Irradiated Graphite Waste - Stored Energy

A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences

2012

Michael Lasithiotakis

School of Materials Materials Performance Centre

1

2 List of Contents

List of Contents List of Contents 3 List of Figures 5 List of Tables 8 Abstract 9 Declaration 10 Copyright Statement 11 Rationale for Submitting the Thesis in Alternative Format 12 Acknowledgements 13 Dedication 14 Chapter 1 - Introduction and Context of Research 15 Graphite 15 Nuclear reactors 17 Decommissioning of a Nuclear Facility 17 Radioactive Waste-Disposal of Radioactive Waste 17 Wigner Energy – An additional hazard during decommissioning. 21 The Windscale fire event – A nuclear accident that directly involved Wigner energy release 23 Chapter 2 - Literature Review 25 Stored Energy Release 25 Defects 27 Annealing of Defects 32 Kinetics of Stored Energy Release 37 Ion irradiation : A Method to Simulate Irradiation Damage. 48 Chapter 3- Methods 51 Differential Scanning Calorimetry 51 X-ray Diffraction 55 Raman Spectroscopy 62 Chapter 4 - Publication I: Application of an Independent Parallel Reactions Model to the Annealing Kinetics on BEPO Irradiated Graphite 67

3 List of Contents

Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite 68 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite 69 Chapter 7 - General Conclusions and Future Work 70 Bibliography 73

Total Word Count : 43,227 words

4 List of Figures

List of Figures

Figure 1.1. Pg 16. A scheme of the manufacturing stages of nuclear graphite.

Figure 1.2. Pg 18. SRF. Schematic of the Swedish Geological Repository for radioactive operational waste. It is the Swedish central disposal facility for all short lived low-and intermediate level waste from the operation of the nuclear power plants. It is located in granitic rock under the sea close to the Forsmark nuclear power plant, around 1 km offshore and 50 m below the seafloor.

Figure 1.3. Pg 19. Examples of dry cask storage containers. Left: Vertical stand alone dry cask storage containers. Right dry cask storage containers in bunkers.

Figure 1.4. Pg 19. Example of a penetration device used in deep sea experiments.

Chapter 2

Figure 2.1. Pg 28. Schematic of the single vacancy (A, unreconstructed and B, reconstructed.)

Figure 2.2. Pg 28. The Stone Wales topological defect, showing the exchange of positions of interstitial atoms.

Figure 2.3. Pg 28. The metastable intimate Frenkel pair defect symbolised by I+V*.

Figure 2.4. Pg 29. Prismatic (left) and basal (right) dislocation.

Figure 2.5. Pg 29. Transmission Electron Micrographs of pyrolytic graphite. The dislocation network shown above, although not created by neutron irradiation, clearly depict dislocation networks lying in the basal planes.

Figure 2.6. Pg 31. Configurations of the interstitials at the various sites A to E and for the free (F) interstitial as obtained with the first principles calculation package CASTEP and GGA. In Figure the light gray atoms are part of graphite; the interstitial is shown in red. For the high symmetry positions D and the free interstitial the top view is given as well. The inset at the top shows the high symmetry sites for an interstitial in graphite.

5 List of Figures

Figure 2.7 . Pg 33. Migration of a single vacancy.

Figure 2.8. Pg 33. A description of the annealing process by Telling et al.

Figure 2.9. Pg 37. Stored energy accumulation as a function of effective dose.

Figure 2.10. Pg 44. Fitting of energy distribution to data from a Windscale Pile 2 dowel graphitic sample at 10oC/min

Figure 2.11. Pg 44. Comparison of constant activation energy models fitted to Iwata’s experimental date using the variable frequency factors from Iwata’s paper and using a constant frequency factor.

Chapter 3

Figure 3.1. Pg 52. (a) Heat flux DSC; (b) power-compensated DSC.

Figure 3.2. Pg 53. The rate of release of stored energy. Hanford cooled test hole graphite 30oC .

Figure 3.3. Pg 53. The effect of irradiation temperature on the shape of DSC curves. In the diagram above three DSC curves at different irradiation temperatures (150oC, 200oC and 250oC)are depicted (heating rate was 10oC/min).

Figure 3.4. Pg 54. A - Layout of a graphite reactor stack (left) and arrangement of sampling points along height of stack (right, a-m are sampling points) from bricks removed during dismantling of the reactor (single-hatched) and cut out from the stack with the aid of remote controlled drill cutter (double-hatched).

Figure 3.5. Pg 54. Curves of behaviour of stored-energy release: Images 1 to 4: Curves for samples cut out of bricks removed during dismantling of a graphite pile; Images 5 to 8: curves for samples cut from stack with drill cutter. Image 1 to 3: Three samples a,b,c (see previous figure) from brick No. 4 in lattice cell 10-03; Image 4: Sample c from brick No. 7 in cell 06-10; Images 5-8: Samples c, d, e, g from cell 09-03. Depiction [------] refers to sample adjacent to channel. Depiction [-∙-∙-∙-∙-∙-] refers to sample remote from channel; C is the specific heat of unexposed graphite.

6 List of Figures

Figure 3.6. Pg 56. Phase identification between two allotropes of carbon, diamond and graphite[109]. A-The X-ray diffraction intensity for diamond nanoparticles B-The diffraction intensity of diamond nanoparticles with a coating of graphite after heat treatment at 1400°C.C- The diffraction intensity for spherical carbon onions after heat treatment at 1700°C. D-The diffraction intensity for polyhedral carbon onions after heat treatment at 2000°C.

Figure 3.7. Pg 57.X-ray powder diffraction patterns of SP-1 pyrolytic graphite and nuclear graphite sample along with silicon standard. Some of the peaks that appear refer to the graphites while others to the silicon standard.

Figure 3.8. Pg 59.Calculation of Integral Breadth β and Full Width Half Maximum of a specific peak of an XRD pattern.

Figure 3.9. Pg 60. Normalised after Ka2 instrumental broadening subtraction of X-ray diffraction patterns of graphite milled in n-dodecane.

Figure 3.10. Pg 61. Photograph of the open (left) and closed (right) DSC/XRD measuring head. The Pt sample and reference cups are occupied by empty graphite pans. Remnants of a sample are visible on the graphite pan and the sample itself can be seen on the support bracket.

Figure 3.11. Pg 62. Schematic diagram of a Raman spectroscoper.

Figure 3.12. Pg 64. Schematic diagram of the E2g and A1g modes. Carbon motions in the (a) G and (b) D modes. The G mode is just due to the relative motion of sp2 carbon atoms and can be found in chains as well.

Figure 3.13. Pg 65. Two characteristic types of spectra from two graphitic materials.[127] On top, Highly Oriented Pyrolytic Graphite (HOPG) undisturbed, without defects, and glassy carbon, containing defects. The peak at the range of 1340cm-1 is indicative of the presence of defects.

7 List of Tables

List of Tables

Chapter 2

Table 2.1. Pg 27. A summation of various types of defects of graphite, and their symbolism.

Table 2.2. Pg 34. A supposed mechanism of the Wigner energy release in irradiated graphite. C, means interstitial carbon molecules. and V means vacancies. Most energy is released by the annihilation of interstitial C2 molecules and vacancies

Table 2.3. Pg 43. Activation Energy and Pre-exponential factors as calculated by various researchers

Table 2.4. Pg 46. Activation Energy and Pre-exponential factors as calculated by Iwata [4] [2] [54] [45] , Simmons , Lexa et al , and Kelly et al,

Chapter 3

Table 3.1. Pg 58. Lattice parameter of SP-1 and nuclear graphite samples.

Table 3.2. Pg 58. Lattice parameter a, c, as correlated with the degree of graphitization (DOG: g) of the as received IG-110 and IG-430 Japanese types of nuclear graphite.

Table 3.3. Pg 63. A collection of characteristic graphitic peaks.

8 Abstract

The University of Manchester Michael Lasithiotakis

Doctor of Philosophy in Materials Science

Irradiated Graphite Waste - Stored Energy

March 2012

Abstract

The cores of early UK graphite moderated research and production nuclear fission reactors operated at temperatures below 150°C. Due to this low temperature their core graphite contains significant amounts of stored (Wigner) energy that may be released by heating the graphite above the irradiation temperature. This exothermic behavior has lead to a number of decommissioning issues which are related to long term "safe-storage", reactor core dismantling, graphite waste packaging and the final disposal of this irradiated graphite waste. The release of stored energy can be modeled using kinetic models. These models rely on empirical data obtained either from graphite samples irradiated in Material Test Reactors (MTR) or data obtained from small samples obtained from the reactors themselves. Data from these experiments is used to derive activation energies and characteristic functions used in kinetic models.

This present research involved the development of an understanding of the different grades of graphite, relating the accumulation of stored energy to reactor irradiation history and an investigation of historic stored energy data. The release of stored energy under various conditions applicable to decommissioning has been conducted using thermal analysis techniques such as Differential Scanning Calorimetry (DSC). Kinetic models were developed, validated and applied, suitable for the study of stored energy release in irradiated graphite components. A potentially valid method was developed, for determining the stored energy content of graphite components and the kinetics of energy release.

Another parameter investigated in this study was dedicated in the simulation of irradiation damage using ion irradiation. Ion bombardment of small graphite samples is a convenient method of simulating fast neutron irradiation damage. In order to gain confidence that irradiation damage due to ion irradiation is a good model for neutron irradiation damage the properties and microstructure of various grades of ion irradiated nuclear graphite were also investigated.

Raman Spectroscopy was employed to compare the effects of ion bombardment with the reported effects of neutron irradiation on the content of the defects. The changes of the of defect content with thermal annealing of the ion irradiated graphite have been compared with the annealing of neutron irradiated nuclear graphite .

9 Declaration

No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning

The Author

10 Copyright Statement

Copyright Statement

i. The author of this thesis (including any appendices and/or schedules to this thesis) owns any copyright in it (the “Copyright”) and s/he has given The University of Manchester the right to use such Copyright for any administrative, promotional, educational and/or teaching purposes. ii. Copies of this thesis, either in full or in extracts, may be made only in accordance with the regulations of the John Rylands University Library of Manchester. Details of these regulations may be obtained from the Librarian. This page must form part of any such copies made. iii. The ownership of any patents, designs, trade marks and any and all other intellectual property rights except for the Copyright (the “Intellectual Property Rights”) and any reproductions of copyright works, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property Rights and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property Rights and/or Reproductions.

Further information on the conditions under which disclosure, publication and exploitation of this thesis, the Copyright and any Intellectual Property Rights and/or Reproductions described in it may take place is available from the Head of the School of Materials (or the Vice-President).

11 Rationale for Submitting the Thesis in Alternative Format

Rationale for Submitting the Thesis in Alternative Format

This PhD thesis describes the use of the independent parallel reactions kinetic model when applied to three different and very versatile types of data. This is the main reason that the results of the thesis were presented in the alternative format.

In the first publication the independent parallel reactions model is tested against various types of historic data, which all had two things in common: They were linear increase temperature runs, and almost all of them referred to specimens that underwent irradiation at low doses. The rate of release was different at many of the runs; however they were sharing commodities such as the appearance of the 200oC peak (with the exception of two runs) which is indicative of low dose and low temperature of irradiation.

The second publication describes a process where the independent parallel reactions model is applied not in Differential Scanning Calorimetry (DSC) data but in Rama data. Another main difference is that the main variable under procession is not used in its derivative form, but in its integral form. Additionally, ion irradiation as a phenomenon is totally different to neuron irradiation as will be explained further.

The third publication shares more commodities with the first publication since it processes Differential Scanning Calorimetry (DSC) data. However, introduces the idea of isothermal analysis, and emphasizes on it. Additionally it displays an integrated kinetic analysis study to the scientific audience and provides with a procedure of calculation and verification of kinetic parameters. Additionally the data are significantly different in comparison with the first publication, because they are isothermal and they contain DSC curves that develop in higher temperatures as a result of different irradiation history.

12 Acknowledgements

Acknowledgements

The author would like to express gratitude to the following:

 The Greek state Scholarship Foundation, for financial support concerning scholarship, fees, and bench fees.  Professor Barry Marsden and Professor James Marrow for their supervision, support and encouragement during the completion of this PhD thesis.  Dr Stephen Preston and Dr. Mark Kirkham of SERCO Assurance for providing the necessary equipment, logistics, and scientific support for completion of this project.  Dr Abbie Jones, Dr Marc Schmidt, Ms Lorraine McDermott for their help in part of the experimental work.  Dr Andrew Willets and Dr. Anthony Wickham for advice, suggestions and support.  Technical stuff of Materials Science Centre, Dr. Judith Shackletton for valuable assistance during the execution and processing of the XRD measurements, as well as Mr Andrew Forrest for his support in completing the DSC work.  The members of the Nuclear Graphite Research Group, William Bodel, David James, Temi Bakenne, Bereket Hagos, Rosie Holmes, Lewis Luyken, Greg Black, Keyun Wenn, Dr Graham Hall, Dr Kwong-Lai Tsang, Dr Mirnaly Saenz De Miera, Dr. Mahmood Mostafavi, Dr Thorsten Becker, Dr Junia Sumita for their suggestions, their encouragement and their friendship.  Professor Andrew Sherry for providing administrative and financial support for laboratory and consumable costs.  Dr. Nicholas Stevens for help and advice concerning academic affairs.  My very close friends during the course of the PhD, Dr Abdulla Faisal Al Shater, Dr. Yannis Bonnis, Dr Anestis Vlysidis, Dr Bostjan Hari, Dr. Gaetano Palumbo, Dr Sallah Rahimi and Dr. Vargese Chacko Nettikaden, for help in academic as well as life matters.  My very close colleagues at the Materials Performance Centre, Dr. John Francis, Dr. Fabio Scenini, Dr. Dirk Engelberg, Dr. Jonathan Duff, Dr. Teruo Hasimoto, Dr. Kuveshni Govender, and Dr. Francisco Jose Garcia Garcia, also for the above.  Special thanks to technical stuff of The Mill and Pariser, Paul Jordan, Stephen Blatch, and Paul Townsend, for their every day technical assistance.  The administrative stuff member of the Mill, Mrs Olwen Richert, and all the Mill administrative stuff for doing their job properly, as well as for breaking the rules when someone needed help.  Finally I would like to thank the Corrosion and Protection gang members that enriched my everyday life with their friendship and acquaintance and gave me wonderful memories to reminisce.

13 Dedication

Dedicated to my father, mother and sister, my aunt Fotini, and in memory of my beloved aunt, Anna Lasithiotaki

14 Chapter 1 Introduction and Context of Research

Chapter 1 Introduction and Context of Research Graphite Graphite is one of the carbon allotropes [1]. Unlike diamond, graphite is an electrical conductor due to its sp2 hybridism that allows electron flow between the graphitic planes. Natural graphite may be considered the highest grade of coal, just above anthracite, thus it is often called meta-anthracite, although it is not used as fuel because it is very difficult to ignite [1].

Graphite follows a rhombohedral Bravais lattice and crystallizes by the hexagonal crystal system with lattice parameters of a=2.4612 Å (Angstroms) and c=6.7079 Å. According to [2] Wyckoff (Wyckoff Vol I, p 26, in ), graphite may be either flat, space group P63/mmc

(#194) or buckled, space group P63mc (#186). If it is buckled, the buckling parameter is small, less than 1/20 of the c parameter of the hexagonal unit cell.

In 1942 Enrico Fermi used graphite as a neutron moderator in an unsuccessful attempt to create a self sustaining nuclear reaction. Other tests were carried out in USA and USSR leading to similar but more successful results [1].

Graphite is an important structural material for the construction of graphite moderated nuclear reactors. It is one of the purest materials manufactured at industrial scale because it retains its properties at high temperatures.

Due to neutron bombardment, large changes in many properties of graphite need to be taken into account during design of graphite components of nuclear reactors, and not all effects are well understood yet. Despite that, graphite reactors have successfully operated in the last 60 years. Two major incidents (Chernobyl disaster and Windscale fires) involved graphite reactors. The Chernobyl incident did not directly involve graphite failure but the Windscale fire was caused by overheating of fuel elements during the uncontrolled release of stored energy that was accumulated in graphitic components, which led to fuel cladding damage and a uranium fire.

15 Chapter 1 Introduction and Context of Research

Nuclear graphite is manufactured using the same production techniques as graphite electrodes, with special attention given to purity. The main constituent is the filler, generally a petroleum or natural based coke. A hydrocarbon based binder is mixed with the blended filler particles and formed into the required shape using extrusion or pressing. This is then baked at ≈1000 C (calcination) and impregnated with pitch to increase its density. Further heating to ≈2800°C graphitizes the material, and after cooling, it will be machined to its required dimensions. [2,3]

RAW PETROLEUM OR PITCH COKE

CALCINED AT 1300°C

CALCINED COKE

CRUSHED, GROUND & BLENDED

BLENDED PARTICLES PITCH

MIXED

EXTRUDED OR MOULDED

COOLED

GREEN ARTICLE

BAKED AT ~1000°C

BAKED ARTICLE

IMPREGNATED WITH PITCH

FURTHER IMPREGNATION AND BAKING AS REQUIRED

GRAPHITISED AT ~2800°C

GRAPHITE

Figure 1.1. A scheme of the manufacturing stages of nuclear graphite [1,2]

16 Chapter 1 Introduction and Context of Research

Research on the influence of fast neutron radiation on strength, thermal expansion, dimensional stability, electrical and thermal conductivity, the storage of internal energy (Wigner energy) and other properties has been carried out since the early 1940s.

Nuclear reactors Decommissioning of a Nuclear Facility Nuclear power stations have a life limit of 30 to 40 years for older generations and it is propose for design lives of up to 60 years for newer designs[4]. At the end of their life all reactors need to be decommissioned and demolished so that the site can be made available for other uses.

International Atomic Energy Agency defined five stages of decommissioning of a nuclear facility[4]. These stages can be described broadly as 1) Plant cleanout 2) Decontamination 3) Dismantling, 4) Demolition and Site Clearance, 5) De-licensing and Release of the Site to alternative use.

Radioactive Waste-Disposal of Radioactive Waste

The concentration and level of radioactivity in the waste produced by decommissioning determines how the waste is treated. Due to International Atomic Energy Agency [4,5] there are three main categories of radioactive waste dealt with by the nuclear industry

1. High Level Waste (HLW) Wastes which produce heat due to their radioactivity. This factor has to be taken into account in the design of storage or final disposal facilities. 2. Intermediate Level Waste (ILW) Wastes that do not need the heat release be taken into account in the design of storage or disposal facilities, but unsuitable for ordinary disposal and have a lower limit of radioactivity of 4 GBq/ tone. 3. Low Level Waste (LLW) Wastes with limited radioactivity (4GBq/tone of alpha or 12 GBq/tone of beta/gamma activity).

17 Chapter 1 Introduction and Context of Research

A fourth category, called Very Low Level Waste [4] (VLLW), can be issued for waste that can be disposed as conventional waste, if the amounts are less than 0.1 m3 and their radioactivity is below 400 kBq of beta/gamma activity or single items containing less than 40 kBq.

The categorization of graphite is still an issue under dispute since the presence of radionuclides (mainly tritium, 60Co and 14C) [6,7] classifies the nature of graphite as an intermediate level waste and as such it is considered by the British nuclear regulations [4]. The probability of Wigner energy release adds arguments to the above. Despite that, graphite is at present considered as low level waste by the French regulations, and therefore becomes suitable for shallow geological disposal.

The following are most of the different possible methods of treating and disposing of nuclear waste: Deep geological repository.[8] A deep geological repository is a nuclear waste repository excavated below 300 metres (980 ft) within a stable geologic environment. It entails a combination of waste form, waste package, engineered seals and geology that is suited to provide a high level of long-term isolation and containment without future maintenance.

Figure 1.2. Schematic of the Swedish Geological Repository (SRF in Swedish, Slutförvar för Radioaktivt Forsmarks) for radioactive operational waste. It is the Swedish central disposal facility for all short lived low-and intermediate level waste from the operation of the nuclear power plants. It is located in granitic rock under the sea close to the Forsmark nuclear power plant, around 1 km offshore and 50 m below the seafloor[9].

18 Chapter 1 Introduction and Context of Research

Dry cask storage[10]. Dry cask storage is a method of storing high-level radioactive waste, such as spent nuclear fuel that has already been cooled in the spent fuel pool for at least one year. The fuel is surrounded by inert gas inside a large container. Usually they are cylinders that are either welded or bolted closed. Ideally, the steel cylinder provides leak- tight containment of the spent fuel. Each cylinder is surrounded by additional steel, concrete, or other material to provide radiation shielding to workers and members of the public. Some of the cask designs can be used for both storage and transportation.

Figure 1.3. Examples of dry cask storage containers. Left: Vertical stand alone dry cask storage containers. Right dry cask storage containers in bunkers. [9].

Ducrete[11]. Ducrete is a version of concrete investigated for use for construction of casks for storage of radioactive waste. It is a composite material with depleted uranium dioxide aggregate used instead of conventional gravel and a Portland cement binder.

Ocean floor disposal[12]. Ocean floor disposal is a method of sequestering radioactive waste in ocean floor sediment where it is unlikely to be disturbed either geologically or by human activity. Several methods of depositing material in the ocean floor have been

Figure 1.4. Example of a penetration device used in deep sea experiments.[12]

19 Chapter 1 Introduction and Context of Research proposed, including encasing it in concrete and as the United Kingdom has previously done, dropping it in torpedoes designed to increase the depth of penetration into the ocean floor, or depositing containers in shafts drilled with techniques similar to those used in oil exploration.

Saltcrete. [13] Saltcrete is a mixture of cement with salts and brine, usually originating from liquid waste treatment plants. Its role is to immobilize hazardous waste and in some cases lower-level radioactive waste in the form of solid material. It is a form of mixed waste. Saltcrete is being replaced by saltstone, which is less permeable and leachable. Saltstone is a mixture of the salt cake (mostly sodium nitrate and other salts) with concrete and fly ash.

Spent fuel pool [14]. Spent fuel pools (SFP) are storage pools for spent fuel from nuclear reactors. Typically 40 or more feet deep, with the bottom 14 feet equipped with storage racks designed to hold fuel assemblies removed from the reactor. These fuel pools are specially designed at the reactor in which the fuel was used and situated at the reactor site. In many countries, the fuel assemblies, after being in the reactor for 3 to 6 years, are stored underwater for 10 to 20 years before being sent for reprocessing or dry cask storage. The water cools the fuel and provides shielding from radiation.

Synroc [15]. Synroc, a portmanteau of "synthetic rock", is a means of safely storing radioactive waste. It was pioneered in 1978 by a team led by Dr Ted Ringwood at the Australian National University, with further research undertaken in collaboration with Australian Nuclear Science and Technology Organization (ANSTO) at research laboratories in Lucas Heights.

Nuclear transmutation[16]. Nuclear transmutation is the conversion of one chemical element or isotope into another, which occurs through nuclear reactions. Natural transmutation occurs when radioactive elements spontaneously decay over a long period of time and transform into other more stable elements. Artificial transmutation occurs in machinery that has enough energy to cause changes in the nuclear structure of the elements. Machines that can cause artificial transmutation include particle accelerators and tokamak reactors as well as conventional fission power reactors. Nuclear

20 Chapter 1 Introduction and Context of Research transmutation is considered as a possible mechanism for reducing the volume and hazard of radioactive waste.

Waste Isolation Pilot Plant[17]. The Waste Isolation Pilot Plant, or WIPP, is the world's third deep geological repository (after closure of Germany’s Repository and the Schacht Asse II Salt Mine) licensed to permanently dispose of transuranic radioactive waste for 10000 years that is left from the research and production of nuclear weapons. It is located approximately 26 miles (42 km) east of Carlsbad, New Mexico.

Wigner Energy – An additional hazard during decommissioning

Eugene P. Wigner in 1942 studied the displacement of atoms in solids caused by neutron irradiation, and proposed a phenomenon known as Wigner effect [5]. The Wigner effect describes the alterations produced by fast particles (such as fast neutrons) on crystalline solids suggesting that neutrons can displace atoms from lattice positions, affecting most of the solid properties. This effect is of most concern in graphite moderators which receive considerable displacement damage. The basic assumption suggested that during operation of a reactor enough energy would be deposited in the graphite to open all the chemical bonds several times. Even the possibility that the graphite parts might break into small pieces could not be ruled out at the time.

It is now known that fast neutron damage causes dimensional changes and changes to Young’s modulus, coefficient of thermal expansion, thermal conductivity, electrical conductivity and also stores energy in the crystalline lattice. Additionally graphite “creeps” when under combined load and irradiation.

The main reason behind the occurrence of these phenomena lies in collisions of neutrons and atoms. Neutrons that collide with the atoms of the lattice will create a cascade of displacements in a matrix via elastic or inelastic collisions, and produce defects. Some of these atoms that come to rest in non-ideal locations, have an energy associated with them, which qualitatively can be characterized as potential energy. This energy contained inside the lattice is called Wigner energy. Large amounts of defects that accumulated pose a risk

21 Chapter 1 Introduction and Context of Research of releasing all of their energy suddenly. Sudden increases in temperature are an issue for nuclear reactors while in operation or under decommissioning.

Estimates of the graphitic waste that will be produced from the decommissioning of the first and second generation nuclear reactors of the UK (mainly Magnox and Advanced Gas-cooled reactors, AGRs) raise this number to 90000 tonnes of graphitic waste. More specifically, according to the Nuclear Decommissioning Authority (NDA)[18], around 56,000 tonnes Magnox, 25,000 tonnes AGR and other quantities of graphite from other various sites (e.g. the Windscale piles and other experimental reactors) add up to the number of 90,000 tonnes of nuclear waste graphite, only in the UK. This number is relatively high for a single country [19, 20], therefore decommissioning is a long standing problem to be dealt with in the UK, and it will involve advanced techniques of rector core dismantling, transportation and final storage of the graphitic waste, as well as the management complications that will arise from an operation of such magnitude.

The main problems arise from the large volumes of the waste. Irradiated graphite, which is regarded as Intermediate Level Waste, will be packaged and transported to deep geological repositories for final disposal. It is planned to provide a deep geological disposal site designed to suitable standards of safety, contamination and other environmental issues, as well as cost related issues.[21]

The possibility of Wigner Energy release during handling, adds an additional parameter in choosing an adequate method of reactor core dismantling, transportation of material and final disposal. As previously discussed the first graphite moderated reactors constructed in the UK operated at temperatures below 150oC whilst the next generation (Magnox and AGR) were designed to operate at temperatures above this. It is generally assumed that the higher the temperature the less stored energy is accumulated due to annealing effects. The amount of stored energy in an AGR is insignificant, however in some parts of the Magnox reactors significant amounts of stored energy may accumulate. However, the stored energy stored in Magnox reactors will not lead to a sustainable

22 Chapter 1 Introduction and Context of Research release as the rate of release in Magnox graphite is always less than the specific heat of graphite.

The Windscale fire event – A nuclear accident that directly involved Wigner energy release.

Graphite reactors have successfully operated in the last 60 years. However two major [22-25] incidents (Chernobyl disaster and Windscale fire) involved graphite reactors . The Chernobyl incident did not directly involve graphite failure but the Windscale fire was caused by uncontrolled release of stored energy. This led to overheating of the graphite core, damaged the fuel cladding, oxidised the uranium metal fuel and eventually led to a uranium fire.

The Windscale fire event is classified as the second most serious accident in nuclear power history after the Chernobyl explosion in Ukraine, and the worst nuclear accident in [22-25] Great Britain . It involved a British nuclear reactor at Windscale, Cumberland (nowadays known as Sellafield, Cumbria). The Windscale fire accident was directly attributed to a routinely planned Wigner energy release, in one of the two reactors operating at the site (Windscale Pile I).

When the Windscale reactors were built, there was little knowledge available about the effects of Wigner energy release and other changes in graphite due to neutron irradiation. Shortly after the Windscale Piles went critical, an inexplicable temperature rise phenomenon occurred, that was later on attributed to the release of Wigner energy accumulation in the graphite cores. In order to secure the safe performance of the reactors, operating engineers decided to perform consecutive annealing procedures. The reactor was heat treated at around 250oC using “nuclear heating” in order to restore the neutron damage in the graphite core [25]. During the anneal Wigner energy was gradually released as heat, which it was hoped would spread throughout the core. The aim of annealing was to prevent accumulation of Wigner energy that had been initiated by the previous operational stage [25]. Initially the engineer’s efforts were reasonably successful, although some pockets in the core remained un-annealed due to a low thermal

23 Chapter 1 Introduction and Context of Research conductivity of the graphite. However, the reactor designers had not seen the need to anneal the cores, therefore the measuring instrumentation, the design of the reactor itself and the cooling system were not ideal for this operation. In addition the nature of the irradiation damage to the graphite was such that each annealing stage required slightly higher temperatures and annealing out the damage became progressively more difficult.

Additionally pockets within the reactor had been observed to contain significant amounts of Wigner energy that it was not feasible to anneal at previous stages. Thermocouples did not comprehensively cover the whole of the reactor core, as the need for annealing had not been predicted [23]. The thermocouples were installed at the zones of peak operating temperatures which did not necessarily coincide with zones of maximum accumulation of stored energy.

Furthermore, during annealing (and operation) air was directly supplied into the reactor, as a cooling medium, and graphite and uranium metal will oxidize in air, increasing the possibility of a fire hazard. In addition the fuel element caps were soldered using a lead based solder with a relatively low melting point[22-25].

It was during one of the planned anneals, on the 7th of October 1957, that Windscale Pile I set on fire, causing the permanent damage of the reactor and the release of radionuclides over the immediate territory around the Windscale site.

When the accident took place though, graphite did not massively oxidize (only parts of the graphite core directly next to the oxidising uranium that ignited were damaged). What caught fire was the fuel elements that consisted of uranium metal, which is also flammable to air after reaching of a certain temperature (170oC in air under certain conditions[26]). In later reactors uranium oxide fuel is used as it considered safer.

The aftermath of the incident lead to the necessity of gaining better knowledge about the nature and characteristics of Wigner energy accumulation and its release.

24 Chapter 2 Literature Review

Chapter 2 Literature Review

Stored Energy Release

The mechanism of reducing defects by thermal relaxation is described as an annealing process, and is followed by the release of the surplus energy that accumulated in the lattice. This is effectively the Wigner energy that has been accumulated in graphite during irradiation. Wigner energy can be expressed as the summation of the energy of the number of the defects.

[27-32] Many measurements of Wigner energy release have been undertaken , mostly, before the advent of modern computational facilities for data analysis. These measurements were aimed at assessing the parameters of the annealing process in reactors operating at low temperatures for use in safety assessments.

A description of the behaviour of the samples over a wide range of experimental conditions is required in order to have confidence in the ability to predict the behaviour outside the domain of experimental investigation. Such a wide database can be used to establish a deeper insight into the processes involved.

The problem with most of the data is that although the irradiation time (fluence) and temperature of the samples in which stored energy was measured is known, the affect of the annealing programmes on the subsequent behaviour of the samples is not well understood.

There have been numerous attempts [29-35] to measure Wigner energy release over the years. Researchers have also tried to correlate the irradiation conditions such as fluence and temperature with overall energy released, with marginal success. The magnitude of Wigner energy in graphite was first measured using a simple DTA apparatus [33]. Samples irradiated at the Oak Ridge graphite pile operating at 54 MW/day at a temperature lower

25 Chapter 2 Literature Review than 100 C and at 175 MW/day at a temperature lower than 130 C exhibited an energy release of 9 Jg−1 and 29Jg−1, respectively, when heated from room temperature to 300 C at 2 C min−1. Heating to 500 C increased these values by an estimated 10%. Iwata[30] investigated the magnitude and the kinetics of the Wigner energy release from graphite irradiated to a fluence of 4×1017ncm−2 at around 80°C by Differential Scanning Calorimetry (DSC) between room temperature and 350 C at heating rates from 1 to 100°Cmin−1 calculating a value of 8±1Jg−1 . Preston et al. [34] have measured samples from a Windscale Pile 2 dowel1 by Differential Scanning Calorimetry (DSC) between 40 and 150°C at heating rates between 0.1 and 30 Cmin−1 followed by an isothermal stage at the final temperature. The highest Wigner energy release observed by them was 135 Jg−1. They heated a sample to 600°C at 10 C/min−1 and observed a Wigner energy release of 262 Jg−1. Unfortunately, the dose history and location of the dowel in the Pile are unknown in order to make correlations with the irradiation dose. Additionally, all specimens taken from the Windscale Piles have received several annealing cycles while in use. Wörner et al. [35] studied Wigner energy release from Windscale Pile 2 graphite by DSC between 50 and 400 C at 25 C/min−1. They found that for a sample with a Wigner energy release of 220 Jg−1 between 50 and 500 C, the fraction of energy released by heating to 300 C is 90%. Based on the above they proposed treatment of the Windscale Pile graphite by heating to 300°C for 30min as a more economically feasible alternative way of restoring irradiation damage that would additionally result in lower 3H emissions. The 3H emissions parameter they have also examined. The above conclusion, Lexa et al. [29] applied when they performed their own sets of experiments.

In conclusion, there are a lot of controversial approaches regarding the results from Wigner energy release experiments. This can be attributed to the variety of irradiation conditions taking place (Temperature, irradiation dose). The history of the samples is also another important parameter (eg. sample annealing history). Finally the various

1 A graphite dowel is a bar of graphite originally located in the isotope channels in order to increase moderation and restrict coolant flow. They were pushed out of the pile from time to time in order to make way for isotopes or to make measurements of stored energy accumulation. This particular dowel was found in lying the air duct during clean-up operations. Therefore its irradiation the history was not known.

26 Chapter 2 Literature Review approaches regarding the annealing test itself, (heating program, devices used etc.) reveals the different scope of every individual research.

Defects

The source of Wigner energy is the defects that are created in graphite by neutrons. Neutrons that collide with carbon atoms must have enough energy to displace them from the lattice to create defects. Fast neutrons with a significant amount of energy, above about 0.1MeV (a thermal reactor has neutron energies up to about 10 MeV, with an average of around 2MeV) will create a cascade of displacements in a matrix via elastic collisions (a 1 MeV neutron striking graphite can create 900 displacements).[36]

Carbon atoms that come to rest in non-ideal locations are referred to as interstitial atoms or simply interstitials and have an associated potential energy. This energy, when released, is Wigner energy. The damaged regions of the graphitic lattice that are left behind the displaced atoms are characteristic molecular gaps which are named vacancies. Vacancies can effectively move trough the lattice but are less mobile than the interstitials, which can also move.

The simplest defect type is the Frenkel pair which is a combination of a vacancy and an interstitial, as described previously[37]. More complicated structures have been described [37] such as the did-vacancies, did-interstitials, the metastable NN third did-vacancies, first and second interplanar di-vacancies and the Stone-Wales defects (Metastable defects with interstitials exchanging positions) (Table 2.1 and Figures 2.1, 2.2 and 2.3).

Table 2.1. A summation of various types of defects of graphite, and their symbolism [36].

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Figure 2.1. Schematic of the single vacancy (A, unreconstructed and B, reconstructed.) [36].

Figure 2.2. The Stone Wales topological defect, where there is an exchange of positions between atoms that do not emigrate and remain in the same ring[36].

Figure 2.3. The metastable intimate Frenkel pair defect symbolised by I+V*.[36]

The description of the results of the formation process of the defects is still a subject of research. The atomistic-level details of structure and interaction are now only starting to be better understood. The base from which all researchers start is the impact of the formation of the simplest type, the Frenkel pair (V-I). Despite that, the scenarios for the formation process and the mobility of defects vary. A more complicated phenomenon that needs to be taken into account is that the defects migrate and agglomerate, producing

28 Chapter 2 Literature Review layer dislocations (with more characteristic the prismatic and the basal dislocation, Figure 2.4). Consequently they have a longer term impact on the carbon structure that leads to further changes in internal energy, microstructure and physical properties.

Figure 2.4. Prismatic (left) and basal (right) dislocation [36] on the graphitic planes.

Figure 2.5. Transmission Electron Micrographs of pyrolytic graphite. The dislocation network shown above, although not created by neutron irradiation, clearly depicts dislocation networks lying in the basal planes. [38]

Telling et al [36, 39] present findings on the structure, formation activation energies and behaviour of defects in irradiated graphitic carbon materials (Table 2.1). According to these authors, defect production is generally a result of changes in internal energy, with affects in microstructure and physical properties. Another area of investigation by Telling et al. [39] is the study of defects produced using electron beams. They studied the irradiation effects by applying control upon irradiation parameters, with a scope to invent a method to engineer the properties of carbon nanostructures. In both cases they used computational and not experimental methods of damage investigation (the tools of density functional theory) and applied it to a model system of perfect crystalline graphite. They used first-principles calculations, to track the details in the behaviour of defects.

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Niwase [40] focuses on the migration rather than formation of defects and the alteration of grain boundaries. He proposes a possible formation process of the di-interstitial, the accumulation of which, leads to the destruction of the long range order of graphite. Niwase [40] claimed that after knock-ons, di-vacancies and dislocation dipoles are reconstructed at the ends of crystallites.

Antonio da Silva et al. [41] studied two types of defects: (i) the Wigner defect in graphite and (ii) a vacancy in an isolated nanotube. They also study the defect’s stability, indicating that the defect is significantly more stable in nanotubes bundles than in graphite. The above could indicate that the lower the crystalline size, the better the defect stability. Their scope though is to clearly engineer the defects in order to be used as conjunctive elements in carbon nanomaterials.

From all the above studies mentioned, it is generally admitted that at the start of irradiation the crystalline changes are associated with interstitial and vacancy defects, but the progressive migration, aggregation and inter-conversion of al those different types of defects and dislocations create a complex defect system. Conclusively, the crystalline change due to irradiation refers to a very complicated phenomenon. The bulk structure of a polycrystalline material such as nuclear graphite adds with additional degrees of complexity, and out of the engineering point of view it is hypothetically better to be studied with statistical values.

The topology of the defects is also another area of interest. Asari et al. [42-44] assume that there is no interaction between the layers during the production of the defects. The produced defects are distributed between the layers and the interstitial atoms do not bridge the gap between them. However, Li et al.[45] claim the exact opposite, stating that there are cases that interstitial atoms come to rest to pre fixed positions between the layers. (Figure 2.6).

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[45] Figure 2.6 . Configurations of the interstitials at the various sites A to E and for the free (F) interstitial as obtained with a first principles calculation package. In the Figure the light gray (red) atoms are part of graphite; the interstitial is shown in red. For the high symmetry positions D and the free interstitial the top view is given as well. The inset at the top shows the high symmetry sites for an interstitial in graphite.

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A summary of the defect categories as well as their formation mechanism, was attempted by Kelly et al [46] and is presented below:

(a) Circular or hexagonal dislocation loops. These loops grow with increasing radiation dose but do not increase in number after a relatively small nucleation dose. Vacancy loops of similar form, but not necessarily fully collapsed, occur at irradiation temperatures above 650°C; these loops are often associated with the larger interstitial loops, e.g. they descriptively “decorate” them. The number of interstitial loops is known to depend upon the displacement rate, temperature and impurity content [47].

(b) Lattice vacancies in the form of single vacancies which can trap diffusing interstitials, and collapsed lines of vacancies which contract the basal planes and which, to a good approximation, do not absorb diffusing interstitial atoms [48,49].

(c) Crystallite boundaries perpendicular to the basal planes defining a crystallite size La, parallel to the basal planes, in which diffusing vacancies can be trapped and collapse to contract the basal planes. The boundaries are assumed not to accept interstitials.

Physical characteristics of the solid are also being altered by this displacement of atoms at non-lattice points and the creation of the vacancies. As a result, there is a decrease in thermal conductivity, an increase in elastic modulus, a change in a and c lattice parameters, and also in electrical resistance, breaking strength et.c.[33].

Annealing of Defects.

The mechanism of reducing defects by thermal relaxation is generally referred as the annealing process, and is followed by the release of the surplus energy that accumulated in the lattice. This is effectively the Wigner energy and is the total increase of the system during irradiation. Wigner energy can be expressed as the summation of the potential energy of the number of the defects.

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Efforts to describe the mechanisms for reducing of defects by thermal relaxation have been attempted by some researchers, leading to different scenarios. Some researchers propose a more general mechanism, while others are even attempting to describe the process with exact reactions. The overall procedure is generally assumed to initiate by the migration and diffusion of interstitials and vacancies[36] (Figure 2.7).

Figure 2.7 . Migration of a single vacancy.[36]

[36] Figure 2.8. A description of the annealing process by Telling et al . I2 is the di- interstitial, a duplication of the single interstitial.

Iwata [30] proposed another more complex mechanism, based on vacancies and interstitials. (Table 2.2). Asari, et al. [44] also suggests that the thermal relaxation of lattice disorder consists of three relaxation stages. Stage I is dominated by the recombination of single-vacancies and single-interstitials through the diffusion of single-interstitials. Stage II is dominated by the recombination process of single-vacancies and di-interstitials. Stage III is dominated by combination of other slower processes, like clustering of single-

33 Chapter 2 Literature Review vacancies and/or related process of migration of larger interstitial clusters and vacancies clusters.

Table 2.2. A supposed mechanism of the Wigner energy release in irradiated graphite as proposed by Iwata [30]. C, means interstitial carbon molecules. and V means vacancies.

Most energy is released by the annihilation of interstitial C2 molecules and vacancies

Elsewhere, Asari, et al [42] propose a more complicated mechanism of annealing with four stages which briefly are (i) vacancy diffusion to grain boundaries (ii) recovery of bond angle distortion, e.g. sp3 to sp2, (iii) vacancy clustering due to diffusion of vacancies on the graphite plane, and (iv) recombination process between vacancies and interstitials through the diffusion of interstitial atoms in graphite planes. Processes (i) and (ii) are regarded as first order reactions for reducing defects, while (iii) and (iv) are second order reactions.

Kolling et al [50] focused on dislocations and claimed that they can be examined by the use of the concept of generalized driving forces which act on the defect. A statistical and a deterministic approach were proposed. An approach on the thermodynamic driving forces on defects were computed with analytical methods in anisotropic materials. Finite element methods were also used to compare with analytical and semi-analytical solutions. They proposed a simple constitutive kinetic law to relate this force with the velocity of the defect.

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Ewels et al [38, 51] examined structures and recombination routes for interstitial vacancy (I- V) pairs in graphite. Among their findings is that interaction results in the formation of a new metastable defect (an intimate I-V pair) or a Stone-Wales defect. Similar defects are expected to form in carbon nanostructures such as nanotubes, nested fullerenes, and onions under irradiation. In summary, they claim that irradiation of graphite results in the production of I-V pairs and depending on the structure of the interstitial, these interact to form either an intimate I-V pair or a Stone-Wales defect. For the majority of cases this defect represents a final barrier to recombination which must be overcome, and they suggest this complex to be the cause of the major 200oC Wigner energy release peak in graphite.

Fast neutron fluence is the key element of quantitative assessments regarding irradiation damage and consequently Wigner energy release. As Early as 1942 Wigner[52] proved that fast neutrons in the fission of uranium fuel are supplied with enough energy to displace around 2×104 carbon atoms per neutron while Seitz[53] calculated this number closer to around 2×103.

Fluence and irradiation temperature as a correlation of Wigner energy accumulation and release have been reviewed by Kelly et al[45]. They assumed that Wigner energy accumulation reaches a saturation point at higher fast neuron fluence. Irradiation temperature is also assumed to play a role, with rate of energy accumulation decreasing with increasing temperature. A correlation between the fast-neutron fluence Φf was attempted, and the number of atoms displaced, i.e., the number of Frenkel defects formed, is provided by the displacement cross section, σd: [45] nF=σd·Φf (2.1)

nF is the displacements per atom (dpa).

Other researchers [53] proposed a simple mathematic formula between Wigner energy, −1 ΔHWigner (Jg ), Frenkel defect energy, hF (eV), and number of Frenkel defects nF:

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M C Wigner nF   19 (2.2) N A 1.60210 hF -19 where NA is Avogadro’s number, 1.602x10 comes form the charge of the electron, and

MC is the molecular weight of graphite. This equation enables the calculation of dpa

(displacements per atom) from experimentally measured ΔHWigner and the theoretical value of Frenkel defect energy hF.

The recombination of interstitials and vacancies, also known as Frenkel pairs, is considered to be the initial step of Wigner energy release [36]. The recombination of the intimate Frenkel pair is specifically suggested as the initial cause of the Wigner energy release peak which has been observed in Differential Scanning Calorimetry (DSC) measurements at around 200oC

Thrower and Mayer [55] reviewed the potential energy of a widely spaced Frenkel pair and calculated it as 14±1 eV. In their study based on quantum-mechanic theory, Telling et al. [56] calculated the energy released in a Frenkel pair recombination as 13–15eV per pair. In another work they concluded that a number of defect species form strong covalent bonds between the graphite atomic layers forms[39]. They also introduced a close-bound or intimate Frenkel pair with an energy of formation of 10.6eV. In another quantum- mechanical study, Ewels et al. [57] calculated the energy of formation of a widely separated Frenkel pair as 13.7eV, while that of the intimate Frenkel pair is given as 10.8eV.

Mitchell et al [58] conducted studies on electron-irradiated graphite. They calculated the

Frenkel pair energy is 13.5 eV for an atomic displacement energy of Ed = 60 eV. The work of Bochirol et al.[59] ,and later on Bonjour[60] ,yielded Frenkel pair formation energies of 9.5 and 8.5 eV, respectively. The determinations of Frenkel pair energy from Wigner energy measurements[58-61] have been reviewed by Thrower et al [55]. Their result, [58-70] 14 ± 1 eV for a displacement energy Ed = 40 eV is in accordance with other studies . From the above studies a Frenkel paid energy around 10-15 eV should be expected.

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Brocklehurst et al. [71] and Bell et al [72] produced a graph correlating the total Wigner energy yield with irradiation dose. (Figure 2.9).

Figure 2.9. Stored energy accumulation as a function of effective dose, A: by Bell et al [74], and B: by Brocklehurst et al[72].

Kinetics of Stored Energy Release

The release of Wigner energy can be described using chemical kinetic models. These models rely on empirical data obtained either from graphite samples irradiated in material test reactors or data obtained from small samples obtained from the reactors themselves.

Data from these experiments is used to derive activation energies and characteristic functions used in kinetic models. The thermal annealing of graphite is understood through the use of kinetic models that essentially require determination of the activation energy Ea and pre-exponential factor A in the Arrhenius equation. The activation energy Ea refers to the energy barrier needed to overcome in order to make the annealing procedure-reaction self sustainable.

The basic relation from which all the kinetic approaches begin is the following [28-32,73-76]:

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dx  kf (x) (2.3) dt where x is a variable that follows the Arrhenius distribution with linear increase of time, f(x) is a mathematical function of x, which characterizes the sample, and k is the constant of proportionality. In the annealing kinetics of Wigner energy release x = S, where S is the energy released during the linear increase of temperature in a DSC experiment. Various forms of the functions f(x) have been considered, such as f(x) = x, which is the simplest, the function f(x) = xn is used to consider a reaction of n-th order, and the most complex is, f(x) = xn (1-qx) m [68]. In addition variations of these have been considered, e.g. f(x) = x(1-x) with n, q, m=1. In the annealing kinetics of graphite, it has been generally assumed by previous researchers [27,28,30,73,74] that a first degree equation of form f(x) = x or f(S) = S can be used to reasonably simulate the process and in general this has been preferred for the interpretation of the data due to its simplicity. Despite these possibilities, there have been few attempts at applying the non-first degree models of the form of f(S) = Sn[31]. This thesis does attempt to use non first degree models.

The objective of these methods is to assess the activation energy Ea, and pre-exponential factor or factor of Arrhenius A, for each process as expressed in the form of a standard Arrhenius equation:

  Ea  k  Aexp  (2.4)  RT  or

  Ea  k  Aexp  (2.5)  kBT  where k = factor of rate of reaction (specific rate) A = Arrhenius factor or pre-exponential factor, or frequency factor

Ea = energy of activation, expressed in Joule/mol or Kev/molecule R = Universal Constant of Ideal Gases,

kB = Boltzmann constant

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T = Absolute temperature. The above equation via natural logarithms gives: E 1 ln k  ln A  a R T (2.6)

The release of Wigner energy can be described using kinetic models similar to chemical kinetic ones. These models rely on empirical data obtained either from graphite samples irradiated in material test reactors or data obtained from small samples obtained from the reactors themselves. Data from these experiments is used to derive activation energies and characteristic functions used in kinetic models. The thermal annealing of graphite is understood through the use of kinetic models that essentially require determination of the activation energy Ea and pre-exponential factor A in the Arrhenius equation. The activation energy Ea refers to the energy barrier needed to overcome in order to make the annealing procedure-reaction self sustainable.

The kinetics of Wigner energy release can provide a better understanding of radiation damage in graphite and a robust prediction of stored energy release, particularly for new conditions outside the scope of present understanding, such as for decommissioning purposes. Kinetic analysis is a useful tool for gaining an understanding of the characteristics of the annealing procedures-reactions especially if it can be correlated with microstructural analysis using surface characterization techniques and spectroscopic methods.

Most of previous researchers considered the annealing procedure as a one stage reaction [27,28,30]. Some very simple models have been applied by them [27,28,30-32] in an effort to simulate experimental data obtained from irradiated graphite samples. A common problem in these early models was their simplicity and the assumptions necessarily made due to the absence of computational power. This prohibited previous researchers from applying more complicated models that should be capable of deriving more realistic results.

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Vand [68] first studied stored energy, but in metallic films instead of graphite. He gave a formula of the basic energy-release equation, describing it with a Boltzmann distribution:

dN(E,t)  E   N (E,t)exp  (2.8) dt  kT  where N is the number of displacements per unit volume, v is a constant frequency factor (given by ν=4fn) , E is the activation energy for the decay process and t is time, n is the number of atoms or vacancies forming the distortion and 1/4f is the average time required for the initiation of the decay, and f is the Debye maximum frequency of the thermal oscillations of the lattice atoms.

Vand [68] examined the credibility of using of 1/4f, and found it to be more valid for non- irradiated material, rather than distorted material. He found that the above formula is far more sensitive to changes in the exponential term than to changes the linear term. Therefore he concluded that ν may vary between different types of defects that were present in a sample irradiated material.

Primak[78] was among the first to apply the above relationships to irradiation damage in graphite. Primak[78] looked very specifically at processes with distributions of activation energy and provided with a very crude analysis with many simplifications made necessary due to lack of computational power. He analyzed the situation which later was described as isothermal annealing. He described a mathematical relationship, of an non dimensional number Θn, given by

1    E 1n n  1 1 nBt exp  (2.9)    kT  1-n with B=A(p/S0) .

Here, A, which is the pre-exponential constant, and B, have both the dimensions of frequency. n is the order of reaction. S0 represents the initial total stored energy before

40 Chapter 2 Literature Review annealing. p, is the main Wigner energy coefficient and has energy dimensions. It relates the change in stored energy to the change in the number of defects.

The situation of linear increase of temperature was also analyzed. In that case S0 is not stable any more and must now become a distribution function of temperature T (or time t as T=at) and the mathematical relationship now becomes

1   T  E  1n   1 1 nB  E2   2.10   a  kT 

where E2(-E/kT) he has found to be one of a class of functions of the form:

 E (x)  x m1 u meu du m  2.11 0 Nomograms of solutions to these functions are available but for the range of x=(E/kT), of interest, which is between values of 20 to 50, a E (x)=(x+m)-1e-x is sufficient to assume. Primak’s model was a good addition to knowledge of Wigner energy release, but it contained very crude numerical simplifications, due to lack of computational power.

Primak in a later work [79] applied the above relationships specifically to nuclear graphite and introduced the concept of annealing out irradiation damage. This work contributed to the understanding of the distribution of displaced atoms, at higher irradiation doses.

Primak [79] also examined the impact of irradiation temperature particularly in the range of activation energies between 2 and 5 eV and demonstrated that there is an auto- annealing effect. He found that at 135oC the accumulation of irradiation damage is about one half that at 650o for the same amount of irradiation dose. He suggested that these temperatures can only anneal damage in the range of 1.1-1.3 eV activation-energy, which is close to what is nowadays admitted. He showed that generally the irradiation annealing is temperature dependent.

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Iwata [30] made an advancement by proposing a kinetic model of the Wigner energy release involving three activation energies. Based on studies of Wigner energy release from Windscale Pile 1 and 2 graphite, while Minshall et al [80] (Figure 2.10) developed a kinetic model of Wigner energy release involving a spectra of activation energies which was used to assess the significance of the Wigner energy for the disposal of irradiated graphite waste [81].

Selected values of atomic activation energy and Frenkel pair energy are summarized in Table 2.3. Telling et al. [39] calculated a barrier to recombination of 1.4 eV. In another quantum-mechanical study, Ewels et al. [57] examined the structures and recombination routes for Frenkel pairs in irradiated graphite and assessed a barrier to recombination of 1.3 eV.

Kelly [82] summarized the preceding developed theories of stored-energy release. He examined the various possibilities for the kinetics of the release process, and classified them as:

1) the constant activation energy model

2) the variable activation-energy model with a constant frequency factor

3) the variable frequency-factor model with a constant activation energy.

He validated with more credibility the variable activation energy model with a fixed frequency factor.

Minshall et al. [80] applied a hypothetical model of a big number, more precisely a swarm of individual separate first order reactions with unique characteristics as described by activation energies and pre-exponential factors. Their attempt provided with a very good fit while simulating experimental data. (Figure 2.10). They also conducted comparisons between their model and the variable frequency factors and a constant frequency factor.

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Iwata [30 ] tested a more simple scenario with only three first order reactions (Figure 2.11).

Table 2.3. A collection of literature data of activation energies (in eV) of annealing of various types of defects , as calculated by first principles and theoretical calculations.

Simmons[83] examined DSC data from two specimens of graphite taken from the Windscale piles, one sample with a fast neutron fluence of 9.0×1020n/cm2 Equivalent Dido Nickel Dose (EDND, the equivalent radiation dose that a dido constructed of nickel would receive, if exposed at the same conditions as the specimen under investigation) at an irradiation temperature of 95 C, and one sample with a fluence of 3.0×1020n/cm2 EDND with an irradiation temperature of 76 C. For the kinetic assessments Simmons

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Figure 2.10. Fitting of energy distribution to data from a Windscale Pile 2 dowel graphitic sample at 10oC/min a very big number of small individual reactions is added in order to cumulatively simulate observed rate of release[80]

Figure 2.11. Comparison of constant activation energy models fitted to Iwata’s experimental date [30] using the variable frequency factors from Iwata’s paper and using a constant frequency factor [80].

44 Chapter 2 Literature Review used three models, the Constant Activation Energy Model, the General Model and the Constant Frequency/Variable Energy Model. The first model is based on the assumption that Activation energy remains constant over the temperature range of the release. The General Model assumes that Activation Energy is a function of temperature, and the Constant Frequency/Variable Energy Model assumes a dependence of activation energy to temperature or time, through the mathematical relationship:

  E0  A exp dt 1 (2.12) 0  kBT(t) where A is the frequency, E0 is the activation energy, kB is Boltzmann’s constant and T(t) is the temperature as a function of time t. The activation energy in this model is not consequently stable and is supposed to be a function of temperature and time. The DSC experiments reported were at heating rates of 2.5, 25, and 50 C/min. The Windscale data from Simmons shows a peak in the rate of release curve around 200 C. He then assumed activation energy of between 1.2eV and 2.0 eV for all three models.

The irradiation damage is generally assumed to initiate from simple nanoscale clusters of a few atoms into interstitial loops, the complexity of which is gradually increasing [74]. The defects begin to develop as monomers, transforming into dimers and then into whole collapsed regions of layer planes developing in-plane vacancy loops. As a consequence different microscopic regions develop, with different energy accumulation and different annealing characteristics. Therefore theories based on the variable activation energy assumption are believed to be more credible in the interpretation of the annealing process [82]. In the case of more than one reaction the need for optimization of the kinetic parameters arises. This can be achieved by the use of curve fitting[85]. Curve fitting is generally considered a process of curve construction based on a mathematical function that provides with the best fit to an equation or a series of data points. In curve fitting a function is constructed that approximately fits a set of data points. It can either involve interpolation, where an exact fit to an equation is required. In literature, especially in Thermogravimetry studies, where a similar Arrhenius equation describes the signals

45 Chapter 2 Literature Review produced by Differential Thermogravimetry, an optimization technique involving the Generalised Reduced Gradient has been often used [86-89]. The concept of the algorithm mainly relies on alterations of a vector’s dimensions (usually this involves the optimisation parameters, or units directly connected with them), and evaluation of their effect by a control function. This process is usually subjected to constraints that assure reasonable values on estimated parameters[90].

A description of the behaviour of the samples over a wide range of experimental conditions is required in order to have confidence in the ability to predict the behaviour outside the domain of experimental investigation. Such a wide database can be used to establish a deeper insight into the processes involved. The correlation between the kinetic analysis of data from irradiated samples, and studies of microstructure can lead with certainty to the verification or rejection of an annealing scenario.

46 Iwata n A(1/sec) Ea (eV) n A(1/sec) Ea (eV) n A(1/sec) Ea (eV) n A(1/sec) Ea (eV) [4] 1 3.7x1010 1.30 1 1.42x1011 145 1 2.5x1012 172 Constant Simmons Activation 1.16 General 1.16- Energy [2] Model Model -1.93

7.5 1013 Lexa et al. 1 7.5 1013 1.31 1 7.5 1013 1.47 1 sec-1 1.57 1 7.5 1013 1.72 [54]

7.5 1013 Kelly et al. 1 7.5 1013 1.47 1 7.5 1013 1.51 1 sec-1 1.74 [45] [4] [2] [54] [45]. Table 2.4. Activation Energy and Pre-exponential factors as calculated by Iwata , Simmons , Lexa et al , and Kelly et al,

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Ion irradiation : A Method to Simulate Irradiation Damage.

Ion irradiation is a possible technique to simulate neutron irradiation damage, because it can allow study of irradiation damage without producing radio-active isotopes. It may also be necessary due to the limited availability of neutron-irradiated samples.

A wide range of ion irradiation techniques has been used in the past[91-114]. Typically ions from noble gases such as Ar , He or Xe and Kr have been used [101-107] because they are inert. They are used in a simple ion jet form sometimes defocused [108] and sometimes in a plasma form[109]. Ions from different noble gases are sometimes used [103] (or even the same ion in different molecular states [106]) in order to execute comparative studies about the effect of size of particle in the induced damage. There are some examples where two different ions have been used simultaneously such as the work of Asari et. al [101] who used He+ as the basic irradiation ion, together with some incident irradiation of Ar+. Other types of ions can be used as well such as the work of Liu et al [109] who irradiated highly oriented pyrolytic graphite (HOPG) with a variety of heavy ions, mostly from metals (Ne, Cr, Fe, Ni, Zn, Xe and U). Briand et al. [110] used either high intensity ion beams with closed shells, such as Ar8+ to quickly induce their desired surface modifications and also low intensity beams of ions (Ar17+) to observe, off-line or on-line, the X-rays emitted during the interaction. Ishioka et. al. [111] used light 5 keV He+ of a flux of 9.8×1010 cm−2 s−1 to induce irradiation on HOPG [102] + surfaces. Kushita et al. irradiated graphite samples with 10 keV H 2 ions at ambient temperature in an electron microscope combined with an ion gun. Tokunaga [113] 21 2 et al. used D2, with ion energy 4 keV and fluence of 3.6X 10 ions/m . Begrambekov et al.[114] performed He+ ion bombardment of graphite and graphite compounds containing Ti and B. The ion energy was comparatively low, 800 eV. Chernikov et al. [115] used carbon ions directly simulating neutron damage by 200 keV C+. Tokunaga et al. [113] irradiated specimens in a high vacuum chamber with deuterium ions at 4 keV using a differential ion gun. Borisov et al [116] performed + irradiation mainly with 30 keV N2 ions at normal incidence with an ion current density was 0.1–0.3 mA/cm2.

48 Chapter 2 Literature Review

The energy of the ions also varies in accordance to the desirable extent of irradiation damage, the penetration depth and the equipment available. It may vary from some keV (Ishioka et al [111] used a 5 keV helium ions) to even MeV (Liu et al [107]). Biró et al. [117] used HOPG that was irradiated with low dose, but with very high energy, heavy ions: 1012ions cm−2, at 215 MeV Ne+ or 246 MeV Kr+, with 1011 ions.cm−2 at 156 MeV Xe+. Oku et al. [118] used Argon ions (40Ar8+) with 175 MeV and 1 μA for irradiation of various carbon materials. They used a beam flux was 2.6 × 108 ion/mm2. Daulton et al.[119] bombarded sheets of fine-grain polycrystalline graphite at 20°C with 350 ± 50 MeV Kr ions to fluences of 6×1012 cm−2 at a rate of 2×1010 ions.cm−2 s−1. [120] + Gouzman et al. used low energy 500 eV N 2 ion irradiation of diamond and graphite surfaces. On the opposite side, Meguro et al. [121] used slow Arq+ (q=1–8) ions only with 400 eV of kinetic energy, that were directed onto the HOPG surfaces. The kinetic energy of Argon was fixed at 400 eV, independent of its charge state.

The temperature of irradiation has also been another area of study and there are examples of researchers who have irradiated graphitic materials in different temperatures as well as room temperature in order to assess the impact of temperature to irradiation damage[115,120]. Liu et al [107] for example, used a defocused Xe ion beam of 3 MeV. Their irradiations were performed at temperatures of 500 and 800oK.

Various are also the sources of ions beams, from electron cyclotron resonance plasma sources (Hida et al.[109]), simple plasma ion sources with electrostatic accelerators (Compagnini et al [105]), sector focused cyclotrons (Liu et al [107]). Meguro et al. [121] used a 10 GHz electron cyclotron resonance plasma system with a Ar+ discharge (approximately 50W of microwave power), and were extracted from the plasma column by 10 kV of extraction voltage.

In some of the studies large scale facilities were utilized. Some of them used multiple sources. Briand et al. [110] performed experiments in various places using the Highly Charged Ion beams provided by sources of the University of Nevada, Reno, in Grenoble and also in Santa Clara, at energies ranging between 5 and 20 keV/q. Oku et al. [118] used a cyclotron, in Takasaki, at installations of the Japanese Atomic Energy Association.. Daulton et al. [119] used the Argonne Tandem Linear Accelerator System (ATLAS). Chernikov et al. [115] performed ion irradiation with implanters at the

49 Chapter 2 Literature Review

Institute of Thin Film and Ion Technologies (Jiilich, Germany), and at Sandia National Laboratories (Albuquerque, New Mexico, USA).

In some of the studies facilities that originally were designed for purposes other than producing irradiation damage, have been used. Smith et. al [122] used an argon ion source from a modified sputter cleaning source, with a potentiometer added to allow the ion potential to vary from 0 to the nominal maximum of 500 eV. Borisov et al. [116] performed ion irradiation using a Mass-monochromator of the Institute for Nuclear Physics of Moscow State University. Gotoh et al. [97] used mass-separated 3 keV D3+ beam of a 7 mm diameter, incident to the specimen surface at a fluence of 6 x 1015 D/(cm2 s) to a fluence 0.3-8.1026 D/(cm2 s)

In summary, previous studies mentioned, display a wide range and variety of ion irradiation methods with various types of ions, and experimental conditions available and their results have been used for proposing mechanisms of irradiation damage creation. However, many drawbacks accompany ion irradiation techniques, and if used for the purpose of simulating neutron irradiation damage, they have to be evaluated. Appropriate methods have to be developed in evaluation of irradiation damage in order to be able to use them for simulating neutron damage. The main differences between ion irradiation and neutron irradiation are the large size of the colliding particle (massive Ar+ ions of 39 Molecular Weight which are very frequently used, are gigantic compared to neutrons of a Molecular Weight of unity), the charge, and the lower energies applied (usually ions have energies of the range of keV, reaching some hundreds of keV, while neutrons reach higher energies). Despite these drawbacks, researchers insist in using ion irradiation as a primary technique of study of irradiation damage in graphite. Although in literature there is an absence of comparative studies of the irradiation damage produced by ions against the one produced by neutrons, ion irradiation is generally considered to be a sufficient method that can provide information about the irradiation effects in graphite. An attempt in evaluating the credibility of the above assumption is within the scope of the current work.

50 Chapter 3 Methods

Chapter 3 Methods Differential Scanning Calorimetry Differential Scanning Calorimetry (DSC) is a technique for measuring the energy necessary to establish a zero temperature difference between a substance and an inert reference material, as the two specimens are subjected to identical temperature regimes in an environment heated or cooled at a controlled rate. In this method the data obtained is usually a curve of the rate of energy released or absorbed versus time or temperature.

There are two main types of DSC systems[123] (Figure 3.1). The heat flux DSC and the power compensated DSC. In power-compensated DSC the temperatures of the sample and reference material are controlled independently using separate, identical furnaces. The temperatures of the sample and reference are made identical by varying the power input to the two furnaces; the energy required to do this is a measure of the enthalpy or heat capacity changes in the sample relative to the reference.

In heat flux DSC, the sample under examination and a reference sample are connected by a low-resistance heat flow path (a metal disc). The assembly is enclosed in a single furnace. The temperature difference between the reference sampler and the sample under examination is recorded and related to enthalpy change in the sample. The method is using calibration experiments. Enthalpy or heat capacity changes can be monitored. Power compensated DSC is more accurate over lower temperatures but can not generally achieve higher temperatures (above 1000oC). Heat flux on the other hand is capable achieving higher temperatures but in cost of accuracy over lower temperatures.

In DSC, it is expedient to conduct experiments either isothermally or with the temperature changing at a constant rate. In the former case, the ordinate value would be plotted against time at isothermal temperature, whereas in the latter case it could be plotted against time or temperature.

51 Chapter 3 Methods

Figure 3.1. (a) Heat flux DSC; (b) power-compensated DSC. [123].

Wigner energy release is usually measured using Differential Scanning Calorimetry techniques. Many measurements of Wigner energy release have been undertaken [27- 32] mostly before the advent of modern computational facilities for data analysis. These were aimed at assessing the parameters of the graphite annealing process in reactors operating at low temperatures in order to ensure safe operation of the particular reactor. The shape of the Wigner energy release curve varies according to irradiation dose, irradiation temperature, and consequently the position of the specimen inside the reactor.

The temperature of irradiation plays also a significant role in the shape of the DSC curve [35]. An example of a typical study is that of Kelly [124] in which it is proposed that when irradiation takes place at higher temperatures thermal and irradiation annealing occurs and the shape of the DSC curve is shifted to higher temperatures. It is also predicted that the higher the irradiation temperature the higher the initiation of the annealing process.

At low irradiation doses a characteristic peak at around 200oC arises[27-32, 79, 124]. In longer-term irradiation the low-temperature peak reduces in magnitude and is shifted to a higher temperature. Studies of Pile Grade A (PGA) graphite from the commercial Magnox reactors[124], showed that no low temperature (~200oC) peak in rate of release curves is visible at high irradiation doses, and the rate of release curve

52 Chapter 3 Methods slowly rises to a plateau value with increased temperature. At high irradiation doses, defect concentration reaches a thermodynamic limit, a saturation point, and the curves that depict a release that occurs at lower temperatures are gradually diminished[124] (Figure 3.2). Studies of Wigner energy release from specimens derived from the Windscale piles [124, 125] suggest some indication of the effect.

Figure 3.2. The rate of release of stored energy. Hanford cooled test hole graphite 30oC [125].

Figure 3.3. The effect of irradiation temperature on the shape of DSC curves. In the diagram above three DSC curves at different irradiation temperatures (150oC, 200oC and 250oC)are depicted (heating rate was 10oC/min)[125].

Position of sampling of the graphite specimen in the reactor also plays a role into the form of DSC profile. In different regions inside the reactor different irradiation

53 Chapter 3 Methods

Figure 3.4. A - Layout of a graphite reactor stack (left) and arrangement of sampling points along height of stack (right, a-m are sampling points) from bricks removed during dismantling of the reactor (single-hatched) and cut out from the stack with the aid of remote controlled drill cutter (double-hatched). [126]

Figure 3.5. Curves of behaviour of stored-energy release: Images 1 to 4: Curves for samples cut out of bricks removed during dismantling of a graphite pile; Images 5 to 8: curves for samples cut from stack with drill cutter. Image 1 to 3: Three samples a,b,c (see previous figure) from brick No. 4 in lattice cell 10-03; Image 4: Sample c from brick No. 7 in cell 06-10; Images 5-8: Samples c, d, e, g from cell 09-03. Depiction [------] refers to sample adjacent to channel. Depiction [-∙-∙-∙-∙-∙-] refers to sample remote from channel; C is the specific heat of unexposed graphite. [126]

54 Chapter 3 Methods conditions and different gradients of irradiation dose as well as temperatures, occur. Consequently the Wigner Energy release parameters change accordingly. The DSC profiles from specimens taken from different parts would display different shapes, as a result.

A characteristic study by Klimenkov et al. [126] is displayed in the figures of previous page (Figure 3.4 and 3.5). They collected samples from various parts of an experimental reactor built in the former Soviet Union and at the time of the study had undergone decommissioning. The operating conditions of this particular reactor were an operational average power of 50 MW and graphite temperatures of 400-600o C at the centre of the pile. The integral thermal flux at the centre was 6.7x1021 neutrons/cm2.

In Figure 3.4, the layout of the reactor is depicted with the positions of sampling pointed. Figure 3.5 shows Wigner energy release curves as well as rate of release curves. The overall conclusion of their work is that samples taken from areas close to the centre of the reactor are exposed to higher irradiation doses and temperatures. Therefore at higher irradiation doses the DSC signal would resemble a monotonic curve that would reach a plateau. At low irradiation doses the characteristic peak at around 200oC appears. Higher temperature of irradiation or higher irradiation dose shifts the post irradiation DSC curves onto higher temperature frames shaping the form of the characteristic plateau.

X-ray Diffraction

The development of X-ray Diffraction (XRD) and X-ray Powder Diffraction, (XRPD) was a major evolution in solid-state science and provided much of the present understanding of chemical bonding. Among the applications of powder X-ray diffraction are the qualitative, and under specific conditions quantitative identification of the phases present in a specimen, quantitative analysis of the concentrations of each phase present in a multiphase specimen, the unit cell features and dimensions, the determination of crystallite orientation in polycrystalline materials, the determination of residual and applied stress, microstructural features of a polycrystalline material, microstrain within crystallites, and defect densities may be determined, in situ techniques under controlled gaseous atmosphere, temperature, pressure, field, and

55 Chapter 3 Methods mechanical loading can be applied, full structure solution from powders may be determined[127].

Diffraction occurs when X-rays scattering from an object interfere with each other, exactly analogously to the diffraction of visible light from a grating. Based on the work of von Laue (who first determined that X-rays diffract from the periodic arrangement of atoms in a crystal), W. H. and W. L. Bragg showed in 1913 that diffraction from a crystal is described by the equation now known as Bragg's law[127]:

  2d hkl sin (3.1)

This equation allows the measuring of the perpendicular distance (dhkl) between imaginary planes which form parallel families and which intersect the repeating unit cell filled with atoms in a way described by the Miller indices (hkl). X-rays may be thought of as reflecting from these imaginary planes at the measurable angle θ. A powder pattern therefore contains a set of diffraction peaks at 2θ positions that correspond to the interplanar spacings in the crystal.

Figure 3.6. Phase identification between two allotropes of carbon, diamond and graphite[128]. A-The X-ray diffraction intensity for diamond nanoparticles B-The diffraction intensity of diamond nanoparticles with a coating of graphite after heat treatment at 1400 C.C- The diffraction intensity for spherical carbon onions after heat treatment at 1700 °C. D-The diffraction intensity for polyhedral carbon onions after heat treatment at 2000 C.

56 Chapter 3 Methods

In carbonaceous materials XRD has undertaken usage initially in phase identification between different allotropes of carbon.(Figure 3.6) Particularly in graphite, XRD has been used to measure lattice parameters[120,121]. The precision of the measurement is affected by instrumental drift, therefore samples often are being measured in a pulverized form mixed in a 50/50 analogy with a standard, usually silicon or silicon oxide, and the resulting XRD pattern is accordingly corrected[132]. Usually d spacing of various peaks is calculated and unit cell parameters are being extracted after cell refinement.(Figure 3.7 and 3.8)

Figure 3.7. Graphite unit cell.

Figure 3.8. X-ray powder diffraction patterns of SP-1 pyrolytic graphite and nuclear graphite sample along with silicon standard. Some of the peaks that appear refer to the graphites while others to the silicon standard[129].

57 Chapter 3 Methods

Table 3.1. Lattice parameter of SP-1 and nuclear graphite samples.[129]

Table 3.2. Lattice parameter a, c, as correlated with the degree of graphitization (DOG: g) of the as received IG-110 and IG-430 Japanese types of nuclear graphite[130].

Another property of XRD that is undertaking usage is diffraction broadening. This is a well-known feature for finite-sized crystallites and results from the restricted range of the contributions from the correlated layers of the crystal. The extent the XRD reflection function, given by peak broadening can be expressed with two different concepts: Integral breadth β and Full Width Half Maximum (FWHM). Integral breadth is the surface or peak area, occupied between the XRD curve and horizontal axis, divided by the peak maximum value. Full width half maximum is the difference between the two extreme values of the intensity at which the dependent variable is equal to half of its maximum value.

The width of the peak as well as the integral breadth, is inversely proportional to the dimensions of the particle and can be represented by the Scherer equation[130]: K K   FWHM  L cos or L' cos (3.2)

58 Chapter 3 Methods

Figure 3.8. Calculation of Integral Breadth β and Full Width Half Maximum of a specific peak of an XRD pattern.

Where β is Integral Breadth, FWHM is the full width half maximum in radians, K is a constant referred as crystalline shape factor, λ is the X-ray wavelength (for copper it is 1.542 Angstroms), L and L΄ is crystalline diameter in Angstroms and θ is the Bragg angle at peak maximum in radians. The use of integral breadth β instead of FWHM would lead to a slightly more accurate value of L,. The basic assumption for the calculation of crystalline size parameters is that crystallines are approximated by ellipsoidal particles [131]. Therefore the Scherer parameter, K, is best defined as the ratio by which the apparent crystallite size must be multiplied to obtain the true size, i.e. True crystallite size /Apparent crystallite size [132]. K is usually considered to have the values 1.0 for integral breadth and 0.89 for half-width method.

In polycrystalline materials, the experimental profile is the convolution of the instrumental profile and the intrinsic profile (pure diffraction profile). The intrinsic profile can be obtained by correction. This is done by unfolding the experimental profile. The simplified method is based on assumptions that the intrinsic and instrumental profiles can be approximated by the Cauchy (Lorentz) or Gaussian function or a bell shaped function in general[133,134]. A set of relations emerge according to the assumption of Cauchy or Gaussian assumptions. The integral breadths can be calculated using the Cauchy–Cauchy, Gaussian–Gaussian, or Cauchy–Gaussian relationship

59 Chapter 3 Methods

 exp     ins (3.3) 2 2 2  exp     ins (3.4)    1 exp (3.5) ins ins

where βexp, β, and βins are the integral breadth of experimental profile, intrinsic or true profile, and instrumental profile, respectively[133,134].

Using XRD, Kelly et al. [46] reviewed the dimensional changes and the thermal expansion coefficient of irradiated graphite. X-ray diffraction patterns of highly irradiated graphite that has been studied by them exhibited broad and asymmetric peaks suggesting a decrease in the degree of crystallinity. The lattice parameter changes seemed to be linear with fluence, up to a relatively low fluence of 3×1018ncm−2. An irradiation experiment performed by them, at 150 C yielded a 13% increase in c lattice parameter (Δc/c).

Figure 3.9. Normalised after Ka2 instrumental broadening subtraction of X-ray diffraction patterns of graphite milled in n-dodecane [135].

It is possible to observe the effects of irradiation in graphitic materials since it is well accepted that the interlayer spacing of graphite carbon d(002) decreases as the degree of crystallinity increases[136,137].Wang et al. measured crystalline sizes of various types of graphite in the range of 300-400Å, both for Lc (002) and La (110).[130]

60 Chapter 3 Methods

Worth referring to, is the work of Lexa et al [138] who constructed a hermetic sealed sample enclosure that enabled simultaneous X-ray Diffraction measurements in combination with Differential Scanning Calorimetry measurements in order to monitor the thermal annealing of graphite with real time measurements. The sample enclosure was adjusted so as to fit in a Perkin – Elmer DSC 2C power compensated calorimeter.

Using this device they took measurements on irradiated graphite while it was being annealed from 25 to 525 oC [29]. They observed that between 25 and 180– 190oC, the samples underwent thermal expansion in line with the literature values. They also observed a disruption of this continuity at 180–190oC, indicating a crystal lattice relaxation. The occurrence of this anomaly at 180-190oC coincides with another graph: The inflection point of the rate-of-heat-release peak at 200 oC in the DSC curves. Their conclusion was that Wigner energy peak at 200oC is clearly a result of lattice relaxation.

Figure 3.10: Photograph of the open (left) and closed (right) DSC/XRD measuring head. The Pt sample and reference cups are occupied by empty graphite pans. Remnants of a sample are visible on the graphite pan and the sample itself can be seen on the support bracket[138].

In the work presented in this thesis X-ray Diffraction is used to verify the crystalline changes upon irradiation initially, as well as to monitor the restoration of the damage produced by ion irradiation.

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Raman Spectroscopy

The basic experimental apparatus of a Raman spectroscopic device consist of the radiation source, dispersion element, detector and filter [139].

The radiation sources include Ar+, Kr+, He–Ne, Ti: sapphire, Nd: YAG and diode laser beams. The dispersion element is a single monochromator. The scattered light enters the monochromator through a slit and is reflected from a mirror to a fixed diffraction grating. This diffraction grating disperses the scattered light spatially on the basis of frequency. Then it directs it to another mirror which sends the separated light to a charge-coupled detector (CCD). A CCD is a multichannel detector made up of large arrays of individual metal–oxide–silicon capacitors. Optical filters play an important role in Raman spectrometers. An interference filter is usually inserted before the laser beam reaches the sample in order to improve the beam’s monochromatic features. Interference filters block all but a small number of incoming wavelengths centred at the laser resonance. Holographic notch filters are inserted after the Raman light is scattered from the sample in order to filter the Rayleigh line from the detected light[139].

Figure 3.11. Schematic diagram of a Raman spectroscoper. [139]

There has been a wide range and value of Raman spectroscopy applications. Some applications could be briefly described as investigation of the symmetry of vibrations from single-crystal spectra, semiconductors research and phase transitions

62 Chapter 3 Methods

Research aimed at investigating the Raman spectra of different varieties of carbon materials [101, 106, 108, 109, 140, 141] are focused on investigating Raman spectra of intact (virgin) graphite as well as processed (polished, neutron or ion irradiated, deposited etc) materials. Raman spectra have proven very sensitive to even slight alterations of the surfaces, and this fact makes Raman spectroscopy a very useful technique for monitoring the changes of molecular states after irradiation.

The basic peaks that are observed in a Raman spectrum of a graphitic material are shown in Table 3.3 [101- 107, 109, 140- 153].

Table 3.3. A collection of characteristic graphitic Raman peaks [101- 105, 109, 140- 153].

The main peaks that appear are one at 1580 cm-1 attributed to the ordered Raman- active E2g peak which in named as the G mode (the name refers to the space symmetry part E2g from which it is produced), three additional extra first-order lines approximately at 1340-1346 (D1 or D as will be named for the specific purposes of -1 this work), 1367 (D2) and 1622 (D0) cm designated as D modes which originate from disordered graphitic materials (cumulative general disorder). The region of second-order Raman spectra shows four distinct lines at 2680 (2D1), 2730 (2D2), 3250 -1 (2D0) cm appeared in the pristine and ion irradiated HOPG samples. The D1 or D peak around 1340 cm-1 is a breathing mode of A1g symmetry [154]. This mode is forbidden in perfect graphite and only becomes active in the presence of disorder. One of the basic Raman techniques used in tracking changes in molecular states of graphite is the relative intensity ratio (D:G peak intensity ratio ), usually before and after a process. It has been observed[99] that the D:G peak intensity ratios on pristine HOPG samples are increasing after ion irradiation, due to the produced disorder. An example is shown in Figure 3.13.

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Figure 3.12. Two characteristic types of spectra from two graphitic materials.[155] On top, Highly Oriented Pyrolytic Graphite (HOPG) undisturbed, without defects, and glassy carbon, containing defects. The peak at the range of 1340cm-1 is indicative of the presence of defects.

The D:G ratio (symbolised as I(D)/I(G)) is also reported to be increasing due to other types of damage induced. For example Nakamizo et al [155] report that by simply polishing a graphitic surface, the D:G ratio increased extensively from 1.0 to 2.1, indicating the introduction of additional defects with polishing. The D mode has been observed [109] to arise when the irradiation fluence surpasses a critical value, which is smaller for heavier ions with higher energy loss. The charge state of the colliding particle is also supposed to affect the I(D)/I(G) ratio. Hida et al.[109] investigated how the charge state of ions affects surface disordering on HOPG. Irradiation occurred by single impacts of slow Ar+ and Ar8+. The intensity ratio of the D peak with respect to the G peak, I(D)/I(G), for Ar8+ irradiation was larger than that for Ar+ irradiation.

It would be ideal if a quantitative link between features that are provided by the Raman spectrum and number or nature of the defects could be established. This was not explored systematically in the past. This was because the main interest in nanographites and carbon fibres was to have a crude estimation of disorder.

64 Chapter 3 Methods

Figure 3.13. Schematic diagram of the E2g and A1g modes. Carbon motions in the (a) G and (b) D modes. The G mode is just due to the relative motion of sp2 carbon atoms and can be found in chains as well [154].

Nowadays however, there is consistent and ongoing research for electric and magnetic properties of graphene. Therefore the experimental identification of the precise nature of the disorder and defects is of great interest. This is because their presence can be linked to changes in the electrical characteristics. Thus a more detailed investigation is certainly needed.

Tuinstra et al. [157] were the first to establish a rule between the amount of disorder and characteristics of the Raman spectrum. They found that the I(D)/I(G) peak intensity ratio was inversely proportional to crystalline size La:

ID C()  (3.6) IG La where C(λ) for a wavelength of 488 nm-1 has been calculated by them as well as others as 4.4 nm [157-160].

The original idea behind the equation above was to link the D peak intensity to phonon confinement. The intensity of the non allowed vibration/phonon, (D peak) would be a function of the amount of breaking. The amount of breaking would not affect the allowed phonon which generates the G peak. Considering La as an average

65 Chapter 3 Methods inter-defect distance, one can assume that the higher the defect quantity, the higher the D peak intensity and, consequently, the smaller La.

There has been up to now enough evidence of the validity of the Tuinstra et al [157] relation, where La has been measured independently by Raman spectroscopy and X- ray diffraction [156,160–164].

For small La however, a new relation has been developed for nanocrystalline materials [153, 166]: ID  C΄()L2 I G a (3.7) For nanocrystalline materials such as amorphous carbons the D mode strength can be assumed to be proportional to the sole existence of six fold rings. Therefore, the development of a D peak in that case, is indicative of order than disorder, exactly the opposite to the case of graphite.

In the case of polycrystalline graphite such as nuclear graphite examined in this work, it can be assumed that crystalline size is simply inversely proportional to defect quantity. This is further explained as order increases as defects decrease, and therefore crystalline size increases. Therefore, despite the fact that reasonable amount of research will be undertaken in the future, it is a reasonable assumption that I(D)/I(G) ratio can be considered as a direct proportion of defect quantity.

In this work presented in this thesis Raman spectroscopy plays a key role in investigating the production of defects after ion irradiation as well as the reduction of their quantity after consecutive thermal annealing steps. This has not been studied previously, and one of the aims of this work is to understand the evolution of the defects during this annealing process.

66 Chapter 4 - Publication I: Application of an Independent Parallel Reactions Model on the Annealing Kinetics to Irradiated Graphite Waste Chapter 4 - Publication I: Application of an Independent Parallel Reactions Model on the Annealing Kinetics to Irradiated Graphite Waste Michael Lasithiotakis. Barry Marsden, James Marrow, Andrew Willets.

Published in Journal of Nuclear Materials 381 (2008) 83–91

Chapter 4 - Publication I: Application of an Independent Parallel Reactions 67 Model on the Annealing Kinetics to Irradiated Graphite Waste Chapter 4 - Publication I: Application of an Independent Parallel Reactions Model on the Annealing Kinetics to Irradiated Graphite Waste

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Chapter 4 - Publication I: Application of an Independent Parallel Reactions Model on the Annealing Kinetics to Irradiated Graphite 75 Waste Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Chapter 4 - Publication I: Application of an Independent Parallel Reactions Model on the Annealing Kinetics to Irradiated Graphite Waste 67

Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Michael Lasithiotakis. Barry Marsden, James Marrow.

Submitted to Carbon, Elsevier. Ref. No.: CARBON-D-11-01944

68 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Title: Annealing of ion irradiation damage in nuclear graphite

Authors: Michael Lasithiotakis*2,a,b, Barry J. Marsdenb and T. James Marrowc.

a-Materials Performance Centre, Corrosion and Protection Centre, School of Materials,

The University of Manchester, Manchester, M13 9PL, UK b-Nuclear Graphite Research Group. School of Mechanical, Aerospace and Civil

Engineering, The University of Manchester, Manchester M13 9PL, UK. c- Department of Materials. University of Oxford, Parks Road, Oxford OX1 3PH, UK

2 *-Corresponding author: Tel: +44(0)161 306 4840. e- mail:[email protected]

1 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Abstract

The changes with annealing of properties and microstructure of various grades of ion- irradiated nuclear graphite have been investigated and compared with changes reported in fast neutron irradiated graphite of various grades. Raman spectroscopy has been used to compare the effect of ion bombardment with the reported effects of neutron irradiation on physical properties such as the lattice defects. The kinetic parameters of the thermal annealing of defects in ion irradiated graphite have been compared with the energy release kinetic parameters from annealing of neutron irradiated nuclear graphite, provided in the literature and a qualitative kinetic model in terms of activation energy and order of reaction is proposed. The activation energies obtained for the annealing of ion-irradiation and mechanical defects are found to be close to those reported for neutron irradiation.

1. Introduction

Ion irradiation is an attractive technique often used to simulate neutron irradiation, because it can allow study of irradiation damage without the need to deal with radioactive materials. High dose can be achieved in relatively short times. It is also attractive as access to neutron-irradiated samples is often difficult and limited.

There is a wide range of ion irradiation techniques available. Typically ions from noble gases such as Ar , He or Xe and Kr are used [1-8]. The technique normally employs a simple ion beam, sometimes defocused [7] and sometimes in a plasma form [4]. Ions can be obtained from different noble gases directly [2] or even the same ion in different molecular states [5] in order to execute comparative studies with respect to size of the

2 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite particle inducing damage. There are some examples where two different ions have been used simultaneously such as in the work of Asari et. al [1] who used He+ as the basic irradiation ion, together with some incidental irradiation by Ar+. It is also possible to use other types of ions such as in the work of Liu et al [3] who irradiated highly oriented pyrolytic graphite with heavy ions, mostly from metals (Ne, Cr, Fe, Ni, Zn, Xe and U).

The main differences between ion irradiation and neutron irradiation are: a) the larger size of the colliding particle compared to neutrons (Ar+ ions of 39 molecular weight are very frequently used, and are gigantic compared to the molecular weight of a neutron), b) the charge (neutrons have no charge), and the lower energies applied (usually ions have energies of the range from a few keV to a few hundred keV, while neutrons reach higher energies up to ~10 MeV in a fission system or 14MeV in a fusion system). Despite these differences, researchers have persisted in using ion irradiation as a primary technique of study of irradiation damage in graphite.

Ion irradiation in this work is examined as a method suitable to produce specimens that would resemble the thermal annealing behaviour of neutron irradiated samples. The comparison between neutron and ion irradiation will take place through the study of the kinetic characteristics of thermal annealing process of ion irradiation induced damage, and it’s comparison with kinetic characteristics of neutron irradiation annealing. In the literature there is an absence of comparative studies of the kinetics of the annealing process of irradiation damage produced by ions against kinetics of the annealing process of irradiation damage produced by neutrons.

3 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Graphite grades used in this study were Gilsocarbon3 (Gilso) and Highly Oriented

Pyrolytic Graphite (HOPG). Gilsocarbon is polycrystalline artificial graphite manufactured from a spherical, onion-like coke produced from naturally occurring asphalt mined in the USA called Gilsonite. The spherical shape of this coke ensures that moulded Gilsocarbon graphite has no strong preferential alignment. This type of graphite was used as a moderator in the UK Advanced Gas Reactors [9].

HOPG is manufactured by a vapour deposition method, which produces a lamellar structure of stacked planes. When graphitised under compression HOPG4 is highly crystalline, consisting of layers of two-dimensional graphitic planes. HOPG is often used in ion irradiation studies [5,7,8]. The main advantage of studying irradiation in HOPG is that HOPG is considered to be a good approximation of a graphitic single crystal, and the resulting damage in HOPG is relatively easily observable using microscopy techniques.

2. Experimental

2.1. Sample preparation

2.1.1. Gilsocarbon

A specimen of Gilsocarbon was embedded in a cylindrical mould of resin and machined with a diamond impregnated cutting disc into pieces approximately 0.3mm x 0.3mm x 2 cm. Then the resin mould was cut into slices of approximately 0.5 mm thickness, and

3 Supplied by British Energy Generation Ltd 4SPI Supplies. Mr. Harry Hargreaves. Aztech Trading, 12 Kernan Drive, Swingbridge Trading Estate, Loughborough Leicestershire LE11 5JF England. UK.

4 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite final graphite specimens (3mm x 3mm x less than 0.5 mm) were separated from the resin manually. During cutting, water was used for cooling and lubrication therefore the separated specimens were dried for 24 hours at room temperature.

The Gilsocarbon specimens were then manually ground using silicon carbide grinding paper of P800 grade (21.8 μm) followed by silicon carbide grinding paper of P4000 grade

(5μm). At a second stage, the samples were polished with diamond paste (Preparationes

Diamantee Mecaprex) with a nominal mean grain size of 3μm then 1μm consecutively to further remove scratches and artefacts. The purpose of polishing was: a) to prepare the surfaces for ion irradiation b) to explore the effect of the production of defects introduced on the surface of the material by polishing.

2.1.2. Highly Oriented Pyrolytic Graphite

A specimen of HOPG was similarly immersed in resin and cut into pieces of 3mm x 3mm x 0.5mm approximately. Then, the resin was removed and each specimen was cleaved with an adhesive tape in order to produce many specimens of thickness less than approximately 0.5mm. Finally, the surfaces obtained were smoothed by a simple technique of removing damaged surfaces layers with adhesive tape to produce a clear

“mirror” surface [10].

2.2. Ion irradiation and annealing

2.2.1. Irradiation method and penetration depth

Ion irradiation was achieved using a Gatan PIPS ion beam milling device designed to prepare specimens for TEM. This device uses two Argon beams directed from opposite

5 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite directions. The available energy of irradiation is between 1 and 6 keV, and the angle of irradiation can be between -10° and 10°. The irradiation chamber is maintained in a vacuum (10-4-10-7torr) at ambient temperature. Five samples of Gilsocarbon and five of

HOPG were irradiated using Argon beams. The energy range for this device is between 0 to 6keV, and the maximum achievable current intensity varies between 30-40 mA. It was found that during the irradiation, the device could not maintain stable beam intensity.

The beam intensity was observed to periodically vary (approximate sinusoidal variation of five seconds time period) between 4 and 30 mA. During the irradiations, a pressure of

10-5torr was maintained throughout. The samples were irradiated with an energy of 6keV for four hours. The angle of irradiation was maintained at 5° from horizontal position.

Samples were rotating at maximum speed available, which was 6 rpm. Atomic displacements caused by the ions and subsequent cascades was calculated using the

TRIM code5 (Transport of Ions in Matter) This is a software that was developed in order to calculate penetration depth when various materials are bombarded by ions. This is executed by involving parameters that refer to both material and bombarding particle

[11]. Damage depth was found to be well within the optical depth of a He - Ne Raman

(40nm)[12]. Penetration depths of less than 80-90 nm for HOPG and less than 120-130 nm for Gilsocarbon were predicted respectively, due to the difference in density between the two graphite grades. The irradiation damage intensity significantly decreases after 50-

60nm for HOPG and 70-80 nm for Gilsocarbon.

5 Transport of Ions in Matter (TRIM). Software by Ziegler JF, Ziegler MD, Biersack JP. 2008. Available at http://www.srim.org

6 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

2.2.2. Annealing

Annealing took place under an argon atmosphere in a cylindrical furnace. The input gas was 99.999% pure with traces of oxygen, which were removed using activated copper.

The heating program took place in steps of 50ºC from 100 to 600ºC with an annealing time of 30 minutes. I consisted of three stages, heating to the chosen temperature at a rate of approximately 10ºC/min, then holding the furnace at temperature for at least half an hour, before cooling down to room temperature. Before annealing, and after the completion of each step, Raman spectroscopy was carried out, as will be described in section 3.3.

Borisov et al [12] on ion irradiated (at 35 keV) and annealed samples of graphite, observed restoration of initial conditions after one hour. Therefore in this work, it has been assumed that an annealing time of 30 minutes for specimens that were bombarded with 6keVAr+ ions would be sufficient to assure termination of annealing reactions occurring up to the annealing temperature.

2.3. Raman spectroscopy

Raman spectroscopy is a useful technique for monitoring the changes of molecular states after ion-irradiation. Previous research efforts have investigated the Raman spectra for different varieties of carbon materials [1,5,7,8,13] obtaining Raman spectra of intact

(virgin) graphite as well as processed (polished, neutron or ion irradiated, deposited etc).

The Raman spectra proved to be very sensitive even to slight alterations to the surfaces.

The basic peaks that are observed in a Raman spectrum of a graphitic material [1-

6,8,10,13] are a first order peak at 1580 cm-1 attributed to the ordered Raman-active peak

7 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite which is designated the G mode (after the space symmetry E2g), and three other first-

-1 -1 -1 order peaks approximately at 1340-1346 cm (D1), 1367 cm (D2) and 1622 cm (D0).

These last three peaks are designated as D modes, which originate from disordered

-1 graphitic structures. For example, the D1 peak around 1340 cm is a breathing mode of

A1g symmetry [14]. This mode is forbidden in perfect graphite and only becomes active in the presence of disorder. It is assumed [15] that the production of defects results in creation of diamond like clusters formed by sp3 hybridism bonds. The region of second- order Raman spectra shows four distinct peaks at 2680 (2D1), 2730 (2D2), 3250 (2D0) cm-1

One of the basic Raman techniques used in tracking changes in molecular states of graphite is the relative intensity ratio of D1/G peak intensity ratio of the D1 and G first order peaks. For example, it has been observed [8] that this ratio for pristine HOPG increases after ion irradiation. The D1 mode has been observed [7] to occur when ion irradiation fluence reaches a critical value, which decreases for heavier ions. Hida et al.

[8] showed how the charge state of the colliding particle affected the D1/G ratio in

HOPG. The D1/G ratio is also reported to vary with other types of damage. For example

Nakamizo et al [15] reported that by simply polishing a graphitic surface, the D1/G ratio increased significantly. In this paper, for simplicity, the D1 peak will be referred to as simply the D peak, and the D1/G peak ratio will be symbolized as ID/IG.

In this work, Raman spectroscopy has been used to investigate the production of defects after ion irradiation as well as polishing, and the reduction of their quantity with consecutive thermal annealing steps. This has not been studied previously, and one of the aims of this work is to understand the evolution of the defects during the annealing

8 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite process. Raman spectroscopy measurements were carried out using a Renishaw Wire

633nm UV laser source Raman spectrometer.

The Raman spectra of polished Gilsocarbon, ion irradiated Gilsocarbon and HOPG, were compared with the spectra from non irradiated HOPG, fractured Gilsocarbon, and a neutron irradiated nuclear graphite machined from British Experimental Pile Zero,

(BEPO6) at Harwell which was irradiated in air to an irradiation dose of 11.3 x 1020 n/cm2 at temperatures between 100 and 120o C (During operation BEPO graphite was annealed several times in an attempt to reduce the levels of stored energy [16]). A collection of the characteristic Raman spectra are shown in Figure 1.

Figure 1: Raman spectra of neutron irradiated BEPO graphite compared to ion irradiated

HOPG, ion-irradiated Gilsocarbon, and polished Gilsocarbon

6 Irradiated BEPO graphite was supplied by the United kingdom Atomic Energy Authority with permission of the United Kingdom Nuclear Decommissioning Authority.

9 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Optical microscopy observations and collection of Raman spectra on fractured

Gilsocarbon were made on reflective facets. These are assumed to be pre-existing calcination or graphitisation cracks. Such cracks arise from the anisotropy of thermal expansion and are therefore deduced to be close to the basal plane. By using fracturing to expose pre-existing cracks, no deformation is introduced to the surface.

In non-irradiated HOPG and on the facets of fractured Gilsocarbon, there is a complete absence of the D peak indicating a presence of no significant disturbed zones on the surfaces of these samples. Ion irradiated HOPG and Gilsocarbon have extensive D peaks, similar to neutron irradiated graphite in terms of peak height and shape. This is indicative to the similarities to the phenomena of neutron and ion irradiation. Polished Gilsocarbon produced an extensive D peak, almost double in size compared to the G peak. This illustrates that the polishing process produces large quantities of surface defects, as has also been reported by previous authors [15].

At a second stage, specimens of ion irradiated Gilsocarbon, ion irradiated HOPG, and polished Gilsocarbon, were annealed to 100oC for 30 min, as described previously. After annealing and cooling down to room temperature, Raman measurements were repeated on the same specimens followed by another annealing cycle at 150oC. This cycle of consecutive annealing and Raman measurements continued until 600oC, with a step increase of 50oC each time.

Initial Raman measurements taken at different locations on the same samples showed small but noticeable differences in the spectra. An optical micrograph was used to accurately locate the same position on the sample surface for each Raman measurements after each annealing cycle (Figure 2). Attention was focused on the peaks

10 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 2 A comparison between two spectra of Gilsocarbon irradiated with Argon ions (left) and the same specimen annealed at

600ºC (right). I/IG versus wavelength. Below each spectrum diagram is an optical microscopy photograph of the measurement area

(scale in μm). A noticeable reduction in the heights of D and G peaks is observed after annealing at 600oC

11 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite attributed to the D band and G band (1340 and 1580cm-1 respectively) and the ratio of their intensities. All the measurements took place three times to assure reproducibility.

Reproducibility was observed to be very high, with a variation of less than 0.1% in peak intensity ratio.

Raman spectra collected for various annealing temperatures on the ion-irradiated

Gilsocarbon specimen are shown in Figure 3. All the measurements exhibit both D and G peaks and the ID/IG peak intensity ratio decreases after each annealing cycle. Similar data were generated for ion irradiated HOPG and polished Gilsocarbon, depicting practically the same phenomenon, the decrease of ID/IG ratio with increasing of annealing temperature. A comparison between Raman spectra of ion-irradiated HOPG and

Gilsocarbon polished and the same specimens after the end of the annealing cycles, when they have been annealed at 600ºC, is given in Figure 4. The decrease of relative intensity of the D peak after the completion of all the annealing cycles is evident.

The annealing temperature versus the ID/IG ratio at each temperature, normalised by the initial ratio before the annealing, is given in Figure 5 for all three specimens that were subject to annealing cycles.

In the figure a decrease in the ID/IG ratio with annealing temperature for all the specimens tested is evident. This decrease is more significant for the irradiated Gilsocarbon and

HOPG specimens than for the polished Gilsocarbon sample, indicating qualitative differences in the defect type, for ion irradiated and polished samples respectively.

12 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 3 A collection of all Raman spectra for various annealing temperatures (in oC) of the Ar+ ion-irradiated Gilsocarbon specimen

13 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 4 A comparison between two spectra of Gilsocarbon polished (top), and HOPG irradiated with Argon ions (bottom) and the same specimens annealed at 600ºC

14 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 5: Annealing temperature versus ID/IG normalised by the ratio initial ID/IG stage after irradiation for Gilsocarbon irradiated with Argon ions, HOPG irradiated with Argon ions and Gilsocarbon polished

3. Analysis of results

The decrease of relative intensity of the D peak observed in the spectra is considered to be an effect of a decrease in defects due to thermal treatment (annealing). A general assumption is made that by calculating the ID/IG ratio it is possible to extract quantitative information about the population of defects present.

ID/IG ratio can be a measure of damage since the intensity of the Id mode is related to

E2g symmetry which appears in disturbed graphite, and IG peak can be assumed to be directly connected to the A1g symmetry, which is unaffected by irradiation damage

[1-6,8,13,14]

I D Q   (1) IG

15 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite where λ is a factor of proportionality, ID is the intensity of the D band, and IG the intensity of the G band.

3.1. Kinetic model

The process of annealing of defects can be considered as a phase change reaction, which may be described using kinetic models [17-20]. Previous graphite annealing models have relied on data obtained from neutron irradiated graphite samples. . This work uses kinetic models to describe the annealing process in ion irradiated graphite.

Data from the experiments reported in the previous section has been used to derive the activation energies and characteristic functions in kinetic models. The objective is to show that thermal annealing of graphite defects can be understood through the use of kinetic modelling to determine the activation energy Ea and pre-exponential factor A in the Arrhenius equation. The activation energy Ea is a measure of the energy barrier needed to be overcome in order for the annealing reaction to be self sustainable.

The basic relation from which all kinetic approaches begin is defined as [17-24]: dx  kf (x) (2) dt where x is a variable that is described by the Arrhenius distribution, f(x) is follows the

Arrhenius distribution with a linear increase in time a mathematical function of x, which characterizes the sample, and k is a constant of proportionality. Various forms of the function f(x) have been considered, such as f(x) = xn which is used to consider a reaction of nth order or the more complex f(x) = xn (1-qx) m [24]. The objective of these methods is to obtain the activation energy Ea, and pre-exponential factor A, for each process as expressed in the form of a standard Arrhenius equation:

16 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

  Ea  k  Aexp  (3)  RT  or

  Ea  k  Aexp  (4)  kBT  where

k= factor of rate of reaction (specific rate)

A = Arrhenius factor or pre-exponential factor, or frequency factor

Ea= energy of activation, expressed in Joule/mol or keV/molecule

R = universal constant for an ideal gases (8.314 m2 kg s-2 K-1mol-1)

-23 2 -2 -1 kB= Boltzmann constant (1.381 × 10 m kg s K )

T = absolute temperature. (degrees Kelvin)

The process of annealing defects is assumed to be a reaction, and as such obeys the laws of thermodynamics and chemical kinetics (strictly, the annealing of defects resembles mostly a change of phase due to the increased mobility of defects).

Consequently the rate of reduction of defect quantity Q follows an Arrhenius law: dQ  Ea  Ae RT Q n dt (5)

Where :

Q =the quantity of defects at a given state of the annealing at time t

(Preferably the normalized quantities expressed as a ratio of initial quantity

content at the beginning of annealing)

A= again the pre-exponential factor of Arrhenius equation referring to number

of collisions per second. However, in the case of the annealing reaction the

17 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite analogy would be number of reacting (vanishing or moving) of defects per

second.

n= the order of the reaction when used to describe a chemical reaction, the

relation between reactants and compounds. In the case of annealing of defects,

a similar physical meaning can also be attributed.

The parameters of activation energy Ea, pre-exponential factor A, and order of reaction n are the kinetic parameters of the annealing reaction. It is to be expected that n may be affected by other parameters such as diffusion, rate of heating, microstructure characteristics, or the general condition of sample and experimental conditions. Some authors [19] have used the function f(x)=xn or f(Q)=Qn to describe the annealing of defects in graphite to analyse results obtained using Differential

Scanning Calorimetry (DSC).

By solving the differential equation in Equation 5 we obtain:

Ea n dQ  Ae RT Q dt (6) and by replacing dT  adt (7) where ‘a’ is the heating rate in oC/min, we obtain:

 Ea A RT n dQ  e Q dT (8) a

The solution of this differential can give the quantity of defects as a function of temperature or time:

1 T  Ea  1n Ae RT 1 nT Q 1   a  (9) o   T0 0 K  

18 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite A graphic form of Equation (8) is given in Figure 6 (normalized quantities).

Figure 6. The defect quantity Q at temperature T normalised by the initial defect quantity Qo .Graphic depiction of Equation 8

In figure 6 it can be observed that the shape of this curve follows same trend with the decrease of ID/IG versus temperature obtained from Raman spectroscopy (Figure 5).

This suggests that the variation of the ID/IG ratio may be described in terms of annealing of the quantity of defects.

A more useful quantity that will be utilized further in the analysis of the present work is the portion of the defect quantity that was annealed at every temperature ‘%q’, which can be expressed as a ratio of the existing proportion of defects Q subtracted of the final remaining quantity Q∞, divided by initial Q0 versus final proportion of defects Q∞:

 Q  Q  q    (10)  Q0 Q 

19 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite The divergence between calculated and experimental results, as provided by the fitting, can be expressed as a percentage, associated with the largest rate of reaction observed in experimental curve, of the following type [20,21,23]:

SUM Q /(Z  N) Dev1(%) 100 (11) max[(q)exp ]

Where Z is the total number of measurements used to represent the curve and N is the number of parameters that were used in the model, i.e activation energy Ea, pre- exponential factor A, and order of reaction n. (q)exp refers to the normalized quantity of defects as calculated by the ID/IG ratios.

In this work, the parameter N was excluded due to the small number of measurements associated, and thus Equation 10 becomes:

SUMq /(Z ) Dev1(%)  100 (12) max[(q)exp ]

The parameter SUMQ can be described as:

N 2 exp calc SUM Q   qi   qi   (13) i1

(q)calc refers to the normalized quantity of defects as calculated by using Equation 12

The problem of minimising the parameter Dev1 is a non-linear optimization problem, and can be solved by a non linear optimization algorithm [20, 21, 22, 24] by controlling the activation energy Ea, pre-exponential factor A, and order of reaction n namely the kinetic parameters. Results are generally considered satisfactory when

Dev1 is less than 3% [20, 21, 22, 24]. In this work, the Generalized Reduced Gradient

[25] implemented within the Solver Add-in of Microsoft Excel 2003, was utilized.

Previous researchers [17,18, 26, 27], using variations of the above equations, conducted kinetic analysis on neutron irradiated graphite samples taken from British

20 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite and Japanese nuclear reactors. These samples were annealed in Differential Scanning

Calorimeters (DSC). During annealing, measurable amounts of energy are being released from the graphite samples. This phenomenon, also known as Wigner energy release, is the release of accumulated energy that was stored in the graphite in the form of potential energy, during the irradiation stage. DSC experiments provide data on the rate of energy release in a specimen versus temperature or time. It is now known [16-20] that Wigner energy is the potential energy of the carbon atoms that have been displaced from their original lattice position, as a consequence of irradiation during neutron bombardment conditions (similar to the conditions taking place inside a nuclear reactor). The population of defects Q is proportional to the energy yield S.

Q  ΄  S (14) where λ΄ is again a similar proportionality factor.

That energy yield can be measured during an annealing experiment in the DSC.

Consequently by measuring the energy yield of a DSC experiment of neutron irradiated graphite, direct conclusions about the population of defects can be made.

From the above mentioned, the equations to describe Wigner energy release are also presumed to follow the Arrhenius law [24]: For example, in a DSC experiment where the temperature rises linearly, the release of stored energy is given by: dS  Ea  n  Aexp S (15) dt  RT  where S is the energy released, and n the reaction order, and are the same kinetic parameters as in the Equation (9) above. Therefore, by measuring Wigner Energy release in a DSC, and by measuring the ID/IG ratio in a Raman experiment two

21 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite different aspects of the same phenomenon, which is the reduction of the defects with thermal annealing can be monitored.

Consequently by analyzing DSC data from neutron irradiated graphite, and Raman data from ion irradiated graphite, a comparison between the annealing processes of ion irradiation and neutron irradiation is achievable. Previous researchers [17, 18, 26,

27] applied a similar kinetic algorithm to DSC data that had been obtained from neutron irradiated nuclear grade graphite.

3.1.1. Single reaction kinetic model (neutron damage)

For the kinetic analysis Simmons [17] tested a constant activation energy model. It assumes that activation energy remains constant over the temperature range of the release. dS  E   S.Aexp  (16) dt  kT 

Nightingale [19] proposed a model based on the assumption of constant frequency/constant activation energy and introduced the order of the reaction, n, as an additional variable. He assumed that there can be an order of reaction different from unity and estimated it to be around 6-8. dS n  E   S Aexp   (17) dt  kT 

The constant activation energy model has been discussed in detail in [28]. For comparison this paper analyses the ID/IG reduction ratio data using the Simmons general model and the Nightingale model. The scope of this examination was to identify the proximity of the Simmons and Nightingale scenarios to the experimental

22 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite curves derived in this study, in order to assess the need of further analysis with more complicated scenarios.

3.1.2. Multiple reaction kinetic models (neutron damage)

Other researchers over the past have made efforts towards interpreting the Wigner energy release reaction with multiple reactions [18, 26, 27] despite difficulties of limited computational power. The more characteristic works include that of Kelly et al [27] who proposed a three reactions model assuming three first order reactions taking place with the same pre-exponential factor each. Recently Lexa et al [26] based on the above studied the release of Wigner energy from graphite irradiated by fast neutrons at a TRIGA Mark II research reactor. They examined a model with four first order reactions also with the same pre-exponential factor. Iwata [18], testing specimens of pyrolytic graphite irradiated at the JAERI JRR-2 experimental reactor in

Japan, proposed a model with three first order reactions but on different pre- exponential factors each. All the aforementioned studies, including recently that of

Lexa et al [26], assume first order reactions. Additionally they do not assess the efficiency of their simulations, with the exception of Iwata [18] who attempted a curve fitting exercise. He tried to reconstruct the experimental DSC curve by the use of the calculated reactions.

The values of activation energy and pre-exponential factor of the works referred above for both the single reaction kinetic model and multiple reaction kinetic model are presented in Table 1.

23 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Table 1. Activation energy and pre-exponential factors as calculated by Simmons

[17], Iwata [18], Lexa et al [26], and Kelly et. al, [27].

3.2. Single reaction kinetic model: Ion and mechanical damage

Based on the assumptions of Simmons [17] and Nightingale [19] a single reaction kinetic model was applied to the Raman data for ion and mechanical damage. To investigate the single reaction model, Equation (8) was fitted to the experimental results for the consecutive annealing and Raman spectroscopy experiments of ion irradiated and mechanically polished graphite.

The model applied above can be described as a single reaction kinetic model, due to the fact that it is based on the assumption that the annealing process can be simulated by only one reaction. Therefore only one set of values of A, Ea, and n have to be calculated,

The results of the fitting process are shown at Table 2 and Figure 7.

24 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Table 2: Overall results for one reaction

Figure 7 shows the remaining fraction ‘q’ of defects versus the annealing temperature obtained by this analysis. The results were satisfactory for the data derived from the annealing of ion-irradiated HOPG. For HOPG the value of Dev1 reached a minimum of 3.3 and the model convergence criteria were almost satisfied. The other two sets of data, from ion-irradiated and polished Gilsocarbon did not achieve good convergence, and the values of Dev1 in both cases exceeded 3%. For the ion irradiated Gilsocarbon data and polished Gilsocarbon data the results were 4.6% and 8.6% respectively .

A comparison between the aforementioned previous researcher’s DSC kinetic analysis results and this work’s Raman peaks kinetic analysis results shows that the values for Ea and n do not closely agree. Simmons [17], Iwata [18], Lexa [26] and

Kelly [27], found activation energies of the order of 1.2 to 1.5eV. In this work, for ion-irradiated HOPG,

25 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 7 HOPG irradiated with Ar ions (top) Gilsocarbon irradiated with Ar ions

(middle) , and Gilsocarbon polished (bottom): Scenario with one reaction

26 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite and mechanically polished Gilsocarbon, the activation energy was around 1 and

0.9eV respectively. The reaction order n as reported by Nightingale [19] was between

6 to 8, which is in agreement with the value of 6.7 calculated on this work for ion irradiated HOPG. For ion irradiated and mechanically polished Gilsocarbon, however, the values of n lay outside these limits (10 and 1 respectively).

As a general conclusion, the single reaction model can not adequately fit the experimental data, considering the fact that for Gilsocarbon ion irradiated the score exceeds the 3% limit. Moreover the fitting process for polished Gilsocarbon has failed

(score 8,6%). . Additionally the obtained parameters between the three different sets of experiments do not agree with each other. This is indicative of the inadequacy of the model considering the fact that there should be a minimal agreement between the kinetic parameters obtained for ion irradiated Gilsocarbon, and ion irradiated HOPG at least. These two different types of graphite receive exactly the same doses and types of irradiation, therefore the damage induced should be similar in terms of quality. This is further supported by the fact that before ion irradiation both types of graphite produce the same signal, but even after ion irradiation their Raman signal is also very similar (figure 1). So, their annealing kinetic parameters are not expected to vary extensively.

3.3. Independent parallel reactions model

The assumption that more reactions take place during the annealing process is not new. It has been proposed by Kelly et al [27], Iwata [18], and Lexa et al [26], for neutron induced damage and therefore needs to be considered for ion irradiation damage as well.

27 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite Additional reasons for supporting the existence of more than one reaction lie in the graphs themselves. Observation on the Gilsocarbon irradiated graph (figure 7 middle) would reveal a major thermal event taking place between 100 to 150oC, reducing vastly the ID/IG ratio an consequently the number of defects (territory A). Another hypothetical territory between 200 to 300oC, although subjectively visible, is a possible region that a second annealing reaction occurs. Another territory of disturbance between 350 to 500oC could also suggest that a possible third reaction takes place at higher temperatures. Some of these territories are merely visible in the

Gilsocarbon polished diagram (territories A and B), therefore there is a possibility that similar defects in terms of quality, are produced during polishing as well.

In the previous single activation model it was assumed that the annealing process has only one reaction process. Therefore in order to produce an adequate fit to the experimental data, one needed to optimize the kinetic parameters for only one reaction. The basis of this assumption is that only one type of defect was produced by irradiation and consequently only one thermal relaxation process for defect annealing is required.

Other researchers have used the independent parallel reactions model to study heterogeneous reactions in biomass and fossil fuels [21, 22]. These models pre- suppose the existence of independent parallel reactions without interactions between them. For this particular analysis the independent reactions, also called partial reactions or “pseudo-reactions”, can take place sequentially implying that each pseudo-reaction begins when another finishes, or in parallel, supposing that pseudo- reactions develop simultaneously, without interactions. Combinations of these two possibilities can also be selected for the analysis of more complex systems.

28 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite In the multiple reactions approach to the analysis of defects, it is assumed that the overall result is the sum of each reaction: q  qi (18) i where qi are the individual reactions taking place. The summation of the qi produces an overall result of the reduction in the quantity of defects given by:

1 T E  ai 1ni A e RT 1 n T q  1 i i  i  a  (19)   T0  

where qi is the reduction in the quantity of defects from an individual partial reaction.

The application of the independent parallel reactions model to the annealing of defects, due to its complexity, can provide with a variety of scenarios for a single set of data. There are some general guidelines [20- 22, 24] for the use and acceptance of results from a kinetic analysis scenario. In summary; a model is considered valid when a model fitted to one set of experimental data can predict another independent set of data; In general the simplest model available should be chosen; results between different experiments may vary slightly, so it is considered essential that they produce results of the same order; The shape of the predicted curve must follow the experimental shape, since even when the target of Dev1<3% is achieved, the shapes of experimental and calculated curves can still show significant differences when the model is incorrect.

In the independent parallel reactions model, a parameter that refers to the percentage of participation of every each partial reaction to the overall process (symbolized with c) is added. This parameter is explained in detail elsewhere [20]. As a result, four parameters are taking part in the optimization process for every partial reaction,

29 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite namely activation energy Ea, pre-exponential factor A, order of reaction n, and percentage of participation c.

Two possible scenarios were examined for the ion-irradiated and mechanically damaged samples. In the first, the intensity ratio and the normalized intensity ratio were assumed to be directly proportional to the quantity of defects. In the second, a non-linear square root dependence was examined.

3.3.1. Scenario I. Linear relation between quantity of defects and

ID/IG ratio

The aforementioned previous researchers [18, 26, 27] used a kinetic approach scenario of three partial reactions. Based on the above, and the assumption that the relation between defect quantity and ID/IG is indeed linear, a three partial reactions model was chosen and applied to the ion-irradiation and mechanical damage data. A three reactions scenario was chose because the three different territories that were observed in figure 7 indicate the existence of three reactions. The starting point values of the optimization were chosen from Table 1, and the results from this analysis are given in

Figure 8 and on Table 3.

The overall activation energies for the three reactions have been calculated as 1.5 eV,

1.9 and 2.9 respectively. The values for the first two reactions are in accordance with the second and the third reaction values reported by Iwata [18], Lexa et al [26] and

Kelly et al [27]. The third reaction exceeds these values, but for the ion-irradiated

HOPG and Gilsocarbon does not have a very high contribution (percentage ‘c’) which implies that there is not high confidence in the value for this reaction. The first reaction that is obtained by Iwata [18], Lexa et al [26] and Kelly et al [27], is not

30 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite found in the data of this work. This implies that the ion irradiation and mechanical processes do not create defects

Figure 8. HOPG irradiated with Ar ions (top) Gilsocarbon irradiated with Ar ions

(middle) , and Gilsocarbon polished (bottom): Scenario with three reactions

31 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Table 3: Overall results for the three reactions (Scenario 1).

that anneal at such low temperature, and reveals a clear difference between neutron irradiation and ion irradiation in particular.

The values of the reaction orders are calculated in all reactions to exceed unity.

However they have been found to be the same for all three sets of experiments and therefore there is an indication that they can be considered as reproducible and characteristic. The value of the reaction order n for the second reaction is higher than the first and the third reactions. However, these values are in accordance with values reported by Nightingale [19] and can reach values between 6 to 8.

The third reaction does not have a very high contribution to ion irradiated Gilsocarbon and HOPG (percentage ‘c’ was 6 and 11% respectively). This can imply that there is

32 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite not high confidence in the values obtained for this reaction, as well as the fact that the reaction itself can be omitted. However, it was included in the presented analysis since it is extensively present in the annealing graph of polished Gilsocarbon. Thus it was proposed in an overall three reaction scenario basis, as has also been proposed by literature [18, 26, 27]. However this is subjective to discussion and the authors would suggest further research efforts towards the direction of proving the evidence of this reaction’s existence. Additionally it is also possible that the annealing of polished

Gilsocarbon can be interpreted as a two reactions step under the aforementioned assumption. The first two reactions covering the area between 0 to 250oC can be merged into one that covers the whole area.

Therefore another possible variation in this scenario is developed in this paper. In this scenario the third reaction was omitted in the ion irradiated specimens, and in the polished Gilsocarbon annealing the second reaction is also omitted, and the first is expanded to contain the territory left uncovered. The results are presented in Figure 9 and Table 4.

In the case of HOPG, DEV1 was marginally outside of the acceptable limits and for ion irradiated Gilsocarbon the overall score was worse (4.2%). However for polished

Gilsocarbon there was a major improvement (2.0 % for the two reactions against 2.6 for the three reactions).

33 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 9 HOPG irradiated with Ar ions (top) Gilsocarbon irradiated with Ar ions

(middle) , and Gilsocarbon polished (bottom): Scenario with two reactions

34 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Table 4: Overall results for the two reactions (Scenario 1).

3.3.2. Scenario 2 – Square root relation between quantity of defects and ID/IG ratio

In the first scenario and also the simple kinetic model, it was assumed that the intensity ratio and the normalized intensity ratio were directly proportional to the quantity of defects. However this is assumption has been. Kitajima et al.[29] and

Asari et al.[30,31], in their interpretation, have produced a model where the quantity of defects is proportional to the square root of the relative intensity ratio (square root proportionality assumption).

Their approach was based by them on the several assumptions. Firstly, the mean distance L between the in-plane defects is proportional to the square root of the quantity of defects within a graphitic layer QL.

35 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

1  2 L  (QL ) (20)

Secondly, there is no interaction between the layers during the production of the defects. The produced defects are distributed between the layers and the interstitial atoms do not bridge the gap between them (It is noted that Li et al.[32] claim the opposite, stating that there are cases where interstitial atoms come to rest to pre-fixed positions between the layers).

As a result of the assumption of Kitajima et al.[29] and Asari et al. [30,31], the overall quantity of defects produced QD can be expressed as a linear function of the in-layer defects QL:

QL  fQD (21)

Where f=0.335 (0.335 nm is the distance between the graphitic layers)

It is also assumed that the in-plane phonon correlation length La corresponds to the mean distance L between the defects.

Consequently, since the in-plane phonon correlation length is related to the relative intensity ratio of the D to G mode, as is given by the relation below [33]:

I D C  (22) IG La

(for a wavelength of λ=514.5 nm and an optical depth of C(λ)=4.4 nm) where the quantity of defects per layer NL can be correlated with the relative intensity ratio as:

I D  C() QL (23) IG

By combining Equation (20) with (17) the overall defect quantity is expressed as

36 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

I D  C() f QD (24) IG and

2 1  I  Q   D  D 2   (25) fC ()  IG 

Consequently, f·C2(λ) is cancelled, and the normalized quantity q becomes:

2 2 2 2  Q  Q   I   I    I   I   q       D    D   / D    D    Q  Q   I   I   I   I  (26)  0    G   G    G 0  G   By application of the above assumption to the kinetic parameter calculation algorithm, the results show better agreement of the calculated overall curve with the experimental values assessed (Figure 10 and Table 5).The values of Dev1 for all ion- irradiated HOPG and Gilsocarbon ion-irradiated and polished are 2, 1.8 and 2.2 respectively, whereas for the scenario I they were 2.8, 2.5 and 2.6 respectively, suggesting that the assumption the ID/IG ratio is proportional to the square root of the defect density produces better results than the assumption of linear proportionality.

The values of activation energies remain the same and the reaction orders decrease slightly.

The assumption of Kitajima et al.[29] and Asari et al.[30,31] produces better results.

But can not obviously rule out the existence of interactions between the layers during the production of the defects. Bonding between layers by irradiation induced interstitials in double walled carbon nanotubes has been proved by TEM studies [34] and their annealing characteristics were also monitored. Therefore in the deterioration of the ID/IG ratio, annealing of intralayer bonding also takes part. The adequacy of this model can only give an indication of a preference of interplanar accumulation of the

37 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 10 HOPG irradiated with Ar ions (top) Gilsocarbon irradiated with Ar ions

(middle) , and Gilsocarbon polished (bottom): Scenario with three reactions and assumption of square root proportionality

38 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Table 5: Overall results for the scenario of the three reactions, with the assumption of square root proportionality (Scenario 2). defects against the formation of bridges between layers. However it is reasonable to assume that both phenomena take place and the interplanar accumulation preference of defects is probably due to the irradiation method chosen. The angle of incidence of the ion jet was very low, around 5 degrees. This fact would deteriorate the in-depth damage and produce more damage along the basal planes, particularly in the case of

HOPG, and this is the main reason that the square root proportionality scenario was chosen to be tested.

In both of the scenarios, despite the fact that calculated activation energies were close to values reported by literature, the pre-exponential factors are higher (Table 3). It therefore can be assumed that ion irradiation can describe the same phenomenon as neutron irradiation in qualitative but not in quantitative terms, therefore pre-

39 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite exponential factors may be expected to vary. The defects introduced by ion- irradiation, mechanical damage and neutron irradiation anneal with the same activation energies, but are introduced in different proportions (as shown by the reaction orders and relative contributions). There may also be synergies between the defect types that are not revealed by this analysis. This is even more profoundly evident in the case of annealing defects produced by mechanical polishing, by comparing the overall contribution of each reaction assessed with the scenarios that have been calculated for ion irradiated samples. Therefore the annealing processes of ion irradiation induced damage tested in this work, and neutron irradiation induced damage reported in literature differ. However, an indication exists, that there is an overall qualitative resemblance between the calculated kinetic parameters of this work’s ion irradiation data, and a combination of the kinetic scenarios that have been reviewed in the literature.

The third reaction also does not have a very high contribution to ion irradiated

Gilsocarbon and HOPG (percentage ‘c’ was 4 and 5% respectively) similarly to the

Scenario 1. Therefore a second trial was executed, this time by omitting the third reaction in ion irradiated HOPG and Gilsocarbon. The results this time were adequate and within acceptable limits (2.4 and 2.5 for HOPG and Ion irradiated Gilsocarbon respectively). This is indicative that under the assumption of no interaction between the layers during the production of the defects a simpler two reaction scenario is capable of producing adequate results, contrary to scenario 1.

Additionally, in the case of polished Gilsocarbon a two reaction fit was implemented by merging the first two reactions into one, similarly as to scenario 1. The deviation also improved, reducing by 0.2%.This indicates that a two reaction scenario can better fit polished Gilsocarbon. The results are demonstrated on Table 6 and on Figure 11

40 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Table 6 Overall results for the scenario of the two reactions, with the assumption of square root proportionality (Scenario 2).

41 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite

Figure 11 HOPG irradiated with Ar ions (top) Gilsocarbon irradiated with Ar ions

(middle) , and Gilsocarbon polished (bottom): Scenario with two reactions and assumption of square root proportionality

42 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite In all three models tested the first two reactions with activation energies of 1.5-1.6 and 1.8-1.9 eV, due to Iwata [18] correspond to a di-interstitial annihilated by two mono-vacancies. Reynolds [35] claims that an activation energy estimate of 1.8 to 2.6 eV corresponds to mobilization of defect aggregates and Telling et al.[36] amongst other authors claims that a 1,7 eV activation energy corresponds to vacancy migration.

3.4. The assumption of the very low constant heating rate

The Arrhenius equations that have been used to describe the annealing evolution in all models tested above are used in experiments with constant heating rate. Therefore the experimental data produced in this work are unsuitable for analysis with the equations above. However, a very slow heating rate, at around 1oC/min, would allow plenty of time for the annealing reaction to complete. Therefore in a hypothetical annealing experiment with constant heating rate, for every each temperature point, a completion of the annealing reaction can be assumed. Consequently, if a very low heating rate is assumed, then the sets of data produced in this work can be interpreted by using the equations aforementioned.

In the analysis that follows it was assumed that the hypothetical heating rate was so low that the annealing reaction would be complete at every stage. The ID/IG points derived at each stage could then be considered to coincide with a continuous single annealing experiment taking place under a very low but constant heating rate. The heating participated as an additional parameter, during the optimization, and an optimum value of about 1.4oC/min was calculated.

43 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite 4. Conclusions

The kinetic analysis of the annealing of ion-irradiated and polished graphite samples and the investigation of the decrease of the Raman ID/IG ratio showed that it is possible to interpret the annealing process as a convolution of two and possibly three different processes, using a parallel reactions kinetic model. The magnitudes of these processes differ in the two types of damage.

The investigation provides a simple analysis that is shown to be closer to reality than the assumption of a single reaction. The assumption that the ID/IG ratio is proportional to the square root of the defect quantity also produces better results than assuming a simple linear dependence.

The ability to interpret the annealing reaction of an ion-irradiation technique with a kinetic scenario previously used for stored energy release from neutron irradiated specimens is indicative of a qualitative similarity in the phenomena of ion and neutron irradiation. Therefore ion irradiation, together with Raman spectroscopy, with the vast variety of irradiation methods and ion beams available has the potential to serve as an alternative technique to the analysis of neutron damage annealing.

Acknowledgements.

The authors wish to express gratitude to British Energy Generation Ltd. for the supply of non-irradiated (virgin) Gilsocarbon specimens and the UKAEA (United Kingdom

Atomic Energy Authority) for the supply of neutron irradiated BEPO graphite with the permission of UK NDA (Nuclear Decommissioning Authority). They would also wish to express gratitude to the Greek State Scholarships Foundation for financial and laboratory expenses support. They would additionally like to thank Professor P.

44 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite Mummery of The University of Manchester and Professor A. Carley from University of Cardiff for valuable help and support.

References

[1] Asari E, Nakamura K G, Kawabe T, Kitajima M. Observation of relaxation processes of disorder in ion-irradiated graphite using Raman spectroscopy. J Nuc

Mater, 1997; 244, 173-175.

[2] Asari E. An effect of the extended cascade on the Raman spectra of ion-irradiated graphite. Carbon 2000; 38, 1857–1861.

[3] Liu J, Yao H J, Sun Y M, Duan J L, Hou M D, Mo D, Wang Z G, Jin Y F, Abe H,

Li Z C, Sekimura N. Temperature annealing of tracks induced by ion irradiation of graphite. Nucl Instrum Meth B. 2006; 245, 126–129.

[4] Compagnini G, Puglisi O, Foti G. Raman spectra of virgin and damaged graphite edge planes. Carbon 1997; 35, 1793-1797.

[5] Ishioka K, Hase M, Ushida K, Kitajima M. Coherent acoustic phonon-defect scattering in graphite. Physica B 2002; 316–317, 296–299.

[6] Liu J, Hou M D, Trautmann M, Neumann C R, Muller C, Wang Z G, Zhang Q X,

Sun Y M, Jin Y F, Liu H W, Gao H J. STM and Raman spectroscopic study of graphite irradiated by heavy ions. Nucl Instrum Meth B. 2003; 212, 303–307.

[7] Niwase K.. Formation of dislocation dipoles in irradiated graphite. Mat Sci Eng A

Struct 2005; 400–401, 101–104.

[8] Hida A, Meguro T, Maeda K, Aoyagi Y. Analysis of surface modifications on graphite induced by slow highly charged ion impact. Nucl Instrum Meth B. 2003;

205, 736–740.

45 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite [9] Hall G, Marsden B J, Fok S L. The microstructural modelling of nuclear grade graphite. J Nucl Mater 2006; 353, 12-18.

[10] Brülle T, Stimming U. Platinum nanostructured HOPG – Preparation, characterization and reactivity. J Electroanal Chem 2009; 636, 10-17.

[11] Ziegler J F, Ziegler M D, Biersack J P. SRIM – The stopping and range of ions in matter (2010). Nucl Instrum Meth B. 2010; 268, 1818-1823

[12] Borisov A M, Mashkova E S, Nemov A S, Virgiliev Y S. Sputtering of HOPG under high-dose ion irradiation. Nucl Instrum Meth B. 2007; 256, 363–367.

[13] Asari E, Kitajima M, Nakamura K G. A kinetic study of the recovery process of radiation damage in ion-irradiated graphite using real-time Raman measurements.

Carbon 1998; 36, 1693–1696.

[14] Ferrari A C, Robertson J. Interpretation of Raman spectra of disordered and amorphous carbon. Phys Rev B 2000; 61, 14095-14107

[15] Nakamizo M. Tamai K. Raman-spectra of the oxidized and polished surfaces of carbon. Carbon 1984; 22, 197-198.

[16] Dickson J L, Kinchin G H, Jackson R F, Lomer W, Simmons J H W. BEPO

Wigner Energy Release. A- U.K Atomic Energy Authority, A.E.R.E. Harwell. Second

United Nations International Conference on the Peaceful Uses of Atomic Energy.

A/Conf.15/P/1805. United Kingdom. 13 June 1958.

[17] Simmons J H W. Stored energy in the Windscale piles. AEA Technology. AEA

RS 5283. March 1994.

[18] Iwata T. Fine structure of Wigner energy release spectrum in neutron irradiated graphite. J Nuc Mater 1985; 133-134, 361-364.

[19] Nightingale R E. Irradiation annealing in graphite 1. An experimental study.

TID-7565(Pt.1) Dec. 1957 US/UK Graphite Conference St., Giles Court, London.

46 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite [20] Lasithiotakis M, Marsden B J, Marrow J T, Willets A. Application of an independent parallel reactions model on the annealing kinetics to irradiated graphite waste. J Nucl Mater 2008; 381, 83–91.

[21] Varhegyi G. Aims and methods in non-isothermal reaction kinetics. J. Anal.

Appl. Pyrol 2007; 79, 278–288.

[22] Sorum L, Gronli M G, Hustad JE. Pyrolysis characteristics and kinetics of municipial solid waste. Fuel 2001; 80, 1217-1227.

[23] Joraid A A. The effect of temperature on non isothermal crystallization kinetics and surface structure of selenium thin films. Physica B. 2006; 390, 263-269.

[24] Varhegyi G, Szabó P, Jakab E, Till F. Least squares criteria for the kinetic evaluation of thermoanalytical experiments. Examples from a char reactivity study. J

Anal Appl Pyrol 2001; 57, 203-222.

[25] Hwang C L, Williams J L, Fan L T. Introduction to the generalized reduced gradient method. 1972 Institute for Systems Design and Optimization, Kansas State

University in Manhattan. Report no. 39.

[26] Lexa D, Dauke M. Thermal and structural properties of low-fluence irradiated graphite. J Nucl Mater. 2009; 384, 236–244.

[27] Kelly BT, Marsden BJ, Hall K, Martin DG, Harper A, Blanchard A. Irradiation damage in graphite due to fast neutrons in fission and fusion systems. IAEA TEC

DOC-1154, 2000.

[28] Minshall P C, Wickam A J. The description of Wigner energy and its release from Windscale pile graphite for application to waste packaging and disposal. IAEA

TCM-Manchester99, 47-64.

47 Chapter 5 - Publication II: Annealing of ion irradiation damage in nuclear graphite [29] Kitajima M, Asari E, Nakamura K G. Real-time observation of thermal relaxation of initial damage in graphite under ion irradiation. J Nucl Mater 1994; 212-

215, 139-142

[30] Asari E, Kitajima M, Nakamura K G, Kawabe T. Thermal relaxation of ion irradiated damage in graphite. Phys Rev B 1993; 47, 147-156

[31] Asari E, Kamioka I, Lewis WA, Kawabe T I, Nakamura K G, Kitajima M. Ion mass effect on lattice disordering rate of graphite under low energy ion irradiation.

Nucl Instrum Meth B. 1994; 91, 545-548

[32] Li L, Reich S, Robertson J. Defect energies of graphite: Density-functional calculations. Phys Rev B 2005; 72, 184109-184119

[33] Tuinstra F, Koenig J L. Raman Spectrum of Graphite. J Chem Phys 1970; 53,

1126-1130

[34] Urita K,. Suenaga K, Sugai T, Shinohara H, Iijima S. Phys. Rev. Let .94, 155502

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[35] W.N. Reynolds, P.A. Thrower. Philos. Mag. 12, (1965) 573-593

[36] R.H. Telling, C.P. Ewels, A.A. El-Barbary, M.I. Heggie, Nature Materials 2

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48 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Chapter 6 - Publication III: Application of an Independent Parallel

Reactions Model on the Annealing Kinetics of BEPO Irradiated

Graphite

Michael Lasithiotakis. Barry Marsden, James Marrow.

Accepted for publication to Journal of Nuclear Materials, Elsevier. Ref. No.: CARBON-D-11-01944

69 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Application of an Independent Parallel Reactions

Model on the Annealing Kinetics of BEPO Irradiated

Graphite

Michael Lasithiotakis*7,a,b, Barry J. Marsdenb and T. James Marrowc.

a-Materials Performance Centre, Corrosion and Protection Centre, School of

Materials, The University of Manchester, Manchester, M13 9PL, UK b-Nuclear Graphite Research Group. School of Mechanical, Aerospace and Civil

Engineering, The University of Manchester, Manchester M13 9PL, UK. c- Department of Materials. University of Oxford, Parks Road, Oxford OX1 3PH, UK

Abstract

Stored energy release rates have been determined for neutron irradiated graphite samples machined from an early air-cooled nuclear reactor (British Experimental Pile

Zero or BEPO). The rate of release of stored energy was measured for both isothermal and linear rise heating rate differential scanning calorimetry experiments.

The rate of release data were analysed using a thermal kinetics, independent parallel reactions model. The effect of annealing on the graphite crystalline structure was evaluated by investigating changes to X-ray diffraction spectra. A correlation between the calculated crystallite size and stored energy release is presented. A

7 *-Corresponding author: Tel: +44(0)161 306 4840. e- mail:[email protected]

1 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite method for calculating the kinetic parameters for the annealing reaction is proposed and tested against the data. The method shows excellent consistency for both the isothermal and linear heating rate experiments (with less than 3% standard deviation).

Key words: Wigner energy, kinetics, graphite, irradiation, annealing.

Introduction

During operation of graphite moderated nuclear reactors, the physical properties of the graphite components are altered due to damage by fast neutron irradiation. This damage is the result of cascades of atomic displacements in the graphite lattice, forming defects [1]. A restoration of some physical properties is achievable by thermal annealing above the temperature at which the graphite was irradiated. During the annealing process, accumulated energy is released in the form of heat. This ‘stored energy’ is often referred to as Wigner energy [2]. Whist stored energy is not an issue for modern power reactors which operate at high temperatures, significant amounts of stored energy are accumulated in graphite irradiated at temperatures below ~100°C

[3]. Examples of such reactors in the UK are BEPO (British Experimental Pile Zero) and the two Windscale Piles, which are now shut down. The potential for heat generation from accidental low temperature annealing of graphite from these reactors needs to be accounted for during decommissioning and waste disposal. This is done using thermal kinetic models to simulate the release of energy from graphite that are fitted to experimental data.

Various methods have been used to measure Wigner energy release and to define the parameters for the thermal kinetic models used in graphite core decommissioning safety cases [4-12]. A differential scanning calorimeter (DSC) is normally used to measure the rate of release of stored energy as a function of temperature normally up to a temperature of 600°C, although some authors have measured energy release to

2 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite 1600°C [13]. The presence of a significant amount of stored energy in a sample can lead the energy release rate to exceed the rate of heat absorption by the specific heat.

This makes the reaction self-sustaining until the rate falls back below the specific heat. This energy release can produce a measurable rise in graphite temperature, which can be as much as ~350°C [14]. Annealing up to 600°C does not remove all the stored energy; temperatures up to around 2100°C are required to do this [13].

The kinetic models used to model the release of stored energy are all based on the

Arrhenius equation, requiring the determination of activation energy Ea and frequency factor A. Some authors consider annealing as a single stage reaction [5, 9] whereas others treat annealing as a more complex process [6, 15-17]. All of these models have been fitted to experimental DSC data, obtained from irradiated graphite samples.

Some models gave reasonable fits to the data [10,14,16], however the various authors did not attempt to verify their models in a systematic way.

In this work, measurements and kinetic analysis of the stored energy release spectra in samples of neutron-irradiated graphite obtained from British Experimental Pile Zero

(BEPO) have been investigated. The classical theory of kinetic analysis has been applied using sophisticated models, which assume independent parallel reactions to describe the various energy release processes, defined by different activation energies and pre-exponential factors. These models are designed to allow the application of an increased number of reactions to simulate the experimental DSC data and to provide a systematic verification of particular scenarios.

Having successfully fitted the independent parallel reactions kinetics model to linear heating rate data from irradiated BEPO graphite, the models have been used to investigate the kinetics of isothermal annealing of other irradiated BEPO samples to demonstrate consistency in the model parameters.

3 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite Experimental

Material and Sample Preparation

The United Kingdom Atomic Energy Authority (UKAEA), with permission from the

Nuclear Decommissioning Authority (NDA), supplied a sample of irradiated graphite from the decommissioned BEPO reactor. This sample had been extracted from section 20 (Figure 1) of a four-inch diameter cylinder that had been bored through the reactor bio-shield and core in 1975 [12]. This section had received a thermal neutron fluence of 11.3 x 1020 n/cm2 EDND (Equivalent Neutron Dose) at an estimated irradiation temperature of between 100 and 120°C [4]. The specimen was machined inside a glove box in the active facilities at SERCO Ltd. (Warrington, Risley), where the specimens were also stored between observations. A Secotom Diamond Cutting machine, operating at 2500 r/min, was used. No cooling liquid could be used, in order to avoid radioactive contamination. A 6 mm diameter cylinder was cut into disks approximately 1.5 mm thick. The mean sample weight was around 70 mg.

Differential Scanning Calorimetry Measurements

Linear Heating Rate

Rate of release of stored energy measurements were made on two nominally identical samples of irradiated BEPO graphite. The measurements were made in a power compensated Perkin–Elmer DSC-7 using Perkin–Elmer Pyris Diamond software, with

99.9999% Ar purge gas at 20 cm3 min-1. The temperature was ramped from 25° to

600°C at a linear heating rate of 10°C min-1 with an isothermal end state of 600°C that was then held for 30 minutes. Then, as is the common practice for measurement of

Wigner energy release in graphite [5-11], the heating ramp is repeated. The first sets

4 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

NARROW WIGNER WIGNER NARROW WIGNER WIGNER LAYER 20 BLOCK FRACTURED SAMPLED MISSING SAMPLED BLOCK SAMPLED SAMPLED 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 END OF CORE BRICK LAYER 19 FRACTURED MISSING NARROW FRACTURED FRACTURED FRACTURED FRACTURED FRACTURED BLOCK JUNCTION

LAYER 18

LAYER 17

REMOVEABLE CORES

Figure 1: Location of the four-inch core section taken from BEPO [12]. Samples were obtained from section 20. All graphite supplied to NDA by the UKAEA came from the lower section of the core, which is shaded (light blue).

5 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite of measurements was subtracted from the second in order to produce a graph of energy release as a function of temperature that determines the Wigner energy release rate characteristic for the specimen (“linear heating rate thermographs”). In each case the sample was left to cool down to room temperature before the second run was executed.

In order to verify that for each sample that all the Wigner energy was released (to

600°C) during the first run, the specific heat capacity of annealed BEPO samples was measured. The specific heat capacity for two BEPO samples was obtained, according to standard methodology [18], using the data from the second run for both samples, a baseline DSC run (an empty run without any samples) and a run with a standard sapphire sample at the same heating rate. For comparison, the specific heat capacity of non-irradiated Pile Grade A graphite sample (PGA), was also measured at the same heating rate. PGA is a nuclear graphite grade used in the UK Magnox reactors, which is manufactured from a needle-coke and is similar in structure to BEPO graphite [19].

It was used for comparison because samples of unirradiated BEPO graphite are not available. The specific heat capacity versus temperature data for well graphitised artificial graphite grades should be very close [20]. The specific heat capacity graphs of PGA and both annealed BEPO samples, coincide with each other as well as a standard graphite specific heat capacity as derived by Preston et al (Figure 2 and

[7,8]). The maximum standard deviation between all specific heat capacity curves is

3.3% indicates that practically all Wigner energy in this temperature range was released during the first DSC anneal. Therefore two consecutive runs were adequate to remove all Wigner energy content, and no additional annealing to remove residual

Wigner energy was necessary. Results are depicted in Figure 3.

6 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 2: Specific heat capacity of PGA and BEPO graphite, after the first annealing up to 600°C, compared with a graphite specific heat capacity standard [7,8]

7 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 3: Non-isothermal experimental thermographs. BEPO graphite, DSC, rate of heating 10°C/min, from 0 to 600°C. Territories A, B and C reveal different thermal processes going on. This is an indication that more than one reaction occurs during annealing.

8 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite Isothermal annealing

A set of eleven isothermal DSC runs were performed on irradiated BEPO samples, each ending with an isothermal anneal of one hour (Figure 4). Each sample was first heated at the same rate as before (10°C/min) to various final isothermal temperatures ranging from 100°C to 600°C at 50°C intervals. As before, each sample underwent the same heat treatment twice, and in each case the sample was left to cool to room temperature before the second heating treatment. The two sets of data were subtracted from one another to isolate the thermal effect of the Wigner energy release.

Thus, eleven plots of Wigner energy release rate against temperature (“isothermal thermographs”) were produced, one for each sample.

X-ray Diffraction Measurements

X-ray diffraction (XRD) characterisation was performed on a non-irradiated PGA specimen, an irradiated BEPO graphite specimen and the BEPO irradiated specimens that had been annealed isothermally (twice) at 100°C to 600°C in 100°C intervals to monitor the effect of annealing to crystalline properties. A Philips X’Pert MPD θ/2θ

X-ray diffractometer was used (CuKa, λ = 1.542 Å) to scan the whole range between

5-95° 2θ with rate of 0.75°/min.

Results

Differential Scanning Calorimetry

The Wigner energy linear release rate thermographs (“linear heating rate thermographs”) obtained reveal three characteristic regions with increasing temperature (Figure 3). These can be identified as: a distinct peak between 180°C to

340°C (Figure 3, peak A), another peak followed by a rapid decrease in the rate of

9 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 4: Isothermal runs on elevated temperatures from 150°C up to 600°C in 50°C intervals. The non-isothermal part (Non Iso) and isothermal part (Iso) are separated with a dashed line.

10 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite release from about 220°C to 500°C (Figure 3, peak B) and a territory of an approximately constant rate of release above 500°C to the end of the run at 600°C

(Figure 3 plateau C). These features appear in both the linear heating rate and the isothermal thermographs.

The linear heating rate thermographs for the two samples differ in shape (standard deviation between heat release rate plots was 38%, Figure 3). This variation may be due to partial annealing during sample preparation, as a coolant liquid could not be used. Variations may also be due to fluence and temperature gradients across the block during irradiation, although these are not expected to be significant.

The data for the rate of Wigner energy release obtained by the subtraction of isothermal annealing runs (“isothermal thermographs”) are given in Figure 4. Two regions are identified, separated by the dotted line, the first part comprises data where the linear heating rate was applied (“Non Iso”). The second region is the isothermal heating stage (“Iso”) where the rate of the reaction decreases.

The characteristic regions described by the linear heating rate thermographs are also observed in the initial temperature rise parts of the isothermal thermographs. The higher the final temperature the more obvious this region becomes, particularly in the isothermal thermographs of 550°C and 600°C. This is a further evidence for the energy release characteristic in this region.

X-ray Diffraction

There are two overlapping peaks in the region from 25 to 26° (2θ), which correspond to the (002) graphite interlayer spacing, ‘c’ [21]. The more intense primary peak, at the lower angle, is sharper and appears in all specimens. In the irradiated BEPO specimens the position of this primary peak tends to move towards lower angles by

11 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite approximately 1 to 1.5° when compared to the unirradiated PGA (Figure 5). This suggests an increase in the graphite interlayer spacing with irradiation.

The interlayer spacing has been observed to decrease as the degree of order increases in graphite [22, 23], and a decreasing trend in the interlayer spacing has also been associated with the restoration of irradiation damage from annealing at similar temperatures to this work (up to 525°C compared to 600°C) [11]. However, a clear trend relating the interlayer spacing to annealing temperature was not observed in our data. It was not possible to measure precisely the interlayer spacing in this work.

Calibration would have required the radioactive graphite and a silicon standard to be mixed in powder form and measured simultaneously [21]. This could not be done due to radioactivity contamination restrictions applied to the instruments used.

Consequently, a correlation between angle at peak maximum and annealing temperature, transformed to inter-planar spacing and annealing temperature could not be extracted.

The broader secondary peak, which has an average separation from the (002) peak of

0.6° (2θ), with a standard deviation of 0.06°, was observed in all the irradiated BEPO graphite specimens (Figure 5). Broadening of the (002) peak with irradiation was previously reported by Lexa et al [11], who did not resolve the secondary peak. Peak broadening is generally described in terms of crystallite size, such as in the (002) direction [24]. The assumption is that the accumulation and concentration of irradiation-induced crystal defects disturbs the inter-crystalline homogeneity. This decreases the size of homogenous clusters with consequent peak broadening. The variation of the (002) peak width is therefore commonly used to characterise radiation damage in terms of the crystallite dimension.

12 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 5: XRD spectra of non irradiated PGA, irradiated BEPO, and irradiated BEPO annealed with final temperature at 100 up to 600°C with 2θ at peak points.

13 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite The crystalline size was calculated using the Scherrer equation [25, 26], following the standard integral breadth method [26].

K   Dcos (1)

Where β is integral breadth of the peak, K is a constant referred as the crystalline shape factor, which is set to unity in the case of integral breadth calculation method

[27], λ is the X-ray wavelength (1.542 Angstroms for copper in this case), D is crystallite dimension, and θ is the Bragg angle at the peak maximum. For (002) diffraction peaks, the graphite crystallite dimension is commonly referred to as Lc.

The observed primary and secondary peaks overlap, so deconvolution was used to separate them. This was accomplished using the PC-APD (version 3.6) software [28].

The deconvolution technique applied (Figure 6) involves fitting a squared Lorentzian profile to represent the experimental XRD profile. A Marquardt non-linear least squares optimisation algorithm, based on the statistical χ2 test, adjusts the squared

Lorentzian profile so as to fit the experimental XRD profile.[28,29]. The profile fitting achieve convergence when the difference in the χ2 test value is less than or equal to 0.3 [28]. Integral breadth was then obtained from the integrated area between each peak and the normalised baseline, divided by the maximum peak height.

Part of the peak broadening was due to inevitable instrumental effects. To account for this, a separate run of a silicon standard was carried out and the instrument integral breadth (of the order of 0.20°) for the (111) peak at 28.45° was obtained. This was subtracted from the previously calculated integral breadth, to remove instrumental error [27]. The resulting peak integral breadth for the primary peak was of the order of 0.23°, with a standard deviation of 9.5%, and 2° for the secondary peak with a standard deviation of 5%.

14 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 6. Final stage of deconvolution of the double peak at 25 to 26°. XRD spectrum of BEPO irradiated graphite, annealed at 100oC. (χ2 test value is less than or equal to 0.3).

15 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Using the primary peak data, the crystalline size, Lc increased with annealing temperature from 200 Å (non-annealed) to 1200 Å at 600°C. The crystallite size defined using the secondary peak was between 39 Å and 51 Å (Figure 7 A, and C).

The non-irradiated data are consistent with literature data; a typical polycrystalline nuclear graphite (PCEA) is reported to have crystallite size in the range of 200-300 Å.

[21]. The dimensions calculated here for irradiated and annealed samples can be regarded as statistical parameters that serve as an index of crystallinity with respect to irradiation damage. The data show that the apparent crystalline size increases with annealing temperature, from which it is concluded that ordered territories are increasing in size with respect to disordered territories. The effect of annealing temperature on the percentage increase of crystalline size correlates with the percentage Wigner energy released (Figure 7, B and D). This indicates that Wigner energy release is directly related to changes in the graphite’s crystalline microstructure.

Kinetic Analysis

The thermal annealing of graphite can be described using thermal kinetic models.

Various mathematical kinetic models have been proposed and their parameters obtained by fitting to DSC data. All kinetic characterisations are variations on the

Arrhenius equation [5-11,15-17]: dx  kf (x) dt (2) where x is a variable that follows an Arrhenius equation, f(x) is a mathematical function of x, which characterises the sample, and k is the constant of proportionality.

In the case of Wigner energy release x = S, where S is the energy released during an

16 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 7. A and C: crystalline size Lc with annealing temperature for primary peak (A) and secondary peak (C) together with their calculated integral breadths. B and D: Normalised phenomenal crystalline size Lc, increase of specimens and normalised Wigner energy release S, with final annealing temperature from 0 up to 600°C. B: primary peak. D: secondary peak. 17 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite annealing experiment. Previous researchers assumed a first order reaction [9, 10, 14,

16] or higher degree models [5]. Therefore various forms of f(x) have been considered, including f(S) = S and the more general function f(S) = Sn where n is the reaction order.

The requirement in a kinetic analysis is to calculate the activation energy Ea, and pre- exponential factor or factor of Arrhenius A, for each process:

  Ea    Ea  k  Aexp  or k  Aexp  (3)  RT   kBT  where k = factor of rate of reaction (specific rate)

A = Arrhenius factor (also known as pre-exponential factor, or frequency factor)

Ea = energy of activation (expressed in Joule/mol or KeV/molecule)

R = Universal Constant of Ideal Gases, (8.314 J K−1 mol−1)

−23 −1 kB = Boltzmann’s constant (1.380 x10 J K ).

T = Absolute temperature.

The authors chose to use the universal gas constant R instead of Boltzmann’s constant

K because the size of the resulting numbers is more suitable for numerical calculations. Taking natural logarithms gives:

E 1 lnk  ln A a (4) R T

The least squares method was used to calculate the activation energy and frequency factor by an appropriate linear fit to experimental data. In carrying out the fit a measures of convergence that was defined using the divergence between the calculated and experimental results, expressed as a percentage of the largest rate of reaction observed in experimental DSC curve [30-35]:

18 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

SUM DSC /(Z  N ) DEV 1(%)  100 exp max[( dS / dt) ] (5) where Z is the total number of measurements that were used to represent the DSC curve and N is the number of parameters that were used in the model, i.e. A, Ea.

The parameter SUMDSC is be described be the equation:

2  exp   calc  N  dS   dS  SUM   i   i   DSC     i1  dt   dt      (6)

A further convergence criteria is the divergence between the experimental and calculated values of Sf :

(S )exp  (S )calc DEV 2(%)  100.abs[ f 0 ] (S )exp f (7)

The optimization of parameters DEV1 and DEV2 is achieved by use of a non-linear optimization algorithm. In this work, the Generalized Reduced Gradient [38], which is implemented within the Solver Add-in of Microsoft Excel 2003, was utilized.

Seven different forms of kinetic model have been investigated, denoted as scenarios I to VII. These are summarized in Table 2, where activation energies are also given, together with frequency factors and other parameters such as order of reaction, temperatures at peak maximum, and percentages of reaction participation on the overall experimental curve. The results from the kinetic models are described in detail in the following sections.

Single Reaction Models (Scenarios I and II)

As early as 1945, Vand [39] describes the stored energy release in metallic films by a first order reaction with constant activation energy. Simmons [9] calculated the

19 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite energy release graphite by similarly assuming that activation energy remained constant over the temperature range of the release. dS  E   S.Aexp  dt  KT  (8)

Nightingale [5] proposed an alternative model, based on the assumption of constant frequency/constant activation energy, and introduced the order of the reaction n as an additional variable, which was estimated it to be around 6-8.

dS n  E   S Aexp  dt  KT  (9)

Primak [38] described a model of variable activation energy with constant frequency factor. Based on this, Simmons [9] developed an additional general model for graphite irradiation damage annealing, from which he calculated activation energies in the range of 1.2 to 2 eV (Table 1).

In this paper, we first analyse the rate of release thermographs using both the constant activation energy model of Simmons (referred to as Scenario I) and the Nightingale model (referred to as Scenario II) in order to determine how well these scenarios fit the measured energy release data, and to assess the need for analysis with more complex scenarios.

The results for the Scenarios I and II are shown in Figure 8 (A and B) from which it is clear that including the reaction order as a parameter significantly improves the fit for scenario II. There are large differences in both the frequency factor (7 orders of magnitude) and the activation energies (1 and 1.7 eV) for the two scenarios. The reaction orders also differ (8 and 10 respectively). Furthermore, the standard deviation (DEV1) in both cases is unsatisfactory (14% in each case); for adequate fitting a well established limit of standard of differentiation 3% is recommended [30-

20 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Table 1. Activation energy and frequency factors due to Simmons [9], Lexa et al [10], Kelly [15] and Iwata [17].

21 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 8: The application of a first-order single reaction model to the experimental non-isothermal data A: Fitting process of one first order reaction (Scenario I). B: Fitting process of one reaction with higher order (Scenario II). C: Three first order reactions (Scenario III). D: Four first order reactions (Scenario IV). E: Six first order reactions (Scenario V). F: Three reactions with reaction order higher than 1(Scenario VI). G: Fitting process with five reactions with reaction order higher than 1 which was the most successful fit (Scenario VII). 22 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite 35]. It is clear that single reaction scenarios are not adequate. Hence the more sophisticated Independent Parallel Reactions Model was investigated.

The Independent Parallel Reaction Model (Scenarios III to VI)

The independent parallel reactions model is based on the assumption that independent parallel annealing reactions exist and take place without interacting. These reactions are also called partial reactions or “pseudo-reactions” and in general may occur sequentially or in parallel. This model has been applied to study the chemical kinetics of heterogeneous reactions [30-35], but has not been applied previously to Wigner energy release.

The total energy released and the rate of energy released for N overall reactions can be described as:

S  si i (10) i=1,2,3,…N

dS dsi,t  ci dt dt i (11)

The factor ci accounts for the contribution of partial reaction i to the total energy released So-Sf (a similar term was used by Iwata [17]). c  S  S i f ,i 0,i (12)

The fraction si is the energy released for each component is given by:

S  S s  f ,i i i S  S f ,i 0,i (13) where Sf, Si,t and S0i, are: the final energy released, energy released at time t (or temperature T), and the initial stored energy, respectively.

23 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite For the kinetic analysis of Wigner energy release it is assumed that each pseudo- reaction represents a different type of defect that anneals within different temperature ranges, releasing different amounts of Wigner energy. The defects are assumed to anneal independently, contributing to the overall energy content: ds  E  i  A exp ai sn dt i RT i   (14)

Calculation of Kinetic parameters

The kinetic analysis of the DSC data for stored energy release is performed as follows

[30-35]. Initial values of Eai, Ai and ci, are required for each of the pseudo-reactions.

Examining the thermographs, the regions with clear peaks or shoulders can be defined

(Figure 9, A). These are considered as regions where a partial reaction dominates and, to a first approximation, it is assumed that only one reaction takes place. Thus there are no significant contributions from other reactions and that there are no sequential reactions.

Differentiating the Arrhenius equation gives:

dS dsi  Eai   ci  (S f  S)Aexp  dt dt  RT  (15) and rearranging and taking logarithms gives:

 dS     ds E  dt   i  ai ln  ln c i   ln A   S  S   dt  RT  f    (16)

The parameter ci is manually adjusted to match the calculated curve to the experimental curve (Figure 9 D). The same procedure is applied to all the regions with obvious shoulders or peaks (Figure 9, B and C).

24 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 9 . The consecutive steps of the algorithm to determine the partial reactions. Isolation of peaks and shoulders (parts A to C) and optimisation of kinetic parameters in order to reconstruct the experimental curve (D and E). Initiation(D) and finalisation (E) of optimisation

25 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite The partial reactions are then added to reconstruct the stored energy release curve

(Figure 9, D) using the relationship:

 calc dS dsi    ci dt dt   i (17) where:

 T    Eai si 1expAi /   exp dT  RT   To    (18) and ds  E  i  A exp ai  s dt i RT  i    (19)

T  E  where β is the heating rate. The integral  exp ai dT is calculated numerically. To  RT 

The approximate thermograph calculated by this method is then compared with the experimental results and a non-linear optimization algorithm applied to achieve convergence between experimental and calculated values (Figure 9, E). During this latter stage, the values of ci were adjusted for each reaction.

To assess convergence, conventional guidelines [31-36] were applied to both the kinetic analysis and the independent parallel reactions model. When DEV1 is less than 3%, the results are generally considered satisfactory. The parameters DEV1 and

DEV2 converge independently and DEV1 is usually chosen as the main indicator of convergence for use in the fitting algorithm since it refers directly to the quality of the differential curve. The value of DEV2 can then be examined as a separate indicator of convergence. A model is considered valid when the comparison between the experimental data and the fit shows little variation and the model is shown to fit another series of experimental data. As a general rule, simpler models are preferred

26 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite over more complicated ones since simple models with fewer parameters show less variation when applied to different experimental data and behave better when extrapolated. Good model solutions when applied to different experimental data are expected to produce results of the same order, although experimental variations (i.e. heating rates, sample mass, shape and physical conditions) may cause slight differences. The parameter c gives an indication of the number of reactions needed to reconstruct the experimental curve, and the summation of parameters ci for all reactions should approach unity.

Previous researchers have attempted to interpret the Wigner energy release reaction with more than one reaction using similar models to the independent parallel reactions model [6, 10, 17]. Kelly [15] by examining data from Windscale piles graphite, was among the first to address the concept that a single reaction model is not suitable where energy release occurs over a wide temperature range. Lexa et al [10] studied the release of Wigner energy from graphite irradiated by fast neutrons at the TRIGA

Mark II research reactor with a four first order reaction model with the same frequency factor for each reaction. Despite the lack of information about their efficiency in reproducing experimental curves, their kinetic analysis results coincide with Iwata’s findings (Table 1)[17]. Iwata examined pyrolytic graphite irradiated with thermal neutrons in the JAERI JRR-2 experimental reactor. He proposed a model using three first order reactions but with different frequency factors, which fitted the data with limited success and he tried to improve by varying activation energies. Minshall et. al. [16], used a multiple activation energy theory that achieved good fits to Windscale Piles DSC data. Instead of the small number of distinct well defined reactions addressed in this paper, Minshall et. al. [16] assumed the existence of an activation energy spectrum for many reactions.

27 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite Analyses by Lexa and Iwata ([10, 17]) were applied to graphite specimens with different irradiation doses and irradiation temperatures than the work presented here.

A summary of the results discussed above is presented in Table 1. The Lexa and

Iwata ([10, 17]) thermographs depict a characteristic peak at around 200°C followed by two shoulders at around 250 and 300°C and have different shapes compared to these BEPO thermographs. Additionally annealing was observed to begin at temperatures between 100 to 150°C in their work, while in this work it was observed to start around 200°C. Therefore direct comparison between their kinetic analysis results and the results presented here is not possible. We therefore examine the effect of the assumptions and simplifications in previous work by testing equivalent model scenarios against the BEPO thermographs.

Constant Frequency Factor (Scenarios III, IV and V)

The details for these three scenarios are given in Table 2. In each of these scenarios, the frequency factor, A, is the same for all reactions. Scenario III (Figure 8, C) is based on the assumptions of Kelly [6] in which the reaction order is unity, there is one frequency factor for all the partial reactions and it is assumed that three reactions take place. Scenario IV (Figure 8, D) follows that of Lexa [10] who constructed and tested a scenario with four reactions, based on Kelly’s [6, 15] assumptions. Scenario V assumes 6 reactions on the same basis (Figure 8, E).

The addition of a fourth reaction in Scenario IV, when compared to Scenario III, did not give a significant improvement in the fit; DEV1 was high (31% and 26% for

Scenario III and 26% and 23% for Scenario IV). The summation of the parameters ci, in both the scenarios, did not reach the target of unity, suggesting that additional reactions were required.

28 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

29

Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite Table 2 : Kinetic parameters calculated for all the scenarios evaluated. The best fit is given by scenario VII (bottom) by 2.84 and 2.89 respectively.

30 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite Scenario V was a 6 reaction model, based on the four reaction scenario (Scenario IV) with two additional reactions. From examination of the DSC curves there were no obvious additional peaks, so they were assumed to be in the centre of the gaps between the first three reaction peaks. The results for Scenario V are shown in Figure

8, E, where the fit to the experimental data is improved. The peak temperatures for the pseudo reactions are also within reasonable agreement. However the convergence is not adequate, with DEV1 values of only 13 % and 10% achieved and the summation of ci is less than 100% (94% and 90% respectively).

Three reactions with n≠1 (Scenario VI)

Scenario VI applies the Iwata [17] approach (three first order reactions with different frequency factors) to the BEPO data. In the earlier evaluation of the single reaction models in this paper, comparison of scenario I and scenario II showed that a model that included higher order reactions (n≠1) achieved an improved fit compared with the n=1 fit. Therefore it was decided to test a modified Iwata [17] model that would allow the reaction orders to vary during optimisation. The results are shown in Figure

8, F. Simulations made on both sets of data achieved convergence of around 5 and

6% respectively, which is a significant improvement compared to scenarios I to V.

However, the target, to reduce DEV1 to less than 3%, was not achieved. Furthermore the summation of c parameters is 109% and some of the calculated parameters differ significantly between samples. The reaction orders for the second reaction vary substantially; from 7.2 for the first set of data to 3.7 for the second. The frequency factors for the third reaction also vary, and are 6.4 x 1024 and 4.9 x 1020 sec-1.

Activation energies for the third reaction vary giving 2.8 eV for the first thermograph and 2.3 eV for the second. Scenario VI is therefore considered to be unsatisfactory.

31 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite Integrated 5 Reaction Model (Scenario VII)

Scenario VII uses a model with five reactions (Figure 8, G). Two additional reactions were added as before, one in the middle between the second and the third reaction, plus another one covering the territory between 500 and 600oC. The DEV1 parameter was less than 3% for both the two thermographs. A comparison is made between the different scenarios tested in the optimization in Figure 10, which also shows that target values of DEV1 were achieved for the two sets of data (both ~3%).

Unsurprisingly, increasing the number of reactions and the order of reaction improves fitting. Scenario VII that only involved 5 reactions (compared to the more complicated Scenario V), achieved the lowest DEV1 and provides the best description of the data. A diagram displaying the success of every model graphically is given in

Figure 10 where all models are displayed against their success (DEV1) and their number of reactions.

The validity of a calculated set of values is also judged on the variation between different sets of values calculated for similar experiments. There are no standard parameter variation limits in such analyses [31-36]. The variation limits are subjective, and depend upon parameters such as signal noise and material variation.

In our case, the most successful scenario, the integrated 5 reactions model examined above, displayed good agreement between the two sets of kinetic parameters, despite the fact that partial annealing during specimen fabrication may have occurred (Table

2).

The difference between the various frequency factor values is small. For example the highest differentiation was displayed in the last reaction where frequency factors are

1.43x1025 and 1.65x1025 sec-1 or 15% respectively. These are assumed to be very close, especially considering that at some of the previous models frequency factors

32 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 10: Summary of the kinetic analysis scenarios applied to both DSC experiments and the scores of DEV1 achieved for each. An increase of the reactions involved may lead to better fitting, but the addition of order of reaction In optimization parameters, improves the fit drastically (Scenarios VI and VII).

33 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite displayed a difference of several orders of magnitude (Scenario II and Scenario VI, third reaction). Activation energies were also found to be very close or even identical for all reactions, differing only by 0.1 eV or 1%. Lexa et al [10] also found stability in activation energy values during their own curve fitting procedure. Greater differences were found for the c cofactor, partial annealing that may have taken place during cutting and polishing could affect the relative contributions of reactions.

Nevertheless, they are still quite close, with greater variation displayed between the c values obtained for the third reaction with a difference of 7% or 40%. Temperatures at peak maxima almost coincide in value, only differing by 2 or 3°C. The maximum difference was about 11°C or 2% and was observed at the fourth reaction.

A comparison between the calculated kinetic values of scenario VII and the values reported in literature shows that the values do not agree. This is to be expected, since the thermographs in this work exhibit peaks at higher temperatures compared to the literature [10, 15, 17]. This is possible due to partial annealing during machining of our samples. The different irradiation histories of the specimens may also be important.

The highest temperature reactions reported by Kelly [15], Lexa [10] and Iwata [17]

(Table 1) give activation energies around 1.7-1.8 eV, which may coincide with the first reaction of scenario VII which is approximately 1.6 to 1.7 eV. This partial reaction has been described in detail by Iwata [17] as taking place between 250 to

350°C with a peak maximum at 280°C (for a linear heating rate of 10°C). Iwata [17] attributes this reaction to the annihilation of a di-interstitial with two mono vacancies.

However El Barbary et. al [40], and Telling et al [41], using first principle calculations, suggest that an energy barrier of 1.7 to 1.8 refers to single vacancy migration.

33 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite The reaction orders are also very close in magnitude to the greatest variation in the fifth reaction, differing only by 0.4 (12% difference). The first three reactions the activation energies were calculated to be around 6 to 7 which is in accordance with the work of Nightingale [5]. The physical meaning of such a high number could be explained by the mobilisation of single vacancies, a process that would require the adjustments of the carbon rings in order to accommodate vacancies [40, 41]. This type of reaction would require the collaboration and mobilisation of all carbon atoms contained within a ring [40, 41, 42]. The physical meaning of a number higher than 6 to 7 (during the optimization course numbers up to 10 have appeared) is considered by the authors unrealistic, given also the fact that this scenario has been rejected by the authors due to bad fit.

In this work the first distinct peak territory is between 180°C to 340°C (Figure 3 part

A) with the peak maximum of the first partial reaction at 270°C. This suggests that the last occurring reaction in the literature thermographs coincides with the first reaction in this work.

The second reaction, with activation energy around 2 eV may refer to interstitial motion, since Krashenikov et al [43] calculated similar energy barriers to interstitials motion at nanotubes of around 2 eV. The region between 2.4 and 3.4, where the activation energies of the next three reactions are observed, is not extensively explored by literature. They could be due to mobilisation of defect aggregates, which are reported to occur at relatively higher temperatures [44], or possibly due to through-layer migration of interstitials [45].

Isothermal Analysis: Application of Scenario VII on isothermal data

The integrated 5 reactions model (Scenario VII) was applied to the isothermal thermographs. The objective of the incremental isothermal treatment was to prevent a

34 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite temperature rise at an earlier stage of annealing, and hence to isolate the reactions that were taking place at that temperature from the reactions that had occurred at an earlier and lower temperature. Kinetic analysis for the energy released during each isothermal hold was performed. The energy released at 100, 150, and 200°C was too low to perform a reliable kinetic analysis, and these data have been excluded from the evaluation.

The differential Arrhenius equation was used:

E ds   Ae RT sn dt (20)

By solving the and re- integrating one obtains:

For n≠1

1 n E ds 1   1n  t 1n 1 nAe RT  dt 1 n   (21) and for n=1:

Ea  Ea ds RT   AeAte e RT dt (22)

A similar form of equation (20) has been developed by Primak as early as 1955 [46].

For simplicity, the fraction of heat released before the initiation of the isothermal stage was assumed to be zero.

Applying the Independent Parallel Reactions Model to the isothermal thermographs the above equations become:

For n≠1

1 ni E ds   i 1ni i 1ni 1 RT  t 1 ni Aie  dt 1 n i   (23) and for n=1:

35 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Eai  Ea RT  i dsi Aite RT  Aie e dt (24)

With s   si i (25) i=1,2,3,…N and ds ds  c i dt  i dt i (26)

The values of A, Ea, c, and n were not recalculated. The values from the Scenario VII analysis of linear heating rate thermograph, the most successful scenario, were chosen as a starting point for a new optimisation process that was applied to all the sets of isothermal data. An average of the previously calculated sets of A, Ea, c, and n values from Scenario VII was applied. This was achieved by dividing the isothermal thermographs into two regions; the linear rate temperature increase and the isothermal anneal. Optimisation for both regions was executed simultaneously using a single set of A, Ea, c and n parameters.

Example results are shown in Figures 11, 12 and 13. The isothermal regions show a better fit compared to the linear ramp regions. This is attributed to the lesser significance of noise in the isothermal range. For example, in the analysis of an isothermal thermograph with a final temperature of 500°C (Table 3), the overall scores (DEV1) of the linear heating rate parts and isothermal parts were 3.8% and

0.6%. The results for the isothermal part were excellent, and the values of DEV1 were always better than 1%. The results for all the temperatures and their standard deviation are summarised in Table 4.

The parameter values obtained did not vary significantly and displayed low deviation, with the exception of the 300°C thermograph. Deviation in frequency factors was

36 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite even smaller than the deviation observed in the linear heating rate experiments (1.3% of standard deviation at most), with only one exception for the first reaction in the isothermal annealing of 300°C. Activation energy variation was about 8% of standard deviation at most (at the fourth reaction). The order of reaction displayed greater variation especially for the first two reactions, where it varied between 6 to 8 (8 and

6% of standard deviation). The third, fourth and fifth reactions displayed better consistency, with values of reaction order varying only about 0.5 at the most (4, 6 and

7% standard deviation).

Additionally, in Table 5, the differences are given as the percentage between all the values calculated for the isothermal thermographs and the non isothermal thermographs. The table expresses the change in values between initial and final stage of optimisation. With the exception of kinetic results from the isothermal thermograph of 300°C, which displayed the highest differentiation with optimisation for values of frequency factor, the remaining experiments displayed very low differentiation in kinetic parameters. Highest differentiation occurred for reaction order values of less than 15% in some instances. Activation energy differentiation was generally lower although in an instance it reached 15%. Frequency factors remained generally stable with optimisation (displaying 3% differentiation at most).

The parameter ci for reactions in some instances is zero, even before the optimization.

This indicates that since the heating was interrupted at lower temperatures, the reactions that would take place at later heating stages have not occurred, i.e. they do

37 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 11. An example evaluation of the kinetic model of five integrated reactions for the non isothermal part of the DSC run that ended at 500°C with four reactions. It is important to note that fourth reaction appears at higher temperatures than reaction four despite the fact that it’s activation energy is lower.

38 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 12. Example evaluations of the kinetic model of five integrated reactions for the isothermal part of the DSC run that ended at 550°C (A) and at 350°C (B). In A the isothermal run starts after 50 minutes of beginning of annealing and in B after 33 minutes.

39 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Figure 13: Examples of isothermal kinetic analysis with final isothermal stage of 300°C (A) and 500°C (B). In these diagrams the non isothermal and isothermal parts are presented at the same graph.

40 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Table 3. The evaluation of the kinetic model for integrated five reactions for the non-isothermal and isothermal parts of the DSC run at 500°C.

41 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Table 4: Kinetic parameters calculated during the optimisation process for the isothermal kinetic experiments, derived by optimisation of Scenario VII’s parameters with their standard deviation.

42 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite

Table 5: The change in the Scenario VII values after the isothermal optimisation, expressed as a percentage of change from the initial values that were obtained by the linear heating rate optimisation.

43 Chapter 6 - Publication III: Application of an Independent Parallel Reactions Model on the Annealing Kinetics of BEPO Irradiated Graphite not participate in the reconstruction of the experimental curve. The optimised value for ci was recalculated for a fraction of the reactions that participated up to the final temperature level, neglecting the reactions that would occur at higher temperatures.

The summation of the ci parameters remains close to unity when this is done. The analysis shows, therefore, that model parameters obtained from DSC linear heating rate experiments describe well the isothermal annealing behaviour.

Conclusions

An independent parallel reaction model has been presented and applied to the kinetics of Wigner energy release. Kinetic scenarios of different complexity have been applied to Differential Scanning Calorimetry data obtain on neutron irradiated BEPO graphite.

A kinetic model using five reactions with different frequency values gives the most consistent results and best fits the data. Three dominant reactions of orders of reaction between 6 to 8 have been investigated in addition to two more of order 2.5 to

3 and 3.2 to 3.7. The parameters obtained by the model, were tested with two different thermographs constructed of sets of data from linear heating rate DSC experiments and achieved convergence with less than 3% divergence, and also good agreement between the two different sets of values. The independent parallel reactions model was also tested against thermographs obtained by isothermal experiments, with successful convergence and agreement with the parameters for the reactions obtained in the DSC measurements.

The annealing effect in the microstructure is evaluated with X-ray diffraction, and a correlation between crystallite size along the c-axis and stored energy release is presented, indicating that Wigner energy release is directly related to changes in graphite crystalline microstructure.

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48 Chapter 7 - General Conclusions and Future Work

Chapter 7

General Conclusions and Future Work This present research involved the development of an understanding of the release of stored energy and has been conducted using kinetic models. A potentially valid method was developed, for determining the stored energy content of graphite components and the kinetics of energy release. The classical theory of kinetic analysis is used as the basis for these models applied to the study of stored energy release.

In the first publication the use of an independent parallel reactions model is evaluated and several kinetic model scenarios are tested. The independent parallel reactions model was able to describe the annealing kinetics of stored energy release. In particular a model with 5 pseudo reactions, was able to give good quality fits to stored energy data made on samples for various types of polycrystalline nuclear graphite originating from different types of coke, manufacture process and irradiation histories.

The variation in the predicted model parameters A, Ea, n and c for each of the five reactions were within acceptable limits for most of the grades of graphite investigated and a relative stability model has been achieved.

In the second publication, a qualitative kinetic model in terms of activation energy and order of reaction is proposed by applying the independent parallel reactions model to the changes with annealing of microstructure properties of various grades of ion-irradiated and mechanically damaged nuclear graphite. The kinetic parameters obtained have been compared with the Wigner energy release kinetic parameters of neutron irradiated graphite, provided by literature. The activation energies obtained for the annealing of ion-irradiation and mechanical defects are found to be close to those reported for neutron irradiation

In the third publication, the parameters obtained by the independent parallel reactions model, were tested with two different linear heating rate DSC thermographs and achieved convergence with less than 3% divergence, with good agreement between the two different sets of values. The independent parallel reactions model was also tested against thermographs obtained by isothermal experiments, showing excellent

70 Chapter 7 - General Conclusions and Future Work consistency (with less than 3% standard deviation) with additional good agreement between isothermal and linear heating rate parameters. . In all cases examined, the independent parallel reactions model has been able to produce accurate results. The flexibility of the model is also displayed, as it was successfully utilized in linear heating rate experiments as well as isothermal heating experiments, and it could even be adjusted to fit Raman measurements. The ability to verify calculated parameters with more than one types of measurements, or more than one technique can provide with the appropriate level of confidence, for applications in decommissioning safety cases.

The flexibility and versatility of independent parallel reactions model could provide with the opportunity to apply older kinetic scenarios that have been provided by first principle calculation studies in the past [39, 51, 56-57, 70], as well as DSC studies [2, 4, 38, 45- 47, 54] in order to evaluate the applicability of all scenarios provided in literature and the validity of their accompanying theories.

Further research on Wigner energy release on higher annealing temperatures is suggested, up to 1600oC as a distinct peak at 1200oC has been reported[167] and application of independent parallel reactions model to these conditions. Research on Wigner energy release at higher temperatures would be useful not only for decommissioning issues but additionally for safety cases of nuclear reactors operating at higher temperatures.

The main tool of the present work has been Differential Scanning Calorimetry, since it could provide with isothermal and linear rise heating rate data of a variety of graphite samples irradiated either in material test reactors or trepanned from the reactors themselves.

However, the kinetics of the annealing of ion-irradiated and polished graphite samples has been investigated by the decrease of the Raman ID/IG ratio and showed that thus, it is possible to interpret the annealing process. Additionally Raman spectroscopy can be used to compare the effect of ion bombardment with the reported effects of neutron

71 Chapter 7 - General Conclusions and Future Work irradiation on physical properties such as the lattice defects. Therefore Raman can also serve as an alternative technique to DSC for evaluation as well as verification of kinetic results.

The effect of annealing on the graphite crystalline structure can also be evaluated by investigating changes to X-ray Diffraction spectra. In our work a correlation between crystalline size along the c-axis and stored energy release displayed that Wigner energy release is directly related to changes in graphite crystallite microstructure. Therefore XRD can serve as an alternative technique to DSC particularly because it can directly track changes in the microstructure with annealing.

Finally a qualitative similarity in the annealing phenomena between ion and neutron irradiation has been concluded. The simulation of annealing reaction kinetics of ion- irradiation with a kinetic scenario derived from stored energy release of neutron irradiated specimens is indicative of the qualitative similarities in the produced damage between ion and neutron irradiation. Therefore ion irradiation, with the variety of irradiation methods, conditions and ion beam sourced available has the potential to serve as an alternative technique to the analysis of neutron damage annealing.

72 Bibliography

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