MTEX-Intro-EBSD-2014-Pittsburgh

FeaturesofthefreeandopensourcetoolboxMTEXfortextureanalysisRalfHielscher1FlorianBachmann2HelmutSchaeben2DavidMainprice31AppliedFunctionalAnalysis,TechnischeUniversit¨atChemnitz,Germany2GeoscienceMathematicsandInformatics,TechnischeUniversit¨atBergakademieFreiberg,Germany3G´eosciencesMontpellierUMR5242,Universit´eMontpellier2&CNRS,FranceMicroBeamAnalysisEBSD2014meetingatCarnegieMellonUniversityinPittsburghCentralthemeinEBSD?• Therelationshipvectorinspecimencoordinates(r)andparallelvectorincrystalcoordinates(h).• IndetailedanalysisofEBSDdataweneedtofrequentlyapplytheserelationshipsr=g.handh=g-1.rwhereg=orientation(e.g.phi1,PHI,phi2)ThisisveryeasywithMTEXPost-processing:MTEXismorethanEBSD…• Initiallydevelopedforpolefigureinversion• LinkscurrentlybeingdevelopedwithMAUDRietveldX-ray(Texture)package–MTEXcanimportanODF• Centralmathematicalconceptistheaxialradialkernels:individualorientationstoODF• Originalgrainmodellingconceptin2Dand3D• Completequantitativetextureanalysis• BasedonMATLABscripts,freeandopensource.• IdealfortheanalysisoflargedatasetsandbatchprocessingwiththeflexibilityofprogramminglanguageOverviewoftheMATLAB®EnvironmentorMatrixLaboratory:Strongchoice• High-level(linebylineinterpreter)languagefortechnicalcomputing• Advantage–fastdevelopmentcycles.• Disadvantage–slowerthancompiled,butthisisbeingreducedbyoptimizationofmatrixandvectorbasedMATLABformulti-corecomputers• Mathematicalfunctionsforlinearalgebra,statistics,Fourieranalysis,filtering,optimization,andnumericalintegration,plus2-Dand3-Dgraphicsfunctions• Advantage–manyoptimisedfunctionsbuilt-in• Extensionsusingcommercialtoolboxsorfreeopensourcetoolboxs(e.g.MTEX),pluslargeuserbasewithMATLABCentral,FileExchange,forumsetc• Advantage–solutionstomanyproblemsalreadycodedinMATLABandfreelyavailablesourcecodeavailable• …OverviewoftheMATLAB®EnvironmentorMatrixLaboratory:Strongchoice• FunctionsforintegratingMATLABbasedalgorithmswithexternalapplicationsandlanguages,suchasC,C++,FORTRAN,Java™etc• Advantage–somespeedcriticalfunctionsarecodedinCandcompiledforMTEX)• …MATLABopeningscreenEnlargementofcommands1.OriginallydevelopedbyRalfHielscheraspartofthisPh.D.thesisTheRadonTransformontheRotationGroup:InversionandApplicationtoTextureAnalysis”underthedirectionofHelmutSchaeben.2.Thetoolboxhasbeenextendedtoincludetheanalysisof2Dand3DEBSDdatabyFlorianBachmannaspartofhisMastersandThesisdegreeswithothers.3.Thephysicalpropertiesof2nd,3rdand4thranktensorshavebeenincorporatedbyDavidMainpriceandothers.HistoryofMTEX2nd  rank    tensors  3rd  rank    tensors  Imports  EBSD  data    *.c7      Oxford-­‐HKL  &  Bruker    *.ang    EDAX-­‐TSL    (Spherical  Harmonics)  4th  rank    tensors  EBSD–spatiallyreferencedorientationdata:grains,sizes,shapesandorganizationMTEX  –  Three  reference  frames                                associated  with  crystals  Directlatticea,b,cReciprocalLatticea*,b*,c*Cartesianframex,y,zFordirectionsForpoletoplanesForEuleranglesϕ1Φϕ2 u=ua+vb+wch=ha*+kb*+lc*andTensorsr=ix+jy+kzConversionsinMTEX%%Definehkloruvw%poletoplanehklh=h.a*+k.b*+l.c*h=Miller(1,1,1,CS,'Forsterite','hkl')%directionu=u.a+v.b+w.cu=Miller(1,1,1,CS,'Forsterite','uvw')%anglesbetweenhandvangle_between_h_and_u=angle(h,u)/degree%%conversionbetweenhklanduvw%N.B.converteduvwandhklnotalwaysintegervalues%changehkl(h)touvwuvw=uvw(h)%changeuvw(u)tohklhkl=hkl(u)%%conversionofhklanduvwtospecimencoordinates%N.B.converteduvwandhklnotalwaysintegervalues%changehkl(h)tovector3dr1%Millerindiceshparalleltospecimendirectionr1r1=vector3d(h)%changeuvw(u)tovector3dr2%Millerindicesuparalleltospecimendirectionr2r2=vector3d(u)%%conversionofspecimencoordinatestohklanduvw%N.B.converteduvwandhklnotalwaysintegervalues%changevector3d(1,1,1)tohklhkl_111=Miller(vector3d(1,1,1),CS,'Forsterite','hkl')%changevector3d(1,1,1)touvwuvw_111=Miller(vector3d(1,1,1),CS,'Forsterite','uvw')!MTEX  –  symmetrise  :  (hkl)  WithsymmetrisecommandFourhkls2inupperand2lowerhemisphereSinglehklinupperhemisphereGrainmodellinginMTEXEBSDGrainsmisorientationboundariesofallanglesplot(ebsd,'property','bc');colormap(gray)colorbarholdonplotBoundary(selected_grains,'linecolor','w','linewidth',1)holdoffXYYEBSDmapsinMTEXmicrostructureatthepixellevel• Orientations–variationswithposition,gradients…• Grains,sub-grainsandtwinsandtheirboundaries• Phases• Properties:indexingquality• Properties:diffractioncontrast(bandcontrast)• Properties:2ndranktensorse.g.chemicaldiffusivity• Properties:3rdranktensorse.g.piezoelectricity• Properties:4thranktensorse.g.Young’smodulus• Schmidfactorsforslipsystems• Superposedmapswithtransparency• Selectindividualgrainsandlineprofilesinteractively• Selectcomplexsub-regionsinteractively• Chosefromanextensiverangeofcoloroptionsormakeyouowncolorscales• Andanythingelseyoucaretoadd!EBSDMapsinMTEXBandContrastmapPhaseMap%**********************************************************************%usefigurekeepsplotopenandsetsdimensionsofplotfigure('position',[200200plot_wplot_h])plot(ebsd,'property','phase')savefigure('/MatLab_Programs/Francoi