衍射花樣指數(shù)化與應用概述

衍射花樣指數(shù)化與應用概述第1頁，課件共28頁，創(chuàng)作于2023年2月Thefirststepinanalysingunknownpowderpatternisoftenanattempttofindaunitcellthatexplainsallobservedlinesinthespectrum.Youdonotneedadditionalcrystallographicdata,althoughifitexistsitmakesforfasterandmorereliableresults.Thematerialtobeanalysedmustbesinglephasedandtheexperimentalmaterialmustbeveryaccurate.第2頁，課件共28頁，創(chuàng)作于2023年2月Indexingprogramsuseonlythepositionalinformationofthepatternandtrytofindasetoflatticeconstants(a,b,c,a,b,g)andindividualMillerindices

(hkl)foreachline.Theformofequationstosolveiscomplicatedforthegeneralcase(triclinic)indirectspacebutisstraightforwardinreciprocalspace.Inthelatterthesetofequationsis：第3頁，課件共28頁，創(chuàng)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頁，課件共28頁，創(chuàng)作于2023年2月Therearetwogeneralapproachestoindexing,theexhaustiveandtheanalyticalapproach.Bothoftheseapproachesrequireveryaccurated-spacingdata.Thesmallertheerrors,theeasieritistotestsolutionsbecausethereareoftenmissingdatapointsduetointensityextinctionsrelatedtothesymmetryorthestructuralarrangementorduetolackofresolutionofthed-spacingthemselves.Theearliestapproacheswereoftheexhaustivetypeandweredonebygraphicalfittingornumericaltablefitting.第5頁，課件共28頁，創(chuàng)作于2023年2月IndexingProgramsThemethodscurrentlyimplementedareshownbold.TheyareselectedthroughtheitemIndexinginthemainmenu.Program Author Type ITO Visser analytical TREOR Werner exhaustive POWDER DICVOL CUBIC第6頁，課件共28頁，創(chuàng)作于2023年2月Theprogramsuseasetofcommonparameters,e.g.thewavelengthandamethodspecificset.Afteryouhaveclickedonaprogramwiththeleftmousebuttonindexingisimmediatelystartedwiththeactiveparameterset.Dependingontheproblemandcomputertypetheprogramruncantakefromsecondstomanyminutes.Allsolutionsarecomputedandstoredinternally.The"best"oneisdisplayedatthetopofthescreen,thenexttobestatthebottom.ForanoverviewofallsolutionsselectSolutionsinthemainmenu.第7頁，課件共28頁，創(chuàng)作于2023年2月MillerIndicesTripletofintegernumbersuniquelyassignedtoaBraggreflection.Thenotationisusuallyintheformof(hkl).Formallyspoken,MillerIndicesrepresentcoordinatesoflatticepointsinreciprocalspace.第8頁，課件共28頁，創(chuàng)作于2023年2月ReciprocalSpaceDirectspaceiscomposedofunitcellsanditscontents,whereasreciprocalspaceisalatticewhoselatticepointsareBraggreflections.Directandreciprocalspacearetightlycoupled.第9頁，課件共28頁，創(chuàng)作于2023年2月

LatticeconstantsAsetofmaximallysixfloatingnumbersrepresentingtheunitcell.Ascrystalsymmetrygrowsthenumberoflatticeconstantsneededtodescribethemetricsofaunitcellreduce.Inthecubicsystemthereisonlyoneconstant.第10頁，課件共28頁，創(chuàng)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頁，課件共28頁，創(chuàng)作于2023年2月d-SpacingThed-spacingisoneofseveralpossibleformstorepresentthepositionalinformationofpeaksinpowderpattern.OtherformsaretheangleQ,or2Q,orQ-values.Win_DIFFRACassumesinputintheformofd-spacings.Theyareinternallyconverted,e.g.ITOworksonlywithQ's.第12頁，課件共28頁，創(chuàng)作于2023年2月TREORThisprogramusestheexhaustiveapproach.Itiswidelyusedforindexingofpowderpatternthroughouttheworldandisbelievedtobeoneofthemostpowerfulenginesforsolvinghighandmediumsymmetries.Itisusefulaswellforlowsymmetryatthecostofratherhightimeconsumption.第13頁，課件共28頁，創(chuàng)作于2023年2月Werecommendthatyoustartwithadiffractionpatternwhoseresultiswellknowntoyou.IfyouarealreadyfamiliarwiththeTREORprogramyoumaydecidetostraightforwardindexing,usingthedefaultparameters.Incaseyouareanoviceuseryoushouldswiftlygothroughtheparametersandchangesettingsonlywhentheyareobviouslywrong.Withtheresultsobtainedyoumaythenturntothemoresophisticatedparameters,e.g.SelectBaselineSet.TheparametersaredescribedindetailundergeneralandTREOR-specificparameters.第14頁，課件共28頁，創(chuàng)作于2023年2月IncontrasttoITOamultitudeofnon-systematicextinctionsamongthefirstlinesmaynotappreciablyaffectthepoweroftrial-and-errormethods.However,'powderindexingisnotlikestructureanalysis,whichworkswellongooddata,andwillusuallygetbyonpoordatagivenalittlemoretimeandattention.Powderindexingworksbeautifullyongooddata,butwithpoordataitwillusuallynotworkatall.'(op.citRef.[4]).第15頁，課件共28頁，創(chuàng)作于2023年2月ThestandardprocedureusingTREORistostartwiththehighsymmetries:cubic,tetragonal,hexagonalandorthorhombicinonerun.Nextthemonoclinicsymmetryshouldbetried.Morethanonerunmaybenecessary,successivelyincreasingthenumberofbaselinesets,thecellvolumeandcelledge.Iftheformulaweightanddensityareknown,theyshouldbeused.TheCPU-timeneededwillthenusuallybestronglyreduced.Unfortunatelytheyaremostlynotwellknownandthereforenotoftenusable.IfallprevioustestshavefailedthetriclinictestremainsforwhichingeneralwerecommendITO.第16頁，課件共28頁，創(chuàng)作于2023年2月AnalyticalApproachThecrystalisassumedtobetriclinic.Solutionsareapproachedinthreesteps.Inthefirst,onetriestofindreasonablezonesfromthediffractiondata.Eachpairoflines,togetherwiththeoriginformsacrystallographiczone.Azoneisrelevanttothesolutionfindingalgorithmifsomeotherdiffractionlineslieonit,ifnotitisdiscarded.Inthesecondstepthebestzonesarethentriedincombinationstofindcompletelattices.ThismethodisknownastheITOmethod.Oncealatticeisfoundthatsatisfiestheexperimentald-spacingdata,thegeometryofthelatticeisexaminedforpossiblehighermetricsymmetry.Thisisthefinalstep.第17頁，課件共28頁，創(chuàng)作于2023年2月衍射分析應用物質對射線的衍射產生了衍射花樣或衍射譜，對于給定的單晶試樣，其衍射花樣與入射線的相對取向及晶體結構有關；對于給定的多晶體也有特定的衍射花樣。衍射花樣具有三要素：衍射線（或衍射斑）的位置、強度和線型。測定衍射花樣三要素在不同狀態(tài)下的變化，是衍射分析應用的基礎。第18頁，課件共28頁，創(chuàng)作于2023年2月衍射分析應用基于衍射位置的應用⑴點陣參數(shù)的精確測定，膨脹系數(shù)的測定；⑵第一類（即宏觀殘余）應力的測定；⑶由點陣參數(shù)測定相平衡圖中的相界；⑷晶體取向的測定；⑸固溶體類型的測定，固溶體組分的測定；⑹多晶材料中層錯幾率的測定；⑺點缺陷引起的Bragg峰的漂移。第19頁，課件共28頁，創(chuàng)作于2023年2月衍射分析應用基于衍射強度測量的應用（1）物相的定量分析，結晶度的測定

(2)

平衡相圖的相界的測定；

(3)

第三類應力的測定；

(4)

有序固溶體長程有序度的測定；

(5)

多晶體材料中晶粒擇優(yōu)取向的極圖、反極圖和三維取向分布的測定；

(6)

薄膜厚度的測定。第20頁，課件共28頁，創(chuàng)作于2023年2月衍射分析應用基于衍射線型分析的應用

(1)多晶材料中位錯密度的測定，層錯能的測定，晶體缺陷的研究；

(2)第二類（微觀殘余）應力的測定；

(3)晶粒大小和微應變的測定；第21頁，課件共28頁，創(chuàng)作于2023年2月衍射分析應用基于衍射位置和強度的測定

(1)物相的定性分析

(2)相消失法測定相平衡圖中的相界;(3)晶體(相)結構,磁結構,表面結構,界面結構的研究

第22頁，課件共28頁，創(chuàng)作于2023年2月衍射分析應用同時基于衍射位置、強度和線型的Rietveld多晶結構測定

需輸入原子參數(shù)（晶胞中各原子的坐標、占位幾率和濕度因子）、點陣參數(shù)、波長、偏正因子、吸收系數(shù)、擇優(yōu)取向參數(shù)等。

第23頁，課件共28頁，創(chuàng)作于2023年2月衍射分析應用RietveldprofilerefinementWhatistheRietveldmethod?Acomprehensive,computerbasedmethodfrotheanalysisofX-rayandneutronpowderdiffractionpatternsbyleastsquaresfittingofacalculateddiffractionpatterntotheobserveddata.WhatisspecialforRietveldmeth