衍射花样指数化与应用概述

衍射花样指数化与应用概述第1页，课件共28页，创作于2023年2月Thefirststepinanalysingunknownpowderpatternisoftenanattempttofindaunitcellthatexplainsallobservedlinesinthespectrum.Youdonotneedadditionalcrystallographicdata,althoughifitexistsitmakesforfasterandmorereliableresults.Thematerialtobeanalysedmustbesinglephasedandtheexperimentalmaterialmustbeveryaccurate.第2页，课件共28页，创作于2023年2月Indexingprogramsuseonlythepositionalinformationofthepatternandtrytofindasetoflatticeconstants(a,b,c,a,b,g)andindividualMillerindices

(hkl)foreachline.Theformofequationstosolveiscomplicatedforthegeneralcase(triclinic)indirectspacebutisstraightforwardinreciprocalspace.Inthelatterthesetofequationsis：第3页，课件共28页，创作于2023年2月Q=h2A+k2B+l2C+hkD+hlE+klFwheretheQ-valuesareeasilyderivedfromthediffractionangleQ.Thissethastobesolvedfortheunknowns,A,B,C,D,E,F,whichareinasimplewayrelatedtothelatticeconstants.Findingthepropervaluesforthelatticeparameterssothateveryobservedd-spacingsatifiesaparticularcombinationofMillerindicesisthegoalofindexing.Itisnoteasyevenforthecubicsystem,butitisverydifficultforthetriclinicsystem.第4页，课件共28页，创作于2023年2月Therearetwogeneralapproachestoindexing,theexhaustiveandtheanalyticalapproach.Bothoftheseapproachesrequireveryaccurated-spacingdata.Thesmallertheerrors,theeasieritistotestsolutionsbecausethereareoftenmissingdatapointsduetointensityextinctionsrelatedtothesymmetryorthestructuralarrangementorduetolackofresolutionofthed-spacingthemselves.Theearliestapproacheswereoftheexhaustivetypeandweredonebygraphicalfittingornumericaltablefitting.第5页，课件共28页，创作于2023年2月IndexingProgramsThemethodscurrentlyimplementedareshownbold.TheyareselectedthroughtheitemIndexinginthemainmenu.Program Author Type ITO Visser analytical TREOR Werner exhaustive POWDER DICVOL CUBIC第6页，课件共28页，创作于2023年2月Theprogramsuseasetofcommonparameters,e.g.thewavelengthandamethodspecificset.Afteryouhaveclickedonaprogramwiththeleftmousebuttonindexingisimmediatelystartedwiththeactiveparameterset.Dependingontheproblemandcomputertypetheprogramruncantakefromsecondstomanyminutes.Allsolutionsarecomputedandstoredinternally.The"best"oneisdisplayedatthetopofthescreen,thenexttobestatthebottom.ForanoverviewofallsolutionsselectSolutionsinthemainmenu.第7页，课件共28页，创作于2023年2月MillerIndicesTripletofintegernumbersuniquelyassignedtoaBraggreflection.Thenotationisusuallyintheformof(hkl).Formallyspoken,MillerIndicesrepresentcoordinatesoflatticepointsinreciprocalspace.第8页，课件共28页，创作于2023年2月ReciprocalSpaceDirectspaceiscomposedofunitcellsanditscontents,whereasreciprocalspaceisalatticewhoselatticepointsareBraggreflections.Directandreciprocalspacearetightlycoupled.第9页，课件共28页，创作于2023年2月

LatticeconstantsAsetofmaximallysixfloatingnumbersrepresentingtheunitcell.Ascrystalsymmetrygrowsthenumberoflatticeconstantsneededtodescribethemetricsofaunitcellreduce.Inthecubicsystemthereisonlyoneconstant.第10页，课件共28页，创作于2023年2月Q-valueTheQ-valueisoneofseveralpossibleformstorepresentthepositionalinformationofpeaksinpowderpattern.Theyaredefinedas:Q=1/d2=(4sin2Q)/l2Qcanberepresentedasaquadraticformofthe(hkl)'s.Q=h2A+k2B+l2C+hkD+hlE+klF,whereA,B,C,D,E,Farerelatedtothelatticeconstants.InITOeachQ-valueismultipliedby10000.第11页，课件共28页，创作于2023年2月d-SpacingThed-spacingisoneofseveralpossibleformstorepresentthepositionalinformationofpeaksinpowderpattern.OtherformsaretheangleQ,or2Q,orQ-values.Win_DIFFRACassumesinputintheformofd-spacings.Theyareinternallyconverted,e.g.ITOworksonlywithQ's.第12页，课件共28页，创作于2023年2月TREORThisprogramusestheexhaustiveapproach.Itiswidelyusedforindexingofpowderpatternthroughouttheworldandisbelievedtobeoneofthemostpowerfulenginesforsolvinghighandmediumsymmetries.Itisusefulaswellforlowsymmetryatthecostofratherhightimeconsumption.第13页，课件共28页，创作于2023年2月Werecommendthatyoustartwithadiffractionpatternwhoseresultiswellknowntoyou.IfyouarealreadyfamiliarwiththeTREORprogramyoumaydecidetostraightforwardindexing,usingthedefaultparameters.Incaseyouareanoviceuseryoushouldswiftlygothroughtheparametersandchangesettingsonlywhentheyareobviouslywrong.Withtheresultsobtainedyoumaythenturntothemoresophisticatedparameters,e.g.SelectBaselineSet.TheparametersaredescribedindetailundergeneralandTREOR-specificparameters.第14页，课件共28页，创作于2023年2月IncontrasttoITOamultitudeofnon-systematicextinctionsamongthefirstlinesmaynotappreciablyaffectthepoweroftrial-and-errormethods.However,'powderindexingisnotlikestructureanalysis,whichworkswellongooddata,andwillusuallygetbyonpoordatagivenalittlemoretimeandattention.Powderindexingworksbeautifullyongooddata,butwithpoordataitwillusuallynotworkatall.'(op.citRef.[4]).第15页，课件共28页，创作于2023年2月ThestandardprocedureusingTREORistostartwiththehighsymmetries:cubic,tetragonal,hexagonalandorthorhombicinonerun.Nextthemonoclinicsymmetryshouldbetried.Morethanonerunmaybenecessary,successivelyincreasingthenumberofbaselinesets,thecellvolumeandcelledge.Iftheformulaweightanddensityareknown,theyshouldbeused.TheCPU-timeneededwillthenusuallybestronglyreduced.Unfortunatelytheyaremostlynotwellknownandthereforenotoftenusable.IfallprevioustestshavefailedthetriclinictestremainsforwhichingeneralwerecommendITO.第16页，课件共28页，创作于2023年2月AnalyticalApproachThecrystalisassumedtobetriclinic.Solutionsareapproachedinthreesteps.Inthefirst,onetriestofindreasonablezonesfromthediffractiondata.Eachpairoflines,togetherwiththeoriginformsacrystallographiczone.Azoneisrelevanttothesolutionfindingalgorithmifsomeotherdiffractionlineslieonit,ifnotitisdiscarded.Inthesecondstepthebestzonesarethentriedincombinationstofindcompletelattices.ThismethodisknownastheITOmethod.Oncealatticeisfoundthatsatisfiestheexperimentald-spacingdata,thegeometryofthelatticeisexaminedforpossiblehighermetricsymmetry.Thisisthefinalstep.第17页，课件共28页，创作于2023年2月衍射分析应用物质对射线的衍射产生了衍射花样或衍射谱，对于给定的单晶试样，其衍射花样与入射线的相对取向及晶体结构有关；对于给定的多晶体也有特定的衍射花样。衍射花样具有三要素：衍射线（或衍射斑）的位置、强度和线型。测定衍射花样三要素在不同状态下的变化，是衍射分析应用的基础。第18页，课件共28页，创作于2023年2月衍射分析应用基于衍射位置的应用⑴点阵参数的精确测定，膨胀系数的测定；⑵第一类（即宏观残余）应力的测定；⑶由点阵参数测定相平衡图中的相界；⑷晶体取向的测定；⑸固溶体类型的测定，固溶体组分的测定；⑹多晶材料中层错几率的测定；⑺点缺陷引起的Bragg峰的漂移。第19页，课件共28页，创作于2023年2月衍射分析应用基于衍射强度测量的应用（1）物相的定量分析，结晶度的测定

(2)

平衡相图的相界的测定；

(3)

第三类应力的测定；

(4)

有序固溶体长程有序度的测定；

(5)

多晶体材料中晶粒择优取向的极图、反极图和三维取向分布的测定；

(6)

薄膜厚度的测定。第20页，课件共28页，创作于2023年2月衍射分析应用基于衍射线型分析的应用

(1)多晶材料中位错密度的测定，层错能的测定，晶体缺陷的研究；

(2)第二类（微观残余）应力的测定；

(3)晶粒大小和微应变的测定；第21页，课件共28页，创作于2023年2月衍射分析应用基于衍射位置和强度的测定

(1)物相的定性分析

(2)相消失法测定相平衡图中的相界;(3)晶体(相)结构,磁结构,表面结构,界面结构的研究

第22页，课件共28页，创作于2023年2月衍射分析应用同时基于衍射位置、强度和线型的Rietveld多晶结构测定

需输入原子参数（晶胞中各原子的坐标、占位几率和湿度因子）、点阵参数、波长、偏正因子、吸收系数、择优取向参数等。

第23页，课件共28页，创作于2023年2月衍射分析应用RietveldprofilerefinementWhatistheRietveldmethod?Acomprehensive,computerbasedmethodfrotheanalysisofX-rayandneutronpowderdiffractionpatternsbyleastsquaresfittingofacalculateddiffractionpatterntotheobserveddata.WhatisspecialforRietveldmeth