters and the bulk. Indeed, the p. 168 Quantification of the results density of the short positron lifetime traps increases (more free vacancies in the bulk material) as well as the size of the clusters. As it was found that the density of the clusters diminishes with dose, it is (as mentioned before) understandable that the amount of vacancies, which are still present in the bulk, increases. The supply of new vacancies requires them to diffuse for longer distances to reach a previously formed cluster.
Pure Fe Fe-C
Figure 104 The estimated values are given for the size of the clusters and the density of both the short positron lifetime traps and the clusters, for pure iron (left) and for the binary Fe-C alloy (right).
The estimated diameter of the irradiation-induced defects in pure iron given in Figure 104 agrees roughly with the one observed by Eldrup et al. (see figure 4 of [167]) for pure iron irradiated to approximately the same dose. The number density of the defects published by Eldrup et al. (see figure 5 of [167]), on the other side, is about 10 times higher than the one found here. This might be the effect of the irradiation temperature, as the alloys in the paper of Eldrup et al. were irradiated at 70 °C, while in the current work an irradiation temperature of 300 °C was chosen. Indeed, at higher temperatures, vacancies will be more easily emitted from clusters and small clusters will be more mobile, increasing recombination and annihilation to sinks, with consequent decrease of the overall amount of clusters.
p. 169 Chapter 5
When carbon is added to the alloy, the size of the clusters is smaller than in pure iron, as carbon hinders the growth of the vacancy clusters. This size seems to saturate at higher doses. The density of both the short positron lifetime traps and the clusters show a peak at about 0.025 dpa. This might be due to the assumption of the model. However, the presence of carbon may also explain this peak to a certain extent. The vacancy-carbon complexes with only 1 vacancy are rather stable and reduced in their mobility [168]. Therefore, the agglomeration will only start after the supersaturation of vacancies. Once they are formed, the clusters grow up to about 5 vacancies and then stabilize again. Newly produced vacancies will especially be present in the bulk material, combined again with the carbon, but also some new clusters will be formed. { TC "Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper" \f C \l "4" }
Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper
In appendix F, it is argued that the correlation of the positron lifetime component and the size of the clusters changes, if copper is added to the positron annihilation sites. It is therefore necessary to estimate the average copper coverage of the clusters, using the approach developed by Nagai et al. [169], [170], as also discussed in appendix F. Figure 105 illustrates the estimated fractions of the positrons annihilating with copper electrons for the two Fe-Cu alloys after irradiation to the different doses. This was obtained by the use of equation 100. This fraction is varying between zero when no Cu atoms are surrounding the positron annihilation site and one when the shell (first and second nearest neighbours) surrounding the positron annihilation site is entirely made of Cu atoms.
Figure 105 The estimated average fraction of the copper at the positron annihilation sites.
p. 170 Quantification of the results
It is found that for the alloy containing 0.1 % of copper, the degree of coverage is low, i.e. lower than 50 %, while, for the alloy containing 0.3 % of copper, it increases to about 100 % at low irradiation doses. This is easily understood, as more copper is available in the latter alloy. The copper in the alloys combines with the relatively small amount of vacancies, produced at low doses. With increasing irradiation dose, the average fraction of copper decreases steadily, as more and more vacancies are available that can reach the already formed clusters.
Based on the obtained degree of coverage, it becomes possible to identify the V-Cu clusters associated with the second component of the positron lifetime measured in the Fe-Cu alloys. In fact, these second positron lifetime component results of the PALS analysis can lead to an estimation of the average size of the clusters, including both the number of vacancies and those of copper atoms, co-clustering together. It should be noticed that an increasing amount of vacancies will lead to an important increase of the positron lifetime of the defect, while an increasing amount of copper atoms will slightly decrease this positron lifetime.
As for the alloys containing copper, the results for the average size of the clusters and the number density of both the clusters and the short positron lifetime traps are given in Figure 106. Here, it is assumed that the clusters are spherical Cu-V co-clusters where the vacancies are in fact covered by Cu atoms. In red, the average size of the clusters is expressed as the average number of vacancies in the clusters, while the curve in purple is the apparent size of the clusters, including both vacancies and Cu-atoms (i.e. the degree of copper coverage is added to the values in red).
In the alloy containing 0.1 wt% of copper, the vacancy clusters seem to be very stable with dose. Nevertheless, a decrease of number density is found after about 0.05 dpa. Again, this might be due to the assumption of the model, but it can also be partially explained by the agglomeration of the small clusters. Thereafter, the amount of clusters remains almost constant. Newly produced vacancies will thus be trapped by the clusters, as proposed by Verheyen et al. [118]. Indeed, the number of short positron lifetime traps is constant after 0.05 dpa, while the size of the clusters seems to grow very slowly.
p. 171 Chapter 5
Fe-0.1% Cu Fe-0.3% Cu
Figure 106 The estimated values are given for the size of the clusters and the density of both the short positron lifetime traps and the clusters, for the Fe-0.1% Cu alloy (left) and the Fe- 0.3% Cu alloy (right).
For the alloy containing 0.3 wt% of copper, the same observation can be made, except that the number density of the short positron lifetime traps keeps on growing with irradiation dose. This indicates that there is still copper available in the matrix with which new short positron lifetime traps are formed. As more clusters (and short positron lifetime traps) can be formed in this alloy, the clusters will remain smaller in term of the included amount of vacancies. Nevertheless, the total V-Cu clusters will be bigger due to a larger amount of copper atoms. { TC "Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy" \f C \l "4" }
Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy
The estimated size and density of the clusters observed in the irradiated Fe-Mn-Ni and Fe-Mn-Ni-Cu alloys are shown in Figure 107, as well as the estimated density of the short positron lifetime traps.
p. 172 Quantification of the results
Fe-Mn-Ni Fe-Mn-Ni-Cu
Figure 107 The estimated values are given for the size of the clusters and the density of both the short positron lifetime traps and the clusters, for the Fe-Mn-Ni alloy (left) and the Fe-Mn- Ni-Cu alloy (right).
In the alloys containing manganese and nickel, the observed vacancy cluster sizes are extremely small, while the density of the defects is much higher compared to the other alloys. The vacancies form clusters containing only a few vacancies and their size does not seem to grow with increasing irradiation dose. The density of the clusters, on the other hand, grows drastically with dose in the Fe-Mn-Ni alloy. So the newly inserted vacancies under irradiation will be stabilized by an element in the matrix and form new small clusters.
When also copper is available, the average density of the defects remains a little lower, compared to the alloy without copper. Therefore, it is believed that some clustering occurs, namely the formation of copper-vacancy complexes. Nevertheless, the amount of vacancies in these complexes remains very low. It is thus believed that next to the copper-vacancy complexes, a large number of monovacancies stabilized by the alloying elements are detected by the second PALS component, which decreases the estimated average size.
p. 173 Chapter 5
It is thus believed that the presence of manganese and nickel prevent the vacancies to agglomerate. This is due to their mutual repulsion. When clusters are formed, a lot of vacancies are needed to stabilize them. If this is not the case, the cluster will dissolve again.
Low-Cu RPV steel{ TC "Low-Cu RPV steel" \f C \l "4" }
In Figure 108, the average size of the defects in the RPV steel is illustrated, as well as the number density of the defects and the short positron lifetime traps.
Figure 108 The estimated values are given for the size of the clusters and the density of both the short positron lifetime traps and the clusters, for the RPV steel.
Also the results of the RPV steel indicate a great deal of very small vacancy clusters. At early irradiation only monovacancies are produced. These will then agglomerate to form divacancies stabilized by alloying elements. This will of course slightly reduce the number of defects. Once the divacancies are formed, their size stabilizes, while the number density increases and short positron lifetime traps appear. For the results of the irradiation to the highest dose, no changes seem to occur.
p. 174 Quantification of the results
5.1.2. Second attempt It was mentioned before that a two-component analysis was found to give a fairly sufficient fitting of the obtained spectra, while a three-component analysis is necessary for irradiated samples. In order to comply with the model, the two experimentally obtained components should be considered as a combination of the three theoretical components. In the previous attempt, it is assumed that the experimentally found first component consists of both the bulk component and a short positron lifetime trap component at the same time. This is however a very rough assumption. In addition, the positron community considers this assumption to be physically not correct. Nevertheless, up to now this is the only attempt made in literature.
In this part of the work, a generalization of the first attempt is made. It is assumed that the theoretical second component can be decomposed into two. Equations 66 and 67 illustrate how it contributes to both experimental components, starting from the PAS' characteristic equations, equations 64 and 65. Here, the parameters, a and b , are fitting parameters, having a value between 0 and 1, to obtain the best fit to the two component analysis. Parameter a is the fraction of the intensity of the second theoretical component that is included in the first experimental component. Parameter b is an analogue parameter for the contribution of the positron lifetime of the second theoretical component included in the one of this first experimental component. In this attempt, also τ 2,theor is not fixed, but fitted within a range that is physically understandable.
I1,theor + I 2,theor + I 3,theor = I1,exp + I 2,exp = 1 (64)
τ 1,theor ⋅ I1,theor +τ 2,theor ⋅ I 2,theor +τ 3,theor ⋅ I 3,theor = τ 1,exp ⋅ I1,exp +τ 2,exp ⋅ I 2,exp = τ mean (65)
I1,theor + a ⋅ I 2,theor = I1,exp (66)
τ 1,theor ⋅ I1,theor + b ⋅τ 2,theor ⋅ I 2,theor =τ 1,exp ⋅ I1,exp (67)
While fitting the above-mentioned parameters, care should be taken that also equation 68 is satisfied. As the first experimental positron lifetime components are found to be higher than what is expected for a polycrystalline Fe alloy, it is sure that a part of the second theoretical component should be included in this experimental one. Indeed, τ 1,exp is also expected to fulfil equation 68, which shows that this positron lifetime should be lower
p. 175 Chapter 5
than the bulk positron lifetime (τ B ) which is equal to 107 ps. This is not always the case for the experimentally found values.
−1 −1 τ 1 = (λ1 ) = (λB + κ1 + κ 2 ) (68)
In the case when two types of defects are present, the trapping rates can be expressed as given in equation 69 and 70.
τ 2,theor −τ 1,theor κ1 = I 2,theor ⋅ (69) τ 2,theor ⋅τ 1,theor
τ 3,theor −τ 1,theor κ 2 = I 3,theor ⋅ (70) τ 3,theor ⋅τ 1,theor
Furthermore, the parametric study, given in appendix F, is still valid. It determined that the theoretical second positron lifetime will be due to the presence of some single vacancies, combined (or not) with a foreign element or a dislocation, and should therefore be between 160 and 175 ps. In this model, also this second theoretical component can be fitted freely, considering this range. Also this assumption makes this second model physically more correct.
Fitting of the parameters{ TC "Fitting of the parameters" \f C \l "4" }
Using the above given equations, it was possible to estimate the parameters a and b , to obtain the best fit to the two component analysis. The results obtained are given in Figure 109. When the parameters are smaller than 0.5, most of the theoretical second component is converged to the second experimental component. If, on the other hand, the parameters are larger than 0.5, the biggest part is converged into the first experimental component. When both parameters are equal to 1 (and τ 2,theor equal to 160 ps), this model corresponds to the first attempt.
p. 176 Quantification of the results
Figure 109 The intrinsic parameters from Equations 66 and 67 are estimated, to obtain the best fit to the two component analysis.
It is found that both parameters increase with dose. This indicates an increasing experimental second positron lifetime (and therefore also the theoretical third positron lifetime will increase), which causes that more of the monovacancy-component will be converged into the first experimental component.
Figure 110 illustrates the total number of vacancies (in ppm), detected in the alloys after irradiation. This corresponds to the vacancies that are produced at the neutron strike, that did not yet disappear at sinks, or recombine with SIAs. As expected, a global increasing trend can be observed, except for the RPV steel. This can be due to the high activity of this sample (as mentioned in chapter 4), increasing the error of the measurement.
Figure 110 The number of vacancies (in ppm) that survived in the materials after irradiation is estimated by the second model.
p. 177 Chapter 5
Pure iron and the binary Fe-C alloy{ TC "Pure iron and the binary Fe-C alloy" \f C \l "4" }
The obtained results for the pure iron alloy and the binary Fe-C alloy are given in Figure 111. The clusters sizes are shown, as well as the number density of the clusters and the short positron lifetime traps (i.e. the theoretical second positron lifetime component). This positron lifetime is found to be between 160 and 177 ps.
Figure 111 The cluster sizes (a), as well as the number density of the clusters (b) and the short positron lifetime traps (c) are given for pure iron and the Fe-C alloy as functions of dose.
It is shown that, while for pure iron the size of the clusters keeps on growing, this is not the case for the alloy containing some carbon. Indeed, it has already been illustrated (in chapter 4) that carbon reduces the size of the vacancy clusters.
Clusters and short positron lifetime traps are formed in pure iron, at the early stages of irradiation, and their number density does not increase considerably with increasing dose. The carbon will, on the other hand, retard the cluster formation, and the number densities of both clusters and short positron lifetime traps continuously grows during irradiation.
This model, when compared to the previous attempt, indicates the same trends for the sizes of the clusters. Also their density is very similar, while the density of the short positron lifetime traps increases by about a factor 10.
p. 178 Quantification of the results
Nevertheless, no peak is observed for the cluster density at 0.025 dpa in the Fe-C alloy, as was found in the previous attempt. The fact that no peak is detected, is however more reasonable, as it is believed that, at early irradiation, vacancy-carbon pairs are formed, visible by the short positron lifetime component. Once a supersaturation of vacancies is reached, they start to agglomerate and form clusters. This explains why there is still a peak found for the density of the short lifetime traps. A large amount of short positron lifetime traps is understandable, as during irradiation there is a constant supply of new vacancies. { TC "Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper" \f C \l "4" }
Binary Fe-Cu alloys with 0.1 % and 0.3 % of copper
In Figure 112, the clusters sizes are given for the binary Fe-Cu alloys. Both estimated sizes are shown for the vacancies only and also the combined vacancy-copper sizes. In addition, the number densities are plotted of both the clusters and short positron lifetime traps, whose positron lifetime is found to be between 160 and 177 ps.
Figure 112 The cluster sizes of the binary Fe-Cu alloys are given, those concerning only the amount of vacancies (a), as well as those including the copper atoms present in these clusters (b). The number density is also shown for the clusters (c) and the short positron lifetime traps (d).
p. 179 Chapter 5
When copper is added to the alloy, the amount of vacancies does not saturate. A continuous growth of the vacancy clusters is observed. However, the amount of copper atoms in the clusters does not change. The overall size will thus saturate at very small irradiation doses. The alloy containing 0.3 % of copper shows a lower amount of vacancies in their clusters, but the total size, including the copper atoms, is much larger compared to the Fe- 0.1% Cu alloy. In the alloy containing 0.1 % of copper, the clusters are formed instantly, while some delay appears for the short positron lifetime traps. The opposite is visible for the alloy containing 0.3 % of copper. Nevertheless, copper precipitates have been observed with atom probe tomography in the same alloys, for all irradiation doses [42]. It is thus believed that copper precipitates will be formed around 1 vacancy in the higher copper alloy, while more vacancies are necessary to form those precipitates in the alloy with less copper. In the former case, the precipitates will be observed as short positron lifetime traps, while in the latter case they are observed as vacancy-rich clusters. During further irradiation, a saturation like behaviour is observed for the densities of both short positron lifetime traps and clusters in the Fe-0.1% Cu alloy. The supply of new vacancies will agglomerate in the already existing clusters and no new ones will form. For the alloy with higher amount of copper, on the other hand, both densities continue to increase. This indicates that there is still copper available in the matrix with which the newly produced vacancies can interact.
While the observed trend of the size of the clusters is analogue to the one found by the previous approach to calculate sizes and densities, a different trend is found for the obtained densities. Using the previous approach, both clusters and small positron lifetime traps were identified immediately at the start of the irradiation, while the current approach suggests that one of both densities are remaining very small up about 0.05 dpa. In addition, with the current approach more clusters are found and the number density of the short positron lifetime traps is even a factor 10 higher. { TC "Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy" \f C \l "4" }
Ternary Fe-Mn-Ni and the quaternary Fe-Mn-Ni-Cu alloy
Figure 113 illustrates the cluster sizes of the Fe-Mn-Ni alloy and the Fe-Mn-Ni-Cu alloy. The number density of these clusters is given, as well as the number density of the short positron lifetime traps. p. 180 Quantification of the results
Figure 113 The cluster sizes (a), as well as the number densities (b) of the clusters and short positron lifetime traps are given for the Fe-Mn-Ni and Fe- Mn-Ni-Cu alloys.
The cluster's positron lifetimes for all alloys containing manganese and nickel do not increase above the one corresponding to about two vacancies. It can thus be assumed that the short positron lifetime traps are monovacancies combined with nickel and/or manganese, in these alloys, and the clusters are divacancies. Almost no increase of the size with dose can be observed. When only manganese and nickel are present, monovacancies are produced at early stages of the irradiation, but later on they are replaced by divacancies. On the other hand, when also copper is present in the alloy, almost no divacancies are produced, as too many alloying elements are willing to combine with the available vacancies. Both alloys show a dramatic increase in number density of defects with increasing dose.
The results for the alloys containing manganese and nickel are very much comparable to what is found for the previous attempt to calculate the size and density of the defects. However, whereas the monovacanies were included in the clusters (leading to a very small amount of short positron lifetime traps) in the previous attempt, in the current attempt, it was possible to separate the mono- and divacancies. Therefore, more information could be obtained in this second approach.
p. 181 Chapter 5
Low-Cu RPV steel{ TC "Low-Cu RPV steel" \f C \l "4" }
The sizes of the clusters and the number densities of both the clusters and the small positron lifetime traps, found for the RPV steel, are given in Figure 114.
Figure 114 The cluster sizes (a), as well as the number densities (b) of the clusters and short positron lifetime traps are given for the RPV steel.
Also for the RPV steel, the short positron lifetime traps correspond to monovacancies, while the clusters have the size of divacancies.
The RPV steel, on the other hand, produces both mono- and divacancies during irradiation and, in contrast to the model alloys, the clusters are showing some saturation in amount and a little increase in size, with dose. This is also seen in the binary Fe-Cu alloys and therefore it may most probably be due to the presence of the copper precipitates, where vacancies agglomerate. The presence of divacancies will then be located in these precipitates, while the monovacancies may be combined with other alloying elements available in the steel. However, care should be taken for the interpretation of the irradiation at the highest dose, as it was shown previously that the bad statistics may lead to a high error of the obtained results.
p. 182 Quantification of the results
The saturation like behaviour is also found in the first approach, however the defects have been found at smaller irradiation doses. At the smallest dose, the average defect sizes have however been identified as being smaller than 1 vacancy, which is physically not possible.
p. 183 Chapter 5
5.2. Combination with other techniques To obtain a better understanding of the PAS results, they are combined and compared with the results obtained for the same materials by different techniques. In order to understand all results, it is necessary to have an idea about the limitation of each technique and the features each technique can detect.
5.2.1. Limitations of the different techniques After irradiation, the alloys have been sent to different laboratories all over Europe to be examined with state-of-the-art techniques, each characterized by specific advantages and limitations. Each technique is able to detect some of the irradiation induced defects, within certain limits, but not others. All measurements were performed within the European PERFECT project and are summarized in [79]. Detailed accounts of these results are published elsewhere [35], [42], [135], [164]. In this and the following section, the main findings are summarized. { TC "Transmission electron microscopy (TEM)" \f C \l "4" }
Transmission electron microscopy (TEM)
The microstructure of neutron irradiated materials was examined by TEM, at CIEMAT laboratories (Spain). This technique is able to detect clusters of point defects (vacancies or self-interstitials) induced by irradiation, with sizes over 1.5 nm. With this technique, information from the self-interstitial component of damage can thus be obtained. This is a part of radiation damage not detected with other microstructural characterisation techniques in such a direct way. Figure 115 shows, as an example, a TEM image of the microstructure produced in pure Fe by neutron irradiation up 0.2 dpa. The irradiation-induced damage can be found in the form of directly observable defects, identified as small dislocation loops, distributed homogeneously in the matrix. The majority of the loops have a Burgers vector of type <100>, and they are believed to be of self-interstitial nature [171], [172]. However, the fact that some of the smaller dislocation loops are vacancy in nature is not discarded, though it is not probable that large dislocation loops are vacancy type, as pure vacancy clusters are, in general, more stable in a spherical shape. In addition, also some voids are detectable.
p. 184 Quantification of the results
Figure 115 TEM image of neutron- induced microstructure in pure iron, 100 nm irradiated at 0.2 dpa [79].
TEM will not observe small vacancy-type of defects, nor small bcc-type of precipitates, such as the copper-rich precipitates found in neutron irradiated Cu containing materials. Instead, it is used to detect self-interstitial-type of defects with sizes over 1.5 nm. Loop sizes distributions and densities are extracted from this technique.
Atom probe tomography (APT){ TC "Atom probe tomography (APT)" \f C \l "4" }
The kinetic of solute clustering after irradiation was followed by APT experiments, at the University of Rouen (France). APT enables the determination of the atomic-scale chemical microstructure of the materials to be reconstructed in three dimensions. This technique thus is a very efficient tool for the chemical analyses of solute-enriched clusters. Their characteristics (i.e. number density, size, and composition) as well as the matrix composition are achievable. Solute enriched clusters were detected in the alloys studied (Figure 116), but they were found to be very diffuse. The proportion of iron within the clusters is always higher than 50 %, in agreement with irradiation-induced clusters previously reported by atom probe analyses [92], [173]-[176]. This dilution of the clusters may cause an overestimation of the real size. Indeed, the border of the clusters will be spread out and the apparent size may include too many atoms.
p. 185 Chapter 5
Figure 116 3-D atom probe reconstitution of a small volume of the Fe-Mn-Ni alloy after neutron irradiation to 0.2 dpa [79]. Iron atoms are not represented for the clarity of the image (a). Enlargements of manganese and nickel enriched clusters (b) and (c).
APT is able to detect solute-enriched clusters from fairly small sizes, to very big ones. For the interpretation of the reconstructed volume, only clusters containing a minimum of 5 solute atoms were considered. Nevertheless, as only about 60 % of the atoms are detected by the detector, clusters containing only a few atoms (< 10 solute atoms) may be overlooked, and will thus not be included in the average values of size and density. In addition, the presence of vacancies cannot be detected. Although they are obtained starting from very small analyzed volumes (typically 15 × 15 × 100 nm3), the densities estimated from the APT results are, in most cases, very realistic. However, defects with a number density less than 1022 m-3 are unlikely to be observed. { TC "Small angle neutron scattering (SANS)" \f C \l "4" }
Small angle neutron scattering (SANS)
SANS is capable of characterizing the size distribution of nm-sized irradiation-induced defect-solute clusters in ferritic alloys. The experiments were performed at the SANS facilities at PSI Villigen [139] and LLB Saclay [140]. The analyses were conducted at FZD (Germany).
p. 186 Quantification of the results
Figure 117 An example of the magnetic scattering cross sections (a) and size distributions of irradiation-induced scatterers (b) for the Fe-0.1% Cu, irradiated at the different doses [35].
SANS provides complementary information to the other techniques, being sensitive mainly to precipitates and voids. For the analysis, a few assumptions are required, based on the results of the other techniques. The lower detection limit is about 0.5 nm in cluster radius. This causes a global overestimation of the size, while the density will be slightly underestimated. An advantage is the averaging capability resulting from a probed volume of some 10 mm3 and from a number of scattering events of the order of 106. In addition, some integrated information on the average cluster composition is given by the ratio of magnetic and nuclear scattering. Therefore, more statistics are available for the average density calculation compared to APT. { TC "Positron annihilation spectroscopy (PAS)" \f C \l "4" }
Positron annihilation spectroscopy (PAS)
It is known that positrons are very sensitive to all types of vacancy-clusters and vacancy-solute complexes. The positron is trapped by defects with a different electron density than the bulk material, such as vacancies, vacancy clusters, interfaces, second phase particles, dislocations, etc. Moreover, due to the difference in positron affinity of the different atomic species, positrons annihilate with a different probability in the precipitates as compared to the bulk material. The measurements provide information on the size and density of small vacancy-type defects. The power of PAS lies in its possibility to find very small defects (> 0.1 nm) even in very low concentrations (> 1 ppm), its "self-seeking" nature and its non-destructiveness.
p. 187 Chapter 5
Care should be taken about the fact that the size is calculated depending on the average amount of vacancies present in the clusters. Contrary to the APT results, it is expected that, if the clusters are diluted, which is most probably the case for irradiated samples, the size will be greatly underestimated. Indeed, APT measurements have found a much higher amount of iron atoms in the precipitates, compared to any other technique. This could point to dilute precipitates. On top of this, it is known that the vacancy clusters, which are produced during irradiation, are mostly decorated with alloying elements [164]; therefore the real size will still be higher. Using this average copper coverage, a better estimation of the amount of vacancies and copper atoms in the clusters could be performed for the binary Fe-Cu alloys, resulting in a more reasonable defect size. In addition, it should be mentioned that all vacancy-containing defects can be observed by the positron technique. Moreover, even very small defects containing only a few vacancies combined or not with alloying elements will be detected. This will lead to a very high observed number density of defects.
5.2.2. Results In the figures below (Figure 118 - Figure 121), the results of defect concentrations and defect sizes are given for each technique. In this work, the precipitates are also classified as a type of defect. The size is given as the mean radius of the defects of the TEM, APT and PAS results, while the peak radius of the size is indicated for the SANS results. As the Fe-C alloy was not investigated by any technique other than PAS, this alloy is not discussed, here. In addition, not all samples could be examined by every technique. The coloured symbols in the figures indicate the found data, while the empty symbols indicate estimated results. These results are estimated using the data points of the same technique and the same material. If needed, the trend lines of alloys observed by the same technique, but different though similar composition are used. SANS results for pure iron, irradiated up to 0.038 dpa were obtained outside the project. Its result for average defect concentration and size are however used for the estimation of the results for the pure iron, irradiated at different doses. It should however be mentioned that for the alloys containing manganese and nickel, no precipitates were found at low dose by the APT technique. The extrapolation of the results thus assumes that the defects were invisible to APT due to their low density or their low size. This may however be incorrect, as it also may be that no defects were produced at this dose.
p. 188 Quantification of the results
Figure 118 The evolution of the number density (upper panel) and radius (lower panel) of radiation-induced damage in pure iron is given during neutron irradiation from TEM, APT, SANS and PAS measurements. The full symbols correspond the obtained data, while the empty symbols indicate estimated values (see text for more information).
Fe-0.1% Cu Fe-0.3% Cu
Figure 119 The evolution of the number density (upper panel) and radius (lower panel) of radiation-induced damage in the Fe-0.1% Cu (left) and the Fe-0.3% Cu (right) alloy is given during neutron irradiation from TEM, APT, SANS and PAS measurements. The figure on the left side illustrates the results for the Fe-0.1% Cu alloy. On the right side, the results for the Fe-0.3% Cu alloy are given. The sizes obtained by PAS include the copper atoms. The full symbols correspond the obtained data, while the empty symbols indicate estimated values.
p. 189 Chapter 5
Fe-Mn-Ni Fe-Mn-Ni-Cu
Figure 120 The evolution of the number density (upper panel) and radius (lower panel) of radiation-induced damage in the alloy containing manganese and nickel (left) and the alloy containing copper as well (right) is given during neutron irradiation from TEM, APT, SANS and PAS measurements. The figure on the left side illustrates the results for the Fe-Mn-Ni alloy. On the right side, the results for the Fe-Mn-Ni-Cu alloy are given. The full symbols correspond the obtained data, while the empty symbols indicate estimated values (see text for more information).
Figure 121 The evolution of the number density (upper panel) and radius (lower panel) of radiation-induced damage in the RPV steel is given during neutron irradiation from TEM, APT, SANS and PAS measurements. The full symbols correspond the obtained data, while the empty symbols indicate estimated values (see text for more information).
p. 190 Quantification of the results
The results for PAS obtained by both calculation methods are given in the figures. As monovacancies will not be observed by any other technique, only the number densities of the clusters are shown.
TEM versus the other techniques{ TC "TEM versus the other techniques" \f C \l "4" }
The scattering theory of Seeger is applied in order to calculate the scattering cross section expected from the distribution of dislocation loops detected by TEM for the pure Fe irradiated at 0.2 dpa [177]. It turned out that the cross section is orders of magnitude too small to explain the irradiation-induced increase of the scattering intensity, observed by the SANS measurements. The same holds true, if the dislocation loops are interpreted as thin slices characterized by an average magnetic scattering length reduced with respect to the Fe matrix. The conclusion that dislocation loops are not responsible for the observed increase of scattering cross sections is also valid for the other materials and irradiation conditions. In this sense, TEM and SANS are complementary techniques.
As indicated before, TEM observes defects (such as self-interstitial type defects), which are not observable by PAS. Conversely, TEM will not detect the very small defects seen by PAS. Thus, both techniques are to be considered as fully complementary to characterize the matrix damage and no clear similarities can be found. Nevertheless, it should be mentioned that the formation mechanisms of the two types of defects may influence each other.
Also the information given by APT and TEM is distinct but complementary. Solute clusters can be detected by APT while resolvable dislocation loops are visible by TEM. Nevertheless, copper clusters segregated on a 10 nm-sized circular object were detected by APT in the Fe-0.1 Cu alloy, irradiated up to the highest dose. This may correspond to a 10 nm-sized decorated dislocation loop, whose presence was confirmed by the TEM analysis [79].
SANS versus APT and PAS{ TC "SANS versus APT and PAS" \f C \l "4" }
The results coming from SANS and TEM are found to be totally complementary. APT and PAS, on the other hand, do mainly detect the same defects as the SANS technique.
p. 191 Chapter 5
Nevertheless, the approach of the techniques is different and therefore also the results may differ.
Information derived from APT and SANS analyses is partly overlapping. In fact, both methods give information on size, volume fraction and composition of clusters. However, clusters of size lower than 0.5 nm were not detected by SANS. This results in a slight overestimation of cluster sizes by this method and an underestimation of their number density. On the other hand, the error on the volume fractions is lower, since the contribution of small scatterers is reduced. An exception is found for the Fe-Mn-Ni-Cu alloy (the right hand illustration of Figure 120). For this alloy, the number density of the defects observed by SANS is considerably higher than the density of the defects observed by APT. It could be attributed to statistical issues, inherent to APT analysis. Indeed, differences in the number densities, obtained by these two techniques, could also be attributed to statistical issues, as only very small volumes can be analyzed by the APT technique.
The PAS results also give information on about the same defects, but as the positrons will observe even smaller defects than APT, which will not be observed by SANS, as its detection limit is 0.5 nm, even bigger differences are expected in-between those two techniques. The average size of the defects observed by PAS will be lower, while their average density will be higher.
APT versus PAS{ TC "APT versus PAS" \f C \l "4" }
It is known that by APT the solute atoms are detected, while no vacancies can be observed. This is in fact the opposite to what is detected by PAS (except for the copper coverage of the copper-vacancy complexes). Therefore, the size seen by PAS is strongly underestimated. Nevertheless, also for the binary Fe-Cu alloys, where the PAS size has been given as vacancies and copper atoms, the obtained PAS size is smaller than the one of APT. This indicates that the clusters are diluted. Indeed, the APT measurements found some iron present in the clusters [79]. This leads to an additional underestimation of the sizes by the PAS technique, but also to an overestimation of the APT sizes. On the other hand, as only 60 % of the emitted atoms are detected in the APT setup, the very small clusters (containing only few solute atoms) will not be determined in the APT p. 192 Quantification of the results technique. The detected APT density will thus be lower than the one of PAS. Indeed, this is found for all alloys. The differences in trends can therefore be referring to the specific defects. For instance, for the Fe-Mn-Ni alloy, an important increase is observed between the two last irradiation doses in the PAS results, while for the APT results a saturation is observed. This indicates that new defects will be formed, which remain very small. { TC "Comparison of the two PAS calculations" \f C \l "4" }
Comparison of the two PAS calculations
The sizes obtained by the two methods are found to be very much comparable; only small changes are present. Although the second method to calculate the size and density of the defects from the PAS results leads to a better understanding of the distribution of positron annihilated at the short positron lifetime traps and at the clusters, the average trend of the cluster number density seems more reasonable for the calculated densities obtained by the first method. At low irradiation doses, low values for the number density of clusters can be found by the second method, showing that more very small vacancy clusters are present, which are not yet assumed to be clusters, but which, surrounded by alloying elements, may play an appreciable role in the hardening. Indeed, in the Fe-0.3% Cu alloy, the number density obtained by the second method falls down beneath the value found by APT, while, as discussed before [178], it is expected that the found vacancy-type of defects and the copper-rich precipitates are the same. For the alloys (and the steel) containing manganese and nickel, even no clusters were observed by the second method for low irradiation doses. It is thus believed that the results coming from the first method give more reliable results for further calculations concerning the influence of the defects on the hardening. These calculations are given in chapter 6.
p. 193 Chapter 5
5.3. Flux effect The first method to obtain the size and density starting from the qualitative PAS results is also applied for the samples irradiated at lower irradiation flux. Again, the coverage fraction of the copper atoms near the positron annihilation sites should be determined in the binary Fe-Cu alloys.
Table 23 The estimated fractions of the coverage with copper on the inner surface of the defects. Material Low flux High flux Fe-0.1% Cu 19 % 49 % Fe-0.3% Cu 70 % 99 %
For the low flux, the covering of the vacancy clusters with copper is significantly smaller compared to the one of the high flux samples. This was not expected, as it has been shown by APT that the size of the copper clusters increases as the flux decreases [42]. [42] also found a copper concentration in their precipitates of about 41 at% at low flux and about 20 at% at high flux. This apparent contradiction can be explained by the presence of more vacancy-free copper precipitates at the lower flux. Indeed, positrons have a much higher probability to be trapped at defects containing a certain amount of vacancies (as the potential well will be bigger).
The results of the estimated size and densities are summarized in Figure 122. For almost all alloys, it is observed that a higher size and lower number density of defects is present in the materials irradiated at lower irradiation flux. This is expected, as at this flux, the defects have more time to agglomerate into bigger defects before new ones are nucleated. The lowering of the number densities can however not only be explained by the increase of the defect size. Caused by an increase of irradiation time, more vacancies will be able to disappear at sinks or to annihilate with self-interstitials. An exception to this trend is the Fe-0.1% Cu alloy. In this alloy, the obtained vacancy size is smaller at the lower flux, but the differences are tiny anyway.
p. 194 Quantification of the results
Figure 122 The estimated values are given for the size of the clusters and the density of both the short positron lifetime traps and the clusters, for all materials irradiated to the lower irradiation flux. The results of the materials irradiated at the corresponding dose at the higher flux are given as well. For the binary Fe-Cu alloys, the results of the cluster sizes are given for both the vacancies alone and the vacancy-copper complexes in total.
Some selected materials were also examined by other techniques, i.e. TEM and APT. In Table 24, the obtained defect sizes (defect radius) and densities at low flux are given for these measurements. They can be compared to Figure 118 - Figure 121.
Table 24 The obtained size (radius) and density of the low flux irradiated materials are given for the TEM and APT measurements of selected materials. TEM APT Material Size Density (m-3) Size Density Pure Fe -- ~ 1 × 1020 -- -- Fe-0.1% Cu -- -- 1.3 0.8 ± 0.5 × 1023 Fe-Mn-Ni -- -- 0.8 ± 0.2 3.8 ± 1.3 × 1023 Fe-Mn-Ni-Cu -- -- 0.8 ± 0.3 4.6 ± 1.5 × 1023 RPV steel -- -- 0.6 ± 0.1 7.4 ± 1.7 × 1023
TEM found much lower defect density at low flux irradiation as well, compared to the results at high flux for similar dose. Also an effect on the size was found. A smaller defect size was observed in the material irradiated at low flux, but not enough statistics were obtained for a correct estimation of the size, due to the low defect density.
p. 195 Chapter 5
APT found much bigger defect sizes (as mentioned before) in the Fe-0.1% Cu, with much lower defect densities. In the alloys containing manganese and nickel, no precipitates were found at low irradiation doses. Nevertheless, at low irradiation flux and comparable dose, defects were found. For the RPV steel, no comparable dose was investigated at high flux.
Both PAS and APT thus show an increase in defect size and a decrease in defect density of the samples irradiated at lower flux. The lower loop size (observed by TEM) can be explained by a higher probability of recombination of the SIAs, while the vacancy transport remains high enough to make the precipitates grow.
p. 196 Quantification of the results
5.4. Fe-Cr alloys In chapter 4, it was shown that the vacancies seem not to cluster in binary Fe-Cr alloys. Therefore, it is possible to obtain quantitative results with a two-component analysis, i.e. assuming only one type of trapping sites. This assumption makes the calculations much easier. The positron trapping rate can now be given by the following equation, from which the defect concentration can be calculated directly.
I 2 −1 κ V = ⋅(λB − ()τ 1 ) (71) I1
This was, however, not the case for the chromium containing steels, as they show a relatively high first component's positron lifetime. It is not clear what leads to this observed increase of the first component and therefore no calculations could yet be performed for the steels.
Figure 123 shows the amount of vacancies that still remain at the investigated Fe-Cr alloys after irradiation. They are compared with the total remaining vacancies in the pure iron irradiated to a comparable dose, obtained by the two different calculation attempts.
Figure 123 The amount of vacancies that remain in the irradiated Fe-Cr alloys, compared to the total amount of vacancies in the irradiated iron alloy, obtained by the two different calculation attempts.
p. 197 Chapter 5
It is clear that the amount of vacancies in the pure, irradiated iron is higher compared to the amount of vacancies in the Fe-Cr model alloys. The result for pure iron, obtained by the first attempt, shows however only a slightly higher value. The vacancies, present in the iron, occur in clusters, while the in the Fe-Cr alloys they are present in the form of monovacancies. The suggestion that the chromium slows down small SIA clusters, leading to more recombination of vacancies with self-interstitials seem thus to be valid. Nevertheless, it is still unclear why this effect seems to be smaller in the alloy with the highest chromium content.
Figure 124 plots the average size and number density of the vacancies and the self- interstitial atoms observed by PAS and TEM, respectively. The size of the SIA clusters reduces with chromium content, while their number density seems to be stable with increasing chromium concentrations.
Figure 124 The average diameter (left) and number density (right) of the vacancies and the self-interstitial atoms observed by PAS and TEM, respectively. The results are given for the pure iron, the Fe-Cr model alloys and the two chromium containing steels.
The average size and density of the pure iron are very comparable with the findings for the binary Fe-Cr alloys. While chromium slow down the small clusters, these clusters can disappear at sinks. Both effects will lead to a reduction of both average size and density of the clusters. Apparently, at this stage of irradiation, none of the effects is found to be more important.
p. 198 Quantification of the results
In Figure 125, a reduced hardening is observed with increasing chromium content, which demonstrates the above mentioned suggestions on the effect of chromium on the SIA clusters.
Figure 125 The yield strength increase of the pure iron, the Fe- Cr model alloys and the two chromium containing steels.
p. 199 Chapter 5
5.5. Conclusions Two attempts to extract numerical information on the defects detected by PAS have been made, based on the existing knowledge of the interaction between positrons and vacancy-type defects in Fe. It is thus demonstrated that, by applying some assumptions, it was possible to access to the most useful information about the neutron irradiation induced defects, namely size and density of the trapping sites. The effect of several alloying elements, important in RPV steels, on these quantitative data has been illustrated.
These results are then compared to the results of other techniques, namely APT, SANS and TEM, on the same material. The combination of the four experimental techniques for microstructural characterization leads to a detailed assessment of almost all features created by irradiation. Furthermore, their type could be identified according to the sensitivity of each of these methods.
The influence of a different irradiation flux has been examined as well.
p. 200
Chapter 6 Influence of microstructural defects on the hardening
“All truths are easy to understand once they are discovered; the point is to discover them.” Galileo Galilei (Italy 1564-1642)
The results coming from all the techniques described in the previous chapters would not be complete if they were not correlated to the hardening they induce. Indeed, the techniques can investigate all the defects in the materials, but no information is found on their importance within the hardening and embrittlement features.
For the purpose of correlating the defects with their induced hardening, tensile tests were performed for all materials under all irradiation conditions. The obtained results are discussed in detail in the first section of this chapter. These results are then compared to the mechanistic models, proposed in chapter 1 and used for the commercial reactors. Finally, some models are developed to characterize the strengths of the different defects and to estimate the influence of each defect on the hardening. The different sections are then summarized.
p. 201 Chapter 6
Table of content Chapter 6 Influence of microstructural defects on the hardening...... 201 6.1. Hardening results...... 203 6.1.1. Hardening trends with dose of the different model alloys ...... 203 Pure iron and the binary Fe-C alloy ...... 203 Binary Fe-Cu alloys ...... 205 Fe-Mn-Ni and Fe-Mn-Ni-Cu alloys ...... 207 Low-Cu RPV steel ...... 209 6.1.2. Hardening trend of commercial RPV steels...... 210
6.2. Comparison with industrial trend curves...... 213
6.3. Influence of the defects on the hardening...... 216 6.3.1. Superposition of the effect of defect populations on yield strength increase...... 217 6.3.2. Primary calculations using the Orowan equation...... 221 6.3.3. Primary calculations using the best fit method ...... 223 6.3.4. Hardening calculations using the newly developed analysis model ...... 227 RPV-2 model...... 227 Results...... 228
6.4. Conclusions ...... 230
p. 202 Influence of microstructural defects on hardening
6.1. Hardening results In order to be able to correlate the found defects with their induced hardening, tensile tests needed to be performed for all the materials under all irradiation conditions. The results of these tests are described and discussed keeping in mind the chemical composition of the material.
6.1.1. Hardening trends with dose of the different model alloys The tensile test results show a certain trend depending on the chemical composition of the alloys. These trends are observed and discussed in this section of the chapter.
Pure iron and the binary Fe-C alloy{ TC "Pure iron and the binary Fe-C alloy" \f C \l "4" }
It is well established that the increase of the ductile-to-brittle transition temperature (DBTT) in RPV steels is related to the hardening of the material [19]. Therefore the mechanical behaviour in terms of hardening of the model alloys, investigated for the understanding of the embrittlement of RPV steels, is highly important. Figure 126 gives the increase of the yield strength (Δσ) of pure iron and the binary Fe-C alloy, as a function of the square root of the dose (in mdpa ). The data have been fitted to the following equations.
Figure 126 The variation of the shift of yield stress is shown, as well as its fitting as function of the square root of the dose for pure iron and Fe-C.
p. 203 Chapter 6
0.165 Δσ Fe = 53.3 ⋅ (φt) (72) 0.285 Δσ Fe−C = 42.3 ⋅ (φt) (73)
For both the alloys, shown in Figure 126, the irradiation-induced hardening has a clear trend of saturation, already visible at low doses. However the hardening depends strongly on the material composition, as described by Verheyen et al. [118]. In pure iron, the irradiation-induced hardening at low dose is rather high, almost 100 MPa. But only a small increase is observed during further irradiation up to 0.1 dpa. The effect of carbon on the dislocation loops during deformation is visible. The saturation-like behaviour is much less pronounced, when carbon is added to the alloy. At low dose, the hardening is comparable to the one of pure iron, while at the highest dose, an increase of about 50 MPa is found in the Fe-C alloy. It may be speculated that this is the consequence of the presence of a higher density of self-interstitial atom (SIA) clusters. Self- interstitials are believed to be trapped at the carbon atoms, which leads to a larger density of such clusters. These clusters act as obstacles to the dislocation motion, and therefore the material will harden. This accumulation will continue during the whole irradiation-process, as the hardening continues to increase compared to the hardening of pure iron. Unfortunately, this surmise cannot be contrasted with the microstructural data obtained by TEM, as this alloy has not been examined by this technique.
For the results of pure iron, the Orowan equation (equation 74) has been used to evaluate the results. For these calculations the results obtained from TEM of the same material analyzed by CIEMAT (Spain) (Hernandez-Mayoral et al. [135]) is used for the number ( N ) and the diameter size ( d ) of the defects. As discussed in the previous chapter, TEM is believed to give information on the self-interstitial loops. In equation 74, the Taylor factor ( M ) is equal to 3.06, while the shear modulus (G ) is taken equal to 71.8 GPa and the module of the Burgers vector (b ) equal to 0.249 nm. Using the results shown in Figure 126, the obstacle strength (α ) can be fitted.
Δσ Y = M ⋅α ⋅ G ⋅ b ⋅ N ⋅ d (74)
The obtained obstacle strengths are given in Figure 127 in function of the square root of the dose (in mdpa ). For the lowest irradiation dose, the defects were too small for the
p. 204 Influence of microstructural defects on hardening calculation of the average size. The size used in the present calculations was thus obtained by extrapolation of the results at higher dose (see Figure 118 in chapter 5). On the other hand, it was not possible to obtain the tensile results for the irradiation at the second lowest dose. The value obtained by the fitting curve shown in Figure 126 is thus used.
Figure 127 The fitted obstacle strengths found using the tensile results from Figure 126 and the defects found by TEM given in Figure 118 for pure iron.
Figure 127 shows a linear decrease of the strength with the irradiation dose. This is however not expected, as the defect size increases with dose (see the previous chapter). In addition, an α value higher than one is observed for the lowest irradiation dose. The obstacle strength should however be between zero and one. It is thus concluded that the irradiation- induced hardening cannot be explained by the presence of the visible self-interstitial loops only. Other types of defects (such as voids) should also have a certain contribution to the hardening.
Binary Fe-Cu alloys{ TC "Binary Fe-Cu alloys" \f C \l "4" }
The hardening of the binary Fe-Cu alloys, investigated in this paper, is shown in Figure 128. The equation used for the fitting of the data is given in equation 75 and 76.
0.191 Δσ Fe−0.1%Cu = 73.6 ⋅ (φt) (75) 0.076 Δσ Fe−0.3%Cu =164.7 ⋅ (φt) (76)
p. 205 Chapter 6
Figure 128 The variation of the shift of yield stress is shown, as well as its fitting as function of the square root of the dose for the binary Fe-Cu alloys.
It is clear that the hardening of the binary Fe-Cu alloys follow the same behaviour as the one of pure iron. The same kind of saturation is observed. However, the alloys exhibit a clear trend of substantially enhanced hardening with increasing copper concentration. Already at the start of the irradiation of the alloys containing copper, some Cu-rich precipitates are formed, as found by for instance APT at Rouen (France) (Meslin et al. [130]) at the lowest irradiation dose investigated. The dislocation movement is blocked by these precipitates. As in alloys with a higher Cu-concentration more precipitates are formed, they will have a higher hardening component.
In the SANS-measurements, on the other hand, Bergner et al. [35] observed only precipitation after a certain dose. This could probably be due to the fact that the precipitates are very small at low doses. Therefore they could be underneath the detection limit of SANS.
The effect on the hardening of copper has been examined by many authors before. In Figure 129 two different calculations have been used to determine the effect of copper in these alloys. The copper effect has been subtracted from the tensile Fe-Cu results in order to obtain the hardening results for the pure iron. "CRP" is the precipitation hardening proposed by the formula of Chaouadi and Gérard [25]. They believe that the copper contribution is constant with dose, but depending on the initial copper content. "Orowan" stands for the Orowan formula where α is fixed to 0.075 for the precipitates as they have been observed by APT (and shown in chapter 5). Also here, when some data was missing, the extrapolated values given in chapter 5 were used.
p. 206 Influence of microstructural defects on hardening
Figure 129 The variation of the shift of yield stress is shown, as well as its fitting as function of the square root of the dose for Fe-0.1% Cu (left) and Fe-0.3% Cu (right). Two different mechanisms are applied to identify the effect of copper on the hardening (see text for more information).
The sizes and densities of the obstacles found by APT are nearly constant for all the studied doses. Therefore, the constant copper fraction, proposed by Chaouadi and Gérard give very comparable results as those found for the Orowan mechanism. Nevertheless, the Orowan mechanism shows slightly better results, especially at high doses for the low copper alloy.
Fe-Mn-Ni and Fe-Mn-Ni-Cu alloys{ TC "Fe-Mn-Ni and Fe-Mn-Ni-Cu alloys" \f C \l "4" }
The fittings for the curves for the hardening of alloys containing nickel and manganese, which are shown in Figure 130, are given in equation 77 and 78.
0.633 Δσ Fe−Mn−Ni = 6.8 ⋅ (φt) (77) 0.424 Δσ Fe−Mn−Ni−Cu = 31.9 ⋅ (φt) (78)
When manganese and nickel are added to the model alloys, the behaviour is quite different. The hardening does not tend to saturate with the square root of the dose. This can only be explained by different obstacles that induces the hardening. According to Vincent et al. [149], manganese has a strong binding energy with SIAs in iron. So the Mn-stabilized SIA-loops (initiated in the previous chapter) could be the main responsible of the hardening in these alloys.
p. 207 Chapter 6
Figure 130 The variation of the shift of yield stress is shown, as well as its fitting as function of the square root of the dose for the Fe-Mn-Ni and Fe-Mn-Ni-Cu alloys.
An addition of 0.1 % of copper leads to an analogue increase of hardening for the ternary Fe-Mn-Ni alloy, as it appeared when adding similar amount of Cu to pure iron. For both cases, the Cu-containing alloy hardens in the same way as the alloy with no copper, but the presence of copper induces more hardening.
Figure 131 illustrates the effect of copper on the hardening, as proposed by the formula of Chaouadi and Gérard [25]. The effect of copper, calculated by the Orowan formula (using the APT data), could not be obtained by one single obstacle strength for the defects. The needed α's are also given in Figure 131.
Figure 131 (left) The variation of the shift of yield stress is shown, as well as its fitting as function of the square root of the dose. The contribution of copper on the hardening is obtained by the Chaouadi mechanism. (right) The fitted obstacle strengths found using the results from Figure 130 and the defects found by APT.
p. 208 Influence of microstructural defects on hardening
It is clear that the contribution of the copper, proposed by Chaouadi and Gérard, is not sufficient. The contribution of manganese and nickel is thus not negligible. Even the contribution of copper on the hardening seems to change when manganese and nickel are present. The obstacle strengths of the precipitates show again a decrease with dose. The same was observed for the self-interstitial loops in pure iron. This indicates that another type of defects is present, causing hardening.
Low-Cu RPV steel{ TC "Low-Cu RPV steel" \f C \l "4" }
The results on models alloys are now compared to those of a low-Cu RPV steel, containing 0.065% of copper, 0.37% of manganese and 0.69% of nickel (compared to 1.2 % of manganese and 0.7 % of nickel in the model alloys).
The fitting of the hardening curve of this steel is given by equation 79.
0.629 Δσ RPV −steel = 6.1⋅ (φt) (79)
Figure 132 The variation of the shift of yield stress is shown, as well as its fitting as function of the square root of the dose for the RPV steel.
This equation is very similar to those of the alloys containing manganese and nickel only. As the amount of copper is in the middle, it is logical that also the equation is in between those of the two alloys. Figure 132 shows that the hardening of this steel is very
p. 209 Chapter 6 similar to the one of the Fe-Mn-Ni alloy. It is not saturating, contrary to the alloys with no manganese and nickel.
The values for the steel are even lower than those for the model alloys. This may be due to the difference in the as-received, non-irradiated microstructure between model alloys and steels.
6.1.2. Hardening trend of commercial RPV steels In Figure 133, the obtained yield strength increase after irradiation is shown for each alloy. The average error bar to be associated with the data, given in the figure, is ± 6 % of the yield strength value. This error thus varies in-between ± 5 MPa for the non-irradiated pure iron and ± 35 MPa for the steel irradiated to the highest dose. The results are compared to some other low-Cu (empty symbols) and high-Cu (full symbols) RPV steels, found in the literature.
Figure 133 The hardening (change of yield strength of the irradiated measurements compared to the unirradiated measurements) for all materials is illustrated as a function of the neutron fluence. Some results found in literature are added. The empty symbols denote the low-Cu steels, while the full symbols are results for high-Cu steels. For both type of steels a trend curve is given, and for the high-Cu steels a region with an error of 30 % is added.
It can be seen that most of the trends of the steels are similar to what is proposed by the model alloys. The low-Cu steels follow a linear dependency on the irradiation dose, while the
p. 210 Influence of microstructural defects on hardening trend of the copper-rich steels saturates after a certain dose. This indicates that the discussion given above is in good agreement with the real features. This is true up to an irradiation fluence of about 7 × 1019 n cm-2, which corresponds to about 40 years of irradiation. As the probable prolongation of the nuclear power plant operation is only a recent issue, almost no surveillance data are available in literature with a higher fluence. However, Figure 133 suggests that the trends will continue. Copper will not add any additional hardening, while alloys containing manganese and nickel harden still more with irradiation dose. Indeed, the alloy containing both copper and manganese and nickel exceeds the proposed trend for the copper-rich alloys. The hardening does not saturate, as indicated by the high-Cu steels. The effect of manganese and nickel is clearly visible. It may be seen that, after an initial hardening, caused by the copper-rich precipitates, the irradiation-induced hardening of this alloy follows a trend parallel to the one of the low-Cu steels. We thus believe that the hardening mechanism associated with the presence of copper is independent of the one associated with the presence of manganese and nickel.
As the increase of irradiation hardening due to the copper-addition is higher, the effect of this element is the predominant one in medium- and high-copper steels [27]. Therefore, the effect of copper has been specifically investigated for many years (e.g. [37], [50], [179]). It is thus by now well-known that, already at very low dose, some copper-rich precipitates are formed [50], [179]. These precipitates hinder the dislocation motion, thereby causing hardening [60]. Once the precipitates are formed, however, the Cu-rich precipitate contribution to the irradiation-induced hardening saturates relatively quickly [23], [27], [147], [165]. A higher copper concentration in the alloy leads to the formation of more precipitates, and thus to a higher hardening component, but the trend to saturation with dose remains unchanged. In contrast to higher-copper steels, the effect of manganese and nickel is not negligible in low-copper steels. This effect may even become dominant for high enough doses [19], [27]. For this reason, research should now be focused on this hardening effect as well.
The hardening behaviour of the low-copper RPV steel, examined in this work, follows exactly the trend indicated by the results from literature. In addition, it is important to note that this behaviour is very close to the one of the alloy containing manganese and nickel and
p. 211 Chapter 6 no copper. The small difference can probably be explained by the richer chemical composition of the steel and/or the different initial microstructure (the model alloys are purely ferritic, while the steel is ferritic-bainitic).
p. 212 Influence of microstructural defects on hardening
6.2. Comparison with industrial trend curves The results are compared with the mechanistic models, used in the industry, both for the verification of the models and the evaluation of the accuracy of the models at higher neutron fluences. For comparison, the models introduced in chapter 1 for the shift in transition temperature are converted to a change in the yield strength, by using equation 80 [180].
ΔT Δσ = 41J (80) Y 0.63
The results and the trend curves for the RPV steel are given in Figure 134. The obtained transition temperature shift includes the related error, to ensure that all experimental points should be underneath the curve.
Figure 134 The yield strength increase of the RPV steel as a function of the fluence is compared to the industrially used, mechanistic models, for related compositions and irradiation conditions.
At low irradiation doses, all models are above the obtained points. The first two data points are in very good agreement with CR-6551, the ASTM E900-02 and the NUREG-1874 model. These trend curves stay however too low at larger irradiation conditions. The RG 1.99 Rev. 2 and the FIS model, on the other hand, overestimate the increase at lower doses. This is also the reason why they have been used, as it is never unsafe to overestimate the effect. Nevertheless, this method may lead to a premature closure of the reactor. At larger doses, the data points approaches and even exceed the predictive models. The trend curves are thus not valid anymore at these doses.
p. 213 Chapter 6
Although an underestimation is found for the result at the lowest dose, the new RG 1.99 Rev. 3 proposal seems to be the one giving the best results. All other data points stay underneath the curve, and the hardening continues to increase with dose, in a similar way, as found for the data points. This model seems thus to give the safest prediction for irradiation at doses relevant for the currently wanted extension.
Figure 135 The yield strength increase of the model alloys as a function of the fluence is compared to the industrially used, mechanistic models, for related compositions and irradiation conditions.
p. 214 Influence of microstructural defects on hardening
In this thesis, only one RPV steel is examined, and for the examination of the effect of alloying elements, model alloys are used. Therefore, also the hardening increases for the model alloys are compared with the models. This is illustrated in Figure 135.
It should be noticed that almost all trend curves underestimate the results for the model alloys. This may be explained by the difference of starting microstructure between the model alloys and the steels. Nevertheless, the trends may be compared. All trend curves, except the one of the RG 1.99 Rev. 2 model, show realistic trends up to high irradiation doses, for the pure iron, the Fe-C and the Fe-0.1% Cu alloy. The small values of the RG 1.99 Rev. 3 model seems however to strongly underestimate the real values. When 0.3 % of copper is added to the alloy, the RG 1.99 Rev. 2 model seems reasonable, while the FIS model now seems to overestimate the effect of the fluence. With the presence of manganese and nickel, all trend curves seem to show an underestimation of the fluence effect. Although comparable values are found at low doses, at high doses no models follow the data points anymore. All models include a copper and nickel term and in addition the NUREG-1874 includes a manganese term, but none of the models show the behaviour as indicated by the manganese and nickel containing model alloys at higher irradiation fluences.
Physically based models are thus needed for a better prediction of the long-term irradiation behaviour.
p. 215 Chapter 6
6.3. Influence of the defects on the hardening In the first section of this chapter, it was indicated that the prediction of the hardening, applying only one experimental technique, gives in many cases results which are physically not correct. As SANS is known to detect different types of defects (voids, precipitates, etc), it was tried to correlate the hardening with the results of this technique only. A scatter plot of the complete set of measured yield stress increase versus square root of volume fraction deduced from SANS is shown in Figure 136.
Figure 136 The correlation is shown between the yield stress increase and the volume fraction obtained by SANS, assuming non-magnetic scatterers and formal decomposition into three components [178].
The yield stress increase can be empirically decomposed into three components. Component (1) is due to objects not detected by SANS because of weak contrast (e.g. dislocation loops as detected by TEM) or small size (e.g. clusters of size below the detection limit of SANS as detected by APT or PAS) and not correlated with SANS. Component (2) consists of a yield stress increase directly caused by the scatterers detected by SANS. Component (3) may be due to measuring errors and variations of the obstacle strength of the clusters and may be associated with either component (1) or component (2).
Nevertheless, it is unlikely that component (1) will be independent of dose and material composition. Also the obstacle strength can change according to the different defect sizes. It is therefore clear that this method of defining the hardening only with one technique may give p. 216 Influence of microstructural defects on hardening a first indication, but it will not result in a full understanding of the effect of the different classes of defects on the hardening. Therefore, in this work, several attempts are made to add all observed defects in a correlation with the hardening results.
6.3.1. Superposition of the effect of defect populations on yield strength increase The 2-D quasi-static, line-tension code DUPAIR upgrades the original algorithm, suggested by Foreman and Makin [181], by considering defect pinning forces as input parameter and by removing the constant line-tension approximation. This approximation is replaced by an expression explicitly dependent on the angle between the Burgers vector and the dislocation line [182]. Any kind of defect distributions, of different types and sizes, can be easily introduced, randomly distributed on a plane array (dislocation glide plane). The application of a shear stress causes the segments of the single dislocation line to bow into a sequence of arcs of circles, each delimited by two pinning defects. The equilibrium shape of the dislocation line pinned between two defects is obtained setting the force balance at the pinning point between the two line tensions vectors T1 and T2 and the pinning force Fp . The applied stress is increased until breakaway occurs at some defect. The shape of the dislocation line is then accordingly reconfigured and the process of increasing the shear stress is restarted, till one of the three following breakaway criteria occurs.
(i) T1 +T2 > Fp .
(ii) If the angle θ between the two dislocation braces becomes smaller than a critical value, the dislocation line unpins independently of the values of line tensions and pinning force (Orowan mechanism). (iii) Whenever the curvature radius of the dislocation line pinned at two defects becomes larger than half the size of the box, the dislocation is unpinned. Periodic boundary conditions are used.
The highest shear stress applied during the simulation to allow the dislocation to move is taken as the yield stress (YS) increase due to the array of obstacles. Therefore, a number of simulations must be performed in each case in order for the found average maximum value to have statistical significance. The global YS increase is finally estimated by multiplying the average maximum value by the Taylor factor, equal to 3.06. The effect of thermal activation
p. 217 Chapter 6 on dislocation unpinning is also included in the code, by means of a simple model that can be found in, e.g. [182].
Figure 137 A schematic illustration of the two
line tension forces (T1 and T2 ) and the pinning
force ( Fp ) [183].
Figure 138 A schematic illustration of the dislocation movement in a lattice containing many defects [183].
Here, the DUPAIR code is utilized for a purely parametric study, with the aim to identify the best superposition law, used to obtain the effect of a number of different defect populations. In most mechanistic models, different hardening laws are associated with the microscopic mechanisms and the total yield strength increase ( Δσ tot ) under irradiation is obtained as the superposition of the different effects (e.g. [25], [72] and [184]). This superposition can be either linear (equation 81), or as the square root of the quadratic sum
(equation 82) of the single components ( Δσ i ).
L Δσ tot = Δσ 1 + Δσ 2 + ... (81) Q 2 2 Δσ tot = Δσ 1 + Δσ 2 + ... (82)
Neither of these superposition laws is supported by any clear physical reason and it is expected that, in fact, in each case, depending on the involved defect populations, their
p. 218 Influence of microstructural defects on hardening density, their pinning forces, etc, the actual superposition should lie somewhere in between the two laws (equation 83) [185].
L Q Δσ tot = S ⋅ Δσ tot + (1 − S)⋅ Δσ tot (83)
Here, S is a superposition parameter that can vary in absolute value between 0 and 1 (0 corresponds to a purely quadratic sum, and 1 to a purely linear sum). The choice of the value of S is not settled, though. The DUPAIR code is adequate to perform an assessment of which one of the two laws (equation 81 or equation 82) should be used or, if neither proved acceptable, to give some indications about what value for S should be employed in each case.
Simulations were performed with two defect populations, one (weak defects) with a -1 pinning force FW varying from 0.2 to 1.5 eV Å , the other (strong defects) with a pinning
-1 force FS equal to 2 eV Å . In this way, the effect of superposing two hardening contributions, with different FS FW ratios, from 10 to 1.33, was explored. The concentration was made to vary in two ways. In one case both defect populations had always the same concentration (CW C S = 1). The results of these calculations are given in Figure 139 (a). In the other case (Figure 139 (b)), the population of strong defects was kept at a constant concentration of 1021 m-3 and only the concentration of weak defects was increased up to 24 -3 10 m (CW C S = 1 to 1000). For each pair of values of the ratios FS FW and CW C S , the simulation was repeated 50 times with different random spatial distributions of the obstacles, taking the mean maximum shear stress increase as the reference Δσ tot . Finally, a comparison of the calculated total shear stress increase was made with the values obtained by
L summing the separate shear stress increase contributions linearly ( Δσ tot ), as in equation 81 or
Q quadratically ( Δσ tot ), as in equation 82.
In Figure 139 (a), the superposition parameter S is shown as a function of the concentration of the two defect populations (same concentration for both) and the ratio
FS FW . No monotonic trend with concentration is exhibited. However, it can be seen that, with the notable exception of large FS FW ratios and extreme (very low or, to a lesser extent, very high) concentrations, the total shear stress increase is fairly well estimated by the
p. 219 Chapter 6 quadratic summation. The superposition parameter is much more frequently closer to 0 than it is to 1. In fact, it can be said that the only case where a sensible deviation from the general trend is visible is FS FW = 10, which corresponds indeed to a limiting case, where the effect of the weak defect population is essentially negligible and it is as if only the strong defect population was present.
Figure 139 (a) The superposition factor is given as a function of the concentration and the
FS FW ratio, for two populations of defects with equal concentrations. (b) The superposition factor is given as a function of CW C S ratio and FS FW ratio, for two populations of defects [178].
p. 220 Influence of microstructural defects on hardening
Very similar considerations apply to Figure 139 (b), where the same quantities as in
Figure 139 (a) are plotted, in the case of a varying concentration ratio CW C S .
In the following, therefore, a quadratic superposition is always assumed, except for the case where a very weak type of defects is present. In the latter case, their contribution is added linearly.
6.3.2. Primary calculations using the Orowan equation In this section, the hardening is calculated starting from experimental results concerning the evolution of the microstructure of the alloys under irradiation. Simple calculations, using the Orowan equation, are performed to provide a first notion of the strength of the different defect populations. For these first calculations, only the specimens irradiated to 0.1 dpa are considered, as this corresponds to the displacement dose of the planned lifetime of the western reactors.
The contribution of each class of defects to the hardening can be estimated using the Orowan equation (equation 74). N and d are, respectively, the number density of defects and their mean size, as obtained from the different experimental methods. The obstacle strength is given by the constant α. This value can vary between zero and one, and it is strongly dependent on the type of defect.
The hardening contribution due to loops can be estimated inserting the TEM results in equation 74. The contribution to the hardening of the nanovoids, on the other hand, can be obtained using the results of PAS. In pure iron, loops and nanovoids are the only two defect populations observed, and the total hardening will be given by the square root of the sum of the squares of the two contributions, as both loops and nanovoids are assumed to be relatively strong obstacles, of similar strength. In the Fe-Cu alloys, vacancies and copper atoms cluster together [118], [128]. For the size and number density of these vacancy-copper clusters, the APT results are used. Also in this case, the total hardening is the square root of the sum of the squares of the two contributions (the loops and the vacancy-copper clusters). For the alloys containing nickel and manganese some precipitates are formed, as revealed by APT, but PAS results suggest that most vacancies are not inside, but rather
p. 221 Chapter 6 outside the precipitates, forming very small clusters trapped by solute elements [164]. The latter are very small defects and will thus have also a low contribution to the hardening. For the precipitates the APT results are used, while for the very small alloying-element-vacancy defects the number density is given by the difference between the PAS and the APT, and the mean size is given by PAS. In this case, there are thus three contributions, i.e. loops, precipitates and very small vacancy clusters. The first two contributions are superposed quadratically, while the contribution of the very small vacancy clusters, which are much weaker obstacles, is added linearly to the composition of the other two contributions.
The α values from equation 74 for each population were fitted using the following two assumptions. First, the strength of the loops is assumed to be linearly dependent on their size. Secondly, it was assumed that the (pure) vacancy clusters containing less than 10 vacancies were negligible in strength, if any other type of defect is present as well. Therefore, the voids found in pure iron, and the small vacancy clusters observed in the alloys containing nickel and manganese were neglected in first assumption. However, it was found in [79], where the results for all four different techniques were published in more detail, that some bigger vacancy type defects are found in iron for other irradiation conditions. These defects were not taken into account, here. Therefore, the obstacle strength attributed to the loops constitutes an upper bound. The best fit values, using these estimations, are shown in Figure 140 (a). The different hardening contributions of the different defect populations and the total values are given in Figure 140 (b).
It can be observed that the SIA loops are the strongest obstacles in the investigated alloys, but their influence on the hardening is limited due to their low density. The precipitates are found to be very small in size, which makes them behave as rather weak obstacles. However, their high density determines that they are the main hardening features. The small vacancy clusters (called v-clusters in Figure 140) have a very low strength and a negligible contribution to the hardening, due to their small size.
p. 222 Influence of microstructural defects on hardening
Figure 140 (a) The obstacle strength from the Orowan equation is given for the different types of defects in the investigated alloys at 0.1 dpa. (b) The hardening contribution of the different types of defects is shown as a function of the hardening measured by the tensile tests.
A sensitivity assessment of the strength associated with the different defect populations, using the Orowan equation for each contribution, and their combination using the proper superposition law, thus provides a reasonable rationalization of the hardening results.
6.3.3. Primary calculations using the best fit method As first attempt to correlate the microstructurally observed defects with the hardening of material under irradiations, the calculations of the previous section are shown to be reasonable. However, Figure 127 indicates already that this attempt is not sufficient. Indeed, Figure 140 illustrates that, in the previous calculations, the hardening in pure iron is induced by the loops observed by TEM only. This was proven to be physically not realistic by Figure 127. New calculations are thus needed.
For pure iron, now, three hardening contributions are assumed, i.e. the SIA loops visible by TEM (loops), the voids observed by SANS, and very small vacancy clusters seen by PAS (V). It is, however, believed that the contribution of the vacancy clusters is almost negligible. Therefore, the contribution of these clusters will be summed linearly to the square summation of the contributions of the loops and the voids (equation 84), as both loops and voids are assumed to be relatively strong obstacles, of similar strength.
2 2 Δσ Fe = Δσ loops + Δσ voids + Δσ V (84)
p. 223 Chapter 6
The binary Fe-Cu alloys also exhibit loops (TEM) and voids (SANS) with comparable strengths as in pure iron. In addition, copper precipitates (Cu-ppt) are observed (APT), with a strength which may be smaller than the one of the loops and voids, but which is still considerable. Therefore, to add these precipitates to the hardening, also a quadratic summation is found to be the most appropriate (equation 85). These precipitates should however be subtracted from the SANS results to obtain the concentration of voids. The strength of the vacancy clusters may be a little higher than for those observed in pure iron, as it was shown that copper will coat these clusters [50], [118] (V-Cu in equation 85). Nevertheless, still a linear summation is suggested. It should be mentioned that some of the clusters observed by PAS will also be observed by APT in its copper precipitates (where vacancies are present) [178]. Therefore, the number density used in equation 74 for the calculations of the vacancy clusters will be the difference between the PAS and the APT number densities. So, for Fe-Cu binary alloys, the superposition relation is given in equation 85.
2 2 2 Δσ FeCu = Δσ loops + Δσ Cu− ppt + Δσ voids + Δσ V −Cu (85)
When manganese and nickel is added to the alloy, the loops (TEM) are believed to contain a certain amount of manganese atoms (SIA-Mn) [186]. This will of course influence their strength; they will become stronger, as they become pinned by the solute atom. Indeed, manganese and nickel containing precipitates have been observed by APT [42] and SANS (MnNi-ppt). However, no voids were found in this alloy, as the defect density found by SANS is comparable to the number of precipitates found by APT. Furthermore, the vacancy type defects have been found by PAS to be decorated by nickel [164] (V-Ni). Nevertheless, also in this case, the vacancy contribution has been linearly added to the quadratic sum of the loops and the precipitates (equation 86).
2 2 Δσ FeMnNi = Δσ SiA−Mn + Δσ MnNi− ppt + Δσ V −Ni (86)
When also copper is added to the alloy (i.e. Fe-Mn-Ni-Cu), the loops (TEM) are not expected to change. In this alloy, again, voids were observed by SANS (excluding the precipitates) and are expected to have a similar strength as those observed in other alloys. In this alloy, the precipitates were found to consist of both copper and/or manganese/nickel.
p. 224 Influence of microstructural defects on hardening
Although one may believe that the strength of the different precipitates may change a little depending on their composition, this is very difficult to assess at this point, and therefore in this work, an average precipitate strength is considered (ppt). The same approach is assumed for the vacancy type of defects that are found to be associated with either copper and/or nickel (V-CuNi).
2 2 2 Δσ FeMnNiCu = Δσ SIA−Mn + Δσ ppt + Δσ voids + Δσ V −CuNi (87)
In the RPV steel, neither loops nor voids were observed. However, small solute rich precipitates (ppts) were detected by APT and some small vacancy-solute features (V-sol) have been evidenced by PAS. The hardening can therefore be considered as the linear sum of the contributions of these two observed nano-features (equation 88).
Δσ RPV = Δσ ppts + Δσ V −sol (88)
The α values from equation 74 for each population were fitted empirically, as close as possible to the obtained hardening results (with the least squares regression), assuming that the strength of each population is linearly dependent on its size. The different hardening contributions of the defects and their summed effect are shown in Figure 141.
At the same time, the measured yield stress ( Δσ Y ) is given, in comparison with the total obtained microstructural stresses. If needed, the extrapolations proposed in chapter 5 are used.
It can be observed that the loops play an important role in the hardening of the pure iron, but not in the other alloys. Indeed, they appear to play only a secondary role, in spite of their high associated strength. Nevertheless, it can be seen, that for the Fe-Mn-Ni alloy, the influence of the loops is increasing drastically with dose. This indicates that the self- interstitial loops combined with manganese will reduce the dislocation motion much more than those that are free (not combined with any solute).
p. 225 Chapter 6
Figure 141 The hardening contribution of the different types of defects (voids, precipitates, loops and vacancy clusters) in function of the irradiation dose, for pure iron (a), Fe-0.1% Cu (b), Fe-0.3% Cu (c), Fe-Mn-Ni (d), Fe-Mn-Ni-Cu (e) and an RPV steel (f). The measured yield stress is added for comparison, next to the total obtained microstructural stress.
Neutron irradiation induced voids, when present, always play a secondary role in the hardening increase, except for the case when both copper and nickel can stabilize these voids, such as in the Fe-Mn-Ni-Cu alloy.
p. 226 Influence of microstructural defects on hardening
In all cases, most of the hardening appears to be caused by the precipitates. Although the matrix damage contribution becomes more pronounced with increasing neutron dose, it does not yet reach the contribution level of the precipitates, even at the highest dose investigated here. This is in apparent contradiction with the low defect strength attributed to the precipitates compared to the one of the loops, caused by their small sizes. This can be explained by the fact that, whenever precipitates are present, their number density is found to be much higher than the one of the loops observed by TEM. The hardening in the Fe- 0.1% Cu alloy is higher then predicted by the defects. This can be explained by the fact that the copper-rich precipitates are assumed to have the same strength in both binary Fe-Cu alloys, according to their size. Apparently, this is not the case. The precipitates in the Fe-Cu alloy with 0.1 % of copper contain much more vacancies and this can lead to harder defects. As for the vacancy-solute clusters, observed by PAS, it can be seen in Figure 141, that in fact their contribution to the total hardening of the irradiated materials cannot be totally neglected. This is found, despite their very tiny average size that would suggest that they would mostly contribute to the nucleation of bigger clusters rather than the hardening of the material by itself (due to their tiny strength).
6.3.4. Hardening calculations using the newly developed analysis model Within the PERFECT project, a model is made which tries to obtain the microstructural defects in neutron irradiated materials, as well as their effect on the hardening. In this section, some of the obtained results are compared to the experimental results.
RPV-2 model{ TC "RPV-2 model" \f C \l "4" }
The aim of my stay at the EDF research site "Les Renardières" was to study the simulation program made within the European PERFECT project, i.e. RPV-2. This program overlaps every range of the multi-scale modelling (both in time and in size). It consists of four parts. In the first part, a PKA spectrum is produced starting from a neutron spectrum. The second part uses this PKA spectrum to calculate the defects (size and density of each size) produced within the cascades. The real size distribution of each kind of defect (such as copper rich precipitates and matrix damage), caused during the irradiation by the neutron spectrum, is calculated in the third part. In the last part, the change of the hardness is computed, considering the defects found in the previous part.
p. 227 Chapter 6
Results{ TC "Results" \f C \l "4" }
The experimental results, discussed in the previous chapters, were compared with the results from RPV-2, regarding the type, amount and size of defects. On the other hand, starting from the found defects, the expected hardness increase can be calculated.
At first, calculations using the rate theory have been performed for the calculation of the defects. The obtained results are compared with the defects found by the positron technique. The two different attempts to estimate the number densities are shown in Figure 142 for pure iron and the binary Fe-C alloy. The densities of the clusters are shown by dashed lines. The sum of both short positron lifetime trap and cluster number densities are given by full lines. The Fe-C alloy is added for comparison, as the potentials used within the RPV-2 program are based on a certain concentration of carbon in the alloys.
Figure 142 The number densities of vacancies found by the two different calculation techniques for quantifying the PAS results of both pure iron and the binary Fe-C alloy. These densities are compared to the results of RPV-2, using the rate theory.
An overestimating of the density of vacancies by the RPV-2 program is observed. In the rate theory, no space information is used, and therefore a huge underestimation of the recombination is reflected in a higher number density of defects. Therefore, the rate theory calculations have been substituted by kinetic Monte Carlo calculations. These calculations are much more complicated, but they do take into account the position of the vacancies and self-interstitials in the cascades, and therefore more recombination can occur. These calculations are compared to the results obtained by PAS in Figure 143.
p. 228 Influence of microstructural defects on hardening
Figure 143 The number densities of vacancies found by the two different calculation techniques for quantifying the PAS results of both pure iron and the binary Fe-C alloy. These densities are compared to the results of RPV-2, using kinetic Monte Carlo.
The primary results give a much better resemblance to the experimental results, but the parameters should be adapted to this case. The search for the good parameter-set is still going on.
Similar conclusions can be drawn from the comparison of the densities found for the self-interstitial clusters and the results of TEM, as illustrated in Figure 144.
Figure 144 The number densities of self-interstitial atoms (SIA) found by TEM for pure iron and the densities obtained by the RPV-2 program, using both the rate theory and kinetic Monte Carlo.
Calculation of hardening increase seems to be in the correct order of magnitude, but some adaptations of the program should still be performed to insert size distributions not calculated by the program itself.
p. 229 Chapter 6
6.4. Conclusions The experimentally observed defects are correlated to the hardening of the material. For this purpose, the hardening behaviour of the different materials were investigated and compared to the models used for commercial surveillance programs. Using some broad assumptions, it was then possible to correlate the defects found in the previous chapters by the hardening observed in the materials.
p. 230
Chapter 7 General conclusions and outlook
“The noblest pleasure is the joy of understanding.” Leonardo da Vinci (Italy 1452-1519)
In the first section of this chapter, the general conclusions of the thesis are summarized, while some examples of possible future work are initialized in the second section of this chapter.
p. 231 Chapter 7
Table of content Chapter 7 General conclusions and outlook ...... 231 7.1. General conclusions ...... 233 Qualitative results ...... 233 Quantitative results ...... 234 Influence on the hardening...... 235 Fe-Cr alloys ...... 235
7.2. Future work ...... 237 REVE samples ...... 237 New matrix ...... 238 Examination of steels...... 238 Flux effect...... 239 MIRE-Cr matrix...... 240
p. 232 General conclusions and outlook
7.1. General conclusions In this PhD-thesis, it was shown how iron alloys of different chemical composition embrittle and harden during irradiation. This was found to be caused by irradiation-induced defects, such as precipitates, solute-vacancy complexes, voids and loops. To understand the mechanisms driving the evolutions of these defects, model alloys and steels, irradiated to different doses, were investigated. The effect of several alloying elements is observed by using model alloys with increasing chemical complexity.
Qualitative results{ TC "Qualitative results" \f C \l "3" }
State-of-the-art positron setups are able to detect some of the defects created by irradiation. The results that have been obtained by these techniques for highly activated model alloys can be summarized as follows.
¾ In pure iron, vacancy clusters are formed during irradiation and they grow in size with increasing irradiation dose. The supply of new vacancies will both cause the formation of new vacancy clusters and the growth of pre-existing ones. These clusters remain however too small to lead to the observed hardening increase. Together with the formation of these vacancy clusters, self-interstitial atom (SIA) loops are formed, observed by TEM. These loops can be the cause of the hardening. ¾ In the Fe-C alloy, a reduction of the vacancy cluster size is observed, compared to the pure iron. The hardening, on the other hand, increases significantly. Carbon interacts with both vacancies and self-interstitials. This leads to more annihilation of the single vacancies with single self-interstitials. In addition, carbon atoms provide nucleation sites, so that more, but smaller, vacancy clusters and SIA loops are produced.
¾ Copper atoms and vacancies migrate together, as their binding energy is rather high. This leads to the formation of vacancy-copper complexes and copper-rich precipitates that contain a certain amount of vacancies. In the binary Fe-Cu alloys, the formed defects are observed at very low irradiation doses and their size and density seem to saturate already at low dose. The same is observed for the irradiation-induced hardening. Nevertheless, the composition of the defects, which are however stable in
p. 233 Chapter 7
amount and size, seem still to change a little during irradiation. The vacancy to copper ratio keeps increasing with dose, and this influences slightly the defect strength. ¾ This is also observed for the alloy with lower copper concentration. The observed defects in this alloy contain more vacancies compared to the defects in the alloy with 0.3 % of copper. The defects with more vacancies have been found to be stronger.
¾ The alloys containing manganese and nickel show vacancy clusters containing only 1 or 2 vacancies. In addition, it was shown that the binding energy between two manganese and two nickel atoms is negative. So, the formation of clusters by vacancy dragging is difficult and might not occur, as a lot of vacancies are needed to stabilize such nickel or manganese clusters. Nevertheless, nickel and manganese rich clusters have been observed. It could thus indirectly be deduced from the PAS results that these clusters can be caused by the interaction of manganese with the SIAs, as Mn and SIAs have a strong binding energy. Manganese is assumed to stabilize small SIA clusters. In this hypothesis, more manganese or nickel can be added combined with an SIA or even accompanied with a vacancy. Indeed, when a solute-vacancy pair passes by such a Mn stabilized SIA cluster, the vacancy can annihilate with a self-interstitial atom, while the solute remains located at the cluster. This may be the origin of the manganese and nickel containing precipitates observed by APT. ¾ For the alloy containing copper, manganese and nickel, the two described phenomena operate simultaneously. However, the combination of manganese and nickel with some of the provided vacancies will reduce the kinetics of the copper-vacancy complex formation. Copper atoms are as well captured by the Mn stabilized SIA clusters, in a comparable way as the nickel atoms.
¾ In the steel, the above observed features are also visible. The effect of manganese and nickel seem more explicit, compared to the effect of copper. Indeed, the copper concentration in the steel is lower than the one in the investigated model alloys, while the composition of manganese and nickel is comparable.
Quantitative results{ TC "Quantitative results" \f C \l "3" }
Two different methods of quantification of the results have been performed and compared. These results have then be compared to the results obtained by other techniques, p. 234 General conclusions and outlook such as atom probe tomography (APT), small angle neutron scattering (SANS) and transmission electron microscopy (TEM).
It was observed that the results obtained from each technique could not be directly compared, as these techniques use different approaches to detect the defects. While APT observes the atoms located at the precipitates, PAS detects the number of vacancies in the defects and SANS can see the difference in scattering effect of the defects. In some cases, the observed defects are the same, but even then the found sizes and densities can be slightly different, as a consequence of the different detection limits of the techniques. TEM, on the other hand, observes the SIA loops, which are invisible for the other techniques. The obtained results are therefore complementary, showing that the combination of the different techniques leads to a better understanding of the irradiation damage.
Influence on the hardening{ TC "Influence on the hardening" \f C \l "3" }
The strength associated with the different defect populations provides a reasonable rationalization of the hardening results.
The SIA loops are found to be the strongest defects. Nevertheless, they don't play the major role in the hardening of the materials, except for the pure iron alloy. The influence of the precipitates is much more marked in the hardening of all other materials, especially at low irradiation doses. The hardening due to these precipitates is saturating, while the effect of the postulated Mn-stabilized SIA loops continues to increase with augmenting dose. At high doses, they may thus become predominant. For the vacancy-solute complexes, it was believed that they would only play a minor or even negligible role in the hardening, as they are very tiny. However, due to their enormous number density, it appeared that their role is not totally negligible.
Fe-Cr alloys{ TC "Fe-Cr alloys" \f C \l "3" }
In the reactors for future use, the materials are expected to contain a certain amount of chromium. Therefore, chromium-rich materials should be investigated and compared to the more conventional chemical compositions. It is found that the chromium strongly reduces the defect size. The vacancy-type of defects remains in the form of monovacancies. The amount
p. 235 Chapter 7 of vacancy-type of defects seem however to increase with increasing chromium concentration. The coincidence Doppler broadening results show a turning point of the behaviour at about 8 wt% of chromium.
Quantifying the results, leads to the observation that less vacancies are present in the Fe-Cr binary alloys compared to the pure iron, irradiated to a comparable irradiation dose. This could be caused by the slowing down of small SIA clusters, leading to an increased recombination of vacancies with these self-interstitials. This feature can also be observed in the TEM and hardening results. Indeed, the size of the observed SIA clusters, as well as the increase in hardening, is reduced with increasing chromium content, in the binary Fe-Cr alloys.
p. 236 General conclusions and outlook
7.2. Future work It is clear that still more investigations should be performed on the already existing matrices. In addition, more model alloys should be investigated to obtain also the influence of other alloying elements which were not discussed in this thesis. Using the knowledge obtained from the model alloys, some commercially used steels could be investigated to endorse that the found statements are also valid for these materials. More investigations of the effect of the flux on the irradiation-induced defects are needed for a full understanding of this feature. Finally, the chromium containing alloys should be investigated at higher irradiation doses, as their maximum obtained dose will be much higher compared to the conventional reactor steels.
REVE samples{ TC "REVE samples" \f C \l "3" }
The best way to obtain information on the temperature dependence of the irradiation- induced defects is by isochronal annealing of the samples. As shown in the appendix E, this was already done for two Fe-Cu alloys. The annealing time was kept constant to about 30 minutes and the annealing temperature increases from 300 °C to 650 °C. It was found that the copper-rich precipitates lose their vacancies at about 350 °C. From this temperature on, a lower hardening of the material was observed as well. However, questions still arise on the nature of the features causing this hardening decrease. At about 600 °C, the copper precipitates start to dissolve. PAS analyses show that bigger vacancy clusters are present after annealing at high temperatures. It would be interesting to verify if they are also detectable by TEM. This study should be extended to other alloys of the REVE matrix.
It is expected that in the pure iron and the Fe-C alloy, the observed vacancy clusters will disappear after a certain irradiation dose. Post-irradiation annealing will thus not lead to substantial new information on these alloys. It would, however, be interested to investigate the alloys containing manganese and nickel. The observed clusters will behave differently if they are combined with self- interstitials than if they were combined with vacancies. Post-irradiation annealing of such samples can thus additionally confirm the statements made in this thesis.
p. 237 Chapter 7
Post-irradiation annealing (PIA) of the Fe-Mn-Ni alloy will allow the temperature behaviour of the Mn and Ni containing defects to be identified. The results can then be compared to the PIA of the Fe-Mn-Ni-Cu alloy. This second PIA treatment would indicate if copper precipitation as it occurs in the binary Fe-Cu alloys is still appearing, as mentioned in this work.
Any irradiation dose would lead to similar results. Nevertheless, the higher the initial dose, the more explicit the features will be. It is recommended to start from the alloys irradiated to 0.1 dpa, as all techniques were applied on these samples (Figure 120).
New matrix{ TC "New matrix" \f C \l "3" }
The effect of several alloying elements has been investigated in this thesis, but other elements may also influence the behaviour of the steel.
The effect of nickel and manganese has been investigated simultaneously. Indeed, it is assumed that manganese is needed for the nucleation of the defects, while nickel causes the main hardening effect. However, the separate behaviour of these elements in combination with copper is not clearly known. It would thus be interesting to investigate the ternary Fe - Ni-Cu and Fe-Mn-Cu alloys. Some papers suggest that the influence of silicon is not negligible under irradiation. Model alloys containing about 0.4 wt% of silicon could thus also be investigated. The binary Fe-Si should be used as a reference for the ternary Fe-Si-Cu alloy and the quaternary Fe-Si- Mn-Ni alloy. This way, the influence of silicon on both the copper-rich and the manganese and nickel rich defects could be found.
Examination of steels{ TC "Examination of steels" \f C \l "3" }
Model alloys are needed to understand what happens in steels with changing concentrations of alloying element. Nevertheless, the behaviour of the steels with comparable concentrations of alloying elements should also be examined, to observe the effect of the pre- irradiation microstructure. It is therefore highly recommended to investigate with the same level of details steels coming from surveillance programs.
p. 238 General conclusions and outlook
It was however mentioned in chapter 1 that only small quantities of material were inserted in the surveillance programs, due to a lack of space. The applied techniques (especially PAS) should thus be extended to the ability of measuring smaller samples. The interaction of dislocations with the visible and non-visible defects can be observed by in situ deformation during TEM measurements. Also other techniques, such as internal friction, can be applied for this purpose.
Post-irradiation annealing of irradiated commercial steels, can lead to a better visibility of defects which are too small to be observed in their as-irradiated state. Identification of the temperatures of hardening drop is a very good start to identify invisible defects. In addition, some defects may grow, which can lead to more visibility by several experimental techniques, such as APT or TEM.
Flux effect{ TC "Flux effect" \f C \l "3" }
In this thesis, two different fluxes were investigated. Therefore, already some ideas on the flux effect could be developed. However, more fluxes are needed for a full understanding of the behaviour. In addition, the two fluxes investigated in this thesis are on the upper limit of the flux range used in generation II reactors.
It would be interesting to investigate surveillance material, irradiated in a commercial reactor and the same material, irradiated in a material test reactor at different fluxes. Several similar doses should be obtained to trace the effect of the flux on the behaviour of the material with increasing dose.
All over the world, many attempts have been carried out for such examination. However, two major obstacles intervene. The first obstacle is the fact that, in many cases, not enough reference material is available for the additional irradiation in material test reactors. Steels with analogue chemical compositions are then used instead, but the homogeneity, the manufacturing procedures and the subsequent thermal treatments may differ, leading to different pre-irradiation microstructures. The second obstacle is the fact that only very few materials are irradiated at low flux and high neutron dose. The flux effect at high doses is therefore still unknown.
p. 239 Chapter 7
MIRE-Cr matrix{ TC "MIRE-Cr matrix" \f C \l "3" }
Up to now, only one irradiation dose of the MIRE-Cr matrix has been investigated. As the materials for future reactors will be irradiated up to much higher doses, the matrix has been irradiated to higher doses as well. Although these doses cannot be compared with the REVE matrix, the results coming from these analyses could be very interesting for the understanding of the chromium-rich steels at higher irradiation doses. The same materials should then also be characterized with techniques other than PAS and TEM.
p. 240
Appendix A History of the positron
In this appendix, a general introduction on the positron is given.
p. 241 Appendix A
Positron
The positron is the antiparticle of the electron, which is represented as e+ or β+. It is the first theoretically predicted antiparticle. The existence of the positron was first postulated in 1928 by Paul Dirac, as a consequence of the equation that he derived. During his study of relativity consistent quantum mechanics on the behaviour of electrons, Paul Dirac came across this particle with the same mass and spin as the electron, but with an opposite charge. Only in 1932, however, was the positron detected by Carl Anderson. Anderson obtained the first direct proof that positrons exist by shooting gamma rays through a cloud chamber in a Wilson chamber, resulting in the creation of electron-positron pairs, which were separated by a magnetic field, bending differently charged particle trajectories in different directions.
Figure 145 The postulator of the positron, Paul Dirac (left) and the discoverer of the positron, Carl Anderson (right) [1].
Positron formation and annihilation
Positrons are released during the radioactive decay of some isotopes, such as sodium-22. But, they may also be generated by pair production from a sufficiently energetic photon. In principle, the positrons are stable particles, but when a positron and an electron meet, they annihilate. Their mass is then transposed into energy, following the famous equation of Albert Einstein ( E = m ⋅ c 2 ). The energy is emitted in the form of gamma photons. In most cases, two photons are created, but up to five annihilation gamma rays have been observed in laboratory experiments [187], depending on the relative spin configuration of the electron and positron. A single photon decay is only possible if another body (e.g. an electron) is in the vicinity, to which some of the energy from the positron annihilation event may be transferred.
p. 242 History of the positron
The photons are produced with a total energy of 1 022 keV, since each of the two annihilating particles has a mass of 511 keV/c2. In case of two γ-rays, they will move in anti-collinear direction from the positron annihilation site.
Positronium
In specific cases, the positron and electron can occur in a bound state. This binding can be compared with the one between a proton and an electron in a hydrogen atom, except for the enormous differences in total mass. The so-called positronium is however not stable, as the particles will still annihilate after some time. The ground state of positronium, like that of hydrogen, has two possible configurations, depending on the relative orientations of the spins of the electron and the positron. In case of antiparallel spins, the particle is known as para-positronium (p-Ps). In vacuum, the p-Ps has a very short mean positron lifetime of 125 ps and it decays preferentially into two gamma quanta. The state with parallel spins is called ortho-positronium (o-Ps), with a mean positron lifetime in vacuum much larger than that of p-Ps, i.e. 142 ns. The leading mode of decay is in three gamma quanta. The interaction with electrons, outside vacuum conditions, will reduce drastically the positronium lifetime. The formation of positronium is consequently not possible in media with a high electron density (such as metals).
p. 243
p. 244
Appendix B The technical details on the positron lifetime setup
This appendix will focus on the update of the original positron lifetime setup, as proposed by Van Van Hoorebeke et al. [109]. The electronic chain and biological shielding are described, as well as the stability and performance of the setup for radioactive specimens.
p. 245 Appendix B
Detectors and geometry
As the Van Hoorebeke triple detector setup has proven to be very efficient in preventing 60Co events to be collected, the original geometry has been kept. However, some improvements have been introduced.
Firstly, a lead shield has been placed between the different detectors. This reduces the Compton scattering effects between the different detectors (which can transform two 60Co gammas in three gammas and give rise to false triple coincidences). Secondly, the old detectors have been replaced by new ones, based on single crystal barium fluoride BaF2 scintillators and Hamamatsu photomultiplier (PM) tubes. The PM tubes were selected for optimal transit time (0.37 ns at 3 kV), and they operate at a constant high voltage of 2.7 kV. The size of the three crystals has been reduced to obtain a better time resolution. This has also the beneficial effect of lowering the high count rate at short distances, due to the much higher actual activity of the specimens and avoiding pileup and afterglow in the crystals. The three crystals have an identical diameter of 28 mm and a thickness of 20 mm for the start- and 10 mm for the two stop-detectors, as shown in Figure 146. A thicker crystal is used for the start, because the gamma-ray energy for the start signal is higher than that for the stop signal. The diameter of the crystals and their housing determines the minimum distance of 3.5 cm between each detector and the centre of the sample-source sandwich. The detectors are mounted in such a way that this distance can be increased if the sample activity is too high (as it will be described in more detail further on). Finally, the differentiator at the dynode output of the detectors has been removed. Originally, this differentiator was used to eliminate the long decay tail coming from the slow component of the scintillator light. At high count rates, this tail gave rise to pileup of the signals and consequently the energy-amplitude relationship of the signals deteriorates. However, this slow component yields 80 % of the total scintillation light [188] and is essential to obtain a good energy resolution. Additionally, the new electronic chain is capable of filtering the pileup events at a later phase. Therefore, the differentiator was removed to obtain a better energy resolution for filtering the right events after the digitalization.
p. 246 The technical details on the positron lifetime setup
Figure 146 Schematic diagram of the new PALS spectrometer. The specimen with a positron source is placed between the 3 detectors with an angle of 45° to each detector. Three movable photomultiplier (PM) tubes are based on single crystal BaF2 scintillators (28 mm diameter and 20 mm thick for start and 10 mm thick for the two stop detectors) and Hamamatsu H3378-51 (transit time 0.37 ns, optimal selection for transit time, HV = 2.7 kV) PM tubes. A digital oscilloscope LeCroy WaveRunner 6100A (1 GHz band width, 4 channels, 5 GS/s, 4 Mpts, Microsoft Windows XP) is connected directly to PMTs. Constant fraction differential discriminators (Ortec 583 CFDD) are used for the gamma energy preselection and are connected to the coincidence unit (Canberra 2144A).
Electronic chain
A general view of the positron lifetime spectrometer is shown in Figure 146. As first proposed in [110], the time-to-amplitude converter (TAC) and multi-channel analyser (MCA) are replaced by a digital storage oscilloscope (DSO) (LeCroy WaveRunner 6100A, 1 GHz band width, 4-Channel, 5 GS/s, 4 Mpts, Windows XP Pro). The anode outputs of each PM are connected to the channel inputs of the DSO. The waveforms of the output pulse are digitized and stored in the memory of the DSO only when it is triggered by a coincidence signal generated by a Canberra 2144A coincidence unit. This coincidence is used together with the CFDDs to preselect only the signals falling in right energy and time region to minimize the amount of data to be stored.
After collecting the signals, a newly developed software analyses the raw data of each event, and allows a clear visualization of the results, as shown in Figure 147. Four characteristics of every signal, such as peak height, peak intensity, base level and rising time are calculated. The base level is defined as the mean voltage level before the pulse. It is used to monitor the pileup effect. The rise time gives the time needed for the signal to increase from 10 % to 90 % of its maximum amplitude. The peak height is the maximum amplitude of the signal and the peak intensity is defined as the area surrounded by the peak signal.
p. 247 Appendix B
Figure 147 The newly developed "Digital Positron Lifetime Spectrometer v1.0" software written in C#. This screen shows the peak height, peak intensity, base level and rising time analysis of the raw data. The y-axis of the figures represents the number of counts and the x-axis corresponds for the peak height and peak area figures to the energy of the gamma-event. For the base level figure the x-axis represents a voltage and for the rise time figure it represents a time.
The peak height and peak intensity corresponds to the energy of the preselected γ-event. After the calculation of these characteristics, the distributions of them are plotted in histograms and the appropriate value ranges can be selected by the user to filter the signals with no pileup, but within the right energy range. The signals satisfying these ranges are used for the generation of a positron lifetime spectrum. This selection leads to further improvement of resolution function and signal to noise ratio of the positron lifetime setup.
Figure 148 The newly developed "Digital Positron Lifetime Spectrometer v1.0" software written in C#. This screen shows a positron lifetime spectrum, after the selection of the appropriate signals.
Biological shielding
In order to achieve sufficient statistics, it is foreseen that the acquisition will last for at least 24 hours and up to one month. During this time, the radioactive emission in the surroundings of the setup will be very high and will not permit the manipulation of other instrument located in the same room. Therefore, the table on which the 3 detectors are installed is shielded with 4 cm thick lead plates, as shown in Figure 149. The present exploitation license allows a maximum activity of 100 MBq 60Co equivalent.
p. 248 The technical details on the positron lifetime setup
Figure 149 A schematic drawing of the shielding with the transport container on top. The enlargement show the specimen mounted in the holder and positioned between the three detectors.
Maximum detector count rate
To test the performance of the detectors at high count rates, the pileup and afterglow in the crystal were investigated. The afterglow in the crystal comes from the long BaF2 component. At high count rates this component gives rise to a continuous, but fluctuating afterglow in the crystal, which produces a slightly fluctuating bleeder current in the PM-base and thus somewhat varying anode voltages.
A simple experiment was performed, where the detectors were exposed to a fixed point source. By changing the distance of the detectors to the source, the count rate was varied. At fixed positions, the anode waveforms were digitized and the base level before every pulse was calculated and plotted. In Figure 150, it can be seen that from a count rate of 360 kcps the base level starts to show a long tail (graph a), which indicates that pileup of events is becoming a problem.
Figure 150 The base level distribution for different distances of the detectors from the double sandwich with pure iron and irradiated iron. The distance, measured from an initial position, restricted by the diameter and the housing of the detector-crystals, is (a) 0 cm, (b) 1 cm and (c) 2 cm, respectively. The activity of the specimens is 23 MBq.
To minimize this pileup effect a maximum count rate of 200 kcps for the detectors was defined. The distance of the detectors is adapted for every specimen to keep the same count rate over different measurements. Due to the variation of the activity of the specimens, the
p. 249 Appendix B fraction of 22Na-events changes. Thus, also the coincidence count rate and measuring time will change. The typical measurement time to obtain one million counts for specimen with an activity of 23 MBq and a 22Na point source of 2 MBq is seven days.
Stability and fatigue
Two factors play an important role in the long-term stability of the measurements. The first factor is the drift in the peak-positions of the start and stop events, due to fatigue in the detectors. This appears because of large changes in tube current or counting rate. To control these parameters firstly the count rate in the detectors should be kept constant at 200 kcps. Secondly, after the start of a new measurement, one should wait several hours to stabilize the PM-tubes. The second factor in the long-term stability is the change in the window-positions for selecting the right start- and stop-events. This might be caused by a shift in the temperature in the electronics (e.g. CFDD, PM-tube). In order to prevent the variation of the temperature an air conditioning system was installed in the room, which keeps the temperature constant at 22 ± 0.1 °C. This also stabilizes the temperature of the scintillators to avoid any change in the second component of the scintillation light (which is very temperature dependent [188]). Furthermore, a more precise selection of the right energy-windows during the post-processing can be done to eliminate any possible drift of the CFDD windows.
Positron lifetime spectrum shape
Four different spectra were obtained under different conditions to verify that the measured positron lifetime spectra are free of shape distortions due to a prompt 60Co contribution or increased background. A well recrystallized high-purity α-Fe was chosen to be the reference material. In the first spectrum, a 22Na positron source with an activity of 2 MBq was tightly sandwiched between the α-Fe disks with size 10 x 10 x 1 mm3. In the other spectra, the presence of 60Co was mimicked by putting different pairs of neutron activated samples with increasing activity on the outside of the first sample assembly. During the measurements the distance was changed to keep the count rate constant at 200 kcps. Due to the varying activity of the sample assemblies and the fixed count rate, the ratio of 60Co/22Na events changes together with the background. To compare the different spectra, the
p. 250 The technical details on the positron lifetime setup background was subtracted and the data were normalized to a total of 106 counts. The background-ratio (i.e. ratio of background to peak height) for the spectra is given in Table 25.
Table 25 The results of positron lifetime analysis of spectra A to D before random contribution subtraction and normalization (see text): the statistics. Spectrum A B C D Activity 0 MBq 6 MBq 12 MBq 23 MBq Measurement time 236 h 169 h 168 h 161 h Total counts recorded 6 693 465 2 910 510 2 815 603 1 058 280 Counts in lifetime spectra 6 129 527 2 515 520 2 453 075 881 039 Background to peak ratio 0.072 % 0.226 % 0.207 % 0.331 %
As the same α-Fe disks are used for the different spectra, the measured spectra should have the same shape independent of the activity of the outer samples. The different spectra are compared in Figure 151 and are as good as identical up to an activity of 23 MBq.
Figure 151 The positron lifetime spectra for pure iron without and with an additional 60Co- source of respectively 6, 12 and 23 MBq. The random contribution has been subtracted and the net spectra have been normalized to the same total number of counts.
The analysis of the positron lifetime spectra were performed as described a little further, using the LT program [113]. The results are listed in Table 26, and have an error within 1 ps. Also the positron lifetime analysis of the different spectra yields compatible results. The analysis of the spectra was performed before the random contribution subtraction and normalization.
Table 26 The results of positron lifetime analysis of spectra A to D before random contribution subtraction and normalization (see text): the positron lifetime. Spectrum A B C D Activity 0 MBq 6 MBq 12 MBq 23 MBq Positron lifetime 107.2 ps 108.6 ps 107.6 ps 106.9 ps
p. 251 Appendix B
Time resolution
The resolution curve is measured for all specimens as the sum of three Gauss functions as shown in equation 52 (see main text). The results found for each term is given in Table 27. As we expected, the results are very similar. As already mentioned above for high count rates, the probability for the appearance of a pulse in the "tail" region of a previous pulse increases. Such a pulse will display an increased noise level, which deteriorates its timing quality. As the count rate is fixed at a level low enough to avoid severe pileup and filtered in the post- processing, it was possible to keep the time resolution stable.
Table 27 The results of positron lifetime analysis of spectra A to D before random contribution subtraction and normalization (see text): the resolution of the spectra. Spectrum A B C D Activity 0 MBq 6 MBq 12 MBq 23 MBq
FWHM 0 188 ps 191 ps 189 ps 189 ps
FWHM 1 173 ps 171 ps 171 ps 168 ps
f1 14.6 % 14.5 % 14.5 % 14.5 %
Δ1 95 ps 95 ps 95 ps 95 ps
FWHM 2 285 ps 311 ps 343 ps 291 ps
f 2 0.38 % 0.38 % 0.38 % 0.38 %
Δ 2 -88 ps -88 ps -88 ps -88 ps
FWHM sum 202 ps 204 ps 203 ps 202 ps
p. 252
Appendix C The technical details on the coincidence Doppler broadening setup
This appendix will focus on the technical details of the coincidence Doppler broadening setup. The newly installed CDB spectroscope (Figure 55) is comparable to the setup explained by Van Petegem et al. [115], [116], as described with ample details by Verheyen et al. [117]. The electronic chain and biological shielding are described, as well as the stability of the setup.
p. 253 Appendix C
Electronic chain
Figure 152 gives a schematic overview of the experimental setup. To minimize the background, both annihilation photons are detected in coincidence [189]. For this purpose, two movable high purity germanium detectors (coaxial HPGe from Canberra type GC3018) are positioned in an anti-collinear direction. These HPGe detectors are able to measure the annihilation photon energy with a precise accuracy. In addition, the detectors have a high energy resolution of typically 0.8 keV at 122 keV and 1.8 keV at 1332 keV. To prevent pileup, the detectors are movable to larger distances from the sample (up to 1.5 m).
Figure 152 A schematic overview of the CDB setup (HV = high voltage, DSP = digital signal processor and INT = interface card) [115].
The detector signal is then amplified, shaped, filtered and baseline restored by the shaping amplifier (PRE AMP model 2101P). The energy outputs of this preamplifier, built-in both the detectors, are connected to a digital signal processor (DSP from Canberra, model 2060), which contains all the data needed for monitoring the detectors. The digital signals of the DSP-units are further processed by an interface card, which was designed at the University of Ghent by S. Van Petegem. The data is than transferred to the PC by a digital data acquisition card from National Instruments (type PCI-IO-32HS). This card allows a fast data transfer to the computer of up to 10 million events per second. The analysis software on this PC is written using LabVIEW (National Instruments) and can simultaneously record single and coincident spectra from both the DSP-units [115]. On the interface card, the 14 data bits of both DSP units are connected to the upper and lower 16 bit data paths (words) of the 32 bit acquisition card. The 'Data Ready' signals of the DSP units are combined with an OR gate and connected to the 'Request' line of the acquisition card. Additionally, both 'Data Ready' signals are added to their respective data paths as a 15th bit. If the data of the DPSs are synchronized, a valid 15th bit in both data words indicates a
p. 254 The technical details on the coincidence Doppler broadening setup coincident event. The coincidence time window depends on the speed of the handshake protocol which can be altered in the software between 100 ns and 1 µs, which is sufficient in most cases. The coincidence count rate varies between 300 and 500 counts s-1, depending on the thickness of the sample. Important is to note that the DSP units should have a fixed conversion time. Furthermore, every data line on the card is connected to an optocoupler. It provides an adequate isolation from the 'noisy' computer environment. Experiments performed without this isolation give evidence for interference phenomena between the computer and the electronics.
Biological shielding
The shielding consists of a lead tube of 15 cm diameter in the centre of the setup. The sample holder is located in the middle of this tube. This sample holder can be loaded from the same container as used from the positron lifetime setup. For each measurement, more than 1 × 108 counts are accumulated during 2 or 3 days.
Stability
To check the stability of the system during the normal measurements, a 57Co source is added to the setup. 57Co is chosen, to avoid a Compton contribution to the 511 keV peak. Indeed, the photon energies emitted by this source are smaller than 511 keV, i.e. respectively 122 keV and 136 keV. These peaks are used in combination with the 511 keV-peak to monitor the calibration and resolution every hour of the measurement.
p. 255
p. 256
Appendix D The preparation of an adequate APT tip
The emission of atoms toward the APT detector is only possible in case a very sharp needle (< 50 nm tip radius) is available. Therefore, this appendix focuses on the way an adequate atom probe tip is prepared.
The tips are made by the use an electrolytic technique, using an acid which may have different concentrations of HCl. There are two similar possibilities to make a tip, differing mainly by the initial length of the needle. In both cases, for making an adequate atom probe tip, the needle of which the tip is made (usually 0.2 mm thick), should be firstly perfectly fixed in a needle holder in which it may not move at all.
p. 257 Appendix D
"Two layers" technique
The easiest way (from the practical point of view) for making an atom probe tip is the "two layers" technique. It can only be used if the needle is long enough. The needle is positioned vertically (Figure 153) and it may result in two satisfactory needles. Nevertheless, as the second needle will fall down, it is likely that it will break. In this case, the tip can be repaired by the second technique.
This technique is illustrated in Figure 153. In a measuring cup, two insoluble liquids are present, an electrolyte (CCl4; lower liquid) and an acid (25 % of HCl; upper liquid). A power source provides an electric potential between the golden spool inside the electrolyte and the needle. During the electrolysis, the needle will oxidize in the acid. By moving the needle, a constriction is obtained. This process is stopped when the thinnest place reaches a thickness between half and a third of the original thickness. The continuation of the process, after this thickness is obtained, can cause a premature breaking (due to the gravity of the lower needle), leading to unsatisfactory tips.
Figure 153 The setup of the "two layers" technique. The electric chain is realized by connecting a golden spool in the electrolyte and the needle to a power supply.
To split the two needles, another setting is needed, where the two liquids are replaced by only one, consisting of a much weaker acid (with 2 % HCl). Now, the whole needle will thin, until the needles split at the thinnest part. Near the end of this handling, the voltage is kept low, to sharpen the tips as much as possible. Once the tips are formed, the electric chain needs to be switched off immediately. The whole process is controlled by an optical microscope (Figure 154).
p. 258 The preparation of an adequate APT tip
Figure 154 Optical microscope images of the tip before splitting (left) and after splitting (right). This second image illustrates the final tip [42].
"Micro loop" technique
Contrary to the "two layer" technique, the length of the needle is not of significant importance in the "micro loop" technique. This technique is therefore often used for smaller needles, or for adjusting broken or unsatisfactory tips. The principle of this technique is similar compared to the first one, but the practice is rather different, as the needle is positioned horizontally (Figure 155). The biggest difficulty in this setup is the bowing of the tips, due to gravity. To avoid this, the removed part is minimized.
Figure 155 The setup of the "micro loop" technique. The electric chain is realized by connecting a golden ring with an acid and the needle to a power supply.
As visualized in Figure 155, the acid is now a drop in a golden ring. The drop should not be too big or too small and it should be replaced frequently. The golden ring is much closer to the needle compared to the golden spool in the first technique. Therefore, the weak acid is chosen here for the whole process. Also here, the whole process is controlled by an optical microscope.
p. 259 Appendix D
The first part is analogous to the one explained for the "two layer" technique, but the second part is much more complicated. The end of the needle (the part that will be removed) may never leave the drop. The drop namely diminishes the influence of the gravity, reducing the probability of the bowing of the tip. This bowing could lead to premature breaking, or (if the needle is already sharp enough) to the sticking of the removed part to the good tip, leading to a bad tip.
p. 260
Appendix E Post-irradiation annealing of an Fe-Cu alloy
This appendix shows the results of the post-irradiation annealing of a binary Fe-Cu alloy.
The binary Fe-0.3% Cu alloy irradiated at different doses in the material test reactor, BR2, has been sent to Oarai (Japan) to be studied within a bilateral collaboration. This material has been examined to investigate the effect of post-irradiation annealing on the copper-precipitates induced by irradiation. This was done to explore the stability and strength of the defects. For this purpose an isochronal annealing was performed. The temperature was gradually increased in steps of 50 °C, starting from 300 °C to a temperature of 650 °C. The annealing time was set to 30 minutes. The irradiation doses chosen for this investigation were the low dose of ca. 0.025 dpa and the higher dose of ca. 0.1 dpa.
The effects of post-irradiation annealing has been examined by three different techniques, i.e. positron annihilation spectroscopy (PAS), micro-hardness and local electrode atom probe (LEAP). Within PAS, both coincidence Doppler broadening (CDB) and positron annihilation lifetime spectroscopy (PALS) measurements were performed. All measurements are performed at room temperature. The aim of CDB is to analyse the effect of the annealing on the copper clusters, while by positron lifetime measurements the vacancy evolution can be followed. Hardness tests show the influence of the different defects on the mechanical properties. LEAP should confirm the results found by PAS. With LEAP, measurements were only performed for the as-irradiated material and annealed at 350 °C and 500°C.
p. 261 Appendix E
Expected results
It is expected that some changes in the nanostructure will happen in the binary Fe-Cu alloys, especially at two different temperatures. In the literature, it can be found that at less than 400 °C, the vacancy-clusters will become unstable and start to dissolve [190]. While, at ca. 600 °C, also the copper-clusters will dissolve in the iron matrix [37].
During irradiation, one expects that in the Cu-rich alloys, copper precipitates are rapidly formed due to the presence of a concentration of vacancies highly in excess of the equilibrium concentration. Free copper atoms will be transported by these moving vacancies. Due to the existing binding between vacancies and copper atoms, copper-vacancy pairs migrating together are formed. These pairs will meet and thereby form copper-vacancy clusters. At 400 °C, the vacancies will start to leave the clusters and move through the matrix. Some of them will then disappear at sinks. Copper left in solute solution or in smaller precipitates during irradiation will be brought by the remaining vacancies towards the existing clusters and thus the precipitates can grow. This has of course an influence on measurements of the samples. The hardness will decrease by two causes. The strength of the pure copper precipitates is slightly lower than the one of the copper-vacancy clusters, while the number density of precipitates decreases and therefore less pinning obstacles for dislocations are present. Positrons will be able to annihilate more with the inner shell electrons of the atoms near the positron annihilation sites and because of this the W parameter of the CDB results increases, while the S parameter decreases. As a result of the fact that the vacancies are not anymore located in clusters and at the same time the moving vacancies have a higher probability to recombine with self-interstitials, the positron lifetime results will decrease drastically. By LEAP, bigger copper clusters should be found, as well as a lower number density, compared to the as-irradiated state.
At about 600 °C, the copper precipitates dissolve in the iron matrix and therefore at this temperature no more hardening features will remain. The hardening should thus decrease until the pre-irradiation value. Also the W parameter decreases to the value of pure iron, while the S parameter should stay constant. The positron lifetime results are only affected by p. 262 Post-irradiation annealing of an Fe-Cu alloy the vacancies and therefore they shouldn't change at this stage of the annealing. Both the S parameter and the positron lifetime should already approach the value of defect-free iron at lower temperatures. As no precipitates would be found by LEAP, samples annealed above this temperature are not examined.
Hardening results
For the as-irradiated samples, as well as for every annealing temperature, several micro- hardness tests were performed on the backside of the positron samples. The average values of these measurements are given in Figure 156. As expected, the hardness decreases starting at about 400 °C, when the vacancies are emitted from the complexes. At ca 600 °C, the hardness tends to decrease again, as the copper clusters dissolve. From these results on, three annealing temperatures are chosen, on which LEAP is performed. No difference is expected between the as-irradiated sample and the sample annealed at 350 °C, while bigger, copper pure precipitates are expected when the annealing temperature is increased to 500 °C.
Figure 156 The hardness is given with increasing annealing temperature, for the two Fe-Cu binary alloys, irradiated at low (0.025 dpa) and high (0.1 dpa) dose. A good agreement is found with the expected trend. The green circles indicate the specimens, on which LEAP has been performed.
A higher hardness value is found for the specimen with the higher irradiation dose. One expects that this is mainly due to the larger amount of self-interstitial atom loops, present at higher irradiations dose. Also an increasing amount of vacancies is observed in the defects of this material, which may also influence the hardening results. Indeed, after annealing above the vacancy mobility temperature the hardness decreases more in specimen with higher dose. This indicates that a higher recombination of the vacancies with the self-interstitials from the
p. 263 Appendix E loops will occur, as well as a reduction of the number of vacancies in the defects. But, still at 500 C, a difference in hardness is observed. As more vacancies are present in the higher irradiated alloy, it is obvious that during annealing, the amount of copper in the formed precipitates is bigger in this sample. Bigger precipitates should thus be found. At higher annealing temperatures, all defects seem to disappear, as expected. Already at ca 600 °C, the initial hardness (before irradiation) is reached. Further annealing will remove also defects, such as dislocations, which were present before irradiation.
Coincidence Doppler broadening results
Two specimens, with a size of (1 × 10 × 10) mm3, are put together into a sandwich with a sodium-22 source. More than 106 counts are accumulated to obtain a nice spectrum with good statistics. The exact number of collected counts is given in Table 28. The same samples have been annealed at different temperatures for 30 min. The annealing was performed under vacuum to avoid oxidation. The samples were then measured (at room temperature) with the same source and setup. Also for these measurements, the total amount of collected counts is given in Table 28.
Table 28 Amount of counts measured for the CDB results. More than 1 million counts are accumulated for each spectrum. Material Temperature # counts Material Temperature # counts Fe 0 °C 2 744 092 Cu 0 °C 2 934 639 0 °C 1 153 306 0 °C 2 895 175 300 °C 1 623 392 300 °C 2 617 802 350 °C 2 511 902 350 °C 2 062 551 Fe-0.3% Cu 400 °C 4 094 380 Fe-0.3% Cu 400 °C 3 907 389 irradiated to 450 °C 4 169 936 irradiated to 450 °C 3 108 741 0.025 dpa 500 °C 3 094 976 0.1 dpa 500 °C 3 554 790 550 °C 4 172 091 550 °C 3 634 881 600 °C 1 362 679 600 °C 2 922 043 650 °C 7 313 453 650 °C 3 409 241
The spectra are divided by the one of pure iron and compared to the ratio of well annealed pure copper to well annealed pure iron (Figure 157).
p. 264 Post-irradiation annealing of an Fe-Cu alloy
0.025 dpa 0.1 dpa
Figure 157 The CDB spectra are given for all annealing temperatures. For each irradiation dose (i.e. 0.025 dpa (left) and 0.1 dpa (right)), the spectra can be divided into three groups with different behaviour, which are indicated by changing colours.
For both irradiation conditions, vacancy clusters are observed in the as-irradiated specimens, decorated by some copper atoms (red curves in Figure 157). Indeed, the increase of the lower momentum part and the decrease of the higher momentum part of the CDB curves indicate that the positrons annihilate in the neighbourhood of vacancy clusters. At the same time, the copper-specific peak at about 25 × 10-3 mc is clearly observed. The higher low momentum part and lower high momentum part of the CDB spectra, for the samples irradiated at the higher dose (right-hand side of Figure 157), point to a higher vacancy to copper ratio within the copper-vacancy clusters.
Annealing up to temperatures of about 350 °C (yellow curves in Figure 157) tend to slightly increase the high momentum part of the CDB spectra, while low momentum part decreases a bit, however these changes are very minor. This most probably is due to the reorganisation of the defects. At 400 °C, when the vacancies are released from the clusters, the high momentum part increases drastically in the lower dose sample, while its low momentum part returns to the value of non-irradiated materials. Many vacancies break free, and therefore the copper contribution plays a more dominant role, while the vacancies disappear at sinks. Some of the mobile vacancies will recombine with self-interstitial atoms, while others may transport some free copper to the precipitates. For the material irradiated at the higher dose, however, no drastic changes are observed yet at 400 °C. It only reaches the values of the lower dose material in the as-irradiated state. Vacancies thus already left some of the defect clusters, but more annealing is necessary to remove them all. It may thus be concluded that the clusters
p. 265 Appendix E formed at higher irradiation doses are more stable, compared to those formed at the lower doses. At 450 °C already, drastic changes are also observed for the material irradiated to the higher dose. Whereas the changes for the lower dose material are saturating around 450 °C, the higher dose material needs temperatures of about 500 °C to reach the maximum copper peak, what indicates that almost all vacancies are removed (blue curves in Figure 157). This also indicates that the clusters are more strongly bound to the vacancies, in the alloy irradiated at the higher dose. In addition, at the temperature where all vacancies are removed, the copper-specific peak for the material irradiated at the higher dose goes beyond the one for the material irradiated at lower dose. The excess of vacancies, which is higher in the high-dose irradiated alloy, thus leads to the formation of the clusters which contain more copper and which are therefore bigger. It should be mentioned as well that none of the curves reaches the one of pure copper. This can be due to either an insufficient number density (not all positrons annihilate in the clusters), or the presence of stable vacancy-clusters. From ca 600 °C on, the copper-specific peak starts to decrease drastically for both the irradiation conditions (cyan curves in Figure 157). The copper-rich precipitates thus start to dissolve. At 650 °C, all the copper is again in solute solution. However, the CDB spectra observed are not fully identical to those of pure iron. This can be due either to changes in the calibration parameters of the setup during the previous measurements, or to the fact that not all defects are eliminated.
The expected trends can be found in the plots of respectively the S and W parameter as functions of the annealing temperature (Figure 158).
Figure 158 The S (left) and W (right) parameters are given in function of the annealing temperature. The trends are as expected. p. 266 Post-irradiation annealing of an Fe-Cu alloy
The S parameter stays constant until the vacancies are emitted from the clusters, then a drastic decrease is observed. Once all vacancies are dissolved, S becomes constant again. As soon as S decreases, W increases, as more positrons annihilate with electrons coming from the copper atoms in the clusters. The moment S becomes again constant, W temporarily saturates as well. Thus the clusters do not grow due to the annealing when all vacancies have disappeared. Starting from 600 °C, a tremendous decrease of W indicates that the copper-clusters are dissolving as well. It is important to recall that the S parameter does not reach the value of the pure iron, while the W value decreases below the one of pure iron. The material irradiated at the higher irradiation dose, starts with higher S and lower W values, indicating that more vacancies are present at the precipitates. Although some of the precipitates formed in the alloy during irradiation up to higher doses seem to decompose by removing their vacancies, most of them stay stable up to higher annealing temperatures. Nevertheless, once they start decomposing, the S value decreases below the one observed for the sample irradiated to a lower dose, while the W value goes beyond the one of the latter sample. The precipitates found at this annealing stage should thus be bigger for the sample irradiated to the higher neutron dose. At 600 °C, all copper clusters start to dissolve at the same time.
Another interesting finding is that the S value increases unexpectedly at an annealing temperature of 600 °C for the material irradiated at low dose. This feature is clearly visible when the W value is displayed as function of the S parameter, as it is done in Figure 159. The values for pure iron (low W ) and pure copper (high W ) are given as reference.
In Figure 159, all points for S and W are positioned on the same line, up to annealing temperatures of 550 °C, i.e. as long as the copper clusters did not dissolve. This indicates that the type of defects stay the same, only changing the amount of vacancies that they contain. Upon further annealing, it looks like another type of defects is observed, where no copper is present. This may however also be due to changes in the calibration parameters of the setup during the previous measurements.
p. 267 Appendix E
Figure 159 The high momentum part of the CDB results (W parameter) is shown as a function of the low momentum part ( S parameter) for the post-irradiation annealing results of the Fe-0.3% Cu alloys irradiated respectively to 0.025 dpa and 0.1 dpa.
But, the point for the material irradiated to 0.025 dpa and annealed at 600 °C does not fulfil the above described trend. A clear increase in the amount of vacancies is observed. This could be explained by the assumption that big vacancy-clusters are stabilized by the presence of copper. As more copper dissolves into the matrix at higher annealing temperatures, most of these clusters will disappear, as it is seen by further annealing.
Positron annihilation lifetime results
The same samples, as for the CDB measurements, have been used for the positron lifetime measurements. Nevertheless, another source was used, to ensure that the source contribution in the positron lifetime measurements is always the same. In the latter, a two- detector setup is used, and therefore for the same measuring time, an equivalent amount of counts has been detected, thus also for this technique at least 1 million counts are collected. The exact amount of measuring data is given in Table 29.
The mean positron lifetime results are in good agreement with the previous results. The good agreement between the results coming from CDB and positron lifetime is visible in a plot where the positron lifetime results are shown in function of the S parameter. This plot is given in Figure 160. As both the mean positron lifetime and the S parameter give the information about the average vacancy-clusters, a good agreement is expected.
p. 268 Post-irradiation annealing of an Fe-Cu alloy
Table 29 Amount of counts measured for the positron lifetime results. More than 1 million counts are accumulated for each spectrum. Material Temperature # counts Material Temperature # counts Fe 0 °C 5 675 933 0 °C 6 249 351 0 °C 7 907 712 300 °C 7 181 552 300 °C 6 492 362 350 °C 1 680 539 350 °C 1 501 905 Fe-0.3% Cu 400 °C 1 283 170 Fe-0.3% Cu 400 °C 1 164 168 irradiated to 450 °C 1 443 237 irradiated to 450 °C 1 481 203 0.025 dpa 500 °C 1 670 496 0.1 dpa 500 °C 1 656 337 550 °C 1 337 172 550 °C 1 745 668 600 °C 1 367 137 600 °C 1 488 403 650 °C 1 135 805 650 °C 1 499 078
Figure 160 The positron lifetime results are compared to the CDB results ( S parameter). A linear correlation is found for the mean positron lifetime in function of the S value.
Figure 161 illustrates the detailed results of the two-component positron lifetime analysis, in function of the annealing temperature, while in Figure 162 the average trend curves are given.
From the moment the vacancies are emitted from the clusters, the mean positron lifetime decreases, but it doesn’t reach the value of defect-free iron. Again the value of the low dose irradiated material is a little higher than expected for an annealing temperature of 600 °C. The second component of this measurement shows that the stabilized vacancy clusters are not very big, but the number density is relatively high. During further annealing many of them disappear and some seem to agglomerate into bigger cluster, which may become stable at these higher temperatures. For the material irradiated to the higher dose, some big, stable vacancy-clusters are found at the end of the annealing. It would be useful to perform TEM on these samples, to see if voids are visible.
p. 269 Appendix E
0.025 dpa 0.1 dpa
Figure 161 The positron lifetime results are given as functions of the annealing temperature. On the left-hand side the material with the low irradiation dose is shown, while on the right- hand side the high dose irradiated material is given.
Figure 162 The positron lifetime results for the two doses are compared as functions of the annealing temperature.
p. 270 Post-irradiation annealing of an Fe-Cu alloy
For the measurement of the material irradiated to 0.025 dpa, annealed at 450 °C, a strange feature is observed. This is most probably due to some artefacts in the experiments, and it is thus not believed to be truthful. In Figure 162, one can see that the vacancy clusters produced in the longer irradiated samples contain more vacancies. This agrees with the observations of the CDB measurements. As soon as the unstable vacancies are dissolved, the differences observed between the two irradiation conditions are tiny. Therefore, one may conclude that the same stable obstacles are formed, independently of the irradiation dose, which still seem to grow in amount and size at high annealing temperatures.
LEAP results
After making several atom probe tips, a number of measurements were performed until the tip breaks. From each material and annealing temperature, the best measurement is kept for further study. The number of counts cumulated for each measurement is given in Table 30. It can be found that at least 8 million atoms are selected, which is enough for precipitation detection.
Table 30 Amount of counts measured for the atom probe results. More than 8 million counts are accumulated for each measurement. Annealing Number of counts temperature 0.025 dpa 0.1 dpa As-irradiated 8 096 457 8 295 795 350 °C 18 940 453 29 232 781 500 °C 13 743 624 35 940 432
Table 31 gives the number of precipitates found in each measurement and this is enough for a statistically study. For these precipitates, the number density and mean size is calculated (Table 31).
Table 31 The amount of clusters is given as well as the calculated number density and the mean size of the clusters. Annealing Number of clusters Number density (1020 m-3) Mean radius (nm) temperature 0.025 dpa 0.1 dpa 0.025 dpa 0.1 dpa 0.025 dpa 0.1 dpa As-irradiated 28 18 3 272 2 186 1.6 1.5 350 °C 30 62 901 1 412 1.8 1.7 500 °C 30 56 1 312 1 711 1.5 1.7
p. 271 Appendix E
A decrease in the number density is found as well as an increase in the size, when the samples are annealed at 350 °C. The most unstable defects might have joined to form bigger, more stable precipitates. At lower irradiation dose, more unstable defects are found as the number density decreases more drastically. Also in the PAS results, it was found that the clusters disappear much more easily in the low dose irradiated material. Annealing to higher temperatures causes again an increase in the number density, and a minor decrease in size. As by this temperature the vacancies leave the clusters, the decrease of size is expected. The increase of the number density can as well be explained by the mobility of the vacancies. These mobile vacancies can join the copper, which is still in the matrix after irradiation, into new clusters. As expected from the PAS results, at 500 °C more and bigger copper precipitates are found for the alloy irradiated to the highest neutron dose.
Table 32 lists the average concentration of copper in the clusters for all examined samples.
Table 32 The concentration of copper in the clusters. Annealing Copper in clusters (%) temperature 0.025 dpa 0.1 dpa As-irradiated 44.20 39.20 350 °C 36.63 38.27 500 °C 39.94 37.65
Although the average concentration of copper in the clusters is about 40 %, it is found that the centre of the clusters is very rich in copper, until more than 90 %. Both concentrations found (the average and the centre concentrations) are higher than those found for the alloy with the same irradiation conditions, but lower concentration of copper (0.1 % of copper). This material (Fe-0.1% Cu) has been investigated by Meslin [42]. For this latter alloy, the average concentration in the clusters is found to be ca 20 %, and the centre- concentration is enriched up to 73 %. For the Fe-0.1% Cu material irradiated at high dose, Meslin found a volume density of (0.8 ± 0.5) 1023 m-3. This is lower than the one found here. Due to the difference in initial bulk concentration of copper, this is of course reasonable. The radius found for a precipitate located at the middle of the measurement is 1.2 nm. The size as well is thus lower than the one found for the alloy with the higher copper content.
p. 272 Post-irradiation annealing of an Fe-Cu alloy
The same observations are found for the material irradiated at low dose. The volume density found is (1.7 ± 0.9) 1023 m-3 in the Fe-0.1% Cu alloy, which is again lower than the one found here. All clusters, observed by Meslin, were localized at the border of the sample, therefore no average size was determined. In both experiments it is however found that the density for the longer irradiated material is lower.
The results of this paper are shown graphically in Figure 163. The clusters can be observed very easily.
0.025 dpa 0.1 dpa
0 °C
350 °C
500 °C --
Figure 163 The atom probe tomography results are shown for the investigated specimens.
Conclusion{ TC "Conclusion" \f C \l "3" }
Post irradiation annealing is a good method to investigate the stability of the defects produced by irradiation. The three techniques used in this paper give altogether a good insight into these features. However, some of the obtained results require further investigation to be fully understood.
p. 273
p. 274
Appendix F Quantitative calculations of the PAS results
Significant progress in revealing the potential existing vacancy clusters has been made by PAS, during the past decades [191]-[195]. But, effort should also be put on the quantitative estimations of the average size and density of the positron annihilation sites, as this leads to a better comparison with other techniques, such as transmission electron microscope (TEM), atom probe tomography (APT) and small angle neutron scattering (SANS). In addition, the quantitative determination of the defects is necessary for the production and validation of the models predicting the microstructural evolution under irradiation. This appendix focuses on the quantitative calculations performed in literature. They are updated with some own assumptions.
p. 275 Appendix F
Theoretical background{ TC "Theoretical background" \f C \l "4" }
Positron annihilation spectroscopy is an indirect method. A comprehensive theory is needed for a quantitative interpretation of the experiments. This theory is based on the Hamiltonian of the many-ions-many-electrons system. For practical use, this Hamiltonian needs to be simplified drastically. The first reduction in complexity (the adiabatic or Born- Oppenheimer approximation) assumes that the electrons are in their ground state, as their dynamics is much faster than those of the much heavier ions. In this approximation, the
Hamiltonian of the many-electron system ( H n−e ) includes the kinetic energy of N − electrons
(T ), their mutual interaction (Vee ) and their interaction with the external potential of the localized ions (Vext ).
H n−e = H Int + Vext = (T + Vee ) + Vext (89)
⎛ 1 N− ∂ 2 1 N−−N 1 ⎞ N− H = ⎜− ⋅ + ⋅ ⎟ + v r (90) n−e ∑ 2 ∑∑ ∑ ext ()i ⎜ 2 i=1 ∂r 2 i=≠1 j i r − r ⎟ i=1 ⎝ i i j ⎠
For applications in the field of materials, the many-electrons problem is further reduced to an effective one-electron form. This approximation is based on the first attempt of Thomas and Fermi to use the electron density as basic variable instead of the complete wave function. They assumed that the motion of the electrons is uncorrelated and that the corresponding kinetic energy can be described as function of the electron density by a local approximation based on the results for free electrons. This has been further developed in the Honenberg- Kohn theorem [196], [197]. Detailed information on this theory is given in [198]. There, it is shown that vext ()r can be linked to the electron density n− (r).
vext (r) = G[n− (r)] (91)
The ground state energy of the system can be derived by minimizing the following
Schrödinger equation, where ΨG [n− (r)] is the ground state of the system with ground state density n− ()r .
p. 276 Quantitative calculations of the PAS results
E[]n− ()r ;vext (r) ≡ ΨG [n− (r)] H n−e ΨG [n− (r)] (92)
The Honenberg-Kohn theorem shows that this energy has its minimum at the ground state density and can be rewritten as given in equation 93.
E n r ;v r = F n r + v r ⋅n r ⋅ dr (93) []− () ext ( ) [ − ( )] ∫ ext ( ) − ( )
Here, F[]n− ()r ( = T[]n− ()r + Vee [n− (r)] ) is a functional, that only depends on the electron density (density functional theory, DFT).
The determination of the positron states in solids can be made on the basis of the two- component generalization of the previous equations, referred to as the two-component density functional theory. The ground state energy of a system of electrons and positrons in an external potential ( vext ) can thus be given as the sum of one-component functionals for electrons and positrons, together with a coulomb interaction term and an electron-positron correlation energy term, all as functions of the electron ( n− (r)) and positron ( n+ ()r ) densities [199].
E n r ; n r = F n r + F n r + v r ⋅ n r − n r ⋅ dr []− ( )()+ []− ( ) [ + ( )] ∫ ext ( ) ( − ( )()+ ) n ()r ⋅ n (r' ) (94) − − + ⋅ dr ⋅ dr'+E e− p []n ()r ; n ()r ∫∫ r − r' c − + 1 n(r)⋅ n(r') F[]n()r = T[]n()r + ⋅ ⋅ dr ⋅ dr'+E []n()r (95) 2 ∫∫ r − r' xc
e− p Ec []n− ()r ;n+ (r) is the electron-positron correlation energy functional and E xc [n(r)] is the exchange-correlation energy between the indistinguishable particles. The ground state electron and positron densities minimizing this energy functional are then determined.
The positron lifetime τ carries information about the electron and positron density at the positron annihilation site. The annihilation rate λ , the reciprocal of the lifetime, is given by the overlap of the positron density n+ (r) and the electron density n− ()r , according to the following equation [200].
p. 277 Appendix F
1 λ = = π⋅ r 2 ⋅ c⋅ n (r) ⋅γ (n (r)) ⋅n (r) ⋅dr (96) τ 0 ∫ − − +
Here, r0 is the electron radius, c is the speed of light and γ (n− (r)) is the enhancement factor. This enhancement factor assumes a zero-positron limit of the pair correlation. This assumption can be justified by arguing that the positron, together with its screening cloud, forms a neutral quasi-particle that enters the system without changing the average electron density. Theoretical investigations on these values have been carried out for example by J. Kuriplach et al. [146] and others [201].
The positron lifetime is related, amongst other things, to the size of the vacancy clusters, where it annihilates. More specifically, it indicates the number of vacancies near the positron annihilation site. Computer simulations performed by e.g. Kuriplach et al. [146] found specific positron lifetimes for clusters with one, two and more vacancies. To correlate the positron lifetime and the intensity parameters with the real properties of the defects, the following set of differential equations needs to be solved.
k k dnB ⎛ ⎞ = −⎜λB + ∑κ i ⎟ ⋅ nB + ∑δ i ⋅ nDi (97) dt ⎝ i=1 ⎠ i=1 dn Di = κ ⋅ n − ()λ + δ ⋅ n (98) dt i B Di i Di
In these equations, the quantities n (t) and n (t) are the densities of the positrons in B Di respectively the bulk and the defect state at time t , while κ is the trapping rate and δ is the detrapping rate. The indices B and Di denote the free (bulk) and the trapped (defect) state, respectively. When these equations are solved, with the knowledge of all parameters, it is possible to determine the number of each type of defects, using the intensities I i . More detailed information can be found in [94].
Defect size calculations{ TC "Defect size calculations" \f C \l "4" }
Over the last 40 years, many investigations have been performed to determine the specific lifetime of positrons trapped at different types of defects in pure iron and Fe-based alloys. Experimentally, this has been done by recovery experiments on deformed iron [202],
p. 278 Quantitative calculations of the PAS results
[203], as well as by the annealing of vacancies in electron irradiated iron [166], [204]. Moreover, models are produced to correlate a specific trapping site with the observed positron annihilation characteristics [51]. While these calculations have been fairly successful for monovacancies in a wide variety of metals [205], they are not easily generalized to more complicated defect geometries. In metallic systems, vacancies and small vacancy clusters show a well-defined relationship between the positron lifetime and the size of the open-volume region [206]. The local electron density determines the positron annihilation rate. Since the electron density is lower at an open-volume region compared to bulk material, the lifetime is increased for positrons trapped at vacancy clusters. The positron lifetime depends on the size of the open- volume region, so positron lifetime measurements can be used as a measure of the vacancy cluster size. To interpret the experimental results, a theoretical model, providing the positron lifetime, as a function of microvoid size, is vital. Based upon a simple superimposed-atom model, Puska and Nieminen [97] have performed such calculations for positron lifetimes in microvoids consisting of 1 (V1) tot 15 (V15) vacancies, using a fitting parameter to reproduce the experimental bulk positron lifetime. To examine larger microvoids, however, ab-initio based superimposed-atom model calculations have been performed by Hempel et al. [51].
Pure iron{ TC "Pure iron" \f C \l "5" }
The determination of the average size of vacancy type defects, as detected by the positrons, has been performed by many authors.
Figure 164 collects all results found in literature. The available data can be separated in four groups. Each of them used a different approach to estimate the positron lifetime as a function of the vacancy cluster size. Group 1 corresponds to data given by Vehanen, Hautojärvi, Puska and co-workers [97], [166], [202], [204], [207]-[214]. They computed the valence electron density, the electrostatic potential and the total trapping potential for microvoids of varying size. To obtain these parameters, they used the method of minimizing the ground state energy, as discussed above [206]. Group 2 contains the results published by Nagai, Tang and co-workers [18], [50], [51], [90], [119], [169], [203], [215]-[219]. Their calculations are based on the superimposed-
p. 279 Appendix F atomic-charge method. In the calculations, the electron-positron correlation potentials are calculated based on the two-component density-functional theory and the positron wave functions are obtained by solving the positron Kohn-Sham equation using numerical relaxation technique [197]. To simulate the vacancy clusters, they employed the supercell approximation. Blocks consisting of n Fe atoms in a 1024-site bcc Fe matrix are removed in order to simulate the corresponding cluster [203]. Group 3 collects the data given by Kuriplach et al. [146]. The positron calculations were carried out employing the so-called atomic superposition (ATSUP) method, developed by Puska et al. [97]. However, the inserted crystal structures were obtained by a Vienna ab initio simulation package. Within the framework of this package, a pseudopotential approach is used. For the purpose of positron calculations, Kuriplach et al. employed the relaxed defect configuration obtained by using 54 atom supercells (3 × 3 × 3 bcc cell of Fe) performed by [220], [221]. Finally, the results of group 4 were published by Asoka-Kumar and co-workers [222], [223]. They have successfully applied a finite element electronic structure technique to calculate positron distributions and lifetimes [201]. In the finite element method, solutions to differential equations (e.g. electron or positron wavefunctions) are described in terms of strictly local, piecewise polynomial basis functions. The unit cell is partitioned into subdomains called elements. Local polynomials are defined in each element and these polynomials are linked continuously to neighbouring elements and across the domain boundaries to create piecewise continuous functions. This finite element method needs a positron potential in order to calculate the positron wavefunction. This potential was obtained by the method described above.
Figure 164 The results found in literature for the positron lifetime component of vacancy clusters with increasing amount of vacancies inside the clusters.
p. 280 Quantitative calculations of the PAS results
Despite the different origin of the data, from the figure, it can be seen that the same trend is observed for all of them. Especially, the results from group 2 and 3 are almost identical, as they use a similar approach for their calculations. A general trend line has been estimated based on all literature data points. As shown in Figure 164, this trend is pretty close to the most recent results of group 2 and 3, that were obtained using ab-initio type calculations.
Alloyed iron{ TC "Alloyed iron" \f C \l "5" }
All calculations of positron lifetime versus vacancy cluster size and experiments trying to link the observed positron lifetimes with the cluster sizes have been performed for pure iron. Adding alloying elements will lead to a shift of the above curve. As this shift depends on the chemistry and amount of alloying elements at the positron annihilation sites, it is very difficult to determine the correct amount of vacancies inside the defect that gives rise to a particular positron lifetime component.
However, Kuriplach et al. [146] have shown that the presence of certain foreign elements (e.g. copper, manganese, nickel, chromium) close to monovacancies will have no effect on the positron lifetime component, within an error of 1 ps.
As for Fe doped with carbon (the basic component of steels), it is expected that the lifetime of the positron in vacancy clusters, combined with carbon atoms, will change compared to the same vacancy clusters in pure iron. In the literature, however, two contradictory opinions have been found for the positron lifetime component of a carbon- vacancy pair. Hautojärvi et al. [214] found experimentally that this component should be equal to 160 ps (i.e. 15 ps less than the value of a monovacancy), while Asoka-Kumar et al. using their model [222] found that the addition of 1 carbon atom to 1 and 2 vacancies in Fe would lead to an increase of about 5 ps (i.e. 181 ps for the carbon-vacancy pair's positron lifetime component). As it is still questionable which of the two opinions is the most accurate, we have chosen to use the same values for the alloy containing some carbon as for pure iron. Moreover, even for the pure iron differences of more than 10 ps have been found between the different groups, for clusters containing vacancies (see Figure 164). On top of this, it should
p. 281 Appendix F be mentioned that it is very difficult to determine experimentally if carbon is located near the positron annihilation site or not (see for instance [164]).
For the binary Fe-Cu alloys, it is expected that the positron lifetimes found for the vacancy clusters containing some copper atoms will be different from the positron lifetimes found for the copper-free clusters. Indeed, Kuriplach et al. have shown that the positron lifetime component slightly decreases with increasing copper coverage of the vacancy clusters (see Figure 165) [146].
Figure 165 The dependence of the positron lifetime on the vacancy cluster size (left panel) and on the copper coverage of selected vacancy clusters (right panel) [146].
As the presence of copper is well observed in the CDB curves, it is possible to estimate the amount of copper present at the positron annihilation sites, using the approach developed by Nagai et al. [169], [170]. They found that the distribution in the binary Fe-Cu alloy can be approximately expressed as a function of the distributions of pure iron and pure copper, as it is shown in equation 99, where N X (pL ) represents the high-momentum distribution of the CDB spectrum of the alloy. In this equation, x is the coverage of the defects by copper atoms (i.e. the fraction of Cu atoms that substitute Fe atoms in the shell (first and second nearest neighbours) surrounding the positron annihilation site).
N Fe−Cu ()p L ∝ (1 − x) ⋅ N Fe (pL ) + x ⋅ N Cu (pL ) (99)
As the ratio curve is given by RX Y (pL ) = N X (pL ) N Y (pL ) , the ratio curve for the binary Fe-Cu alloy can be expressed with equation 100.
R()Fe−Cu / Fe (pL )∝ (1 − x) + x ⋅ RCu / Fe (pL ) (100)
p. 282 Quantitative calculations of the PAS results
The estimated fractions of the positrons annihilating with copper electrons are determined by fitting the Cu curve to the Fe-Cu curves using equation 100 and taking into account the effect of vacancies that tend to increase the S parameter and decrease the high -3 momentum region ( pL > 7 × 10 mc). Thus, the x -parameter varies between zero when no Cu atoms are surrounding the positron annihilation site and 1 when this first shell is entirely made of Cu atoms.
Based on the obtained degree of coverage and using both the average positron lifetime of vacancies in pure iron from Figure 164 and the results of Kuriplach et al. (Figure 165), it becomes possible to identify the V-Cu clusters associated with the second component of the positron lifetime measured in the Fe-Cu alloys. In fact, these second positron lifetime component results of the PALS analysis can lead to an estimation of the average size of the clusters, including both the number of vacancies and those of copper atoms, co-clustering together. Figure 166 illustrates that an increasing amount of vacancies will lead to an important increase of the positron lifetime of the defect, while an increasing amount of copper atoms will slightly decrease this positron lifetime.
Figure 166 The dependence of the positron lifetime on the amount of vacancies and the copper coverage of the cluster.
Determination of the concentration of positron annihilation sites
In order to extract the real properties of the defects, their size and density, from the experimentally obtained positron lifetime components and their associated intensities, the set of differential equations 97 and 98 needs to be solved. It should be mentioned at this point that the detrapping rate is considered to be negligible in most cases compared to positron annihilation and trapping rates [207]-[213].
p. 283 Appendix F
In most cases, only one trapping state is used (i.e. k is equal to 1). But this situation can not be applied for irradiated samples, as more than one trapping site is expected. Therefore, a second trapping state has to be included, as illustrated in Figure 167. For this model, a 3-component analysis of the positron lifetime spectrum is required, however, for neutron irradiated material, a 2-component analysis gives a fairly sufficient fitting of the obtained spectra, while the analysis with 3 components fails to converge. Therefore, and in order to comply with the model, one of the experimentally obtained components should be considered as a combination of two components.
Figure 167 Two types of defect traps are assumed, i.e. short positron lifetime traps and clusters. The positron lifetime of the short positron lifetime traps is supposed to be experimentally measured in the first component.
It is supposed that the positron lifetime of the short positron lifetime traps is experimentally measured as part of the first component, as illustrated in Figure 167. This has been firstly introduced by Vehanen et al. [166] and in the present work the formulae proposed by Vehanen et al. (equations 101 to 104) will be applied. Here, τ 1,calc is given by equation 105, where λ B is the reciprocal of the bulk positron lifetime (τ B , equal to 107 ps). For clarity, from now on the short positron lifetime traps will be denoted as sh , while the traps with longer positron lifetimes are named clusters ( cl ).
I1,exp = I1,calc + I sh (101)
I 2,exp = I cl (102)
I1,calc ⋅τ 1,calc + I sh ⋅τ sh τ 1,exp = (103) I1,calc + I sh
τ 2,exp =τ cl (104)
−1 −1 τ 1,calc = (λ1,calc ) = (λB +κ sh +κ cl ) (105)
p. 284 Quantitative calculations of the PAS results
With the equations 101 to 104 and the fact that I1,exp + I 2,exp =1, only five equations are available to calculate six unknown parameters. Therefore, one of the parameters should be determined in another way. In this respect, a parametric study has been performed to determine the best value for τ sh . Figure 168 shows the estimated defect densities for both the short positron lifetime traps (Figure 168 (a)) and the clusters (Figure 168 (b)), estimated using the equations given before, inserting the experimental results for irradiated pure iron, as well as a fixed value for τ sh . These calculations have been performed for different values of τ sh , changing from 120 ps to 175 ps, with an interval of 5 ps, using as input values, those provided by Vehanen et al. [166]. The results shown here were carried out for the pure iron experiments, but they were also performed for the other alloys, with comparable results.
Figure 168 The estimated defect density for respectively the short positron lifetime traps (a) and the long positron lifetime traps, i.e. the clusters (b) are shown with changing
assumption for the value of τ sh . τ sh varies from 120 ps to 175 ps for both calculations.
The estimated densities for both the short positron lifetime traps and the clusters show unaccepted trends for very low values of τ sh , while the results for high values of τ sh converge to reasonable values. In order to keep the differences as small as possible, only the high values of τ sh were taken into account. More precisely, the ranges are chosen between 150 ps and 175 ps for the densities of the short positron lifetime traps and between 140 ps and 175 ps for the densities of the clusters.
More information is needed to select the best value forτ sh . Asoka-Kumar et al. [222] found that the value of the positron lifetime for a dislocation combined with a vacancy is between 142 and 165 ps. In addition, as mentioned earlier, Hautojärvi et al. [214] found a positron lifetime of 160 ps for a V-C pair. Furthermore, for the alloys containing copper, it
p. 285 Appendix F has been argued before that the positron lifetime component for vacancies combined with copper is lower than the single vacancy's positron lifetime in Fe (e.g. 175 ps). It therefore emerges that for the short positron lifetime traps in the Fe-based alloys, a value of 160 ps can be assigned whatever its origin.
Now, with a fixed τ sh , it is possible to solve the differential equations (equations 97 and 98) and therefore determine all other parameters. The defect density of both the short positron lifetime traps csh and the clusters ccl can be estimated, using equation 106 and 107.
κ sh = μ sh ⋅ csh (106)
κ cl = μ cl ⋅ ccl (107)
The specific trapping rate for monovacancies μV has been determined by Vehanen et al. [166], to be equal to (1.1 ± 0.2) × 1015 s-1. The same specific trapping rate of single vacancies is used for the short positron lifetime traps ( μ sh = μV ), as they are, as mentioned earlier, considered to be most probably composed of single vacancies associated with a foreign element or a dislocation. As for the clusters, unfortunately no experimental data are available on their specific trapping rate μ cl . In addition, Nieminen et al. [224] have shown that positron lifetime measurements exhibit strong temperature dependence for the positron trapping probability at large voids in aluminium. They also showed that the specific trapping depends linearly on temperature, in the case of large voids at low temperatures, as the trapping process is transition limited (the positron mobility is large and the capture rate is small). At temperature above 200 K, however, the process becomes diffusion limited and the dependence on temperature becomes weak. The same has been observed for an iron-based alloy containing voids with a positron lifetime of 500 ps by Huguenin and Moser [225], ten years later. However, in the latter work, the authors suggest that the variations under consideration are strongly dependent on void size. For small vacancy clusters (with a positron lifetime of 260 ps), no temperature variation could be detected in the samples. In the alloys investigated in the present work, the clusters have been observed to be small [164], with a positron lifetime comparable to the one given by [225]. Therefore, it can be assumed that the dependency on temperature of the specific trapping rate of the clusters found here is negligible. Theoretical calculations by Nieminen and Laakkonen [226] indicated that for these small vacancy clusters p. 286 Quantitative calculations of the PAS results in metals, the positron trapping rate is proportional to the defect volume, i.e. the number of vacancies in the cluster ( N ), given by μ cl ≈ μ v ⋅ N .
Summary
The amount of vacancies in the defects can thus be obtained by the use of the trendline shown in Figure 164. In the binary Fe-Cu alloys, however, the presence of copper at the positron annihilation sites significantly alters this relationship. Therefore, the trend given by Figure 166 is used for these alloys. The overage copper coverage of the positron annihilation sites is calculated using the CDB ratio curves (equation 100).
Solving the differential equations leads to the following equations for the trapping rates of the short positron lifetime traps (κ sh ) and the clusters (κ cl ), respectively.
τ 1,exp ⋅(λB − I 2,exp ⋅τ 2,exp )− I1,exp κ sh = (108) τ sh −τ 1,exp
I 2,exp κ cl = ⋅()λB − λ2,exp +κ sh (109) I1,exp
In these equations, λ B is the reciprocal of bulk positron lifetime (τ B , equal to 107 ps in pure iron) and τ sh is fixed to 160 ps. Using these trapping rates, the concentration of defects
15 -1 can be determined by equation 106 and 107, with μV equal to (1.1 ± 0.2) × 10 s and μ cl given by μ cl ≈ μ v ⋅ N .
p. 287
References
References
[1] This photograph is available online at
[18] T. Toyama, Y. Nagai, Z. Tang, M. Hasegawa, A. Almazouzi, E. van Walle, R. Gérard, Acta Mater. 55 (2007) 6852-6860. [19] G.R. Odette, G.E. Lucas, Radiat. Eff. Defect Solid. 144 (1998) 189-231. [20] L. Malerba, J. Nucl. Mater. 351 (2006) 28-38. [21] D. Terentyev, C. Lagerstedt, P. Olsson, K. Nordlund, J. Wallenius, C.S. Becquart, L. Malerba, J. Nucl. Mater. 351 (2006) 65-77. [22] W.J. Phythian, C.A. English, J. Nucl. Mater. 205 (1993) 162-177. [23] C.A. English, J.M. Hyde, S.R. Ortner, Proc. of International Symposium on the Mechanisms of Materials Degradation and Non-Destructive Evaluation in Light Water Reactors, Osaka (Japan) (2002) 53. [24] G.E. Lucas, G.R. Odette, Proc. of the Second International Symposium on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors (1985) 345-360. [25] R. Chaouadi, R. Gérard, J. Nucl. Mater. 345 (2005) 65–74. [26] B.A. Gurovich, E.A. Kuleshova, Yu.A. Nikolaev, Ya.I. Shtrombakh, J. Nucl. Mater. 246 (1997) 91-120. [27] J.T. Buswell, W.J. Phythian, R.J. McElroy, S. Dumbill, P.H.N. Ray, J. Mace, R.N. Sinclair, J. Nucl. Mater. 225 (1995) 196-214. [28] G.R. Odette, G.E. Lucas, JOM 53(7) (2001) 18-22. [29] R.G. Carter, N. Soneda, K. Dohi, J.M. Hyde, C.A. English, W.L. Server, J. Nucl. Mater. 298 (2001) 211-224. [30] S. Jumel, PhD-thesis at L'Université des Sciences et Technologies de Lille (2005). [31] E. Lucon, M. Lambrecht, M. Scibetta, A. Almazouzi, Restricted Contract Report SCK•CEN R-4540 (2007). [32] ASTM A533 Standard Specification, Annual Book of ASTM Standards, Section 01.04, pp. 258-260. [33] M. Hansen, Constitution of Binary Alloys, Metallurgy and Metallurgical Engineering Series, McGraw-Hill Book Company (1958). [34] A.D. Romig, Jr., J.I. Goldstein, Met. Trans. A 11A (1980) 1151-1159. [35] F. Bergner, M. Lambrecht, A. Ulbricht, A. Almazouzi, accepted for publication in J. Nucl. Mater. (2009). [36] K. Tapasa, A.V. Barashev, D.J. Bacon, Yu.N. Osetsky, J. Nucl. Mater. 361 (2007) 52- 61. [37] M. Perez, F. Perrard, V. Massardier, X. Kleber, A. Deschamps, H. De Monestrol, P. Pareige, G. Covarel, Phil. Mag. 85 (2005) 2197-2210. [38] N. Smetniansky-De Grande, A. Barbu, Rad. Eff. And Def. Sol. 140 (1997) 313-321. [39] J.T. Buswell, P.J.E. Bischler, S.T. Fenton, A.E. Ward, W.J. Phythian, J. Nucl. Mater. 205 (1993) 198-205. [40] M.K. Miller, K.F. Russell, , J. Nucl. Mater. 371(1-3) (2007) 145-160.
References
[41] B.D. Wirth, G.R. Odette, W.A. Pavinich, G.E. Lucas, S.E. Spooner, Effects of Radiation on Materials: 18th International Symposium, ASTM STP 1325, ed. R.K. Nanstad et al. (West Conshohocken: American Society for Testing and Materials) (1999) 102-121. [42] E. Meslin-Chiffon, PhD-thesis at the Université de Rouen (2007). [43] R. Chaouadi, Restricted Contract Report SCK•CEN R-4235 (2005). [44] Workshop on Trend Curve Development for Surveillance Data with insight on Flux Effects at High Fluence: Damage Mechanisms and Modeling, Mol (Belgium), 19-21 November 2008. [45] G. Meyrick, Class Notes and lecture materials (2001) p. 37, 110 and 118. [46] L. Debarberis, B. Acosta, A. Zeman, S. Pirfo, P. Moretto, A. Chernobaeva, Y. Nikolaev, Int. J. of Microstructure and Materials Properties 2(3-4) (2007) 326-338. [47] M.K. Miller, R. Jayaram, K.F. Russell, J. Nucl. Mater. 225 (1995) 215-224. [48] E.A. Little, D.R. Harries, Metal Sci. J. 4 (1970) 195-200. [49] N. Soneda, K. Dohi, A. Nomoto, K. Nishida, S. Ishino, Proc. of the International Symposium on Research for Aging Management of Light Water Reactors (2007). [50] Y. Nagai, Z. Tang, M. Hasegawa, T. Kanai, M. Saneyasu, Phys. Rev. B 63 (2001) 134110. [51] A. Hempel, M. Saneyasu, Z. Tang, M. Hasegawa, G. Brauer, F. Plazaola, S. Yamaguchi, F. Kano, A. Kawai Proc. of 19th International Symposium on Effects of Radiation on Materials ed. M.L. Hamilton et al., American Society for Testing and Materials, West Conshohocken (2000) 560-578. [52] J.R. Hawthorne, A.L. Hiser, Proc. of the Effects of Radiation on Materials: 14th International Symposium (1990) 55-79. [53] K. Kussmaul, J. Föhl, T. Weissenberg, Proc. of the Effects of Radiation on Materials: 14th International Symposium (1990) 80-104. [54] C.A. English, W.J. Phythian, J.T. Buswell, J.R. Hawthorne, P.H.N. Ray, Proc. of the Effects of Radiation on Materials: 15th International Symposium (1992) 93-116. [55] M. Matijasevic, PhD-thesis at the University of Ghent (2007). [56] ASTM A213 Standard Specification, Annual Book of ASTM Standards, Section 01.01, pp. 112-118. [57] G. Bonny, D. Terentyev, L. Malerba, Scripta Mater. 59 (2008) 1193-1196. [58] L. Malerba, A. Caro, J. Wallenius, J. Nucl. Mater. 382 (2008) 112-125. [59] A.H. Cottrell, Steels for reactor pressure circuits, Londen and Bradford: Lund Humphies (1961) 281-286. [60] K.C. Russell, L.M. Brown, Acta Metall. 20(7) (1972) 969-974. [61] U. Potapovs, J.R. Hawthorne, Nucl. Appl. 6 (1969) 27-46. [62] A. Fujii, M. Nemoto, H. Suto, K. Monma, Tans. JIM 9 (1968) 374-380. [63] N. Igata, K. Watanabe, S. Sato, ASTM spec. tech. publ. 529 (1973) 63-74.
[64] J. Burke, The kinetics of phase transformations in metals, Oxford: Pergamon Press (1965) 55. [65] S.B. Fisher, J.T. Buswell, Int. J. Pres. Ves. & Piping 27 (1987) 91-135. [66] T.J. Williams, P.R. Burch, C.A. English, P.H.N. Ray, Proc. of the Environmental Degradation of Materials in the Nuclear Power Systems – Water Reactors (1988) 121- 131. [67] G.R. Odette, E.V. Mader, G.E. Lucas, W.J. Phythian, C.A. English, Proc. of the Effects of Radiation on Materials: 16th International Symposium (1993) 373-393. [68] C.A. English, A.J. Fudge, R.J. McElroy, W.J. Phythian, J.T. Buswell, C.J. Bolton, P.J.H. Heffer, R.B. Jones, J.T. Williams, Int. J. Pres. Ves. & Piping 54 (1993) 49-87. [69] T.J. Williams, W.J. Phythian, Proc. of Effects of Radiation on Materials: 17th International Symposium (1996) 191-205. [70] K. Dohi, T. Onchi, F. Kano, K. Fukuya, M. Narui, H. Kayano, J. Nucl. Mater. 265 (1999) 78-90. [71] U.S. Nuclear Regulatory Commission, Regulatory Guide 1.99 Revision 2 (1988). [72] E.D. Eason, J.E. Wright, G.R. Odette, NUREG/CR-6551, Washington, D.C.: U.S. Government Printing Office, U.S. Nuclear Regulatory Commission (1998). [73] ASTM E900-02, Standard Guide for Predicting Radiation-Induced Transition Temperature Shift in Reactor Vessel Materials, Volume 12.02 (2005). [74] NUREG-1874, ADAMS Accession number ML070860156 (2007). [75] M. Erickson Kirk, U.S. Nuclear Regulatory Commission, Draft Regulatory Guide DG- 1.99, Proposed Revision 3 (2007). [76] G. Bezdikian, Proc. 18th International Conference on Structural Mechanics in Reactor Technology (SMiRT-18), Beijing, China (2005). [77] M.T. EriksonKirk, United States Nuclear Regulatory Commission, in review (2007). [78] J.P. Massoud, S. Bugat, J.L. Boutard, D. Lidbury, S. Van Dyck, F. Sevini, FISA 2006 – EU research and training in reactor systems, ed. G. Van Goethem et al. (European Commission, Directorate-General for Research, Euratom) (2006) 107-122. Information on the FP6_PERFECT project is available online at
References
[87] B. Verboomen, SCK•CEN IR-0013 (2002). [88] C.A. English, Mat. Sci. For. 97-99 (1992) 775-778. [89] R.H. Howell, T.E. Cowan, J. Hartley, P. Sterne, B. Brown, Appl. Surf. Sci. 116 (1997) 7-12. [90] Y. Nagai, M. Hasegawa, Z. Tang, A. Hempel, K. Yubuta, T. Shimamura, Y. Kawazou, A. Kawai, T. Kano, Phys. Rev. B 61 (2000) 6574-6578. [91] P. Asoka-Kumar, B.D. Wirth, P.A. Sterne, Philos. Mag. Lett. 82 (2002) 609-615. [92] K. Fujii, K. Fukuya, N. Nakata, K. Hono, Y. Nagai, M. Hasegawa, J. Nucl. Mater. 340 (2005) 247-258. [93] P. Hautojärvi, Positrons in Solids, Topics in Current Physics 12, Springer, Berlin (1979). [94] M.J. Puska, R.M. Nieminen, Rev. Mod. Phys. 66(3) (1994) 841-897. [95] H. Hessel Anderson, M. Eldrup, N. Hansen, D.J. Jensen, T. Leffers, H. Lilholt, O.B. Pedersen, B. Singh, Proc. of the 5th Intl Riso Symposium of Metallurgy and Materials Science (1984) 133. [96] M. Eldrup, B.N. Singh, J. Nucl. Mater. 251 (1997) 132-138. [97] M.J. Puska, R.M. Nieminen, J. Phys. F: Metal. Phys. 13 (1983) 333-346. [98] Information on the Amira program is available online at
[110] H. Saito, Y. Nagashima, T. Kurihara, T. Hyodo, Nucl. Instr. and Meth. A 487 (2002) 612-617. [111] P. Kirkegaard, M. Eldrup, Comput. Phys. Commun. 7(7) (1974) 401-409. [112] P. Kirkegaard, N.J. Pedersen, M. Eldrup, PASFIT-88, A data processing system for positron annihilation spectra on mainframe and personal computers, Riso National Laboratory, Roskilde, Denmark (1989). [113] J. Kansy, Nucl. Instr. and Meth. A 374 (1996) 235-244. [114] J. Dryzek, J. Kansy, Nucl. Instr. and Meth. A 380 (1996) 576-581. [115] S. Van Petegem, B. Van Waeyenberge, D. Segers, C. Dauwe, Nucl. Instr. and Meth. A 513 (2003) 622-630. [116] S. Van Petegem, PhD-thesis at Universiteit Gent (2003). [117] K. Verheyen, M. Jardin, A. Almazouzi, SCK•CEN BLG-957 (2004). [118] K. Verheyen, M. Jardin, A. Almazouzi, J. Nucl. Mater. 351(1-3) (2006) 209-215. [119] Y. Nagai, Z. Tang, M. Hasegawa, Rad. Phys. Chem. 58 (2000) 737-742. [120] E.W. Müller, J. Panitz, S.B. McLane, Rev. Sci. Instrum. 39(1), (1968) 83. [121] E.W. Müller, Z. Phys. 131 (1951) 136-142. [122] This image is available online at
References
[136] M.L. Jenkins, M.A. Kirk, Characterization of radiation damage by transmission electron microscopy, Institute of Physics, Bristol (2001). [137] J.W. Edington, Practical electron microscopy in Materials Science, ed. Macmillan Philips Technical Library (1965). [138] This image is available online at
[162] F.G. Djurabekova, L. Malerba, C. Domain, C.S. Becquart, Nucl. Instr. And Meth. B 255(1) (2007) 47-51. [163] C.S. Becquart, C. Domain, J.C. Van Duysen, J.M. Raulot, J. Nucl. Mater. 294(3) (2001) 274-287. [164] M. Lambrecht, L. Malerba, A. Almazouzi, J. Nucl. Mater. 378 (2008) 282-290. [165] L. Malerba, E. van Walle, C. Domain, S. Jumel, J.C. Van Duysen, Proc. of the 10th International Conference on Nuclear Engineering, ICONE-10, The American Society of Mechanical Engineers (2002). [166] A. Vehanen, P. Hautojärvi, J. Johansson, J. Yli-Kauppila, Phys. Rev. B 25 (1982) 762- 780. [167] M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun, K. Farrell, J. Nucl. Mater. 307-311 (2002) 912-917. [168] S. Takaki, J. Fuss, H. Kugler, U. Dedek, H. Schultz, Radiat. Eff. 79 (1983) 87-122. [169] Y. Nagai, K. Takadate, Z. Tang, H. Ohkubo, M. Hasegawa, Proc. 21th International Symposium on The Effect of Radiation on Materials, ed. M L Grossbeck et al., American Society for Testing and Materials, West Conshohocken (2004) 590-602. [170] Y. Nagai, T. Nonaka, M. Hasegawa, Y. Kobayashi, C.L. Wang, W. Zheng, C. Zhang, Phys. Rev. B 60 (1999) 11863-11866. [171] A.C. Nicol, M.L. Jenkins, M.A. Kirk, Proc. of Mat. Res. Soc. Symposium (2000) 50-58. [172] F. Ebrahimi, D.T. Hoelzer, D. Venables, V. Krishnamoorthy, Development of a Mechanistic Understanding of Radiation Embrittlement in Reactor Pressure Vessel Steels - Final Report, Department of Materials Science and Engineering, University of Florida. [173] P. Pareige, B. Radiguet, A. Barbu, J. Nucl. Mater. 352 (2006) 75-79. [174] K. Fukuya, K. Ohno, H. Nakata, S. Dumbill, J.M. Hyde, J. Nucl. Mater. 312 (2003) 163-173. [175] M.K. Miller, M.G. Burke, J. Phys. C 6 (1987) 429-434. [176] M.K. Miller, P. Pareige, Mat. Res. Soc. Symp. 650 (2001) R6.1.1-12. [177] F. Bergner, A. Ulbricht, M. Hernandez-Mayoral, P.K. Pranzas, J. Nucl. Mater. 374 (2008) 334-337. [178] M. Lambrecht, E. Meslin, L. Malerba, M. Hernández-Mayoral, F. Bergner, P. Pareige, B. Radiguet, A. Almazouzi, submitted for publication in J. Nucl. Mater. (2009). [179] P.J. Pareige, K.F. Russell, M.K. Miller, Appl. Surf. Sci. 94/95 (1996) 362-369. [180] R. Chaouadi, Restricted Contract Report SCK•CEN R-3676 (2002). [181] A.J.E. Foreman, M.J. Makin, Can. J. Phys. 45(2) (1967) 511-517. [182] J.P. Hirth, J. Lothe, Theory of Dislocations, second ed., New York: Wiley (1982). [183] By courtesy of Gilles Adjanor (EDF, France). [184] M. Kirk, presented at EPRI MRP/NRC PTS Re-Evaluation Meeting, Rockland, Maryland (2000).
References
[185] G.R. Odette, G.E. Lucas, G. Tedeski, B.D. Wirth, Fusion Materials Semiannual Progress Report for Period Ending (1998) 221. This paper is available online at
[208] M.J. Puska, R.M. Nieminen, J. Phys. F: Met. Phys. 12 (1982) L211-L216. [209] P. Hautojärvi, L. Pöllänen, A. Vehanen, J. Yli-Kauppila, J. Nucl. Mater. 114 (1983) 250-259. [210] G. Dlubek, O. Brümmer, V.S. Mikhalenkov, J. Yli-Kauppila, A. Vehanen, P. Hautojärvi, Cryst. Res. Tech. 19 (1984) 627-631. [211] M.J. Puska, J. Phys.: Condens. Matter 3 (1991) 3455-3469. [212] G. Brauer, M.J. Puska, M. Sob, T. Korhonen, Nucl. Eng. Des. 158 (1995) 149-156. [213] B. Barbiellini, M.J. Puska, T. Korhonen, A. Harju, T. Torsti, R.M. Nieminen, Phys. Rev. B 53 (1996) 16201-16213. [214] P. Hautojärvi, J. Johansson, A. Vehanen, J. Yli-Kauppila, P. Moser, Phys. Rev. Lett. 44 (1980) 1326-1329. [215] A. Hempel, M. Hasegawa, G. Brauer, F. Plazaola, M. Saneyasu, Z. Tang, Proc. 9th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors, ed. F P Ford et al., The Minerals, Metals & Materials Society (1999) 835-844. [216] Y. Nagai, M. Hasegawa, Z. Tang, T. Kanai, M. Saneyasu, Mat. Sci. For. 363-365 (2001) 91-93. [217] Z. Tang, M. Hasegawa, Y. Nagai, M. Saito, Phys. Rev. B 65 (2002) 195108. [218] Y. Nagai, K. Takadate, Z. Tang, H. Ohkubo, H. Sunaga, H. Takizawa, M. Hasegawa, Phys. Rev. B 67 (2003) 224202. [219] Y. Nagai, T. Toyama, Y. Nishiyama, M. Suzuki, Z. Tang, M. Hasegawa, Appl. Phys. Lett. 87 (2005) 261920. [220] C. Domain, C.S. Becquart, Phys. Rev. B 65 (2001) 024103. [221] E. Vincent, C.S. Becquart, C. Domain, Nucl. Instr. and Meth. B 228 (2005) 137-141. [222] P. Asoka-Kumar, J.H. Hartley, R.H. Howell, P.A. Sterne, D. Akers, V. Shah, A. Denison, Acta Mater. 50 (2002) 1761-1770. [223] S. Glade, B.D. Wirth, G.R. Odette, P. Asoka-Kumar, P.A. Sterne, R.H. Howell, Phil. Mag. 85 (2005) 629-639. [224] R.M. Nieminen, J. Laakkonen, P. Hautojärvi, A. Vehanen, Phys. Rev. B 19 (1979) 1397-1402. [225] D. Huguenin, P. Moser, Appl. Phys. A 48 (1989) 583-585. [226] R.M. Nieminen, J. Laakkonen, Appl. Phys. 20 (1979) 181-184.
Author Biography
Marlies Lambrecht was born on the 21st of October 1982 in Kortrijk (Belgium). She obtained the engineering degree in Materials Science at the University of Ghent (Ghent, Belgium) in 2005. Following her studies, she started a PhD at the same university, in collaboration with the Belgian nuclear research centre, SCK•CEN (Belgian Nuclear Research Centre, Mol, Belgium). During this PhD study, she presented her work at many different international conferences (also as invited speaker) and published a number of papers in relevant journals.
List of publications
International reviewed papers: 1. M. Lambrecht, L. Malerba, A. Al Mazouzi, M. Hernández-Mayoral, D. Gómez- Briceño, E. Meslin, B. Radiguet, Ph. Pareige, F. Bergner, "On the correlation between irradiation-induced microstructural features and the hardening of reactor pressure vessel steels.", submitted for publication in J. Nucl. Mater. (2009).
2. E. Meslin, M. Lambrecht, F. Bergner, M. Hernández-Mayoral, A. Al Mazouzi, "Characterization of neutron-irradiated ferritic model alloys and an RPV steel from combined TAP, SANS, TEM and PAS analyses", submitted for publication in J. Nucl. Mater. (2009).
3. M. Lambrecht, A. Al Mazouzi, "Positron defect studies of neutron irradiated iron- based materials.", accepted for publication in J. Eng. Gas Turb. Power. (2009).
4. M. Lambrecht, A. Al Mazouzi, "The influence of irradiation-induced microstructure on the hardening of RPV steels.", accepted for publication in J. Eng. Gas Turb. Power. (2009).
5. M. Lambrecht, A. Al Mazouzi, "Positron defect studies of neutron irradiated iron- based materials.", accepted for publication in J. Phys.: Conference Series (2008).
6. F. Bergner, M. Lambrecht, A. Ulbricht, A. Al Mazouzi, "Comparative small-angle neutron scattering study of neutron-irradiated Fe, Fe-based alloys and a pressure vessel steel.", accepted for publication in J. Nucl. Mater. (2009).
7. M. Lambrecht, A. Al Mazouzi, "Positron annihilation study of neutron irradiated model alloys and a reactor pressure vessel steel.", J. Nucl. Mater. 385 (2009) 334-338, doi: 10.1016/j.jnucmat.2008.12.020.
8. M. Lambrecht, A. Al Mazouzi, "The influence of different chemical elements in the hardening-embrittlement of RPV-steels.", Proceedings of SMINS, Karlruhe, Germany, 4-6 June 2007; OECD Handbook: Nuclear Science "Structural Materials for Innovative Nuclear Systems (SMINS)" (2008) p 457–466, isbn: 9789264048065.
List of publications
9. M. Lambrecht, L. Malerba, A. Almazouzi, "Influence of different chemical elements on irradiation-induced hardening embrittlement of RPV-steels.", J. Nucl. Mater. 378, 282-290 (2008), doi: 10.1016/j.jnucmat.2008.06-030.
10. M. Lambrecht, M. Jardin, A. Al Mazouzi, "Positron annihilation study of neutron irradiated pure Fe and Fe-Cu binary alloys.", Phys. Stat. Sol. (c) 4-10, 3477 (2007), doi: 10.1002/pssc.200675798.
11. M. Jardin, A. Al Mazouzi, M. Lambrecht, A. Rempel, Y. Nagai, E. van Walle, "Digital positron lifetime spectrometer for measurements of radioactive materials.", Phys. Stat. Sol. (c) 4-10, 4001 (2007), doi: 10.1002/pssc.200675816.
12. M. Jardin, M. Lambrecht, A.A. Rempel, Y. Nagai, E. van Walle, A. Almazouzi, "Digital positron lifetime spectrometer for measurements of radioactive materials.", Nucl. Instr. and Meth. A 568-2, 716 (2006), doi: 10.1016/j.nima.2006.08.087.
Reports: 1. M. Lambrecht, A. Al Mazouzi, L. Malerba, Y. Houbaert, "Report on status of PhD research: Advanced experimental techniques for the comprehension of hardening and embrittlement mechanisms in RPV steels.", Status report at SCK•CEN (2008).
2. M. Lambrecht, A. Al Mazouzi, "PAS analysis of neutron irradiated model alloys and an RPV steel.", Internal report of Integrated Project PERFECT (Contract No F160- CT-2003-5088-40) (2008).
3. E. Lucon, M. Lambrecht, M. Scibetta, A. Al Mazouzi, "Preliminary Study to consolidate the Surveillance Program of Santa Maria de Garoña in View of Licence Renewal.", Restricted Contract Report SCK•CEN-R-4540 (2007).
4. M. Lambrecht, M. Konstantinovic, "Microstructural characterization of neutron irradiated Fe-Cu binary alloys. Positron annihilation spectroscopy and internal friction experiment.", Scientific Report of SCK•CEN 2007.
5. M. Lambrecht, A. Al Mazouzi, "The effect of irradiation-induced damage on the hardening-embrittlement of RPV-steels.", Scientific Report of SCK•CEN 2007.
6. M. Lambrecht, A. Al Mazouzi, "Characterization of neutron irradiated samples (REVE matrix): Post-irradiation annealing of selected alloys (Final report).", Internal report of Integrated Project PERFECT (Contract No F160-CT-2003-5088-40) (2007).
7. M. Lambrecht, A. Al Mazouzi, Y. Houbaert, "The effect of irradiation-induced damage on the hardening-embrittlement of RPV-steels.", Proceedings of the 8th FirW PhD Symposium, Ghent, Belgium, 5 December 2007.
8. M. Lambrecht, A. Al Mazouzi, "The influence of the alloying elements in the hardening-embrittlement of RPV-steels studied by positron annihilation spectroscopy.", Proceedings of the 37th Polish Seminar on Positron Annihilation, Ladek Zdroj, Poland, 2-7 September 2007.
9. M. Lambrecht, A. Al Mazouzi, "Characterization of neutron irradiated samples (REVE matrix): Positron annihilation and mechanical properties (Final report).", Internal report of Integrated Project PERFECT (Contract No F160-CT-2003-5088-40) (2007).
10. M. Lambrecht, A. Al Mazouzi, Y. Houbaert, "Advanced experimental techniques for the comprehension of hardening and embrittlement mechanisms in RPV-steels.", Proceedings of the 7th FirW PhD Symposium, Ghent, Belgium, 29 November 2006.
Presentations/Posters: - 23 presentations + 1 invited talk - 8 posters Æ 2 best poster awards
1. Lambrecht M., et al. – Topical day (oral presentation accepted)– Mol, Belgium, 13 May 2009.
2. Lambrecht M., et al. – ICONE 17 (oral presentation accepted) – Brussels, Belgium, 12-16 July 2009.
3. Lambrecht M., et al. – ICONE 17 (poster presentation accepted) – Brussels, Belgium, 12-16 July 2009.
4. Lambrecht M., Al Mazouzi A., Malerba L., Houbaert Y. – "Advanced experimental techniques for the comprehension of hardening and embrittlement in neutron irradiated model alloys and an RPV steel." – Internal Symposium DMSE – Ghent, Belgium, 28 November 2008.
List of publications
5. Lambrecht M., Al Mazouzi A., Malerba L., Houbaert Y. – "Advanced experimental techniques for the comprehension of hardening and embrittlement in neutron irradiated model alloys and an RPV steel." – Day of the PhD's – Mol, Belgium, 21 October 2008.
6. Lambrecht M. – "Brief presentation on my current activities." – Group meeting – Mol, Belgium, 6 October 2008.
7. Lambrecht M., Al Mazouzi A. – "Positron Defect Studies of Neutron Irradiated Iron- Based Materials." – International Workshop on Positron Studies of Defects (PSD-08) – Prague, Czech Republic, 3 September 2008. Æ INVITED TALK
8. Lambrecht M., Al Mazouzi A. – "PAS analysis of neutron irradiated model alloys and an RPV steel." – FP6-IP-PERFECT – Paris, France, 16-20 June 2008.
9. Lambrecht M., Al Mazouzi A. – "Positron annihilation study of neutron irradiated model alloys and an RPV steel." – European Materials Research Society 2008 Spring Meeting – Strasbourg, France, 28 May 2008.
10. Lambrecht M., Malerba L., Al Mazouzi A. – "The role of different irradiation-induced microstructural features on the hardening of RPV steels." – European Materials Research Society 2008 Spring Meeting – Strasbourg, France, 28 May 2008.
11. Lambrecht M. et al. – "Presentation on my work." – Talk at EDF –Les Renardieres, France, 14 February 2008.
12. Lambrecht M., Al Mazouzi A., Malerba L., Houbaert Y. – "Advanced experimental techniques for the comprehension of hardening and embrittlement mechanisms in RPV-steels." – 2nd DM2S PhD Symposium. – Ghent, Belgium, 16 January 2008.
13. Lambrecht M., Al Mazouzi A., Houbaert Y. – "The effect of irradiation-induced damage on the hardening-embrittlement of RPV-steels." – 8th FirW PhD Symposium. – Ghent, Belgium, 5 December 2007.
14. Lambrecht M., Al Mazouzi A., "Characterization of neutron irradiated samples (REVE matrix)." – FP6-IP-PERFECT – Paris, France, 19-20 November 2007.
15. Lambrecht M., Al Mazouzi A., "Post irradiation annealing in selected model alloys." – FP6-IP-PERFECT – Paris, France, 19-20 November 2007.
16. Lambrecht M., Al Mazouzi A., Hernández Mayoral M., Gómez Briceñol D., Meslin E., Barbu A., Pareige P., Radiguet B., Bergner F., Ulbricht A. – "The effect of irradiation- induced damage on the hardening embrittlement of RPV-steels." – International School on Modelling of Irradiation Damage – Rochehaut sur Semois, Belgium, 1-5 October 2007. Æ BEST POSTER AWARD!
17. Lambrecht M., Al Mazouzi A. – "The influence of the alloying elements in the hardening-embrittlement of RPV-steels studied by positron annihilation spectroscopy." – 37th Polish Seminar on Positron Annihilation – Ladek Zdroj, Poland, 2-7 September 2007.
18. Lambrecht M., Al Mazouzi A. – "The influence of different chemical elements in the hardening-embrittlement of RPV-steels." – SMINS – Karlsruhe, Germany, 4-6 June 2007.
19. Al Mazouzi A., Lambrecht M. – "Experimental validation of the multiscale approach to model the irradiation damage in RPV-Steels." – SMINS – Karlsruhe, Germany, 4-6 June 2007.
20. Bergner F., Ulbricht A., Hernandez-Mayoral M., Al Mazouzi A., Lambrecht M. – "Combined TEM, PAS and SANS investigation of neutron-irradiated pure Fe." – SMINS – Karlsruhe, Germany, 4-6 June 2007.
21. Lambrecht M., Al Mazouzi A., Malerba L., Houbaert Y. – "Advanced experimental techniques for the comprehension of hardening and embrittlement mechanisms in RPV-steels." – 1st DM2S PhD Symposium. – Ghent, Belgium, 6 December 2006.
22. Lambrecht M., Al Mazouzi A., Houbaert Y. – "Advanced experimental techniques for the comprehension of hardening and embrittlement mechanisms in RPV-steels." – 7th FirW PhD Symposium. – Ghent, Belgium, 29 November 2006.
23. Lambrecht M., Al Mazouzi A., van Walle E. – "Comparative study between low Cu- RPV-steels and Fe-Ni-Mn and Fe-Cu-Ni-Mn alloys after high dose neutron irradiation." – The 13th Meeting of the International Group on Radiation Damage Mechanisms in Pressure Vessel Steels. – Tsukuba, Japan, 15-20 October 2006.
List of publications
24. Lambrecht M., Jardin M., Al Mazouzi A., van Walle E. – "Positron annihilation study of neutron irradiated pure Fe and Fe-Cu binary alloys." – The 13th Meeting of the International Group on Radiation Damage Mechanisms in Pressure Vessel Steels. – Tsukuba, Japan, 15-20 October 2006.
25. Lambrecht M., Al Mazouzi A. – "Positron annihilation study of neutron irradiated pure Fe and Fe-Cu binary alloys." – International School on Experimental Quantification of Irradiation Damage – Rochehaut sur Semois, Belgium, 25-29 September 2006. Æ BEST POSTER AWARD!
26. Lambrecht M., Jardin M., Al Mazouzi A. – "Positron annihilation study of neutron irradiated pure Fe and Fe-Cu binary alloys." – The XIVth International Conference on Positron Annihilation – Hamilton, Canada, 23-28 July 2006.
27. Jardin M., Al Mazouzi A., Lambrecht M., Rempel A., Nagai Y., van Walle E. – "Digital positron lifetime spectrometer for measurements of radioactive materials." – The XIVth International Conference on Positron Annihilation – Hamilton, Canada, 23-28 July 2006.
28. Al Mazouzi A., Lambrecht M., Jardin M., Malerba L., Lucon E., van Walle E., Scibetta M. – "On the correlation between microstructure and hardening evolution under irradiation of low Cu RPV steel in comparison with model alloys." – E-MRS – Nice, France, 31 Mai 2006.
29. Lambrecht M., Al Mazouzi A., Malerba L., Houbaert Y. – "Advanced experimental techniques for the comprehension of hardening and embrittlement mechanisms in RPV-steels." – DAC – Mol, Belgium, 18 Mai 2006.
30. Al Mazouzi A., Lambrecht M., Jardin M., Malerba L. – "On the correlation between microstructure and hardening evolution under irradiation of low Cu RPV steel in comparison with model alloys." – AMES – Héviz, Hungary, 6-8 February 2006.
31. Al Mazouzi A., Rempel A., Verheyen K., Jardin M., Lambrecht M., Hasegawa M., Nagai Y., Kuriplach J. – "Application of positron annihilation techniques for nuclear materials." – JRC – Bergen, Netherlands, 17 November 2005.
32. Al Mazouzi A., Jardin M., Lambrecht M. – "Quantitative Characterization of the microstructure." – FP6-IP-PERFECT – Paris, France, 18 October 2005.
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