Rietveld方法原理

陈小龙中国科学院物理研究所2006 10杭州 Lecturenotes Rietveld方法原理 1 IsostructuralCompounds Nd2CuO4Gd2CuO4a 0 39419nma 3 8938nmc 1 21627nmc 11 8810nmZNd 0 353ZGd 0 349 Nd Gd 2 XRDpatternsofSolidsolutionNaSr4 xBaxB3O9 0 x 4 FirstcubicborateonlywithBO3 Cubicboratesareestimatedbelow1 L Wu X L Chen et al 2004 3 PhasetransitionofBaTiO3fromtetragonaltocubicatabout132 C 4 YBa3B3O9 Phasetransitionandstructuredetermination S G P63cm No 185 a 9 4235 4 c 17 602 1 1100 C S G R 3 No 148 a 13 0441 1 c 9 5291 1 1140 C X Z Li X L Chen et al 2004 5 LiAlB2O5 SearchfornewSHGmaterials B3O7 5 AlB2O7 5 6 StructuralDataforLiAlB2O5 7 FinalRefinementofNewcompoundofLiAlB2O5 8 StructurevsTemperature KCaCO3F 0 8120 3 0 1880 3 0 5byx raydata 9 LiSr4B3O9 Acomparisonbetweenstructuredeterminationfromsingle crystalandpowderX raydiffraction a 14 9470 S G Ia 3d ZB ZSr 2 3 38 2 0 6 Single crystal Rint 0 0745R1 alldata 0 0695wR2 alldata 0 1887withweightingscheme W 1 2 Fo2 0 0000P 2 359 71P whereP Fo2 2Fc2 3SDPD RB 0 07Rp 0 0609Rwp 0 0811Rexp 0 0314 10 WhatisaRietveldRefinement astandardtreatmentofpowderdiffractiondatatomakethefinalstructuralmodelachievetheacceptedcriterion abestknownmethodthatfullymakesuseofthestep modescanneddatatodigoutalotofstructuralandotherinformation aprocedureforstructuralsolutioninnature 11 WhatcanwegettoperformaRietveldrefinement LatticeParametersQuantitativephaseAnalysisAtomicPositionsGrainsizeAtomicOccupancyIncommensurateStructureDebyeTemperaturesStructurefactorsCrystallinityPhasetransitionsMagneticstructures 12 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 13 AminoffPrize Stockholm 1995 H M RietveldActacrystallogr 22 151 1967 H M Riveted J Appl Crystallogr 2 65 1969 14 Structuralmodel Rawdata RietveldRefinement Refinedmodel shift 15 HowRMworks TheRMrefinesastructurebyminimizingaquantitythroughtheNewton Raphsonalgorithm where yiistheobservedintensityatacertain2 yc iisthecalculatedintensityatthesameangle wiisaweight weusuallytakewi 1 yii 1 2 n 1 2 p theparameterstoberefined 16 Givenasolution opt 1 2 p thatapproximatelysatisfytheaboveequation Tofindabettersolution webeginaniterativeprocessbyexpandingintoaTaylorseries 17 A 1 b 1 0 1 1isashift 18 S isthescalefactorofthephase LhcontainstheLorentz polarisationandmultiplicityfactors FhisthestructurefactorAhistheabsorptioncorrectionPhisthepreferredorientationfunction isthereflectionprofilefunctionthatmodelsbothinstrumentalandsampleeffects 19 where fiatomicscatteringfactorforithatomxi yiandzithefractionalcoordinatesforithatom Themeansquaredisplacementoftheatominadirectionnormaltothereflectingplanes 20 WhereRELAXisrelaxtionfactorsthatareusedtocontroltheshiftstoavoiddivergence andCCisamultiplier 21 WhatweneedtoperformaRR Asetofstep modescanneddata usually2 10 120 ormore step 2 0 02 collectingtimeisinstrumentdependentfrom1 20sforlaboratorydiffractometer Aninitialstructuralmodelhavingroughlyaccuratelatticeconstants correctspacegroupandapproximateatomicpositions 22 Howweobtainaninitialstructuralmodel solidsolutionsusuallyadoptsamestructuretypesoftheirparentcompounds NaSr4 xBaxB3O9 0 x 4 CompoundswithsamechemicalformulaYBa2Cu3O7andNdBa2Cu3O7butalwaysalertthatexceptionsarenotuncommonLa2CuO4andNd2CuO4TryanderrorAbinitostructuredetermination 23 Isthecompoundknown CrystallographicStructureDatabases ICSD MineralsandInorganics http www fiz karlsruhe de MineralsandInorganicOver60000entriesCambridgeStructureDataBank http www ccdc cam ac ukOrganics OrganometallicsOver250000entries ICDDdiffractiondatahttp 24 Anewstructuraldatabase 2003 aimedatfreelyretrievingdata 18000Patternsalready 25 ParametersinPCRfile TheparametersinPCRfilecanbedividedintothreecategories relatingonlytosamples refinablesuchasatomicpositions temperaturefactors relatingbothtosamplesandinstrumentssuchasscalefactors FWHM Fullwidthathalfmaximum user specifiedparameterssuchasBKPOS Nba 26 27 Codewords I codewordsareusedtocontrolparameterswhentoberefined whentobefixedandwhentobeconstrainedandetc AcodewordisformedasC S 10P CC WhereSstandsforthesignmark Pisanordinalnumbersetbyusersfrom1top themaximumnumberofparameters 28 Codeword II Forexample anatomCapositionis 0 0 z withztoberefinedfromitsinitialvalue0 1 ThecodewordinyourPCRfilelookslikethefollowing Ca1Ca 20 00 00 1 0 00 0120 5 Here S 1 P 12 andCC 0 5 ThatmeansthatzofCa1isthe12ndparametertoberefinedintheiterativeprocess andxandyofCa1occupyspecialpositionsnotneededtoberefined 29 Codeword III Anotherexample thelatticeconstantsofatetragonalcompoundaretoberefined ThecodewordinyourPCRfilelooksasfollows3 8913 89111 73251 051 061 0Inthiscase constraintisputonaandbbyusingthesamecodewordsincea balwaysholdsintetragonalcompounds 30 Codeword IV Onemoreexample theoccupanciesoftwokindsofatomsatonesitearetoberefined Solidsolutionsarethemostcommonamongthiskindofrefinements ThecodewordsinyourPCRfilearesetasYY 3 0 8 10 3YbYb 3 0 2 10 3OnlyinthiswayaretheoccupanciesguaranteedtosatisfyOcc Y Occ Yb 1 31 Codeword V eachparameterusuallycontrolledbyonecodeword Bealertthatonecodewordshouldbegiventotwoormoreparametersthatareirrelevant thereisnolimittochooseordinalnumbers Butweusuallysetthefirstordinalnumberstoglobalparameterssuchaszeropoint backgroundparametersandtheetc 32 Modelingbackgrounds Thebackgroundintensitybiattheithstepmaybeobtainedbyanyofthefollowingthreemethod aspecifiedbackgroundfunction usuallyapolynomial linearinterpolationbetweenuser selectedpointsinthepatternAuser suppliedfunction 33 Controlflags ThechoiceofbackgroundtypeisindicatedbyacontrolflagCommentline 4 JobNprNphNbaNex 05102Nba 0Refinebackgroundwithapolynomial 1ReadbackgroundfromfileCOFHIL bac 2 3 NlinearinterpolationbetweenNgivenpoints 34 WhereBmareparametertoberefinedBKPOSisauser specifiedparameter originofpolynomialfunction non refinable If2 BKPOS weseebi B0UserscanlookintotheirdatafilestosetthevaluesofBKPOS 35 Profilefunctions I Gaussian G Npr 0 Lorentzian L Npr 1 Parametertoberefined Hk FullWidthatHalfMaximum FWHM 36 Hk 0 2 37 Profilefunctions II Mod ILorentzianNpr 2 Parametertoberefined Hk Mod ILorentzianNpr 3 38 Profilefunctions III Psudo VoigtNpr 5 Parameterstoberefined Hk 0 X 0 shape 39 Pseudo VoigtfunctionsHk 0 2 40 Profilefunctions III PearsonVII Parameterstoberefined Hk m0 X Y 41 Profilefunctions IV Mod TCHZpV L x andG x havedifferentFWHMsHLandHG Parameterstoberefined HGandHL 42 FullwidthathalfMaximum FWHM ForNpr 0 6 Hk HG ForNpr 7 HLisrequiredapartfromHG 43 TypicalvariationsofFWHMvs2 44 Summaryfortheparameterstoberefinedwithdifferentprofiles Npr 0 Gaussian U V W Ig3Npr 5 pv U V W Ig 0 Shape X5NPr 6 PearsonVII U V W Ig 0 Shape X Y6NPr 7 TCHZpv U V W Ig X Y Sz6 45 46 Preferredorientations I Nor 0 Rietveld TorayaModel G1andG2arerefinableparameters Histheacuteanglebetweend Handthenormaltothecrystallites platyhabit Note preferredorientationvectorPr1 Pr2andPr3isneededtospecifyaprioribyusers 47 Preferredorientations II Nor 1 modifiedMarch sModel G1andG2arerefinableparameters G11Needle likehabit 48 49 Systematicline shift Bragg BrentanoGeometrySpecimendisplacementSpecimenTransparency SYCOS SYSIN thelinearabsorptioncoefficientofthesample 50 WDT FWHM WDT 5 preferably 10 51 Monochromatorpolarizationcorrect Incidentangletoamonochromator CTHM cos22 0 8009foragraphitemonochromator CuK 52 Asymmetrycorrectionforprofiles P1 P2 P3 andP4areparameterstoberefined AsymLim peaksbelowthis2 anglelimitarecorrectedforasymmetry 53 54 Occupancy misthesitemultiplicity Misthemultiplicityofthegeneralsiteforagivenspacegroup Forexample KCaFCO3 P 6m2 187 K 1occupies1 a site O 23 k site generalsite12 o Occ K 1 12 0 08333 Occ O 2 0 25 bothatoms chemicaloccupancy 1 0 55 AgreementFactors I ProfileFactor WeightedProfileFactor ExpectedWeightedProfileFactor 56 AgreementFactors II Goodnessoffitindicator BraggFactor CrystallographicRFfactor 57 Variationsofagreementfactorsandesd Hill Madsen PowderDiffraction 1987 58 AnestimationofSforanidealrefinement take S 1sinceN P 59 Gaussian Lorentzian R J HillandH D Flack J Appl Cryst 20 1987 356 361 60 Durbin Watsonstatisticparameters d4 QD negativeserialcorrelation 61 Variationsofd eds RwpandRBvscycles R J HillandH D Flack J Appl Cryst 20 1987 356 361 62 Commentsonagreementfactors RFandRBaremoreindicativeofstructuralmodelfitsRpandRexparemoreindicativeofoverallprofilefitsRF RB RpandRexparenotgoodindicesfortherefinementsofdifferentpatternsSshouldbeascloseas1disamoresensitiveindexoverRF RB RpandRexpAtleastRp RwpandRexpshouldbegivenwhensubmittingapapertoajournal 63 QuantitativePhaseAnalysis where Wjistheweightfractionforthejthphase Sjisscalefactorforthejththephase Zjisthenumberformulaunitspercellforthejthphase Mjisthemassoftheformulaunit Vjistheunitcellvolume tjBrindleycoefficientthatcomesintoeffectwhenthelinearabsorptioncoefficientsofphasesinpowderdifferalottoeachother 64 KCaFCO3 CaCO3 65 MultiphaseRietveldAnalysis 66 Resultin outfile Noabsorptioncorrectionisapplied 67 ToobtainasatisfactoryquantitativephaseanalysisbasedontheRietveldmethod weshouldbecautioned Sampleshouldbecarefullyprepared powderishomogeneousincompositionsandhaveasufficientnumberofgrainswithrandomorientations Structuresofphasesarewellknown Absorptioncorrectionisappliedwheneverthephasesdifferalotintheirlinearabsorptioncoefficients TheBrindleycoefficientscanbeconsultedintheFullprofManual 68 Calculationofbondlength angleandbondvalencesum 69 ESDs 70 Bondvalencesumisagoodindicatorofthestructuralvalidity Fordetails seeI D Brown ActaCrystallogr B48 141 1992 71 EPSandRelaxfactors Forcedterminationwhenshifts EPS esdRecommendedEPS 0 1 R at Atomicparameters includingatomiccoordinatesandetc R an anisotropicparametersR pr profileparameters latticeparameters preferredorientationsandtheetc R gl globalparameters suchaszeroshift backgroundsandtheetc 72 2Excluded2 regions 73 Suggestedturn onsequencesfortheparameters ScalefactorsZeroshiftBackgroundFWHMShape1 X Y 6 Latticeparameters ifaccuratetosomeextentotherwisedoitbeforerefiningFWHM 7 Atomiccoordinates8 Temperaturefactors occupancies9 Preferredorientation GauSiz LorSiz 74 Somefactorsaffectingrefinementresults Lowinstrument sresolution RS 0 1 0 2mmToolowcounts Strongestcounts 10000Toolesssample Sampleshouldfullycoverthesampleholderwindow Overflowinlowangleregion Toolessangleregion2 120 ToolargeEPSthatleadstofalseminimum Improperprofilefunction ToolessWDTvalues 75 Errormessages I HoleinMatrix thenumberofparameterstoberefinedNPRlargerthanthenumberofcodewordsForexample yousetNPR 12 whileonecodeword80 5ismissingor101 0ismistypedas11 0 NegativeFWHM HG2 0 meaningless IncreasingthenegativeU V orWwhilesetsmallerRelaxvaluesintheensuingtherefinements 76 Errormessages II Noscatteringfactor atomidentifier TYP isnotrecognizablebyFullprof Forexample Ca 2isacceptedwhileCa2 isnotaccepted Toomanyreflections Foragivenpoint therearetoomanyreflectionscontributingtotheintensitythatarebeyondthesoftware scapacity UsuallythisresultsfromthefalseFWHM Invalidinteger or Invalidreal ExaminetheformatofparametersNote Thesoftwaredoesnotalwaysgivethecorrectlineswhereerrorsoccur Lookintothenearbylines 77 chenhong MACMXP18A HF FormCon2 0 78 huming 理学DMAX2000 79 RefinescalefactorS 80 Rwp 962138 S 0 5E 20 64E 3 81 RefinezeropointalongwithS 82 Rwp 62 8ZP 0 05 83 RefinebackgroundalongwithSandZP 84 Rwp 32 9 85 Refinelatticeparametersalongwithothers 86 Rwp 28 9 87 Refinepeakprofilealongwithotherparameters 88 Rwp 18 9 89 Refineasymmetry 90 Rwp 16 8 91 Refineatomiccoordinates firsttwoatomsPbandSthenumberofparameterstoberefined 22 92 Rwp 14 0 Furtherrefineatomiccoordinatesof3OatomsRwp 13 1 93 Refinetemperaturefactorsalongotherparameters 94 Rwp 12 5 95 Rp 8 92 Rwp 10 8 Rexp 6 57 96 CalculatethebondlengthsandbondvalencesAndtheresultsarestoredin dis 97 a b a b c PbSO4 98 Fouriersynthesis SetFou 4inyourPcrfile PbSO4 99 Rp 7 3 16 6 5 82 8 91 Rwp 8 2 20 0 7 83 10 8 Rexp 1 5 7 0 4 83 6 71 GodF 1 3 7 41 61 6 ComparewiththeRietveldRefinementRoundRobin Total23respondents Backgroundexcluded 100 Rangemeansinglecrystalthisworka 8 4764 8 48598 4804 4 8 482 2 8 4818 1 b 5 3962 5 40245 3989 3 5 398 2 5 3997 1 c 6 9568 6 96506 9605 4 6 959 2 6 9614 1 ComparewiththeRietveldRefinementRoundRobin R J Hill J Appl Cryst 25 58