Mapping Polycrystalline Materials in 3D: Diffraction Contrast Tomography and Related Techniques

$Mapping Polycrystalline Materials in 3D: Diffraction Contrast Tomography and Related Techniques$

Mapping polycrystalline materials in 3D: Diffraction contrast tomography and related techniques

Andrew King ! Synchrotron SOLEIL

W. Ludwig, P. Reischig, L. Nervo, S. Schmiederer, N. Viganò, Y. Guilhem, G. Johnson and many others…

Outline

• Introduction • Motivation • Underlying techniques • Diffraction contrast tomography – Setup, data acquisition and processing • Application examples • Developments in progress • Related techniques

1 Myself

• Diffraction for strain, stress and damage characterisation – Manchester 2001-2005 • Tomography for 3D morphology of porous and granular materials – INSA de Lyon 2006 • Diffraction Contrast Tomography for mapping polycrystals and materials applications. – Manchester/ESRF/HZG 2009-2013 • At SOLEIL since 2013… – PSICHE beamline, tomography for materials science

Outline

2 450 S. Terzi et al. / Scripta Materialia 61 (2009) 449–452 serted into alumina tubes and fixed with ceramic glue. In The liquid regions have been outlined in blue. At the on- order to localize the deformation of the specimen in the set of deformation, time t0, the liquid of near-eutectic region of interest where X-ray images are recorded, the composition is fairly homogeneously distributed within cross-section of the specimen was locally reduced to the whole specimen. The measured volume fraction of about 1.5 mm in diameter (i.e. a notched zone). The liquid, typically 7–8%, can be compared to the theoreti- specimen was heated by an induction coil and the tem- cal value predicted by two microsegregation models. At perature was controlled and monitored by using a ther- the temperature of 555 °C, the liquid fraction is equal to mocouple 0.5 mm in diameter inserted into the lower 9% under equilibrium conditions, whereas the Scheil– alumina tube and in close contact with the specimen. Gulliver model gives 17%. The measured value is closer 1 The specimen was heated at 0.5 °CsÀ up to 555 °C, to the equilibrium value, which seems to indicate that i.e. aboveWhat the are eutectic we trying temperature to do, (548 and°C), why? and then the heating plus holding times were sufficient to homog- held isothermally for 3 min at this temperature to reach enize the initial copper concentration profiles of the thermal• homogenization. Imaging materials The tensile test was then per- solidified specimen. However, perfect homogenization 1 formed at a displacement speed of 0.1 lmsÀ which should not be achieved if one calculates the correspond- – How are they structured? 4 1 leads to an average strain rate equal to 2 10À sÀ , ing Fourier number Fo (Fo < 0.1). Furthermore, the assuming that– How the gauge does length the structure of the specimen determineÂ is equal propertiesmeasured and liquid fraction is even lower than the equilib- to 0.5 mm. behaviour? rium value. This can be explained by the fact that some During the– How tensile does test, the the structure tensile rig andchange the speci-during use?of the liquid remains in the form of intergranular films men were allowed to rotate through 180° in 16 s, while which are too thin to be detected by X-ray tomography. the heating450 coil itself was fixed. DuringS. Terzi et al. / Scriptathis Materialia rotation, 61 (2009) 449–452 The next three images of Figure 1 show the same

400 transmission450 serted into alumina images tubes of and the fixedS. Terzi zone with etal. ceramic / Scripta of interestglue. Materialia In 61 (2009) ofThe theliquid 449–452 regionsnotched have been outlined region in blue. at At various the on- times (or levels) of deforma- specimen wereorder to localize recorded. the deformation The of pixel the specimen size in wasthe setset of to deformation,tion. time t0 As, the deformation liquid of near-eutectic proceeds, the fraction of liquid serted intoregion alumina of interest tubes where and fixed X-ray with images ceramic are glue. recorded, In theThe liquidcomposition regions have is fairly been homogeneously outlined in blue. distributed At the on- within 2.8 lm.order Such tocross-section localize scans the ofdeformation the the specimen specimen of the was specimen locally were in reduced the recorded toset ofthe deformation, every whole specimen. timeint0, The the measured liquid deformed of near-eutectic volume fraction zone of increases. In other words, since 450 S. Terzi et al. / Scripta Materialia 61 (2009) 449–452 27 s usingregionabout of the interest 1.5 latest mm where in version X-ray diameter images (i.e. of are a notchedthe recorded, Camera zone). the Thecomposition FReLoNliquid, is typically fairly homogeneously 7–8%,the can solid be compared distributed skeleton to within the experiencestheoreti- plastic deformation with 450 serted into alumina tubes and fixedS.cross-section Terzi with etspecimen al. ceramic / Scripta of glue. Materialiawas the In heated specimen 61 (2009) byThe an was liquid 449–452 induction locally regions reduced coil have and been to the outlined tem-the whole incal blue. value specimen. At thepredicted on- The by measured two microsegregation volume fraction models. of At F2kHD-Atmelaboutperature 1.5 mm with inwas diameter controlled a fast (i.e. and readout amonitored notched zone). of by using the The a CCD ther-liquid, camerathe typically temperature 7–8%, ofcan 555 bev° comparedC,> the 0, liquid liquid to thefraction theoreti- flows is equal to into the notched region (i.e. serted intoorder alumina to localize tubes the and deformation fixed with ceramic of the specimen glue. In in theThe liquidset of regions deformation, have been time outlinedt0, the in liquidblue. At of the near-eutectic on- $ s region of interest where X-ray imagesspecimen aremocouple recorded,was heated 0.5 the mm by an1 in inductioncomposition diameter coilinserted is and fairly theinto homogeneously tem- the lowercal value distributed9% predicted under within equilibrium by twoÁ microsegregation conditions, whereas models. the At Scheil– order to localize the deformationset of at the specimen 20 Mpixels in the set sÀ of deformation,[15]. After time t0, data the liquid acquisition, of near-eutectic $ v < 0) in order to ensure global mass conservation. cross-section of the specimen wasperature locallyalumina was reduced controlled tube toand and inthe closemonitored whole contact specimen. by withusing the a The ther- specimen. measuredthe temperature volumeGulliver fraction model of 555 of gives°C, the 17%.‘ liquid The fraction measured is equal value to is closer region of interest where X-ray images are recorded, the composition is fairly homogeneously1 distributed within Á about 1.5 mm in diameterthree-dimensional (i.e.mocouple a notchedThe 0.5 specimen zone). mm Thein (3-D) was diameter heatedliquid, images inserted at typically 0.5 ° intoCs of 7–8%,À the theup lower can to specimen 555 be compared°C,9% underto to were the the equilibrium equilibrium theoreti- conditions,At value, the which whereas longest seems the to Scheil– indicatetime (i.e.that about 900 s or 18% average cross-section of the specimen was locallyalumina reducedi.e. tube above toand the in eutecticthe close whole contact temperature specimen. with the (548The specimen.° measuredC), and then volumeGulliver fractionthe model heating of gives plus 17%. holding The timesmeasured were value sufficient is closer to homog- specimen was heated by an induction coil and the tem- cal value predicted1 by two microsegregation models. At about 1.5 mm in diameter (i.e. a notchedThe specimen zone). The was heatedliquid, at typically 0.5 Cs 7–8%,À up can to 555 be comparedC, to to the the equilibrium theoreti- value, which seems to indicate that perature was controlledreconstructed and monitoredheld by using isothermally using a ther- standard for 3the min temperature° at this reconstruction temperature of 555 °°C, to the reach liquid tools. fractionenize In isthe equal initial to copperdeformation concentration of profiles the specimen) of the a few pores or cracks have specimen was heated by an induction coili.e.• and abovethermalThis the the tem- eutectichomogenization.coverscal temperature value a predictedlot The (548 tensileof by°materialsC), test two and was microsegregation then then per-science!the heating models.solidified plus At holding specimen. times However, were suffi perfectcient to homogenization homog- mocouple 0.5 mm in diameteraddition inserted to into direct the lower post-processing9% under equilibrium ofthese conditions,1 images whereas the to Scheil– already appeared in the notched area. This is shown in perature was controlled and monitoredheld by using isothermallyformed a ther- atfor a displacement 3the min temperature at this speedtemperature of 555 of 0.1°C, tol thems reach liquidÀ which fractionenize istheshould equal initial not to copper be achieved concentration if one calculates profiles the of correspond- the alumina tube and in close contact with the specimen. Gulliver model gives 17%. The4 measured1 value is closer mocouple 0.5 mm in diameterquantify insertedthermal into theleads the1 homogenization. lower evolution to an average9% Theunder strainof tensile equilibrium the rate test equal microstructure, was conditions, to then 2 per-10À whereassÀ solidified, specific theing Scheil– specimen. Fourier number However,moreFo perfect( detailFo < 0.1). homogenization in Furthermore,Figure 2 the, where a sequence of 2-D images The specimen was heated at 0.5 °CsÀ up to 555 °C, to the equilibrium1 value, which seems to indicate that alumina tube and in close contact withformed theassuming specimen. at a displacement that theGulliver gauge speed model length of gives 0.1of thelms 17%. specimenÀ ThewhichÂ measured is equalshould valuemeasured not is closer be achieved liquidfraction if one calculates is even lower the correspond- than the equilib- i.e. above the eutectic temperature1 (548 °C), and then the heating plus holding4 times1 were sufficient to homog- The specimen was heated atvolumetric 0.5 °CsÀleadsup toto digital555 an0.5 averagemm.°C, image strainto the rate equilibrium correlation equal to value, 2 10 which(V-DIC)À sÀ , seemsing to has indicate Fourierrium been value. that number ThisFo canhas(Fo be< explainedbeen 0.1). Furthermore, extracted by the fact thatthe from some the 3-D reconstructed views of i.e. aboveheld the isothermally eutectic temperature for 3 min at (548 this temperature°C), and then to reachthe heatingenize plus the holding initialÂ copper times were concentration sufficient to profiles homog- of the thermal homogenization.applied The tensileassuming to test measure wasDuring that then the the gauge per- tensile3-D length test,solidifieddisplacement of the the tensile specimen specimen. rig andis However, fieldsequal the speci- in perfectmeasured theof homogenization bulk the liquid liquid fraction remains is even in the lower form than of intergranular the equilib- films held isothermally for 3 min at this temperatureto 0.5 mm.men to reach were1 allowedenize to therotate initial through copper 180 concentrationin 16 s, whilerium profiles value.which of This arethe too can thin be explained to be detected by the by fact X-ray that tomography. some formed at a displacement speed of 0.1 lmsÀ which should not be achieved° if one calculates the correspond- thermal homogenization. Theof tensile the test specimen, wasDuringthe then heatingthe per- tensile from4 coil1solidified test, itself which the was tensile specimen. fixed. local rig During and However, strain the this speci- rotation,perfect heterogeneitiesof homogenization the liquidThe remains next three in the images form of ofFigure intergranular 1 show films the same leads to an average strain rate equal to1 2 10À sÀ , ing Fourier number Fo (Fo < 0.1). Furthermore, the formed at a displacement speed of 0.1menlms were400À allowedwhich transmissionÂ to rotateshould images through not of be the achieved 180 zone° in of 16if one interest s, while calculates of thewhich the correspond-notched are too thin region to be at detected various bytimes X-ray (or tomography. levels) of deforma- assuming that the gaugehave length been of the specimen derived.4 1 is equal A specificmeasured procedure liquid fraction has is even been lower thandevel- the equilib- leads to an average strain rate equalthe to 2 heatingspecimen10À coilsÀ , wereitselfing was recorded. Fourier fixed. TheDuring number pixel thisFo size rotation,(Fo was< 0.1). set Furthermore, to Thetion. next As threethe deformation images of proceeds,Figure 1 theshow fraction the same of liquid assumingto 0.5 that mm. the gauge length of the specimenÂ is equal measuredrium liquid value. fraction This can iseven be explained lower than by the factequilib- that some During the tensile test,oped the tensile to400 compute transmission rig2.8 andlm. the Such speci- localimages scans of ofstrainsof the the specimenzone liquid from of interest remains were sparsely recorded of in the the everyform distributednotched of intergranularin region the deformed at films various zone times increases. (or levels) In other of deforma- words, since to 0.5 mm. specimen27 s were using recorded. therium latest value. The version pixel This of cansize the be Camerawas explained set FReLoN to by thetion. fact As thatthe deformation solid some skeleton proceeds, experiences the plastic fraction deformation of liquid with Duringmen the were tensile allowed test, to the rotatedisplacement tensile through rig and 180 the° in speci-measurement 16 s, whileof thewhich liquid points areremains too thinlocated in the to be form detected at of solid–liquidintergranular by X-ray tomography. films the heating coil itself was fixed.2.8 Duringlm.F2kHD-Atmel Such this scans rotation, of withthe specimen a fastThe readout were next recorded three of the images CCD every camera of Figurein the 1$ deformedshowvs > 0, the liquid zone same increases. flows into In the other notched words,region since (i.e. men were allowed to rotate through 180° in 16 s, while which are1 too thin to be detected by X-ray tomography.Á interfaces27 s using[16,17]set at the 20 latest. Mpixels version sÀ of[15] the. CameraAfter data FReLoN acquisition,the solid$ v skeleton‘ < 0) in experiences order to ensure plastic global deformation mass conservation. with 400 transmission images of theMore zone of specifically interest of the notched region at various times (or levels)Á of deforma- the heating coil itself was fixed. DuringF2kHD-Atmel thisthree-dimensional rotation, with a fastThe (3-D) readout next images three of the of images CCD the specimen camera of Figure were 1$showvs >At 0, the liquidthe same longest flows time into (i.e. the about notched 900 sregion or 18% (i.e. average specimen were recorded.Figure The pixel 1 sizeshows was set a to sequence1 tion. As of deformation four 3-D proceeds, images theÁ fraction of the of liquid 400 transmission images of the zone ofset interest atreconstructed 20 of Mpixels the s usingÀnotched[15] standard. region After reconstructionat data various acquisition, times tools. (or levels) In$ v‘ of 0,and liquid everyday flows into materials the notched region (i.e. 27 s using the latest version1 of the Cameraadditionvolumetric FReLoN to direct digital post-processingthe image solidÁ skeleton correlation of these experiences (V-DIC) images plastic has to been deformationalreadyhas appeared been with extracted in the notched from the area. 3-D This reconstructed is shown in views of set at 20 Mpixels sÀ [15]. After data acquisition, $ v‘ < 0) in order to ensure global mass conservation. F2kHD-Atmel with a fast readout of thequantify CCDapplied camera the evolution to measure$ v ofs > 3-D the 0,Á displacement liquidmicrostructure, flows fields into specific in the the notched bulkmore region detail in (i.e.Figure 2, where a sequence of 2-D images three-dimensional1 (3-D) images of the specimen were Á At the longest time (i.e. about 900 s or 18% average set at 20 Mpixels sÀ [15]. After datavolumetric acquisition,of the digital specimen, image$ fromv‘ correlation< 0) which in order local (V-DIC) to strain ensure has heterogeneities beenglobal masshas conservation. been extracted from the 3-D reconstructed views of three-dimensionalreconstructed (3-D) using images standard of the reconstruction specimen were tools. InAtÁ thedeformation longest time of (i.e. the specimen) about 900 a s few or pores 18% oraverage cracks have addition to direct post-processingapplied ofhave these to measure been images derived. 3-D to displacement A specificalready procedure appeared fields in in has the the beenbulk notched devel- area. This is shown in reconstructed using standard reconstructionof theoped specimen, tools. to In compute fromdeformation which local local strains strainof from the heterogeneitiesspecimen) sparsely distributeda few pores or cracks have additionquantify to direct the post-processing evolution of the of microstructure, these images to specificalreadymore appeared detail in in theFigure notched 2, where area. a sequenceThis is shown of 2-D in images volumetric digital image correlationhave (V-DIC) beendisplacement derived. has been A measurement specifichas procedure been points extracted locatedhas been from at devel- solid–liquid the 3-D reconstructed views of quantify the evolution of the microstructure,oped tointerfaces compute specific [16,17] localmore strains. detail from in sparselyFigure 2, distributed where a sequence of 2-D images volumetricapplied digital to measure image correlation 3-D displacement (V-DIC) fields has beenin the bulkhas been extracted from the 3-D reconstructed views of of the specimen, from which localdisplacement strain heterogeneitiesFigure measurement 1 shows a sequencepoints located of four at solid–liquid 3-D images of the applied to measure 3-D displacement fieldsinterfaces innotched the[16,17] bulk area. taken at various times during deformation. of the specimen,have been from derived. which A specific local strain procedure heterogeneities has been developed to compute local strains fromFigure sparsely 1 shows distributed a sequence of four 3-D images of the have been derived. A specific procedurenotched has been area devel- taken at various times during deformation. oped todisplacement compute local measurement strains from points sparsely located• distributed3D, at solid–liquidin-situ measurements displacementinterfaces measurement[16,17]. points located at solid–liquid interfacesFigure[16,17] 1. shows a sequence of four 3-D– imagesMost of “real” the problems are 3D Figurenotched 1 shows area a taken sequence at various of four times 3-D duringimages deformation. of the notched area taken at various times during deformation.– Need techniques to see inside evolving systems

Figure 2. Sequence of 2-D images obtained from the 3-D recon- Figure 1. Sequence of 3-D images of the notched zone of the specimen structed views of the notchedFigure area 2. of theSequence specimen. The of tensile 2-D axis is images obtained from the 3-D recon- after various deformation times. The figure shows the variation of theFigure 2.verticalSequence and the of time 2-D after images deformation obtained is from applied the at 3-D time recon-t0 is indicated Figure 1.FigureSequence 1.liquidSequence volume of of 3-D fraction images images in thisof the zone notchedof (blue the zone regions). notched of the (For specimen zoneinterpretation of thestructed specimenin views each of figure. the notched In order areastructed to of evaluate the specimen. views local strains The of tensile atthe various axis notched is positions area of the specimen. The tensile axis is of colour mentioned in this figure, the reader is referred to the web along the sample, six horizontal slices (average vertical height of about after variousafter various deformation deformation times. times. The figure The shows figure the variation shows of the variationvertical and of the the time after deformationvertical is applied and at the time timet0 is indicated after deformation is applied at time t is indicated liquid volumeversion fraction of this inarticle.) this zone (blue regions). (For interpretation in each125 figure.lm) In have order been to evaluatedefined and local are strains indicated at various in (d). positions 0 liquid volumeof colour fractionmentioned in in this this figure, zoneFigure the reader (blue2. Sequence is referred regions). of to 2-D the images web (For obtained interpretationalong the from sample, the 3-D six horizontal recon- in slices each (average figure. vertical heightIn order of about to evaluate local strains at various positions Figure 1. Sequence of 3-D images of the notched zone of the specimen structed views of the notched area of the specimen. The tensile axis is version of this article.) Figure 2. Sequence of 2-D images obtained from125 l them) have3-D beenrecon- defined and are indicated in (d). after various deformation times.of Thecolour figure shows mentioned the variation in of thethis figure,vertical and the the reader time after deformationis referred is applied to the at time webt is indicated along the sample, six horizontal slices (average vertical height of about Figure 1. Sequence of 3-D images of the notched zone of the specimen structed views of the notched area of the specimen. The tensile axis0 is liquid volume fraction in this zone (blue regions). (For interpretation in each figure. In order to evaluate local strains at various positions after various deformation times. Theversion figure shows of the this variation article.) of the vertical and the time after deformation is applied at time t is indicated 125 m) have been defined and are indicated in (d). of colour mentioned in this figure, the reader is referred to the web along the sample, six horizontal slices (average vertical0 height of about l liquid volume fraction in this zone (blue regions). (For interpretation in each figure. In order to evaluate local strains at various positions 3 version of this article.) 125 lm) have been defined and are indicated in (d). of colour mentioned in this figure, the reader is referred to the web along the sample, six horizontal slices (average vertical height of about version of this article.) 125 lm) have been defined and are indicated in (d). Diffraction Contrast Tomography • X-ray technique • Tomographic concepts and algorithms • 3D, non-destructive mapping of: – Grains (shapes, orientations…) – Sample structure (cracks, pores, inclusions…)

MAX4 Imaging Workshop

Outline

4 Standard tomography

• Absorption or phase (refraction) contrast – Full field radiography + rotation • Reconstruction of ~density

ω ω

Standard tomography: Reconstruction • Filtered back projection – most standard, basic reconstruction technique • 1 / 2 / 4 / 8 / … / 1024 / 1800 projections

Aluminium alloy for DVC. M. Fregonese, MATEIS, INSA de Lyon

5 450 S. Terzi et al. / Scripta Materialia 61 (2009) 449–452 serted into alumina tubes and fixed with ceramic glue. In The liquid regions have been outlined in blue. At the on- order to localize the deformation of the specimen in the set of deformation, time t0, the liquid of near-eutectic region of interest where X-ray images are recorded, the composition is fairly homogeneously distributed within cross-section of the specimen was locally reduced to the whole specimen. The measured volume fraction of about 1.5 mm in diameter (i.e. a notched zone). The liquid, typically 7–8%, can be compared to the theoreti- Standard tomography: Reconstruction specimen was heated by an induction coil and the tem- cal value predicted by two microsegregation models. At perature was controlled and monitored by using a ther- the temperature of 555 °C, the liquid fraction is equal to • Can see pores and precipitates, but not grainsmocouple 0.5 mm in diameter inserted into the lower 9% under equilibrium conditions, whereas the Scheil– 450 S. Terzi et al. / Scripta Materialia 61 (2009) 449–452alumina tube and in close contact with the specimen. Gulliver model gives 17%. The measured value is closer 1 serted into alumina tubes and fixed with ceramic glue. In The liquid regionsThe have been specimen outlined in was blue. At heated the on- at 0.5 °CsÀ up to 555 °C, to the equilibrium value, which seems to indicate that order to localize the deformation of the specimen in the set of deformation, time t0, the liquid of near-eutectic region of interest where X-ray images are recorded, the composition is fairlyi.e. homogeneously above the distributed eutectic within temperature (548 °C), and then the heating plus holding times were sufficient to homog- cross-section of the specimen was locally reduced to the whole specimen.held The isothermally measured volume for fraction 3 min of at this temperature to reach enize the initial copper concentration profiles of the about 1.5 mm in diameter (i.e. a notched zone). The liquid, typically 7–8%,thermal can be comparedhomogenization. to the theoreti- The tensile test was then per- solidified specimen. However, perfect homogenization specimen was heated by an induction coil and the tem- cal value predicted by two microsegregation models. At 7566 C. Landron et al. / Acta Materialia 59 (2011) 7564–7573 1 perature was controlled and monitored by using a ther- the temperature offormed 555 °C, the at liquid a fraction displacement is equal to speed of 0.1 lmsÀ which should not be achieved if one calculates the correspond- 4 1 mocouple 0.5 mm in diameter inserted into the lower 9% under equilibriumleads conditions, to an whereas average the strainScheil– rate equal to 2 10À sÀ , ing Fourier number Fo (Fo < 0.1). Furthermore, the F alumina tube and in close contactundergoes with the specimen.the highest stressGulliver triaxiality model gives state 17%. and The the measured highest value is closer Â r 2 1 assuming that the gauge length of the specimen is equal measured liquid fraction is even lower than the equilib- true ¼ S The specimen was heatedð Þ at 0.5strain°CsÀ duringup to 555 the°C, tensileto test. the equilibriumThe size was value, chosen which to seems be suf- to indicate that i.e. above the eutectic temperature (548 °C), and then the heating plus holdingto 0.5 times mm. were sufficient to homog- rium value. This can be explained by the fact that some F being the measured force during theheld tensile isothermally test. for 3 min at thisficiently temperature large to reachfor the elementaryenize the initial volume copper to concentration be representa- profiles of the thermal homogenization. The tensile test was then per- solidified specimen. However,During perfect the tensile homogenization test, the tensile rig and the speci- of the liquid remains in the form of intergranular films The curvature radius R and the radius of the mini- tive but also1 sufficiently small for the strain and notch formed at a displacement speed of 0.1 lmsÀ which should not be achievedmen if wereone calculates allowed the correspond- to rotate through 180° in 16 s, while which are too thin to be detected by X-ray tomography. triaxiality to be4 spatially1 constant inside this sub-volume. mal section a were measured in orderleads to to an determine average strain the rate equal to 2 10À sÀ , ing Fourier number Fo (Fo < 0.1). Furthermore, the Â the heating coil itself was fixed. During this rotation, The next three images of Figure 1 show the same average stress triaxiality T in the centerassuming of that the the minimum gauge length ofThe the specimenexternal is shape equal of threemeasured different liquid fraction cavities is located even lower inside than the equilib- to 0.5 mm. the sub-region are plottedrium as value. a function This can400 be of explained transmission deformation by the infact images that some of the zone of interest of the notched region at various times (or levels) of deforma- cross-section, using the Bridgman formulaDuring the[44] tensileas test,reas- the tensile rig and the speci- of the liquid remainsspecimen in the form were of intergranular recorded. films The pixel size was set to tion. As deformation proceeds, the fraction of liquid sessed by Wierzbicki and Bao [45]. men were allowed to rotate throughFig. 180 2b,° in showing 16 s, while that inwhich the arefirst too steps thin to of be deformation detected by X-ray cav- tomography. the heating coil itself was fixed.ities During remain this rotation, roughly sphericalThe next and three only2.8 images becomelm. of SuchFigure ellipsoidal scans 1 show of the the same specimen were recorded every in the deformed zone increases. In other words, since 1 p a 400 transmission images of the zonelater, of during interest the of the tensilenotched test. region at27 various s using times (or the levels) latest of deforma- version of the Camera FReLoN the solid skeleton experiences plastic deformation with T 2ln 1 specimen were recorded.3 The pixel size was set to tion. As deformation proceeds, the fraction of liquid ¼ 3 þ þ 2RNotch ð Þ F2kHD-Atmel with a fast readout of the CCD camera $ vs > 0, liquid flows into the notched region (i.e. 2.8 lm. Such scans of the specimen were recorded every in the deformed zone increases. In other words,1 since Á ffiffiffi 27 s using the latest version of the Camera FReLoN the solid skeletonset experiences at 20 plastic Mpixels deformation sÀ with[15]. After data acquisition, $ v‘ < 0) in order to ensure global mass conservation. The relevance of these calculated values of eloc and T 3. Results F2kHD-Atmel with a fast readout of the CCD camera $ vs > 0, liquid flows into the notched region (i.e. Á 1 Á three-dimensional (3-D) images of the specimen were At the longest time (i.e. about 900 s or 18% average was evaluated using finite elementsset (FE) at simulations. 20 Mpixels sÀ The[15]. After data acquisition, $ v‘ < 0) in order to ensure global mass conservation. results of the simulations, detailedthree-dimensional in Appendix A (3-D), show images3.1. of the Macroscopic specimen were measurementsAtÁ the longest timereconstructed (i.e. about 900 s using or 18% averagestandard reconstruction tools. In deformation of the specimen) a few pores or cracks have good agreement with the local strainreconstructed calculated using from standard Eq. reconstruction tools. In deformation of theaddition specimen) a few to pores direct or cracks post-processing have of these images to already appeared in the notched area. This is shown in addition to directAluminium post-processing alloy of for these DVC. images M. to Fregonesealready appeared, MATEIS, in the notched INSA area. de This Lyon is shown in (1) and with the stress triaxiality calculatedquantify the from evolution Eq. (3) of. the microstructure,The force–displacement specific more detail curves in Figure acquiredquantify 2, where during a the sequence evolution the of 2-D images of the microstructure, specific more detail in Figure 2, where a sequence of 2-D images volumetric digital image correlationin situ (V-DIC) tensile has testbeen performedhas been onextracted thevolumetric smooth from the 3-Dspecimen reconstructed digital of image views of correlation (V-DIC) has been has been extracted from the 3-D reconstructed views of applied to measure 3-D displacement fields in the bulk applied to measure 3-D displacement fields in the bulk 2.4. Microscopic measurements of the specimen, from which localeach strain steels heterogeneities are given in Fig. 3a. The slight force relaxation have been derived. A specific procedurevisible has on been these devel- curves is due to the step-by-stepof the specimen, procedure from which local strain heterogeneities In a second processing step the centraloped to area compute of the local tensile strains from(the sparsely displacement distributed was maintained constanthave been and thenderived. the A specific procedure has been devel- displacement measurement points located at solid–liquid specimen was selected for damage quantification.interfaces [16,17] This. sub- force relaxed during the tomographicoped scan). toFig. compute 3b shows local strains from sparsely distributed 3 region was chosen to be a cubic volumeFigure of 300 1 showslm , a as sequence indi- of fourthe 3-Dtensile images true of stress the of the steels studieddisplacement as a function measurement of points located at solid–liquid cated in Fig. 2a, which showsRecent a transparentnotched areatomography takenview at of various the timesthe during work local deformation. tensile true strain. These curves are in agreement • Hotinterfaces tearing in[16,17] Al-Cu. external shape of the sample as well as the location of the with expectations for these materials in termsFigure of 1 strengthshows a sequence of four 3-D images of the cavities. It can be assumed that• thisDuctile central failure sub-region of dualand phase ductility. steel The very high strengthnotched and strain area shown taken in at various times during deformation.

What are the grain orientations? Where are the grains FigureAre 2. Sequencethere of grain 2-D images obtained from the 3-D recon- Figure 1. Sequenceand of 3-D grain images of the notched zone of the specimen structed views of the notched area of the specimen. The tensile axis is after various deformation times. The figure shows the variation of the boundariesvertical and the time after that deformation we is applied at time t0 is indicated liquid volumeboundaries? fraction in this zone (blue regions). (For interpretation in each figure. In order to evaluate local strains at various positions Fig. 2. 3-D views of volumes obtained by tomography:of colour mentioned (a) whole in sample,this figure, with the readerthe outer is referred surface toshown the web in lightalong gray thecan’t and sample, the six outersee? horizontal surface slices of (average the cavities vertical in height of about version ofGrain this article.) orientations? 125 lm) have been defined and are indicated in (d). dark gray; (b) three chosen cavities selected in the center of the sub-region where the morphology of the cavitiesIs the was quantified grain (instructure the cube shown in (a)) at the center of a DP steel sample at various steps of deformation.Where are the evolving? martensite grains?

Figure 2. Sequence of 2-D images obtained from the 3-D recon- C. Landron et al, Acta Mat. FigureS. 1.TerziSequence et al, ofScripta 3-D images Mat. of the notched zone of the specimen structed views of the notched area of the specimen. The tensile axis is 59 (2011) 7564-7573 61 (2009) 449-452 after various deformation times. The figure shows the variation of the vertical and the time after deformation is applied at time t0 is indicated liquid volume fraction in this zone (blue regions). (For interpretation in each figure. In order to evaluate local strains at various positions of colour mentioned in this figure, the reader is referred to the web along the sample, six horizontal slices (average vertical height of about version of this article.) 125 lm) have been defined and are indicated in (d).

6 Fig. 3. Mechanical behavior of the three steels in tension: (a) force–displacement; (b) true stress–local true strain. Mapping grains

• Scanning electron microscope technique electron backscatter diffraction (EBSD) • Electron penetration is very limited (<1µm) • Good 2D mapping • Difficult to extend to 3D, and only possible destructively.

10 µm

How to see the grains?

• Absorption and refraction, but X-rays also diffract • Scattering of radiation from periodic structures (crystals) Bragg’s law: λ = 2d sin(θ)

d θ θ

7 Diffraction • Monochromatic radiation

– discrete values of θ corresponding to dhkl • Only occurs when crystal is aligned correctly – angle θ between incident ray and crystal plane • For us: All parts of the crystal volume diffract with same efficiency – “kinematic scattering”

θ θ

Using X-ray diffraction for grain mapping

• A number of techniques use diffraction of x-rays to image (poly-) crystals • This talk will concentrate on diffraction contrast tomography • Talk tomorrow on scanning microscopies – M. Cotte.

Journal of Applied Crystallography, special issue March 2013 MAX4 Imaging Workshop 16

8 Outline

Diffraction contrast tomography • Setup: – Precise rotation stage – High resolution 2D detector close to sample – Parallel, monochromatic beam

9 Diffraction contrast tomography - requirements • Precise rotation stage – submicron eccentricity, wobble • High resolution 2D detector close to sample – compact design – high dynamic range • Parallel, monochromatic beam – synchrotron source

Instrument High resolution 2D detector Precision rotation stage

Slits to define beam

Incoming beam

10 Data acquisition • 360° rotation, integrated images of 0.05°-0.1° • Near-field – Spots approximate parallel projections of grains • 50-100 spots per grain – Reconstruct grain shapes • Diffraction geometry – Crystallographic orientations • Absorption contrast image in center of detector – Reconstruct cracks, pores, etc

DCT: Closer look at data • Titanium sample under load, 130 grains • 0.05° increments • Showing the diffraction contrasts only • Strain causes distortion and misorientation in grains

• Causes diffraction spots ~3mm to spread over several images • Can also see extinction spots, but significant overlap problems – useful in special cases Integrated image

11 DCT: Data processing 1 (2) Segmentation (1) Acquisition • Identify individual spots • Spots are 3D objects, because they may spread over a few adjacent images • 100,000+ spots • Reduce data volume from 30-60 GB • Record metadata: ! Position (u,v,ω) ω ! Intensity ! Size (u,v,ω) • 3600-7200 images covering ! Integrated image 360°. ! … • Remove background intensity to leave only diffraction contrast. • Moving median filter

DCT: Data processing 2 (3) Extract diffraction geometry Pair Matching • Important step • With a small, high resolution detector, the spot position does not directly tell us the diffraction angles • Sort spots into pairs, with 2θ, η, and ω, and the p scattering vector p (diffracting plane normal)

W. Ludwig et al, Rev. Sci. Instrum. 80, 033905 (2009), P. Reischig et al, J. Appl. Cryst. 46, 297-311 (2013), …

12 DCT: Data processing 3 (4) Indexing • Assign spots (pairs or individuals) to grains • INDEXTER algorithm • Iterative process • Crystallographic, spatial and shape criteria

DCT: Data processing 4 (5) Reconstruction • Reconstruct grains individually • ART/SIRT reconstruction from the diffraction spots • Oblique, parallel beam geometry • Few 1000 individual grains • Assemble the full 3D grain map • Plus absorption reconstruction from direct beam images • Mask for grain map

13 Resulting data (DCT)

• DCT grain map (few 1000 grains), combined with tomographic reconstruction of sample acquired simultaneously. • Rendering to show all the information: Mg fatigue test specimen. Absorption contrast tomography data: High Z precipitates 2 x FIB notches (implanted Ga)

Part of the grain map from DCT - shapes; orientations.

• All acquired non-destructively, so now can perform an in-situ experiment

Limitations Synchrotron DCT case • Access to synchrotron • Sample size – Sample size, grain size, and pixel size all scale together • Number of grains – ~5000 grains illuminated at once • Orientation spread – low mosiacity (<0.1°-1° intragranular orientation spread) – Main limitation in real materials " Developments in progress

14 Outline

Short fatigue cracks • Microtomography to observe short fatigue crack growth in-situ in a grain mapped sample. – FIB notches placed in specific grains – In-situ fatigue using machine from INSA de Lyon – Use radiographs to monitor crack – Use tomograms to record crack evolution in 3D

A. King et al., Acta Mater. 59 (2011) 6761–6771 30

15 Crack and microstructure

• Look at final crack shape compared to microstructure – How does this correspond to the crack growth rate?

Crack plane Basal plane Crack growth rate

Titanium fatigue crack • Similar concept from PhD thesis of Michael Herbig – In Ti-21S, β-Ti alloy (bcc) – Explain facetted crack growth in terms of combinations of slip systems – Ultimate goal of predicting crack behavior in polycrystals

M. Herbig etMAX4 al, Acta Imaging Mater. Workshop 59, 2011, 590-601

16 Babout et al. Intergranular stress corrosion cracking in sensitised austenitic stainless steel Stress corrosion cracking Experimental • InteractionX-ray tomography: of stress, principles sensitised material, andThe corrosive general concept environment of X-ray tomography is an extension of classical X-ray radiography, and is based – onIdentify the attenuation boundaries of the X-ray which beam resist through cracking the specimen. X-ray radiography provides only a projection – ofBridging the sample boundaries volume on one include single plane. low X-raysigma tomography overcomes this disadvantage by combining theboundaries information from and a series low of index many radiographs, plane boundaries each being recorded with different orientation of the sample in front of the detector. The variation of X-ray W 302SS wire; P platinum counter electrode; C environ- attenuationTensile in the axis volume of the sample can be reconstructed by combining a sufﬁcient number of mental cell; S K2S4O6Tensilesolution; axisT tensile machine; D detector radiographs with an appropriate algorithm, such as (d)1 X-ray microtomography set-up on ID19-ESRF ﬁltered back projection.27 The data are obtained in the form of a three-dimensional array of voxels (analogous most grain boundaries surrounded by wide ditches,

to pixels in a two-dimensional digital image), for which which is associated with grain boundary chromium the grey level of each voxel describes the calculated X- carbides.31 The wire was spot welded to 3 mm diameter

ray attenuation at that position. 2008 steel grub screws to form a tensile specimen. During the A tomographic scan requires an X-ray source, a experiment, a length of 0.5 mm of the wire was exposed rotation stage and an X-ray detector. This is usually a . ﬂuorescent detector which changes the X-rays into to the environmental solution, which was 0 15 mol Σ boundaries:potassium tetrathionate (K2S4O6), acidiﬁed with diluted

visible light, and a set of optic lenses that transfers the Science, , light to a CCD camera. Cone and parallel X-ray1 sources (<15°) sulphuric acid (H2SO4) to pH 2. The remainder of the specimen was protected with lacquer paint. are commonly used. The term microtomography3 is et al sometimes used to refer to tomography with an9 image The specimen was mounted in an environmental spatial resolution in the micrometre range, whichOther can be<29 cell, within a specially designed 5 kN tensile machine, developed by Buffie`re and Michaud (respectively achieved if the spot size is of the order of a few King A. Bridge (Σ1) micrometres, or via an adequate set of optics in the GEMPPM and GCP, INSA Lyon, France). The tensile detector. machine base was fixed to a stage where rotation and The results presented in the present article have been translation can be controlled precisely. In the stress obtained at the European Synchrotron Radiation corrosion set-up developed for the present work (Fig. 1), Facility (ESRF), on the ID19 beam line. The main an inner Perspex tube (40 mm diameter and 2 mm wall features of the line are a spectrally and spatially thickness) is used as the solution container, and a second homogeneous, highly coherent, high photon flux beam larger one (70 mm outer diameter and 1 mm wall at the sample position and a tuneable photon energy in thickness) provides the load transfer between the lower the range of 6–100 keV, with most of the experiments and upper grips in the tensile machine. This system carried out in the range of 10–35 keV.28 A state of the allows a full rotation of the device during a tomographic Otherart applications detector, developed at the ESRF, allows radiographs scan as Perspex is transparent to X-rays of the beam to be acquired with a tuneable spatial resolution in the energy used (i.e. 30 keV). range of 0.29–40 mm. Table 1 shows the set-up used for The progress of the in situ stress corrosion test is • Widethe experiment range reported of applications in the present paper. The summarised in Table 2. Before loading, the sample was distance between the sample and the detector was fixed connected for a few seconds to a platinum cathode to –at 40Fatigue mm to generate some phase contrast.29 polarise the sample, which initiated stress corrosion.

Published by Maney Publishing (c) IOM Communications Ltd Cracking then propagated in the sample under an –In situIGSCCstress corrosion cracking applied stress of y100 MPa and open circuit conditions. The tested sample was a 302 stainless steel wire with Each tomography scan was performed under steady chemical composition of 71.51Fe–18.14Cr–8.60Ni– state conditions, obtained by simultaneously reducing –0.07C–1 Deformation.25Mn–0.025P–0.003S–0 .4Si (wt-%). The wire the stress to 10 MPa and cathodically polarising the sample via a connection to a high purity aluminium was solution annealed at 1050uC for 30 min, then 32 exposed• atPlasticity 650uC for 60 min, producing a stress free, anode. Cracking was reinitiated by reapplying a higher fully sensitised microstructure. All heat treatments were stress under open circuit conditions. The applied stress performed• Twinning in argon atmosphere with a subsequent water quench. The degree of sensitisation was assessed with an Table 2 Progress of environmental in situ test* 30 –electrolytic Sintering etching test in 10 wt-% oxalic acid. A Sample Stress, visual inspection of the etched microstructure showed Step polarisation MPa Effect on cracking • Particle rotations Table 1 X-ray microtomography set-up* 0 A 0 Initiation Load 1 OC 100 Propagation r, mm • GrainE, keV growthnt ,s D, mm Scan 1 C 10 Arrest Load 2 OC 60 Propagation 0.7 30 1500 1 40 Scan 2 C 10 Arrest – Snow dynamics Load 3 OC 40 Propagation *r: spatial resolution; E: photon energy; n: No. of radiographs/ Scan 3 C 10 Arrest –scan Paleontology/Biology (during half-full rotation); t: exposure time/frame; D: distance sample detector. *Polarisation type, A: anodic; OC, open circuit; C, cathodic.

Materials Science and Technology 2006 VOL 22 NO 9 1069

17 Outline

Laboratory DCT

• Synchrotron – high flux – monochromatic beam – parallel beam • Laboratory X-ray tube – Low flux – polychromatic beam – cone beam • Commercial development (Xnovo, Zeiss) • Similar developments using cold neutron source at PSI (Switzerland)

A. King et al, J. Appl. Cryst. 46, 2013 S. Peetermans et al, Analyst 139, 2014

18 DCT: 6D reconstruction • Main limitation of technique as I have described it is mosaicity – Grains are not perfect crystals – Intragranular misorientation – Assumption that the spots are parallel projections of the grains breaks down • To deal with this reconstruct both intensity and orientation (rx,ry,rz) as function of position (x,y,z) in each grain – Thesis of N. Vigano

6D reconstruction • Some 6D reconstruction examples • Slice through a grain – reconstruction of misorientation and subgrains • Greatly improved grain shape reconstruction • Good compromise between speed of DCT (reconstruction ~1000 grains), and techniques which solve orientation of every voxel (100 million voxels)

N. Viganò, Scientific Reports 6, 20618 (2016)

19 Outline

A family of techniques

• Diffraction contrast tomography (DCT) • 3D X-ray diffraction microscopy (3DXRD) • Original grain mapping technique, from which DCT was derived • High energy diffraction microscopy (HEDM) – At APS – recently very successful with deformed materials • Diffraction tomography – Point scanning with a focused beam • Differential Aperture X-ray Microscopy (DAXM) – White beam, point scanning, analyser wire for 3D spatial info. • Topography – Classical diffraction imaging for defects in single crystals • Dark field x-ray microscopy – Recent developments analogous to TEM

MAX4 Imaging Workshop 40

20 Visual overview

• From Wolfgang Ludwig….

100 µm 100 µm high res.- slow Cryst. phases medium res. - fast single crystals

MAX4 Imaging Workshop 41