AnalysisofEBSDData(L17)27-750,Fall2009Texture,Microstructure&Anisotropy,Fall2009B.El-Dasher*,A.D.Rollett,

G.S.Rohrer,P.N.KaluLastrevised:7thNov.‘09*nowwiththeLawrenceLivermoreNatl.Lab.《EBSD數據分析》課件共42頁，您現在瀏覽的是第1頁!OverviewUnderstandingtheprogram:ImportantmenusDefinitionofGrainsinOIMPartitioningdatasetsCleaningupthedata:TypesExamplesofNeighborcorrelationOrientation:SystemDefinitionDistributionFunctions(ODFs)PlottingODFs《EBSD數據分析》課件共42頁，您現在瀏覽的是第2頁!OverviewMisorientation:Definitions-Orientationvs.MisorientationDistributionFunctions(MDFs)PlottingMDFsOthertools:PlottingDistributionsInteractivetools《EBSD數據分析》課件共42頁，您現在瀏覽的是第3頁!GrainDefinitionsOIMdefinesasetofpointstoconstituteagrainif:-Apathexistsbetweenanytwopoints(intheset)suchthatitdoesnottraverseamisorientationanglemorethanaspecifiedtolerance-ThenumberofpointsisgreaterthanaspecifiednumberPointswithaCIlessthanspecifiedareexcludedfromstatistics

Note:PointsthatareexcludedaregivenagrainIDof0(zero)inexportedfiles《EBSD數據分析》課件共42頁，您現在瀏覽的是第4頁!PartitioningDatasetsChoosewhichpointstoincludeinanalysisbysettingupselectionformulaUsetoselectbyindividualpointattributesUsetoselectbygrainattributesSelectionformulaisexplicitlywrittenhere《EBSD數據分析》課件共42頁，您現在瀏覽的是第5頁!NeighborCorrelationExampleNoCleanupLevel0Level3NotethatHighercleanuplevelsareiterative(i.e.Level3=Levels0,1,2,3)《EBSD數據分析》課件共42頁，您現在瀏覽的是第6頁!OrientationDistributionFunctionsTheODFdisplayshowthemeasuredorientationsaredistributedinorientationspaceTwotypesofdistributionscanbecalculated:DiscreteODF:Binsizedefinesthevolumeofeachelementinorientationspace(5ox5ox5o)FastcalculationSuitableformosttexturestrengthsbutnotweaktexturesifthenumberofgrainsissmall(considerthenumberofdatapointspercellrequiredtoachievereasonablylownoise)ContinuousODF:GeneralizedSphericalHarmonicFunctions:Rankdefinesthe“resolution”ofthefunctionEquivalenttoaFouriertransformCalculationtimerisessteeplywithranknumber(32isaneffectivemaximum)TimeintensiveMostlyappropriateforweakertexturesSomesmoothingisinherent《EBSD數據分析》課件共42頁，您現在瀏覽的是第7頁!TypesofODF/PoleFigure/InversePFPlotsChoosetextureanddesiredplottypeUsetoaddmultipleplotstothesameimageNB:amoreprehensivediscussionofreferenceframesisgivenlater《EBSD數據分析》課件共42頁，您現在瀏覽的是第8頁!1=0°1=5°1=10°1=15°...max=5.56...ParametersfortextureanalysisCourtesyofN.Bozzolo《EBSD數據分析》課件共42頁，您現在瀏覽的是第9頁!max=5.17Lmax=16max=5.56Lmax=22Effectofthemaximumrankintheseriesexpansion,Lmaxmax=2.43Lmax=5max=4.04Lmax=8max=6.36Lmax=34Resolution 32x32x16Gaussian 3°Lmax 22BinSize 5°CourtesyofN.Bozzolo《EBSD數據分析》課件共42頁，您現在瀏覽的是第10頁!0=8°7.6at{03530}80000grains6.6at{03530}7.1at{03525}8.2at{03025}8.3at{153030}2000grains5.8at{53015}7.3at{3453550}15.5at{-53550}16000grains6.7at{03530}7.9at{03530}6.9at{-53535}9.0at{-53040}Gaussiennede0=4°Triclinicsamplesymmetry0=4°0=8°StatisticalAspectsNumberofgrainsmeasuredWidthoftheGaussian(and/orLmax)InfluenceofthesamplesymmetryZirconium,equiaxedSectionsthrutheODatconstant1(Lmax=34)16.011.38.05.64.02.82.01.40.7Texture=distributionoforientationsProblemofsampling!OrthorhombicsamplesymmetryCourtesyofN.Bozzolo《EBSD數據分析》課件共42頁，您現在瀏覽的是第11頁!Texture–MicrostructureCouplingExample:partialtextureofpopulationsofgrainsidentifiedbyagrainsizecriterion(zirconiumattheendofrecrystallization)partialtextureofthelargestgrainsPartialtextureofthesmallestgrainsImportantfortextureevolutionduringgraingrowth:thelargegrainsgrowattheexpenseofthesmallgrains.Sincethelargegrainshaveadifferenttexture,theoveralltexturealsochangesduringgrowth.D>2D(=11μm)3496grains17.9%surf.D<D/2(=2.75μm)14255grains1.7%surf.Globaltexturej1=0°090060Fj27.4116.011.38.05.64.02.82.01.40.7《EBSD數據分析》課件共42頁，您現在瀏覽的是第12頁!AgainthefunctioncanbeeitherdiscreteorcontinuousMisorientationDistributionFunctionsCalculatingMDFsisverysimilartocalculatingODFsCorrelatedMDF:MisorientationsarecalculatedonlybetweenneighborsIfthemisorientationisgreaterthanthegraindefinitionangle,thedatapointisincludedThiseffectivelyonlyplotsthemisorientationsbetweenneighboringpointsacrossaG.B.UncorrelatedMDF:MisorientationsarecalculatedbetweenallpairsoforientationsindatasetThisisthe“texturederived”MDFasiteffectivelyiscalculatedfromtheODFOnlyeffectivelyusedifthesamplehasweaktextureTextureReduced:RequiresbothCorrelatedandUncorrelatedMDFstobecalculatedforthesameplottypeThisMDFissimplytheCorrelated/UncorrelatedvaluesMaybeusedtoamplifyanyfeaturesinthecorrelatedMDF《EBSD數據分析》課件共42頁，您現在瀏覽的是第13頁!SectionsthroughMisorientationSpace《EBSD數據分析》課件共42頁，您現在瀏覽的是第14頁!ReconstructedBoundariesDataMUSTbeonhexagonalgridCleanupthedatatodesiredlevelChooseboundarydeviationlimitGenerateamapwithreconstructedboundariesselectedExportg.b.dataintotextfileThistypeofdataisrequiredforstereologicalanalysisof5-parametergrainboundarycharacterThesoftwareincludesananalysisofgrainboundariesthatoutputstheinformationasa(long)listoflinesegmentdata.useoftheGBsegmentanalysisisanessentialpreliminarystepbeforeperformingthestereological5-parameteranalysisofGBCD.Thedatamustbeonahexagonal/triangulargrid.Ifyouhaveamaponasquaregrid,youmustconvertittoahexagonalgrid.UsethesoftwarecalledOIMToolstodothis(freelyavailablefortranprogram).《EBSD數據分析》課件共42頁，您現在瀏覽的是第15頁!TSL/OIMReferenceFrames-TD

=-yEulerND

=zEuler-RD

=-xEulerZspatialxspatialyspatialSampleReferenceFrameforOrientations/EulerAnglesReferenceFrameforSpatialCoordinatesCrystalReferenceFrame:Rememberthat,toobtaindirectionsandtensorquantitiesinthecrystalframeforeachgrain(startingfromcoordinatesexpressedintheEulerframe),onemustusetheEuleranglestoobtainatransformationmatrix(orequivalent).+Zspatialpointsintotheplane

ZEulerpointsoutoftheplanexspatialyspatialRD=xEuler

=100sampleTD=yEuler=010sampleImage:

Notethe180°rotation.“+”denotestheOrigin+Physicalspecimen:

MountedintheSEM,thetiltaxis

isparallelto“xspatial”Thepurplelineindicatesadirection,associatedwith,say,ascratch,ortraceofagrainboundaryonthespecimen.《EBSD數據分析》課件共42頁，您現在瀏覽的是第16頁!17TSL/OIMReferenceFrames:

CoordinatesinPhysicalFrame,ConversiontoImage?

ThepreviousslidesmakethepointthatatransformationisrequiredtoalignspatialcoordinateswiththeEulerframe.?

However,thereisalsoa180°rotationbetweenthephysicalspecimenandtheimage.Thereforetoalignphysicalmarkingsonaspecimenwithtracesandcrystalsinanimage,itisnecessarytotakeeitherthephysicaldataandrotateitby180°,ortorotatethecrystallographicinformation.-TD

=-ysampleND

=zEuler-RD

=-xEulerZspatialxspatialyspatialSampleReferenceFrameforOrientations?Howtomeasurelinesetc.onaphysicalspecimen??Answer:usethespatialframeasshownonthediagramtotheleft(whichisNOTthenormal,mathematicalarrangementofaxes)andyourmeasuredcoordinateswillbecorrectintheimages,providedyouplotthemaccordingtotheIMAGEspatialframe.Thepurpleline,forexample,willappearontheimage(e.g.anIPFmap)asturnedby180°inthex-yplane.+《EBSD數據分析》課件共42頁，您現在瀏覽的是第17頁!18TSL/OIMReferenceFrames:LabelsintheTSLsystem?Whatdothelabels“RD”,“TD”and“ND”meanintheTSLliterature??ThelabelsshouldbeunderstoodtomeanthatRDisthex-axis,TDisthey-axisandNDthez-axis,allforEulerangles(butnotspatialcoordinates).?ThelabelsonthePoleFiguresareconsistentwiththemaps/images(butNOTthephysicalspecimen).?Thelabelsonthediagramareconsistentwiththemaps/images,butNOTthephysicalspecimen,asdrawn.?TheframeinwhichthespatialcoordinatesarespecifiedinthedatasetsisdifferentfromtheEulerframe(RD-TD-ND)–seetheprecedingdiagramsforinformationandforhowtotransformyourspatialcoordinatesintothesameframeastheEulerangles,usinga180°rotationaboutthelinex=y.=xspatial

=yEuler=yspatial

=xEulerThediagramisreproducedfromtheTSLTechnicalManual;thedesignationofRD,TDandNDisonlycorrectforEuleranglesinreferencetotheplottedmaps/images,notthephysicalspecimen《EBSD數據分析》課件共42頁，您現在瀏覽的是第18頁!TestofEulerAngleReferenceFramesTSL1AsimpletestoftheframesusedfortheEuleranglesistohavethesoftwaresplotpolefiguresforasingleorientationwithsmallpositivevaluesofthe3angles.Thisrevealsthepositionofthecrystalx-axisviathesenseofrotationimposedbythesecondEulerangle,F.Clearly,onehastoadd90°to1topassfromHKLcoordinatestoTSLcoordinates.NotethattheCMUTSLisusingthex//1120convention(“Xconvention”),whereastheMetzChannel/HKLsoftwareisusingthey//1120convention(“Yconvention”).HKL1Eulerangles:17.2°,14.3°,0.57°Hexagonalcrystalsymmetry(nosamplesymmetry)《EBSD數據分析》課件共42頁，您現在瀏覽的是第19頁!20Diagramsa1//a2//a3//x//[100]Cartesiany//[010]Cartesianx//[100]Cartesiany//[010]Cartesian《EBSD數據分析》課件共42頁，您現在瀏覽的是第20頁!21topbottomEuleranglereferenceframefirstacquiredpixel(Xpix=1,Ypix=1)XpixYpixXpixYpixX1Y1Z1"Virtualchamber"ofHKLsoftware,whichisusedtodefinethespecimenorientationinthemicroscopechamber(=howtoalignframe_0withframe_1);pictureisdrawnasiftheobserverwasthecamera.Notethatthemapsareturnedby180°withrespecttothispicture.-originalEuleranglesaregiveninframe_1(alsocalledCS1)ThectfformatisdesignedtoexportEulerangleintoframe_0(CS0),whichiscorrect,providedthatthespecimenorientationiscorrectlydefined.CS1=rawdataformatCS0ismodifiedbytheusertoalignaxeshowevertheyplease.TheCTFformatalwaysexportsinCS0arrangement.《EBSD數據分析》課件共42頁，您現在瀏覽的是第21頁!Tracesof{10-10}planesbeta-transformedTi(fromNathalieGey,LETAM–nowLEM3)EBSDmapXspatialYspatialXpix,Ypix=spatialframeX0,Y0,Z0=eulerangleframe,supposedtobealignedwithX1,Y1,Z1(μscopeframe)(Z0pointingout)NotethatarotationofthePFaxesby180°aroundZtorecovertheframenumbered3onthePFplots,wouldalsobeconsistentwiththetracebeingperpendicularto<10-10>…EulerframeSpatialframe《EBSD數據分析》課件共42頁，您現在瀏覽的是第22頁!NavigatingthemenusTherearetwomenusthataccessvirtuallyeverything:CreatesnewpartitionsImportsdataaspartitionsAccesstoroutinesthatcleanupthedatasetUsethistoexporttext.angfilesCheckthescanstatsRotatetheorientationsofeachpointaboutsampleframeCutoutscansectionsAccesstomenufor:-Maps-Texturecalculation-TextureplotsExportgrainIDdataassociatedwitheachpointCheckthepartitionstats&definitionChangethepartitionproperties:DecidewhichpointstoincludeDefinea“grain”《EBSD數據分析》課件共42頁，您現在瀏覽的是第23頁!GrainDefinitionsExamplesofdefinitions3degrees15degreesNotethateachcolorrepresents1grain《EBSD數據分析》課件共42頁，您現在瀏覽的是第24頁!GrainCIStandardization:ChangestheCIofallpointswithinagraintobethatofthehighestwithineachgrainMostusefulifaminimumCIcriterionisusedinanalyzingdata(preventslowCIpointswithinagrainfrombeinglost)DataCleanupNeighborOrient.CorrelationPerformedonallpointsinthedatasetForcleanupleveln:Condition1:Orientationof6-nnearestneighborsisdifferentthancurrentpoint(misorientationangle>chosen)Condition2:Orientationof6-nnearestneighborsisthesameaseachotherIfbothconditionsaremet,thepoint’sorientationischosentobeaneighbor’satrandomRepeatlowcleanuplevels(n=3max)untilnomorepointschangeforbestresultsNeighborPhaseCorrelation-SameasGrainDilationbutinsteadofusingthegrainwithmostnumberofneighboringpoints,thephasewiththemostnumberofneighboringpointsisusedOutputOptions:OverwritecurrentdatasetCreate“cleanedup”datasetasanewdatasetWritethe“cleanedup”datasetdirectlytofileNeighborCICorrelationPerformedonlyonpointswithCIlessthanagivenminimumTheorientationandCIoftheneighborwithhighestCIisassignedtothesepointsUsewhenmajorityofpointsarehighCI,andonlyafewbadpointsexistGrainDilation:ActsonlyonpointsthatdonotbelongtoanygrainasdefinedApointbecomespartofthegrainwiththemostnumberofsurroundingpointsTakestheorientationandCIoftheneighboringpointwithhighestCIUsetoremovebadpointsduetopitsoratG.Bs《EBSD數據分析》課件共42頁，您現在瀏覽的是第25頁!DefinitionofOrientationBydefinitionanorientationisalwaysrelative.TheOIMusesthesamplesurfacetodefinetheorthogonalreferenceframe.Quantitiesaretransformedfromsampleframetocrystalframee1se2sj1Fj2NB:amoreprehensivediscussionofreferenceframesisgivenlater《EBSD數據分析》課件共42頁，您現在瀏覽的是第26頁!PlottingOrientationDistributionsOnemustselectthetypesofdatavisualizationdesiredPolefiguresshowthedistributionofspecificcrystalplanesw.r.t.samplereferenceframeForthegenerationofmorethanonePF,theyneedtobeaddedoneatatime.InversePoleFiguresareusedtoillustratewhichcrystalplanenormalsareparalleltosampledirections(generallyRD,TD&ND)Theindicesenteredrepresentwhichsamplereferenceframeplaneisbeingconsidered:100,010and001aretypicalchoicesMultipleplanesalsoneedtobeenteredoneatatimeEulerspaceplotshowsthedistributionofintensityasafunctionoftheEuleranglesUsedtovisualizepocketsoftextureaswellas“fiber”texturesResolutiondefineshowmanyslicesarepossibleintheplot《EBSD數據分析》課件共42頁，您現在瀏覽的是第27頁!TheAverageOrientationofthepixelsinagrain

isgivenbythisequation:RD10000orientationsneartotheBrassponent:representedbya{111}polefigureand,inthepleteEulerspacetoshowthe24equivalentsresultingfromapplicationofcubiccrystalsymmetry{111}Preparationofthedataforanalysisi=1,24CourtesyofN.BozzoloVerysimple,n’est-cepas?However,thereisaproblem...Asaconsequenceofthecrystalsymmetry,thereareseveralequivalentorientations.

Thisexampleillustratesthepoint:ChoJH,RollettADandOhKH(2005)Determinationofameanorientationinelectronbackscatterdiffractionmeasurements,Metall.Mater.Trans.36A3427-38《EBSD數據分析》課件共42頁，您現在瀏覽的是第28頁!max=5.3716x16x83°225°max=4.4432x32x168°225°max=5.56Resolution 32x32x16Gaussian 3°Lmax 22BinSize 5°EffectofthebinningresolutionEffectofthewidthoftheGaussianParametersfortextureanalysisCourtesyofN.Bozzolo《EBSD數據分析》課件共42頁，您現在瀏覽的是第29頁!max=31!Same,with10°

binning:DirectMethodmax=5.56Ineffecttheharmonicmethodgivessome”smoothing".Withoutthis,acoarsebinningof,say,10°,producesavery“lumpy”result.1=5°CourtesyofN.Bozzolo《EBSD數據分析》課件共42頁，您現在瀏覽的是第30頁!SingleEBSDmap(1mm2)Multiplemaps,differentlocations(total=1mm2)RDTDND{10.0}(00.1)2.84.05.68.011.3asymmetryofintensityHomogeneity/heterogeneityofthespecimen...equiaxedTiNotjustthenumberofgrainsmustbeconsideredbutalsotheirspatialdistribution:StatisticalAspectsCourtesyofN.Bozzolo《EBSD數據分析》課件共42頁，您現在瀏覽的是第31頁!DefinitionofMisorientationMisorientationisanorientationdefinedwithanothercrystalorientationframeasreferenceinsteadofthesamplereferenceframeThusamisorientationistheaxistransformationfromonepoint(crystalorientation)inthedatasettoanotherpointxzygA-1gBx,y,zaresamplereferenceaxesgAisorientationofdatapointA(referenceorientation)w.r.tsamplereferencegBisorientationofdatapointBw.r.t.samplereferenceMisorientation=gBgA-1《EBSD數據分析》課件共42頁，您現在瀏覽的是第32頁!PlottingMDFsAgain,youneedtochoosewhatdatayouwanttoseeSelecttheTexturedatasetSelecttheplottype(axis/angle;Rodrigues;Euler)Usetogenerateplotsections《EBSD數據分析》課件共42頁，您現在瀏覽的是第33頁!ChartsChartsareeasytouseinordertoobtainstatisticalinformationIncreasingbin#《EBSD數據分析》課件共42頁，您現在瀏覽的是第34頁!ReferenceFramesThisnextsetofslidesisdevotedtoexplaining,asbestwecan,howtorelatefeaturesobservedinEBSDimages/mapstotheEulerangles.Ingeneral,theEulerframeisnotalignedwiththex-yaxesusedtomeasurelocationsinthemaps.TheTSLandChannelsoftwaresbothrotatetheimage180°relativetotheoriginalphysicalsample.BothTLSandChannelsoftwaresusedifferentreferenceframesformeasuringspatiallocationversusthetheEulerangles,whichis,ofcourse,extremelyconfusing.《EBSD數據分析》課件共42頁，您現在瀏覽的是第35頁!TSL/OIMReferenceFramesforImagesFromHerbMiller’snotes:TheaxesfortheTSLEulerframeareconsistentwiththeRD-TD-NDsystemintheTSLTechnicalManual,butonlywithrespecttomaps/images,notthephysicalspecimens.TheaxesfortheHKLsystemareconsistentwithNathalieBozzolo’snotesandslides.Here,xisinmon,butthetwoy-axespointinoppositedirections.ConversionfromspatialtoEulerandviceversa(TSLonly)Notes:theimage,aspresentedbytheTSLsoftware,hastheverticalaxisinvertedinrelationtothephysicalsample,i.e.a180°rotation.Notethatthetransformationisa180°rotationaboutthelinex=y《EBSD數據分析》課件共42頁，您現在瀏覽的是第36頁!37CartesianReferenceFrameforPhysicalMeasurementyEulerxEulerxCartesianyCartesian?Howtomeasurelinesetc.onaphysicalspecimenusingthestandardCartesianframewithxpointingright,andypointingup??Answer:usetheCartesianframeasshownonthediagramtotheleft(whichISthenormal,mathematicalarrangementofaxesandisNOTtheframeusedforpointcoordinatesthatyoufindina.ANGfile).Applythetransformationofaxes(passiverotation)asspecifiedbythetransformationmatrixshownandthenyourmeasuredcoordinateswillbeinthesameframeasyourEulerangles.Thistransformationisa+90°rotationaboutzsample.Inthiscase,thez-axispointsoutoftheplaneofthepage.《EBSD數據分析》課件共42頁，您現在瀏覽的是第37頁!TSLversusHKLReferenceFrames+Z(x)xspatialyspatialRD

=100sample

=xEulerTD

=010sample=yEulerTSLHKL+Z(x)xspatialyspatialRD

=100sample=xEulerTD

=010sample

=yEulerThetwospatialframesarethesame,exactlyasnotedbyChangsooKimandHerbMillerpreviously.Thefiguresshowimages(asopposedtophysicalspecimen).TheEuleranglereferencesframesdifferbyarotationof+90°(add90°tothefirstEulerangle)goingfromtheTSLtotheHKLframes(intermsofanaxistransformation,orpassiverotation).Viceversa,topassfromtheHKLtotheTSLframe,oneneedsarotationof-90°(subtract90°fromthefirstEulerangle).Thepositionofthe“sample”axesiscritical.Thenames“RD”and“TD”donotnecessarilycorrespondtothephysical“rollingdirection”and“transversedirection”becausethesedependonhowthesamplewasmountedinthemicroscope.《EBSD數據分析》課件共42頁，您現在瀏覽的是第38頁!39TheAxisAlignmentIssueTheissuewithhexagonalmaterialsisthealignmentoftheCartesiancoordinatesystemusedforcalculationswiththecrystalcoordinatesystem(theBravaislattice).Inoneconvention(e.g.popLA,TSL),thex-axis,i.e.[1,0,0],isalignedwiththecrystala1axis,i.e.the[2,-1,-1,0]direction.Inthiscase,they-axisisalignedwiththe[0,1,-1,0]direction.Intheotherconvention,(e.g.HKL,Univ.Metzsoftware),thex-axis,i.e.[1,0,0],isalignedwith