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1、QuickTime™andadecompressorRietveldanalysisareneededtoseethispicture.1RietveldmethodInitially,methodforrefinementofcrystalstructuresfromneutronpowderdiffractiondata中子粉晶衍射数据Rietveldalgorithms算法-1966+…..1stfullpaper-1969Developmentofautomateddiffractometry-early1980sIncreasedcomputin
2、gpowerRiseofdemandforinformationcontainedinpeakshapes,backgroundcrystallitesizemicrostressthermalmotion热运动stackingfaults堆垛层错amorphouscontentotheratomicdisorder1989-RietveldmethodadoptedforusewithX-raypowderdata2RietveldmethodUseseverydatum(y)collected,individuallyobsEachycomparedw
3、ithacorrespondingcalculatedvalue(y)obscalcMustbeabletocalculateycalcNeedmodelsforallscatteringeffects-bothBraggpeaks&backgrdModelsallinvolveparametersChangeparametersaccordingtotheleastsquarescriterion最小二乘准则MinimizeR=Σw(y–y)2iobscalcRefinementparametersWhatparametersarevaried?unit
4、celldimensionsatompositionalparametersatomthermalmotionparametersatomsiteoccupancyparametersscalefactor(s)backgroundfunctionparameterssampledisplacement,sampletransparency,zero-shifterrorspeakshapeparameterspreferredorientation,absorption,porosity多孔性,extinctionparameters,phasecomp
5、osition4RefinementparametersWhatparametersarevaried?atompositionalparametersatomthermalmotionparametersatomsiteoccupancyparameters5AtompositionalparametersI~
6、F
7、2F=Σƒe2πi(hxj+kyj+lzj)hklhklhkljneedx,y,zforallatomsinunitcell–jjjexceptforsymmetry-relatedatompositionscertain"specialpo
8、sition"coordinates6AtompositionalparametersEx.–R3mIfatomsin36i,needx,y,zIfatomsin18g,needxIfatomsin3a,noparameters7AtomicdisplacementparametersDebye-Wallerfactor(seeR.W.James,OpticalPrinciplesoftheDiffractionofX-rays&others)I(T)/I(T)=exp(–16π2µ2(sin2θ)/λ2)omeansquareamplitudeofato
9、micvibrationforisotropic各向同性motion8AtomicdisplacementparametersDebye-Wallerfactor(seeR.W.James,OpticalPrinciplesoftheDiffractionofX-rays&others)I(T)/I(T)=exp(–16π2µ2(sin2θ)/λ2)oUsuallyconsideredpartofatomicscatteringfactorƒ=ƒexp(-8π2µ2(sin2θ)/l2)=ƒexp(-B(sin2θ)/λ2)jojjojjBis"tempe
10、raturefactor"alsoB=8π2UjjGenerall
