Retiveld Refinement-Report in tulane university-te

ReportinTulaneUniversityRietveldRefinement---GeneralStructureAnalysisSystem(GSAS)BinQianReportinTulaneUniversityOutline•IntroductionoftheRM(RietveldMethod)•Todeducetheintensityofthereflectedray(Intheory)•HowRMworks?•Thepoliciesoftherefinement•Thepracticesabout(Sr1-xCax)3Ru2O7refinement(Includingthesampleswithsinglephaseandtwophases)ReportinTulaneUniversity-astandardtreatmentofpowderdiffractiondatatomakethefinalstructuralmodelachievetheacceptedcriterion;-abestknownmethodthatfullymakesuseofthestep-modescanneddatatodigoutalotofstructuralandotherinformation;-aprocedureforstructuralsolutioninnature.IIntroductionoftheRM1.WhatisaRietveldRefinement?ReportinTulaneUniversityLatticeParametersQuantitativephaseAnalysisAtomicPositionsGrainsizeAtomicOccupancyStructurefactorsDebyeTemperaturesPhasetransitionsMagneticstructures……2.WhatcanwegettoperformaRietveldrefinement?IntroductionoftheRMReportinTulaneUniversity3.HistoryReview•RietveldoriginallyintroducedtheProfileRefinementmethod(Usingstep-scanneddataratherthanintegratedPowderpeakintensity)(1966,1967)•RietvelddevelopedfirstcomputerProgramfortheanalysisofneutrondataforFixed-wavelengthdiffractometers(1969)•Malmos&ThomasfirstappliedtheRietveldrefinementmethod(RR)foranalysisofx-raypowderdatacollectedonaGinierHaggfocusingCamera(1977)•Khattack&CoxfirstappliedtheRRtox-raypowderdatacollectedonadiffractometer(1977)•ConferenceonDiffractionProfileAnlysisSponsoredbyIUCrinPoland,suggestedtheterm“RietveldMethod”(1978)•WilesandYangdevelopedageneralcomputerprogram(D.B.W)forbothx-ray&neutrondiffractiondata(fixedwavelength)(1981)•VonDreele,JorgensenandWindsorextendedtotheprogramtotheneutrondiffractiondata(1982)•Fitchetal,193refinedparameters,UO2DAs.4D2O(1982)IntroductionoftheRMReportinTulaneUniversityAminoffPrize,Stockholm,1995IntroductionoftheRMH.M.RietveldActacrystallogr.,22,151(1967).H.M.Riveted,J.Appl.Crystallogr.,2,65(1969).A.C.LarsonandR.B.VonDreele,GeneralStructureAnalysisSystem(GSAS),LosAlamosNationalLaboratoryReportLAUR86-748(2004).ReportinTulaneUniversityIITodeducetheintensityofthereflectedray1.Thomsonformula(onefreeelectron)220sineemrc422420sineemrcII442242242200222sin(2)cos2eepmrcmrcIII422402epmrcIISobyaddingtheintensityofthetwocomponents4224201cos2()2eemrcIIReportinTulaneUniversityTodeducetheintensityofthereflectedray2.ThescatteringintensityofXraybyoneatom)(0SSrjjcoscossin42jjjjkrrcos1jZikraejEEesink4incidentrayscatteredrayReportinTulaneUniversityTodeducetheintensityofthereflectedray)(4)(2rrrUcos0sin()ikraeVeEEedVkrEUrdrkr0sin()aeEkrfUrdrEkrAtomicscatterfactorReportinTulaneUniversityTodeducetheintensityofthereflectedray3.Scatteringbyaunitcellczbyaxrjjjj)(0SSrjj1jnicejjEEfe2()11jjjjnniiHxKyLzcHKLjjjjeEFfefeEwhere,fiatomicscatteringfactorforithatom,xi,yiandzithefractionalcoordinatesforithatom2*ccceHKLIEEIF11cos2()sin2()nnHKLjjjjjjjjjjFfHxKyLzfHxKyLzHKLFAiB222HKLFABReportinTulaneUniversityTodeducetheintensityofthereflectedraySupposedthecellnumbersareM=M1M2M3,andimmergedinthex-ray,sothephasedifferenceis)pnm(rrr)SS(*mnp2204.Perfectsmallcrystal123mnpiMeHKLMMMMEEFe2222331122222123sinsinsinsinsinsinMeHKLMMMIIFWhenMk=0,±1,±2,……,222sinsinkkkkMM22123,MeHKLIIFMMMMMReportinTulaneUniversityIntensitydistributionofonedimensioninterferencefunctionReportinTulaneUniversity112233111111,,HHKKLLNNNNNN22MeHKLIIFMdIIM22eHKLIIFMdddddVsinrdsindd*033122ReportinTulaneUniversity03212VVNNNNdddG32201sin2eHKLIIFVV42320024201cos22sin2HKLeIIFVIQVmcV220324242221HKLFVsincoscmeQThereflectabilityofunitvolumeThetotalintensityisinproportiontotheconcerneddiffractivevolumeReportinTulaneUniversity5.Powderx-raydiffraction-ReflectionmultiplicityCrystalsystemIndicesH000K000LHHHHH0HK00KLH0LHHLHKLPCubic681224*2448*Hexagona62612*24*Tetragonal4248*816*trigonal248Monoclinic2424Triclinic222Forexample:Inthecrystalsystem(Oh),therearesixrelatedplanes:(100),(010),(001),(-100),(0-10),(00-1),theirdiffractionpeaksareseparatedinthesinglecrystal,buttheyoverlapat(100)diffractioninthepolycrystal,Sothereflectionmultiplicityis6.4232024201cos22sin2HKLeIIFPVmcVReportinTulaneUniversity5.Powderx-raydiffraction-AngledependentcorrectionsTheangledependentcorrectionsforpowderdiffractionincludetheLorentzfactorforbothneutronsandx-rays.Forneutrondatathereisanadditionalfactorforthevariationofscatteredintensitywithwavelength.X-raydiffractometerswithamonochromatorinparallelgeometryConstantwavelengthneutronsTOFneutrons4sinLd212sincosL22cos21sincosLReportinTulaneUniversity5.Powderx-raydiffraction-Temperaturefactorrjr'jujThedisplacementofatomjjjjrxaybzc'''jjjjuxaybzc'jjjrruSo,whenthetemperatureisT,thestructurefactorisasfollowing:'()0002exp()22exp()exp()()exp()THKLjjjjjjiFfrssiifrssussFHKLMTReportinTulaneUniversityWhere02exp()exp()iMTussTemperaturefactor222222sinsin8MBuDebyededucethefor