FullProfuser'sguide FullProf Rietveld,ProfileMatching&IntegratedIntensities RefinementofX-rayand/orNeutronData (powderand/orsingle-crystal)
HELPFULLPROF
1.-INTRODUCTIONANDGENERALINFORMATION SHORTREFERENCEGUIDEOFTHEPROGRAM FFFFFFPPPPPP FllPPf FllPPf FFFFllPPPPPPf FuullPrrrooofff FuullProof FuuuuullllllProoof *************************************** *Program:FullProf* *************************************** (Version3.5dOct98-LLB-JRC) JuanRodriguez-Carvajal LaboratoireLeonBrillouin(CEA-CNRS) Tel:(33)169083343,Fax:(33)169088261
Disclaimer: Theauthorisnotresponsibleforerroneousre Theauthorisnotresp onsibleforerroneousresultsobtainedwithFullP sultsobtainedwithFullProf.This rof.This guidecannotsubstitutethelackofknowledgeofusersoncrystallograp guidecannotsubstitutethelackofknowledge ofusersoncrystallography, hy, magnetism,diffractionphysicsanddataanalys magnetism,diffraction physicsanddataanalysis.Thisshortguideism is.Thisshortguideismerelya erelya descriptionoftheinputfileswithminorexpl descriptionoftheinp utfileswithminorexplanationsonhowtoprocee anationsonhowtoproceed.Powder d.Powder diffractionisbecomingmoreandmorepowerfulbutFullProfisnotan diffractionisbecomingmoreandmorepowerful butFullProfisnotan "automatic"(black-box)program,asisusually "automatic"(black-box )program,asisusuallyfoundinsinglecrystal foundinsinglecrystalstructure structure determination.Noattempthasbeenmadeinord determination.Noatte mpthasbeenmadeinordertopredictthebehavio ertopredictthebehaviourofthe urofthe programagainstbadinputdata.Theusermustcheckhis(her)databefor programagainstbadinputdata.Theusermust checkhis(her)databefore e claimingamisfunctionoftheprogram.Theaut claimingamisfunction oftheprogram.Theauthoracknowledgesallsugg horacknowledgesallsuggestions estions andnotificationofpossiblebugsfoundintheprogram. ThemostrecentversionofFullProfiseither Themostrecentversio nofFullProfiseitherin"pub/divers/fullp" in"pub/divers/fullp" orin "pub/divers/fullp" oftheanonymousftp-areaoftheLLBunix-cluster.
UsersinterestedincreatetheirownsubroutinestolinkwithFULLP-lib Usersinterestedincreatetheirownsubroutin estolinkwithFULLP-library rary areaskedtoreadthefile"fpreadme"inthea areaskedtoreadthe file"fpreadme"intheabovementioneddisk-area. bovementioneddisk-area. ToaccessthisareafromInternet,onehasto Toaccessthisareafr omInternet,onehastotypeinthelocalhostth typeinthelocalhostthe e followingcommands: LocalPrompt>ftpcharybde.saclay.cea.fr Answerwiththeword:anonymous,totheLoginrequestandpassword. Answerwiththeword:anonymous,totheLogi nrequestandpassword. Withintheftpprompt,do: FromaUNIXhost: ftp>cdpub/divers/fullp->GotoFullProfarea ftp>getfpreadme->Obtainthedocument ftp>bye->Returntohost FromsomeVMS-VAXhosts: ftp>setdef"pub/divers/fullp"->GotoFullProfarea ftp>get"fpreadme"->Obtainthedocument ftp>ex->Returntohost
---------------------------------------------------1.1:Purpose,authors,referencesand documentation ---------------------------------------------------FullProfisaprogramforRietveldanalysis(s FullProfisaprogram forRietveldanalysis(structureprofilerefineme tructureprofilerefinement)of nt)of neutron(CW,TOF,nuclearandmagneticscatter neutron(CW,TOF,nucl earandmagneticscattering)orX-raypowderdiff ing)orX-raypowderdiffraction raction datacollectedasafunctionofthescattering datacollectedasafu nctionofthescatteringvariableT(2thetaorTO variableT(2thetaorTOF).The F).The programcanbealsousedasaProfileMatching programcanbealsous edasaProfileMatchingtool,withouttheknowle tool,withouttheknowlegdeof gdeof thestructure. SingleCrystalrefinementscanalsobeperform SingleCrystalrefinem entscanalsobeperformedaloneorincombinatio edaloneorincombinationwith nwith powderdata. FullProfhasbeendevelopedstartingfromthe FullProfhasbeendeve lopedstartingfromtheprogramofWiles&Young, programofWiles&Young,J. J. AppliedCryst.14,149(1981),(DBW3.2S,Versions AppliedCryst.14,149(1 981),(DBW3.2S,Versions8711and8804).Themodi 8711and8804).Themodifications fications ofthecodearemainlyrelatedwiththere-organizationofthecentral ofthecodearemainlyrelatedwiththere-org anizationofthecentralroutines routines performingthecalculationofprofilefunction performingthecalcula tionofprofilefunctions,derivatives,structure s,derivatives,structurefactors, factors, andtheintroductionofmanyotherthings.Thetotalsourceismoretha andtheintroductionofmanyotherthings.The totalsourceismorethan1 n1 Megabyte(morethan28.000fortranlines).The Megabyte(morethan28 .000fortranlines).Theformatofthemaincontr formatofthemaincontrolinput olinput file(e.g.acontrolfilecreatedforusewith file(e.g.acontrolf ilecreatedforusewithDBW-8711canbeusedby DBW-8711canbeusedbyFullProf FullProf withminormodifications).Theinputfileisa withminormodificatio ns).Theinputfileisacceptedas"interpretedf cceptedas"interpretedfree ree format". ThesourceiswritteninstandardFORTRAN77l Thesourceiswritten instandardFORTRAN77language,andisorganized anguage,andisorganizedastobe astobe easilyadaptedtodifferentcomputers.Theactualversioncanberunon easilyadaptedtodifferentcomputers.Theact ualversioncanberunonVAX, VAX, AlphaandUnixcomputers,MacIntoshesandonP AlphaandUnixcompute rs,MacIntoshesandonPCs(LaheyComputerSystem Cs(LaheyComputerSystemsInc. sInc. FORTRAN-compiler,minimum386/4Mbwithco-proc FORTRAN-compiler,mini mum386/4Mbwithco-processorrequired).Themigr essorrequired).Themigration ation towardsgenuineFortran90isinprogress. --------------------------1.2:FeaturesofFullProf: ---------------------------Choiceoflineshape(Gaussian,Lorentzian,modifiedLorentzians -Choiceoflineshape(Gaussian,Lorentz ian,modifiedLorentzians, , pseudo-Voigt,Pearson-VIIorThompson-C pseudo-Voigt,P earson-VIIorThompson-Cox-Hastings)foreachpha ox-Hastings)foreachphase. se. -Neutron(constantwavelengthandTOF)a -Neutron(consta ntwavelengthandTOF)andX-ray(laboratoryand ndX-ray(laboratoryand synchrotronsources)
UsersinterestedincreatetheirownsubroutinestolinkwithFULLP-lib Usersinterestedincreatetheirownsubroutin estolinkwithFULLP-library rary areaskedtoreadthefile"fpreadme"inthea areaskedtoreadthe file"fpreadme"intheabovementioneddisk-area. bovementioneddisk-area. ToaccessthisareafromInternet,onehasto Toaccessthisareafr omInternet,onehastotypeinthelocalhostth typeinthelocalhostthe e followingcommands: LocalPrompt>ftpcharybde.saclay.cea.fr Answerwiththeword:anonymous,totheLoginrequestandpassword. Answerwiththeword:anonymous,totheLogi nrequestandpassword. Withintheftpprompt,do: FromaUNIXhost: ftp>cdpub/divers/fullp->GotoFullProfarea ftp>getfpreadme->Obtainthedocument ftp>bye->Returntohost FromsomeVMS-VAXhosts: ftp>setdef"pub/divers/fullp"->GotoFullProfarea ftp>get"fpreadme"->Obtainthedocument ftp>ex->Returntohost
---------------------------------------------------1.1:Purpose,authors,referencesand documentation ---------------------------------------------------FullProfisaprogramforRietveldanalysis(s FullProfisaprogram forRietveldanalysis(structureprofilerefineme tructureprofilerefinement)of nt)of neutron(CW,TOF,nuclearandmagneticscatter neutron(CW,TOF,nucl earandmagneticscattering)orX-raypowderdiff ing)orX-raypowderdiffraction raction datacollectedasafunctionofthescattering datacollectedasafu nctionofthescatteringvariableT(2thetaorTO variableT(2thetaorTOF).The F).The programcanbealsousedasaProfileMatching programcanbealsous edasaProfileMatchingtool,withouttheknowle tool,withouttheknowlegdeof gdeof thestructure. SingleCrystalrefinementscanalsobeperform SingleCrystalrefinem entscanalsobeperformedaloneorincombinatio edaloneorincombinationwith nwith powderdata. FullProfhasbeendevelopedstartingfromthe FullProfhasbeendeve lopedstartingfromtheprogramofWiles&Young, programofWiles&Young,J. J. AppliedCryst.14,149(1981),(DBW3.2S,Versions AppliedCryst.14,149(1 981),(DBW3.2S,Versions8711and8804).Themodi 8711and8804).Themodifications fications ofthecodearemainlyrelatedwiththere-organizationofthecentral ofthecodearemainlyrelatedwiththere-org anizationofthecentralroutines routines performingthecalculationofprofilefunction performingthecalcula tionofprofilefunctions,derivatives,structure s,derivatives,structurefactors, factors, andtheintroductionofmanyotherthings.Thetotalsourceismoretha andtheintroductionofmanyotherthings.The totalsourceismorethan1 n1 Megabyte(morethan28.000fortranlines).The Megabyte(morethan28 .000fortranlines).Theformatofthemaincontr formatofthemaincontrolinput olinput file(e.g.acontrolfilecreatedforusewith file(e.g.acontrolf ilecreatedforusewithDBW-8711canbeusedby DBW-8711canbeusedbyFullProf FullProf withminormodifications).Theinputfileisa withminormodificatio ns).Theinputfileisacceptedas"interpretedf cceptedas"interpretedfree ree format". ThesourceiswritteninstandardFORTRAN77l Thesourceiswritten instandardFORTRAN77language,andisorganized anguage,andisorganizedastobe astobe easilyadaptedtodifferentcomputers.Theactualversioncanberunon easilyadaptedtodifferentcomputers.Theact ualversioncanberunonVAX, VAX, AlphaandUnixcomputers,MacIntoshesandonP AlphaandUnixcompute rs,MacIntoshesandonPCs(LaheyComputerSystem Cs(LaheyComputerSystemsInc. sInc. FORTRAN-compiler,minimum386/4Mbwithco-proc FORTRAN-compiler,mini mum386/4Mbwithco-processorrequired).Themigr essorrequired).Themigration ation towardsgenuineFortran90isinprogress. --------------------------1.2:FeaturesofFullProf: ---------------------------Choiceoflineshape(Gaussian,Lorentzian,modifiedLorentzians -Choiceoflineshape(Gaussian,Lorentz ian,modifiedLorentzians, , pseudo-Voigt,Pearson-VIIorThompson-C pseudo-Voigt,P earson-VIIorThompson-Cox-Hastings)foreachpha ox-Hastings)foreachphase. se. -Neutron(constantwavelengthandTOF)a -Neutron(consta ntwavelengthandTOF)andX-ray(laboratoryand ndX-ray(laboratoryand synchrotronsources)
-Oneortwowavelengths(Ka1+Ka2) -Backgroundrefinement -Multi-phase(upto8phases) -Preferredorientation:twofunctionsavailable -Absorptioncorrectionforacylinder -Choicebetweenthreeweightingschemes: -Choicebetween threeweightingschemes:standardleastsquares, standardleastsquares, maximumlikelihoodandunitwheights. -Choicebetweenautomaticgenerationof -Choicebetween automaticgenerationofhkland/orsymmetryopera hkland/orsymmetryoperators tors andfilegivenbyuser. -Magneticstructurerefinement(crystall -Magneticstruct urerefinement(crystallographicandspherical ographicandspherical representationofthemagneticmoments) representation ofthemagneticmoments).Twomethods:describing .Twomethods:describing themagneticstructureinthemagnetic themagneticst ructureinthemagneticunitcellofmakinguseo unitcellofmakinguseof f thepropagationvectorsusingthecrys thepropagatio nvectorsusingthecrystallographiccell.This tallographiccell.This secondmethodisnecessaryforincommes secondmethodi snecessaryforincommesuratemagneticstructures uratemagneticstructures. . -Automaticgenerationofreflectionsfor -Automaticgener ationofreflectionsforanincommensuratestruct anincommensuratestructure ure withupto24propagationvectors.Refi withupto24p ropagationvectors.Refinementofpropagationvec nementofpropagationvectors tors inreciprocallatticeunits. -h,k,ldependenceFWHMforstrainandsizeeffects -h,k,ldependenceofshiftandasymmetry -h,k,ldependenc eofshiftandasymmetryforspecialkindofdefe forspecialkindofdefects cts -ProfileMatching.Thefullprofilecan -ProfileMatchin g.Thefullprofilecanbefittedwithoutprior befittedwithoutprior knowledgeofthestructure(needsonly knowledgeofth estructure(needsonlygoodstartingcelland goodstartingcelland profileparameters) -Quantitativeanalysiswithoutneedofs -Quantitativean alysiswithoutneedofstructurefactorcalculati tructurefactorcalculations. ons. -Chemical(distances)andmagnetic(magne -Chemical(distan ces)andmagnetic(magneticmoments)slackconstr ticmoments)slackconstraints aints -Resolutionfunction(forpseudo-Voigtp -Resolutionfunc tion(forpseudo-Voigtpeakshape)maybesupplie eakshape)maybesuppliedinafi dinafi le -Structuralormagneticmodelcouldbes -Structuralorm agneticmodelcouldbesuppliedbyanexternal uppliedbyanexternal subroutineforspecialpurposes(rigid subroutinefor specialpurposes(rigidbody,TLS,polymers, body,TLS,polymers, formfactorrefinements,smallanglesc formfactorref inements,smallanglescatteringofamphifilic atteringofamphifilic crystals,descriptionofincommensurate crystals,descr iptionofincommensuratestructuresinreal structuresinreal directspace,etc.) -Singlecrystaldataorintegratedinten -Singlecrystal dataorintegratedintensitiescanbeusedas sitiescanbeusedas observations(aloneorincombinationw observations(a loneorincombinationwithapowderprofile) ithapowderprofile) -Neutron(orX-rays)powderpatternscan -Neutron(orX-r ays)powderpatternscanbemixedwithintegrated bemixedwithintegrated intensitiesofX-rays(orneutron)from intensitiesof X-rays(orneutron)fromsinglecrystalorpowder singlecrystalorpowder data. -------------------------------------------------1.3:Runningtheprogram,inputandoutput files. -------------------------------------------------Toruntheprogramtheuserhastoinvokethenameoftheexecutab Toruntheprogramtheuserhastoinvoke thenameoftheexecutablefile lefile andpresstheENTER/INTROkey.Ofcourse andpresstheENT ER/INTROkey.Ofcoursetheexecutablefilemust theexecutablefilemustbein bein adirectoryincludedinthePATHorana adirectoryinclu dedinthePATHoranaliasshouldexist. liasshouldexist. Forfordoingsequentialrefinementsther Forfordoingseq uentialrefinementsthereisanumberofcommand eisanumberofcommandfiles files thatcanbeused.Thecommandfiles(scri thatcanbeused. Thecommandfiles(scripts)dependontheoperat pts)dependontheoperating ing system.AfacilityisincludedinFullPro system.Afacilit yisincludedinFullProfforversionshighertha fforversionshigherthat3.2 t3.2 thatallowssequentialofcyclicrefinements. Examples: 1:Prompt>FULLPROF 2:Prompt>FullProf,... ----------Inputfiles: ----------Toruntheprogram,youneedatlea Torunthe program,youneedatleastoneinputfile, stoneinputfile, CODFIListhecodeofthecontrolf CODFIList hecodeofthecontrolfilegivenbytheuser. ilegivenbytheuser. CODFIL.PCR:Inputcontrolfile
Itmustbeinthecurrentdirectorytoruntheprogram. Thisfilecontainsthetitleandcrystallographic dataandmustbepreparedbyuserwithafileeditor. Therearetwodifferentformatsforthisfile:thefirst oneisfreeformatandcloselyrelatedtothatof theYoung&Wiles'sprogram.Thesecondisbasedonkeywords andcommands. (thislastformatisnotavailableatpresent) Warning:thisfileisnormallyup-datedeverytimeyouruntheprogram (seeparameterNXTonline3).Inthefirststagesofarefinement, itiswisetosaveacopyofthisfilewithadifferentname. Thefollowingfilesareoptional. FILE.DAT:Intensitydatafile(unit4):formatdependson instrument.IfyoudonotspecifythenameFILE,theprogram takesFILE=CODFIL.Notnecessaryforpatterncalculationmodes. FILE.BAC:Backgroundfile(unit12).Theformatofthisfile isthefollowing(asthatofFILE.DATforINSTRM=0): firstline:2theta(initial)step2theta(final) followinglines:listofintensitiesinfreeformat. CODFILn.HKL:Setoffileswiththereflectionscorrespondingto phase"n"(nistheordinalnumberofaphase).Thesefilesare optionalanddependonthevalueoftheparameterIRF(n)(seebelow) Ifsequentialrefinementshavetobedone,thisfileiscalledHKLn.HKL MYRESOL.INSTRU:Filedescribingtheinstrumentalresolution function.Anynamecanbeusedanditscontentdependonthe valueoftheparamenterIRESO(seebelow). GLOBAL.SHP:Fileprovidinganumericaltableforcalculatingthe orpeakshapeanditsderivative.Thepeakshapeshould CODFIL.SHP:begiveninanormalizedformP(x)wherethevariablexis chosentogiveaFWHM=1andtheareaisequalto1=>Integ{x1,x2}[P(x).dx]= 1. ThatallowstheuseoftheconventionalU,V,Wparametersfor definingtheFWHMasafunctionofangle. Theformatofthisfileisthefollowing: Line1:Anycomment Line2:Np8,nupr,(anpr(j),j=1,nupr) Np8=Numberofpoints nupr=Numberofdifferentprofiles anpr(j)=Angletowhichprofile"j"isbestadapted Therestofthelinesarecolumnswith X,P(X,1),PP(X,1),P(X,2),PP(X,2),...P(X,nupr),PP(X,nupr)infreeformat. PP(X,j)isthederivativeofP(X,j)withrespecttoX. Theprofileofareflectionsituatedbetweenanpr(j)andanpr(j+1) islinearlyinterpolatedbetweentheprofilesP(X,j)andP(X,j+1) CODFIL.COR:Filewithcorrectionsforintegratedintensitiesofprofile intensitiesdependingonthevalueofthevariableICORR.Seebelow. Outputfiles: Exceptfor*.OUTand*.SUM,theircreationdependsonthevalueofaflag whichisquotedinparenthesis.Theordinalnumberontheflaglistisgiven inbrackets. CODFIL.OUT:Thisisthemainoutputfile(unit7)whichcontains
allcontrolvariablesandstructureparameters. CODFIL.PRF:Observedandcalculatedprofile(unit1):tobefed intoPLOTPOW,PLOTR,...(ifIPL2differentfromzero) InthecaseofICRYG=1(Integratedintensitymode)alist ofsin(theta)/lambda,Gobs,Gcalcisoutputaftertwo linesofcomments. CODFIL.RPA:Summaryofrefinedparameters(unit2):short versionofCODFIL.SUM(ifJCIL=1) IfthefileexistthenewdataareAPPENDEDattheend. CODFIL.SYM:Listofsymmetryoperators(unit3) (ifIPL1=JSY=1) (ThelasttwofilesarenecessarytorunDISTANor BONDSTR) CODFIL.SUM:Parameterlistafterlastcycle(unit8):the summaryofthelastparameters,theirstandard deviationsandreliabilityfactors.Ananalysis ofthegoodnessoftherefinementisincluded attheend. CODFIL.FOU:IfJFOU=1 H,K,L,StructureFactorsinCambridgeformat(unit9): tobefedintoFOURTK(FOURPL)toproduceFouriermaps. ItcorrespondstothefileusuallycalledHKLFF.DATbut youmustpreparethesecondfileCRYST.cry IfJFOU=2 (Listof'observed'structurefactorsinSHELXSformat) H,K,L,Fo,sigma(Fo)(3I4,2F8.2) JFOU=-1or-2,asabovebuttheyarecalculatedin anotherway.TheFcalcinJFOU>0maydependonthe peakshapeandtheintegrationinterval,becausethey areobtainedbyintegrationofthecalculatedprofilein thesamewayasthe'Fobs'areobtainedfrom'Iobs'. IfJFOUisnegative,Fcalcarereallythestructure factorsoftheconventionalcellinabsoluteunits. JFOU=3FormatsuitablefortheprogramFOURIER (3I4,2F10.4,f8.5,f10.4) H,K,L,Freal,Fimag,sintheta/lambda,fobs JFOU=4Format(3I4,2F10.4,i8) H,K,L,Fobs,Fcalc,nint(10000.*Phrd) ForJFOU=3,4: Phrdisthephaseinradiansandtheobservedandcalculated structurefactorsoftheconventionalcellareinabsolute units CODFILn.SHX:IfJFOU=2,-2,templateofSHELXS*.INfile. CODFILn.INP:IfJFOU=3,-3,templateofFOURIER*.INPfile. CODFILn.HKL:Filesthatcanbeinputoroutputfiles.Depending onthevalueofIRF(n)
CODFIL.INT:Singleintegratedintensityfilewhentheprogramis usedforrefiningwithICRYG=1,2(seebelow). CODFIL.HKL:(ifJLKH<>0,unit10).Completelistofreflections ofeachphase. JLKH=1 -->IfJOBTYPlessthan2 reflectioncode,h,k,l,multiplicity,dspacing,twotheta, FWHM,Iobs,Icalc,Iobs-Icalc. -->IfJOBTYP>1 h,k,l,multiplicity,Icalc,twotheta,dspacing JLKH=2 -->OutputforSIRPOW92 h,k,l,mul,sint/l,2t,Fwhm,F2,sF2 JLKH=-2 -->OutputforEXPO h,k,l,Fwhm,F2 JLKH=3,-3 -->Outputofrealandimaginarypartof structurefactors(onlyforcrystalstructures) h,k,l,mul,Freal,Fimag,2theta,Intensity IfJLKH<0thestructurefactorsaregivenforthe conventionalcell.Otherwisethestructurefactor correspondstothenon-centrosymmetricpartofthe primitivecell. (theobtainedfilecanbeusedasaCODFILn.HKLfilesfornewruns) JLKH=4 -->Outputof:h,k,l,F2,sigmaF2.WhereF2isthe"observ ed" structurefactorsquared.Thefilecouldbeusedasinpu t fora"pseudo-single"crystalintegratedintensityfile usingICRYG=1andIRF=4 JLKH=5 -->Outputof:h,k,l,mult,Fcalc,T,D-spacing,Q. WhereFcalcisthemoduleofthecalculatedstructurefa ctor. ThisfilecanbeusedasinputforJBT=-3andIRF=2ino rder toperformquantitativeanalysiswithoutre-calcultating thestructurefactorsforeachcycle.TheFcalcarein absoluteunitsfortheconventionnelcall. CODFIL.SAV:(ifJCIL=2) Listofreflectionsbetweentwoselectedangles h,k,l,multiplicity,Iobs,twotheta,dspacing Forbuild-insequentialrefinements(version3.2andhigher)theuser mustpreparethedatafilesusingnamesoftheformCODnnn.dat. CODstandsforthecodeofthesefilesandcanbeformedbywhatever numberofcharacters(compatiblewiththeactualoperatingsystem). nnnstandsforasequenceofintegers.AllCODnnn.datfilesmust beinthesamedirectoryandthenumbersnnnshouldbeinbetween aminimunnumber(first)andamaximunnumber(last)thatareasked byprogram.Holesareallowedbetweenfirstandlast. ThefileCODFIL.PCRcanhaveadifferentcode(CODFILcouldbedifferent ofCOD)anditwillbeusedforrefiningthewholesetofCODnnn.dat files.ThefinalresultsarecontainedintheCODFIL.RPAfile.
ForVaX-usersusingacommandfiletoexecuteFullProfincyclicmode: Forsequentialrefinements,*.DATfileswillnormally bepreparedbySEPFIL.InthiscaseCODFILmusthave threeletters(e.g.XXX)ascodefollowedbyanumber. The*.PCRfilemustbenamedXXXIN.PCR XXXCYC.RES:Inthecaseofsequentialrefinements,alltheabove fileswouldrapidlyyieldaquotaexceedederrormessage.Thusonly condensedresultsaresavedinfilesXXXCYC.RES(similartoCODFIL.RPA) andXXXSUM.RES(similartoCODFIL.SUM). XXXHKL.RES:Listofreflectionsofaselectedzoneofthe diffractionpatern(usefulwithProfileMatchingmode) ThefinalversionofthefileXXX**.PCR(where**correspondstothelast datasetisalsosaved.
2.-DETAILEDDESCRIPTIONOFINPUTFILES
---CODFIL.PCR Thisfileisfreeformat.Thatdoesn'tmeanfreeformatinFORTRAN(,*)-sense Aroutineinterpretstheitemsgivenbytheuserthatmustobeytheorder givenbelow.Aspaceisneededbetweeneachitem(exceptwhenthesecond isanegativenumber).Whentheprogramisrun,messagesoferrorreading alineofthisfilearenormallyduetoapreviouserror.Forexample,the numberofatomsyoureallywrotedoesnotcorrespondtothenumberyouput inthelinefollowingthenameofthephase. Emptylinesaswellaslinesstartingwiththesymbol"!"inthefirstcolumn areconsideredascommentsandareignoredbytheprogram.Iftheuserstarts his(her)CODFIL.PCRfilewiththeleft-ajustedcapital"COMM",thenew CODFIL.PCRfilehascommentswithmnemonicsforeachvariable.Iftheuser introducehis(her)owncomments,theyarenotsavedinthenewversionof thefile.Theunexperiencedusercancreateatemplatebyanswering "starting"(withoutquotes)tothepromptaskingforthenameofthefile. Notethatastarafteralinenumber(oravariable) indicatesthattheline's(orvariable)existencedependsonthevalueof acontrolvariable. ============================================================================ LINE1: TITLE(any70characterstobeusedtolabeltheprintout) IfthefirstfourcharacterofTITLEcorrespondtotheword TITLthefileisgivenin"commandmode"(notavailableyet). IfthefirstfourcharactersofTITLEcorrespondtoCOMM, commentslines(startingwith!inthefirstcolumn)are automaticallyaddettothenewCODFIL.PCR(orCODFIL.NEW). Thecommentlinesgiveakeywordforeachvariableinorder tobeeasilyrecognizedbytheuser.Thiscommentlinehas beenincludedbelowto ============================================================================ LINE2:
JOBTYP,NPROF,NPHASE,NBCKGD,NEXCRG,NSCAT,NORI,IDUM,IWGT, ILOR,IASG,IRESO,ISTEP,NRELL,ICRYG,IXUNIT,ICORR (15integers) (Itisunderstoodthattheyareseparatedbyaspace) --------------Commentline: !JobNprNphNbaNexNscNorDumIwgIloIasResSteNreCryUniCor ---------------------------JOBTYP=0X-raycase (Job)1Neutroncase(constantwavelength,nuclearandmagnetic) 2patterncalculation(X-ray) 3patterncalculation(Neutron,constantwavelength) -1Neutroncase(T.O.F.,nuclearandmagnetic) -3patterncalculation(Neutron,T.O.F.) Ifabs(JOBTYP)>1andIDUM=1(seebelow)acalculatedpatternis createdwiththenameCODFIL.SIMinformatcorrespondingto INSTRM=0.Thispatterncorrespondstoan"idealobserved" patternandcanbeuseforsimulationpurposesinorderto investigatetheeffectofsystematicerrorsonthestructural parametersandonthereliabilityfactors. NPROF=Defaultvalueforselectionofapeakshape.Particular (Npr)valuescanbegivenforeachphase(seeline11-2) 0Gaussian 1Cauchy 2Modified1Lorentzian 3Modified2Lorentzian 4Tripledpseudo-Voigt 5pseudo-Voigt 6PearsonVII 7Thompson-Cox-Hastingspseudo-Voigt 8NumericalprofilegiveninCODFIL.SHP orinGLOBAL.SHP 9T.O.F.Convolutionpseudo-VoigtxDoubleExponential 10Notyetused 11Splitpseudo-Voigtfunction 12Pseudo-Voigtfunctionconvolutedwithaxialdivergenceasymmetry function(Finger,Cox&Jephcoat,J.Appl.Cryst.27,892,1994) NPHASE=numberofphases(max:8)(ifNPHASE<0thenumberofphasesis (Nph)abs(NPHASE)andtheasymmetrycorrectionisappliedfollowingtheapp roximationof C.J.Howard,J.Appl.Cryst.15615-620(1982)withtheSimpsonformulaf orfivepoints) NBCKGD=0Refinebackgroundwithpolynomialfunction (Nba)1ReadbackgroundfromfileCODFIL.BAC.Theformat ofthisfileisexplainedabove. Somecoefficientsarereadbelow. 2,3,.,NlinearinterpolationbetweentheNgivenpoints IfNBCKGD<0butIABS(NBCKGD)>4theinterpolation isperformedusingcubicsplines -1refinebackgroundwithDebye-like+polynomial function. -2BackgroundtreatediterativelybyusingaFourier filteringtechnique.Anextraparameterisread below.Thestartingbackgroungisreadfrom
fileFILE.BACasforNBCKGD=1. -3Read6additionalpolynomialbackgroundcoefficients NEXCRG=numberofexcludedregions (Nex) NSCAT=numberofscatteringsets(zeroinmostcases) (Nsc)IfNSCAT>0,theprogramperformsaninternal fitifatableisgiveninordertogetcoefficients fortheexponentialexpansion(seebelow). IfNSCAT<0,alinearinterpolationismade. NORI=0preferredorientationfunctionNo1 (Nor)1preferredorientationfunctionNo2(March) IDUM=1Ifequalto1andsomeofthephasesaretreated (Dum)withProfileMatchingmodes,thecriteriumofconvergence whenshiftsarelowerthanafractionofstandarddeviations isnotapplied. =2Ifequalto2,theprogramisstoppedincaseoflocal divergence:chi2(icycle+1)>chi2(icycle) =3Ifequalto3thereflectionsnearexcludedregions (excl+/-wdth*2theta)arenottakenintoaccounttocalculate theBraggR-factor.Thesereflectionsareomittedinthe outputfileswithhkl's. IfJOBTYPgreaterthan1andIDUMisdifferentthanzero afileCODFIL.SIMisgenerated IWGT=0standardleastsquaresrefinement (Iwg)1maximumlikelihoodrefinement 2unitweights ILOR=0StandardDebye-Scherrergeometry,orBragg-Brentanoif (Ilo)theiluminatedareadoesnotexceedthesamplesurface. IfBragg-Brentanogeometryisusedbuttheabovecondition isnotfulfilled,theintensitydatamustbecorrectedfor thegeometriceffectbeforeattemptinganyrefinement. (Apartialcorrectioncanbedonebyusingtheparameter SENT0inline5) =1FlatplatePSDgeometry =2Transmissiongeometry.Flatplatewiththescattering vectorwithintheplate(StoegeometryforX-rays) =3Polarizationcorrectionisappliedeveniftheformatof theDATFIL.DATfiledoesnotcorrespondtooneofthe synchrotronexplicitelygivenformats(seebelow). Thismustbeusedforsynchrotrondatagivenina X,Y,Sigmaformat(INSTRM=10). IASG=1SubroutineASSIGNiscalledateachcycle,thenreflections (Ias)arere-ordered. =0SubroutineASSIGNiscalledonlyatthefirstcycle (IfJBT=2foronephase,IASGmustbe=1) IRESO=0Resolutionfunctionoftheinstrumentisnotgiven (Res)IfIRESOisnotzero,thenextlinecontainsthenameofthe filewheretheinstrumentalresolutionfunctionisgiven. TheprofileisassumedtobeaVoigtfunction(NPROF=7). 12parametersoratabledeterminetheresolutionfunction. Ui,Vi,Wi,Xi,Yi,Zi(i=1,2forlambda1andlambda2) Thedifferenttypesoffunctionsare:
=1HG**2=(Ui*tan(q)+Vi)*tan(q)+Wi HL=Xi*tan(q)+Zi =2HG**2=(Ui*tan(q)+Vi)*tan(q)+Wi HL=(Xi*(2q)+Yi)*(2q)+Zi =3HG**2=(Ui*(2q)+Vi)*(2q)+Wi HL=(Xi*(2q)+Yi)*(2q)+Zi =4Listofvalues2q,HG(2q),HL(2q) (alinearinterpolationisappliedforintermediate2q) ISTEP=1,2,3,..IfISTEP>1thenumberofdatapointsisreducedby (Ste)afactorofISTEP.Onlythosepointscorrespondingtothe newstepsizeISTEP*STEP(seeLine#3below)aretaken intoaccountintherefinement.Usefulforspeed-up preliminaryrefinements. NRELLNumberofparameterstobeconstrainedwithingiven (Nre)limits.Attheendofthefileyoumustgivealist ofNRELLlinesspecifyingthenumberandthelimit ofeachparameter. ICRYGIfnotequaltozero,onlyintegratedintensitydata (Cry)willbegiven.Noprofileparametersareneeded. ForICRYG=2noleast-squaresalgorithmisapplied. InsteadaMontecarlosearchofthestartingconfiguration isperformed.AselectednumberofparametersNRELL aremovedwithinaboxdefinedbytheNRELLrelations fixingtheallowedvaluesoftheparameters.Thebest (lowestR-factor)NSOLUsolutionsareprintedandthe CODFIL.PCRfileisupdatedwiththebestsolution. (SeeNRELLvariableinthislineandLine) IXUNITUnitsofthescatteringvariable (Uni)=02thetaindegrees =1T.O.F.inmicro-seconds ICORR (Cor)=0Nocorrectionisapplied =1Afilewithintensitycorrectionsisread. Thecorrectionsareappliedtotheintegratedintensities asamultiplicativeconstant.ThefileCODFIL.CORstarts withacommentandfollowswithalistofpairs:asimple listofabcisaeandcorrectionvalues. TITLE...... Scatteringvariable(T)Valueofthecorrection "" ............................. Dataarereadinfreeformat.Forpeaksbetweenpoints providedintheCODFIL.CORfile,thecorrectionislinearly interpolated.Example: Firstline->ThisismycorrectionFILEfor Followinglines->10.01.3 20.01.1 30.01.0 40.00.9 80.00.8 120.00.7 180.00.7
Theintensityofareflectionatscatteringvariable40is assumedtobeI(calc)*0.9. =2Asimilarfileisreadbutthecoefficientsofanempirical functionandtheirstandarddeviationsarereadinsteadof directlythecorrections. Theformatis: Firstline->TITLE.... Secondline->ITYCORR,ITYFUNC,NPCORR Followinglines->CoefficientSigma(Coefficient) (NPCORRlines) IfITYCORR=1correctionsareappliedtotheintegrated intensities.Standarddeviationsmustnotbegiven. ITYCORR=2correctionsareappliedtotheobserved profile.Thecorrectedobservedprofile andtheirvarianceareobtainedas: y(corr)=y(obs)/cor Sigma2(y(corr))=sigma2(y(obs))/cor^2+sigma2(cor)/y(obs)^2 NPCORR:Numberofcoefficientsoftheempiricalfunction. ITYFUNC=1Polynomialfunction: cor=Sum{i=1,npcorr}{coeff(i)*T**(i-1))} ITYFUNC=2Exponential+MaxwellianforTOFrawdata cor=Coeff(1)+Coeff(2)*Exp(-Coeff(3)/T^2)/T^5+ +Sum{i=4,NPCORR,2}{Coeff(i)*Exp(-Coeff(i+1)*T^2)} Line2-1*:FILERES (A16)Nameofthefilewiththeinstrumentalresolutionfunction. TobegivenonlyinthecaseofIRESO<>0. TheitemsinFILERESarereadinfreeformat. Thefirstlineisconsideredasatitle ForIRESO=1,2,3the12parametersUi,Vi,Wi,Xi,Yi,andZi arereadfromlines2and3(seetheabovelineforthe availableinstrumentalfunctions). Example: Line1:ResolutionfunctionofMyXrayDiffractometer Line2:0.00802-0.009360.010240.00290.00.0!U1,V1... Line3:0.00774-0.005520.008140.00000.00.0!U2,V2... ForIRESO=4,thefileFILERESstartswithalinewhiththe titlefollowedbyalinewiththenumberofpoints(NPOINS) wheretheinstrumentalGaussianandLorentzianFWHMaregiven. NPOINSlinesfollowcontainingthethreeitems:2thet,HGand HL.TheBraggpeaksofthediffractionpatternmustbebetween 2thet(1)and2thet(NPOINS).Forthiscasethesameresolution functionisappliedtobothwavelengths. ThemaximumnumberofNPOINSis30. ============================================================================ LINE3:IOT,IPL,IPC,MAT,NXT,LST1,LST2,LST3,IPL1,IPL2,INSTRM, JCIL,JSY,JLKH,JFOU,ISHOR,IANALY (17integers)
--------------Commentline: !IprPplIocMatPcrLs1Ls2Ls3SyoPrfInsRpaSymHklFouShoAna ---------------------------Listofoutputcontrolflags:normally0=off/anyvalue=on IOT=1obs.&calc.profileintensities-->CODFIL.OUT(0) (Ipr)2ThefilesCODFILn.SUBwiththecalculatedprofileof eachphasearegenerated. 3As2butthebackgroundisaddedtoeachprofile. IPL=1lineprinterplot-->CODFIL.OUT (Ppl)2Generatesthebackground-fileFILE.BAC 3PutsdifferencepatterninfileFILE.BAC IPC=1listofobs.&calc.integr.int.-->CODFIL.OUT (Ioc)=2Thereflectionscorrespondingtothesecondwavelength arealsowritenifdifferentfromthefirstone. MAT=correlationmatrix-->CODFIL.OUT (Mat)IfMAT=2,thediagonalofLSQmatrixisprinted beforeinversionateverycycle. NXT=1CODFIL.PCRisre-writtenwithupdatedparameters (Pcr)2newinputfile-->CODFIL.NEW LST1=reflectionlist-->CODFIL.OUT(usually0) (Ls1) LST2=1correcteddatalist-->CODFIL.OUT(usually0) (Ls2)4InsomeversionsofFullProfaplotofthediffraction patternisdiplayedonthescreenateachcycleofrefinement. LST3=mergedreflectionlist-->CODFIL.OUT(usually0) (Ls3) IPL1=symmetryoperators-->CODFIL.OUT(+CODFIL.SYMifJSY=1) (Syo) IPL2=outputdataforplot-->CODFIL.PRF (Prf)=1FormatsuitableforPLOTPOW,BENSTRAP,PLOTR,etc.. =2"""IGOR(MacIntoshsoftware) =3"""KaleidaGraph(MacIntoshsoftware) &PLOTR(Pcsoftware) =4"""Picsure,Xvgr(Sun-UnixSoftware) INSTRM=0Datasuppliedinfreeformat (Ins)Uptosevencommentlinesareaccepted. Thefirstthreerealnumbersfoundatthebeginningofaline areinterpretedasTi,stepandTf. Thefollowinglinesafter(Ti,step,Tf)mustcontain NPTS=(Tf-Ti)/step+1valuesoftheintensityprofile. DataformatfromArgonnearealsointerpretedbythis valueofINSTRM. 1D1A/D2Bformat(originalRietveld-Hewatformat: thefirstlinemustbe2Thetai,step,2Thetaf,i.e.thefirst fourlinesofthePOWDERfilemustberemoved.Note howeverthatanglesaregivenindegrees2Theta,not inhundredthsofdegree!).
2D1Boldformat(DEC-10) 3newformatforD1B&D20(VaxDataBase) +/-4Brookhavensynchrotron. 4:Firstline:2thetamin,step,2thetamax(freeformat) Restoffile:pairsoflineswith10itemslike Y1Y2.........Y10--(10F8)intensities S1S2.........S10--"sigmas -4:FormatgivenbyDBWSprogramforsynchrotrondata. (VersionDBW3.2S-8711) 5DatafromGENERALFORMATforTWOAXISinstrument 3linesoftextfollowedbytwolineswiththeitems: ->NPTS,TSample,Tregul,Ivari,Rmon1,Rmon2 ->Ti,step,Tf Setoflinescontaining10itemscorrespondingto theIntensitiesinformat10F8.1,uptoNPTSpoints (NPTS=(Tf-Ti)/step+1),followedbythecorresponding sigmasinformat(10f8.2)ifIvari=1.IfIvari=0 thesigmasarecalculatedasSQRT(Yi*Rmon1/Rmon2). 6D1A/D2BstandardformatforfilesMYFILE.SUM preparedbyD1A(D2B)SUMorequivalentprograms. Theextensionofthedatafilemustbe'dat'. 7FilesfromD4orD20L 8DatafromDMCatWurenlingen(PaulScherrerInstitut) 9DataoffileCODFIL.UXDgeneratedbytheSocabim softwareonX-Raysdiffractometer. 10X,Y,Sigmaformatwithheaderlines. Inallcasesthefirst6linesareconsidered ascomments. Ifinthefirstline(leftajusted)appearsthe keywordXYDATA,thenthefollowing5linesare consideredastheheadingofthefile.Among these5linesthefollowingkeywordsandvalues haveameaningtotheprogram: ->INTERfac_xfac_yInterpolStepin ->TEMPtsamp fac_xinternalmultiplierofX-values fac_yinternalmultiplierofYandSigma-values Interpol=0Variablestepisusedintheprogram =1Thevariablestepdataareinterpolated internallytotheconstantstepStepin. =2Dataaresupplieddirectlyatconstantstep Ifnosigmavaluesareprovidedtheprogramassumes thatsigma(Y)=sqrt(Y). Youcanaddcommentstothedatafileifthey startwiththecharacter!inthefirstposition oftheline.Theselinesareignoredbytheprogram. 11DatafromvariabletimeX-raydatacollection Thefirstfourlinesareconsideredascomments Thefollowinglinesare:
->2Thetai,step,2ThetafComment ->(Time,Intensity)informat5(F6,I10) TheprogramusestheinformationcontainedinTime tonormalizetheobservedintensitiestotheaverage timeandtocalculatethevarianceofthe normalizedvalues. 12TheinputdatafileconformstoGSASstandard datafile.BINTYP=LOG6,TIME_MAPandLPSDarenot yetavailable JCIL=1preparesfileCODFIL.RPA (Rpa)Ifthefileexistsbeforerunningtheprogram thenewdataareAPPENDED. 2preparesfileCODFIL.SAV(sequentialrefinements) JSY=1preparesCODFIL.SYM(if1,IPL1mustbesetto1) (Sym) JLKHpreparesCODFIL.HKL (Hkl)=1asexplainedabove =2OutputforSIRPOW.92 =-2OutputforEXPO =3OutputofReal&Imaginary partsofStructureFactors =4Outputofh,k,l,F2,sF2(tobere-usedwithIRF=4) =5Outputofh,k,l,mult,Fcalc,T,D-spacing,Q. (tobere-usedwithJBT=-3andIRF=2) JFOUpreparesCODFIL.FOU (Fou)=1Cambridgeformat =2Shelxsformat (PreparesalsothefileCODFILn.SHX) =3FOURIERformat (PreparesalsothefileCODFILn.INP) ISHOR=1Supresstheoutputfromeachcycle.Onlytheinformation (Sho)fromthelastcycleisprinted. IANALY=1Providesananalysisoftherefinementattheendof (Ana)thesummaryfileCODFIL.SUM. =2Printsalsotheactualdimensionofarrays. ============================================================================ LINE4*:LAMDA1,LANDA2,RATIO,BKPOS,WDT,CTHM,TMR,RLIM,K (9reals)(notneededifICRYGisnot0) --------------Commentline: !lambda1Lambda2RatioBKPOSWdtCthmmuRAsyLimRpolarz ---------------------------OR(forT.O.F.data) BKPOS,WDT,IABSCOR (2real+1integer) --------------Commentline: !BKPOSWdtIabscor ---------------------------LAMDA1=wavelengthl1
LAMDA2=wavelengthl2(=l1formonochromaticbeam) ABS(RATIO)=IntensityratioI(l2)/I(l1) IfRATIO<0theparametersU,V,W(seebelow)forthe secondwavelengtharereadseparately. BKPOS=originofpolynomialforbackground(indeg.2thetaorusecs) WDT=width(range)ofcalc.profileinunitsofHk (typically3.5forGaussianand10forLorentzian,3-3.5forT.O.F.) CTHM=coefficientformonochromatorpolarizationcorrection (seeMathematicalinformation) TMR=absorptioncorrectioncoefficientmR,usedonlyfor (muR)refinementoncylindricalsamplesandflatsamples withsymmetricaltheta-2thetascanning(thescattering vectorlyingwithinthesampleplane). m=effectiveabsorptioncoefficient R=radiusorthicknessofthesample. RLIM=peaksbelowthis2Thetalimitarecorrectedforasymmetry (AsyLim)(seebelowformoredetails) K=polarizationfactor(synchrotron)(Rpolarz) fractionofmosaic-crystal(transmissiongeometry) IABSCOR=TypeofabsorptioncorrectionforT.O.F.data (Iabscor)1:Flatplateperpendiculartotheincidentbeam 2:Cylindricalsample 3:ExponentialcorrectionAbs=exp(-c*Lambda**2) ============================================================================ LINE5:MCYCLE,EPS,RELAX1,RELAX2,RELAX3,RELAX4, THMIN,STEP,THMAX(requiredforpatterncalculationmodeonly), ALPSD(requiredforflatplatePSDgeometryonly) SENT0(requiredforBragg-BrentanoX-rayILOR=0, whenthecrosssectionofthesampleis lowerthanthebeamdimensionsatlowangles) (1integerand10reals) --------------Commentline: !NCYEpsR_atR_anR_prR_glThminStepThmaxPSDSent0 ---------------------------MCYCLE=numberofcyclesofrefinement EPS=forcedterminationwhenshiftslessthanEPS*e.s.d. RELAX=thefourrelaxationfactorsforshifts: 1->Atomicparameters: coordinates,magneticmoments,siteoccupancies &isotropicdisplacement(temperature)factors 2->anisotropicdisplacement(temperature)factors 3->profileparameters,asymmetry,overalldisplacement (temperature),cellconstants,preferredorientation parameters,strains,size,propagationvectors&user-suppliedparam eters. 4->globalparameters,zero-shiftT0,background, displacementandtransparency. THMIN=startingangleforcalculatedpatternindegreesT STEP=stepsizeindegreesT THMAX=endingangleforcalculatedpatternindegreesT
ALPSD=incidentbeamangleatsamplesurfaceindegrees SENT0=Thetaangleatwhichthesampleinterceptscompletely thex-raybeam.BelowSENT0partofthebeamdoesn't touchthesampleandtheintensityofreflections belowSENT0havetobemultipliedbythefactor: sclow=sin(theta)/sin(SENT0) ============================================================================ LINE6*: (2reals)(notneededifICRYGisnot0) --------------Commentline: !2Theta/TOFBackground ---------------------------ifNBCKGD>2orNBCKGDlessthan-3,thereareiabs(NBCKGD)lineswith Pos=positionindegreesT Bck=backgroundcountsatthisposition IfNBCKGDispositive:linearinterpolation IfNBCKGDisnegative:cubicsplinesinterpolation ============================================================================ -LINE7*: (2reals)(notneededifICRYGisnot0) --------------Commentline: !Excludedregions(LowTHighT) ---------------------------ifNEXCRG>0,enterlimitsofexcludedregions: ALOW=lowscatteringvariableboundindegreesormicrosecs AHIGH=highscatteringvariableboundindegreesormicrosecs ============================================================================ LINE8*: 2*NSCATsetsoflines(neededonlyifyouwishtoenteryour ownscatteringlengthorformfactorinsteadofusingthe valuesstoredininternaltable;scatteringfactorsand anomalousdispersioncorrectionsincorporatedintheprogram. --------------Commentline: !Additionalscatteringfactors ---------------------------Line8-1:NAM,DFP,DFPP,ITYM (A4,2realsand1integer) NAM=symbolidentifyingthisset(leftjustified) ThissymbolisconvertedtolowercaseforX-ray diffractionglobaldata. DFP=Df'orneutronscatteringlengthb DFPP=Df"(ignoredintheneutroncase) ITYM=1Indicatesthatyouaregivingamagneticformfactor IfITY=0andandJOBTYP=1or3(neutroncase)the nextlinemustnotbegiven.Youarejustgivingthe FermilengthofthespeciesNAMinDFP. =2IndicatesthatyouaregivingjustDf'andDf" andtheprogramwillusetabulatedcoefficients forthesin(Theta)/ldependentpartoff(X-rays). ThenameNAMmustcorrespondinthiscasetoa
validtabulatedname(SeeNotes(1,2)below). Atvariancewiththenameusedfordeterminingthe scatteringfactorinthedescriptionofatoms,the chemicalsymbolusedinNAMmustbeLOWERCASE. Thisisthemostsimplewayofgivinganomalous dispersionparametersforsynchrotrondata. Line8-2: (9,7or2reals-seebelow-) OnelineoftheformA1,B1,A2,B2,A3,B3,A4,B4,Cgiving thecoefficientsfortheanalyticapproximationtotheX-ray formfactorf. oronelineoftheformA,a,B,b,C,c,Dgiving thecoefficientsfortheanalyticapproximationtothemagnetic formfactorf(P.J.Brown,VolCnewed.ITC) orasetoflinesoftheform:sin(Theta)/l-f Thesetisterminatedbyalinewith-100infirstposition. Ifthefirstformisdesired,A2mustnotbezero. Note(1):Scatteringlength,X-raysandmagneticformfactorsarestored ininternaltables.Tousethemyoumustgivethe"name"ofthe scattererusingUPPERCASEchemicalsymbols(scatteringlength), chemicalspecies(e.g.CU+2,forX-rays)orMfollowedbythe chemicalsymbolandformalchargestate(e.g.MNI2,formagnetic formfactorofNi+2).Thesenamesaregiveninlines11-4behind theatomname(seebelow).Inthecaseofgivingusersupplied Df'andDf''thechemicalsymbolisconvertedtoLOWERCASE.For X-raydiffractiontheformfactorssymbolsbehindtheatomname couldbegiveneitherinLOWERorUPPERcase. Ifthemagneticformfactorsoftherareearthsaretobeused, twooptionsexist.Example: MHO3:magneticformfactorofHo+3as JHO3:magneticformfactorofHo+3as+c2 wherec2hasbeencalculatedusingthedipolar approximation.SevencoefficientsA,a,B,b,C,c,Dare usedforapproximating+c2. Note(2):IfatableissuppliedandNSCAT>0theprogramperformsan internalfittoNINEcoefficientsandthiscouldfails.Ifyou wantalinearinterpolationNSCATmustbenegativeandthe listisgivenas:1000.0*2sin(Theta)/L-f ============================================================================ LINE9: MAXS=numberofparametersvaried (1integer) --------------Commentline: !Numberofrefinedparameters(appearsinthesamelineasMAXS) ---------------------------============================================================================ LINE10*: Globalparameters(notneededifICRYGisnot0) Line10-1:ZER,FLGZER,SYCOS,FLCOS,SYSIN,FLSYN,LAMBDA,FLAMBDA,IGLMORE (8realsand1integer) --------------Commentline: !ZeroCodeSycosCodeSysinCodeLambdaCodeMORE ----------------------------
ZER=zeropointforT(indegrees):Ttrue=Texp.-ZER Notethattheshiftconventionisoppositetothatused inPawley'sprogram. FLGZER=codewordforzeroshift(codewordsaredescribedinthe Mathematicalsectionbelow). SYCOS=systematic2ThetashiftwithcosThetadependence sampledisplacement(Theta-2Thetadiffractometers) FLCOS=codewordforSYCOS SYSIN=systematic2Thetashiftwithsin2Thetadependence sampletransparencycoefficient FLSIN=codewordforSYSIN LAMBDA=Wavelengthtoberefined(only1-wavelengthcanberefined) FLAMBDA=CodewordforLAMBDA.Cellparametersshouldbefixedif wavelengthistoberefined. IGLMOREifdifferentfromzerothefollowinglineisread Line10-1-1:PO, CPO,Cp,CCp,Tau,CTau (6reals) --------------Commentline: !Microabsorptioncoefficients !P0Cod_P0CpCod_CpTauCod_Tau ---------------------------Microabsorptioncoefficientsandcodes.Seemathematicalsection. (onlyusedifILOR=0andJOBTYP=0or2) Line10-1(bis)*:ZERO,FZERO,DTT1,FDTT1,DTT2,FDTT2,TOFTET (ReplacesLine10-1forT.O.F.data) --------------Commentline: !ZeroCodeDtt1CodeDtt2Code2sinTh ------------------------------------------------------------------ZERO:ZeropointforT(inmicroseconds):Ttrue=Texp.-ZER FZERO:Codewordforzeroshift DTT1,DTT2:TheTOFpositionofareflectionwithd-spacingdiscalculatedusi ng theformulaT=ZER+(DTT1+DTT2*d)*d FDTT1,FDTT2:CodewordsforDTT1,DTT2 TOFTET:valueof2sin(Theta)forthedetectorbank UsedforobtainingthewavelengthsandforLorentzfactor. Line10-2*:BACK1,BACK2,BACK3,BACK4,BACK5,BACK6 FBACK1,FBACK2,FBACK3,FBACK4,FBACK5,FBACK6 (6reals/6reals) IfNBCKGD=-3,twolinesmorewithcoefficients: BACK7,BACK8,BACK9,BACK10,BACK11,BACK12 FBACK7,FBACK8,FBACK9,FBACK10,FBACK11,FBACK12 --------------Commentline: !Backgroundcoefficients/codes ---------------------------BACK=backgroundcoefficients(seeMathematicalsection) FBACK=codewordsforbackgroundcoefficients IfNBCKGD=1(backgroundreadfromfile),BACK1cannotbezero Onlyfourcoefficientsareneededifsuchacase.Thecomment
lineinthiscaseis: --------------Commentline: !BackgroundTranf_coefficients/codes ---------------------------Line10-3*:BACKs,FBACKs(OnlyifNBCKGD=-1) (6reals/6reals/6reals/6reals) --------------Commentline: !Additionalbackgroundcoefficients/codes ---------------------------Fourlines(seeMathematicalsection): Bc1,Bc2,Bc3,Bc4,Bc5,Bc6 CBc1,CBc2,CBc3,CBc4,CBc5,CBc6 d1,d2,d3,d4,d5,d6 Cd1,Cd2,Cd3,Cd4,Cd5,Cd6 Line10-4*:FWINDOW(OnlyifNBCKGD=-2) --------------Commentline: WindowforFourierfiltering(appearsinthesamelineasFWINDOW) ---------------------------WindowforFourierfiltering.ThevalueofFWINDOWmustbe muchgreaterthanthenumberofpointssubtendedbythe baseofasingleBraggreflectionsinthewidestregion (afactorgreaterthanfive,atleast!). ThestartingbackgroundisreadfromfileFILE.BAC asinthecaseNBCKGD=1.But,atvariancewiththecase NBCKGD=1,thefileFILE.BACisre-writtenattheendof thesession. ============================================================================ LINE11:NPHASEsetsoflines ---------------------------------------------------------------------------Line11-1:PHSNM=nameofphase (A70) --------------Commentline: !DataforPHASEnumber:n==>CurrentR_Bragg:Rb ------------------------------------------------------------------------------------------------------Line11-2:N,NDIST,NMAGC,PREF(1),PREF(2),PREF(3),JBT,IRF,ISYM, ISTR,IFURT,ATZ,NVK,NPRO,IMORE (3integers,3reals,5integers,1realand3integers) --------------Commentline: !NatDisMomPr1Pr2Pr3JbtIrfIsyStrFurthATZNvkNprMore ---------------------------N=numberofatomsinasymmetricunit Thetotalnumberofatomsforallphasescannotbe greaterthanNATS(definedinPARAMETERstatement ofFUL0.INC) NDIST=numberofdistanceconstraints
NMAGC=numberofmagneticmomentconstraints PREF(1,2,3)=preferredorientationdirection(inreciprocalspace) JBT=0ThephaseistreatedwiththeRietveldMethod,then refiningagivenstructuralmodel. =1ThephaseistreatedwiththeRietveldMethodandit isconsideredaspuremagnetic.Onlymagnetic atomsarerequired.Inordertoobtainthecorrect valuesofthemagneticmomentsthescalefactorand structuralparametersmustbeconstrainedtohave thesamevalues(exceptamultiplicativefactor definedbytheuser)thattheircrystallographic counterpart.(Seenoteonmagneticrefinements) Thethreeextraparameterscharacterizingtheatomic magneticmomentscorrespondstocomponents(inBohr magnetons)alongthecrystallographicaxes. =-1As1butthethreeextraparameterscharacterizingthe atomicmagneticmomentscorrespondstothevalueofM (inBohrmagnetons)thesphericalPhianglewithXaxis andthesphericalThetaanglewithZaxis.Thismode worksonlyiftheZaxisisperpendiculartotheXYplane. (formonoclinicspacegroupsthetheLaueClass112/m) isrequired). =2ProfileMatchingmodewithconstantscalefactor =-2As2butinsteadofintensitythemodulusofthestructure factorisgivenintheCODFILn.HKLfile =3ProfileMatchingmodewithconstantrelativeintensities forthecurrentphase,butrefinablescalefactor.Inthis caseIRFmustbeequalto2. =-3As3butinsteadofintensitythemodulusofthestructure factorinabsoluteunits(effectivenumberofelectrons forX-rays/unitsof10(-12)cmforneutrons) isgivenintheCODFILn.HKLfile.Thisstructurefactoris givenforthenon-centrosymetricpartoftheprimitive cell,soforacentrosymmetricspacegroupwithacentred latticethestructurefactortobereadis: Freduced=Fconventional/(Nlat*Icen) whereNlatisthemultiplicityoftheconventionalcelland Icen=1fornon-centrosymmetricspacegroupsandIcen=2for centrosymmetricspacegroups. =4Theintensitiesofnuclearreflectionsarecalculatedfrom aroutine,suppliedbytheuser,calledSTRMOD. ThedefaultsubroutinehandlesRigidbodygroups. =5Theintensitiesofmagneticreflectionsarecalculatedfrom aroutine,suppliedbytheuser,calledMAGMOD. =+10/-10Thephasecancontainnuclearandmagneticcontributions STFACiscalledforreflectionswithnopropagationvector associatedandCALMAGiscalledforsatellitereflections. CALMAGisalsocalledforfundamentalreflectionsifthere isnopropagationvectorgivenbutthenumberofmagnetic symmetrymatricesisgreaterthan0. Thenegativevalueindicatessphericalcomponentsfor magneticparameters. Forthiscasetheatomparametersareinputinaslightly differentway. IRF=0Thelistofreflectionsforthisphaseisautomatically generatedfromthespacegroupsymbol =1Thelisth,k,l,MultisreadfromfileCODFILn.HKL(wheren
istheordinalnumberofthecurrentphase) =2Thelisth,k,l,Mult,Intensity(orStructureFactorifJBT=-3) isreadfromfileCODFILn.HKL =-1Thesatellitereflectionsaregeneratedautomaticallyfrom thegivenspacegroupsymbol =3Thelisth,k,l,Mult,Freal,FimagisreadfromfileCODFILn.HKL Inthiscase,thestructurefactorreadisaddedtothat calculatedfromthesuppliedatoms.Thisisusefulfor simplifyingthecalculationofstructurefactorsfor intercalatedcompounds(rigidhost). =4,-4Alistofintegratedintensitiesisgivenasobservations forthecurrentphase(InthecaseofICRYG<>0thisis mandatory) ThefileCODFILn.HKLcanalsobenamedasHKLn.HKL,orCODFIL.INT inthecaseICRYG<>0. TheformatofCODFILn.HKLfilesisthefollowing: Forabs(IRF)<4: Thefirsttwolinesarereadastitles(characters) Therestofthelinesconsiston: 1)Nopropagationvectors hklm(IRF=1)(freeformat) hklmCoeff(IRF=1+JSOL=1)(") hklmIntensity(orF)(IRF=2)(") hklmFrealFimag(IRF=3)(") 2)NVKpropagationvectors Inthethirdlineyouhavetogivethenumberofpropagation vectorsinformat(32x,i2),thenyougive NVKlineswith:NvK1K2K3,whereNvistheordinalnumber ofKandKiarethecomponentsofKinfree format. hklnvm(IRF=1)(freeformat) hklnvmCoeff(IRF=1+JSOL=1)(") hklnvmIntensity(orF)(IRF=2)(") hklnvmFrealFimag(IRF=3)(") Note: ThegeneratedfileswhenJBT=2,3maycontentadditionalitems thatarenotusedbyFullprof.Theseitems(sigma,angle,FWHM) canbeusedbyotherprograms. ThecaseIRF=1+JSOL=1istobeusedwhenshiftsofBragg reflectionsareobservedandamodelforitisknown.The usermustprovidethevalueofthecoefficientCOEFFfor eachreflection. Forabs(IRF)=4: -ThefirstlineisconsideredasaTITLE -Inthesecondlinetheformatoftheintensitydatatobe readbelowisgiven. Example:(3i4,2f10.2,i4,3f8.4)(don'tforgetparentheses)
-R_lambda(n),Itypdata,ipow(n)(freeformat) R_lambda(n):wavelengthforphasen Itypdata=0Squareofstructurefactors(F2)and sigma(F2)areinput. =1Structurefactors(F)andSigma(F)are input.Thesequantitiesaretransformed internallytocaseItypdata=0. Ipow(n)=0Singlecrystalobservations. =1Twinnedsinglecrystalobservations. Upto6hkl'scancontributetoa singleobservation. =2Powderintegratedintensities.Inthis caseclusterofpeakscanbegiven. ForthiscaseItypdataisirrelevant. -*cmono,rkks(tobegivenonlyforX-raysandIpow=2) CorrespondtovariablesCTHMandKfor monochromatorpolarizationcorrection. 1)Nopropagationvectors hklGobsSigma(Gobs)Icodec1c2c3 2)Propagationvectors -Nok(numberofpropagationvectors:mustbeequaltoNVK) NVKlineswith:NvK1K2K3,whereNvistheordinalnumber ofKandKiarethecomponentsofKinfree format. hklnvGobsSigma(Gobs)Icodc1c2c3 Theformatofthedatacorrespondstothatgivenexplicitely inline2oftheCODFILn.HKLfile. Nodatareductionisperformed.Theprogramexpects tobeprovidedwithanindependentsetofreflections. nvistheordinalnumberofthepropagationvector correspondingtothecurrentobservation(hkl). GobsandSigma(Gobs)havedifferentmeaningsdependingon thevalueofItypdataandIpow. Ipow=0Itypdata=0Gobs=F2 =1Gobs=F Ipow=1AsabovebutisGobs<0thereflection contributestothenextpositiveobservation. Ipow=2Gobs=Sumsof{jLpF2} Icod:codeforreflectionsindicatingthescalefactor numbertobeapplied(fortwinnedcrystalsor inhomogeneousdata). IfIpow=2andNVK><0Icodisthemultiplicity. IfIpow=2andNVK=0themultiplicityisautomatically calculatedfromthesymbolofthespacegroup. ForIRF=4 c1,c2,c3:Notyetused (coefficientsforextinctioncorrections) ForIRF=-4 c1,c2:RealandImaginarypartofthepartialcalculatedstructure factororthereflection.Theprogramwilladdthis
contributiontothestructurefactorcalculatedwiththe givenatoms->Ftot=F+Fp=(A+iB)+(c1+ic2).Seecomments forIRF=3. Examples: TwinnedOrthorhombiccrystalwithtwodomains (a,b,c)(b,a,c) hklGobsSigmaIcod ............................. 200-1.00.02 0203221.012.11 311-1.00.02 1311221.08.21 Powderclusterofpeaks 11123.20.41Isolatedpeak ............................. 531-1.00.01Clusterofpeaks:four 342-1.00.01independentreflections 441-1.00.01contributeto 503832.19.41<-thisobservation ISYM=0Thesymmetryoperatorsaregeneratedautomaticallyfrom thespacegroupsymbol. =+/-1Thesymmetryoperatorsarereadbelow.Inthecase ofapuremagneticphaseISYMmustbealwaysequalto1. ForJBT=10withmagneticcontributionISYMcouldbe0 butacommentstartingwith"Mag"shouldbegivenafter thespacegroupsymbol(seebelow) Note:ForProfileMatchingmode2,IRFcanbe0inthe firstrun.Inthatcase,aCODFILn.HKLfileis generatedandIRFissetto2inthenewCODFIL.PCR file.Thefileisupdatedateachruninthe caseofJBT=2.OfcourseISYMmustbe0. IfforaphaseIRF.LE.0andISYM=1,thereflections aregeneratedfromthesymbolgivenintheplace reservedforthespacegroup. Inthatcase,afileCODFILn.HKLisgeneratedwith therelevant(non-zero)reflectionsandproper multiplicitiesfortheparticularmodeldescribed byuser-givensymmetryoperators.Inadditionthe calculatedintensitiesaregiveninF2(corrected formultiplicity,scaleandLP-factor)inabsolute units.Theprogramdoesn'tusetheintensitiesin newrunsreadingthisgeneratedfile. Thecontainofthisgeneratedfile,apartfromthe featuresdescribedabove,is: Nok-vectors->hklmF2(calc)F2(obs) k-vectors->hklnvmF2(calc)F2(obs)hrkrlr withobviousmeaning. ISTR=0Ifstrainor/andsizeparametersareused,theyare thosecorrespondingtoselectedmodels(seebelow) =1Thegeneralizedformulationofstrainsparameterswill
beusedforthisphase.Seebelow =2Thegeneralizedformulationofsizeparameterswill beusedforthisphase.Seebelow =3Thegeneralizedformulationofstrain+sizeparameterswill beusedforthisphase.Seebelow IFURTNumberoffurtherparametersdefinedbyuser,tobeused withusersuppliedsubroutines. AZT=Z.Mw.f^2/t (usefultocalculatetheweightpercentageofthephase) Z:Numberofformulaunitspercell,Mw=molecularwheight f:Usedtotransformthesitemultiplicitiesusedonline 11-41totheirtruevalues.Forastoichiometricphasef=1 ifthesemultiplicitiesarecalculatedbydividingtheWyckoff multiplicitymofthesitebythegeneralmultiplicityM. Otherwisef=Occ.M/m,whereOcc.istheoccupationnumber giveninline11-4-1. t:IstheBrindleycoefficientthataccountsformicroabsorption effects.Itisrequiredforquantitativephaseanalysisonly. Whenphaseshavelikeabsorption(inmostneutronuses),this factorisnearly1.IfIMORE=1(seebelow)theBrindley-coeff. isdirectlyreadinthenextline(insuchcaseATZ=Z.Mw.f^2). NVK=Numberofpropagationvectors.IfNVK<0thevector-K isaddedtothelist. NPRO=Integerindicatingthepeakshapeforthepresentphase (seeline2).IfNPRO=0,thedefaultvalueNPROFistaken. IMORE=Ifdifferentfrom0anewlineisread ---------------------------------------------------------------------------Line11-2-1*:JVIEW,JDIST,JHELIX,JSOL,JMOM,JTER,BRIND, RM1,RM2,RM3,JTYP (6integers,4realsand1integer)(ReadonlyifIMORE=1) --------------Commentline: !JviJdiHelSolMomTerBrindRMuaRMubRMucJtyp ---------------------------JVIEW=1afilesuitableforSCHAKALisgenerated =2afilesuitableforSTRUPLOisgenerated (Theextensionofthefileisinbothcases".sch") =11IfJBT=2afileCODFILn.INTwithalistof overlapedpeakclustersisoutput. JDIST=1CreatesafilecalledCODFILn.ATMwithallatoms withinaprimitiveunitcellforamagneticphase.Thenumber "n"correspondstothenumberofthecurrentphase.IfJBT=10o nly thelistofmagneticatomsisgenerated. -1Foramagneticphasecreatesafilecalled CODFILn.ATMwithaformatsuitableforfurther processingwiththeprogramMOMENT.
2As1butforacrystalstructure,allatoms insidetheconventionalcellaregenerated. JHELIX=1Therealandimaginarycomponentsofthe Fouriercoefficientofamagneticatomareconstrained tobeorthogonal.Thefactor1/2isalsoincluded (seemathematicalsection). JSOL=1Additionalhkl-dependentasymmetryandshiftsparameters areread. JMOM-unusedatpresent JTER-unusedatpresent BRIND-Brindleycoefficient(seeline11-2) RM1-UsedwhenIRF=4andIMORE=1.IfRM1=0.0theprogram makesRM1=1.0internally.ThemeaningRM1correpondsto theglobalweightoftheintegratedintensityobservations withrespecttotheglobalprofile.Thecontribution tothenormalequationsoftheintegratedintensitypart ismultipliedbyRM1. RM2-IfIRF=4,RM2isafactorforexcludingreflections onlythereflectionswithGobs>=RM2*Sigma(Gobs)are consideredintherefinement. IfJVIEW=11andJBT=2andIRF<>4seenotebelow. RM3-IfRM3>0.9theweightsaredividedbytheChi2ofthe precedentcycle(nottested!)forintegratedintensity refinements(IRF=4). IfJVIEW=11andJBT=2andIRF<>4seenotebelow. JTYP-Jobtypeforthephase.Allowstherefinementofhetero geneousdata(SamevaluesastheglobalvariableJOBTYP inline2).ForthemomentisonlyusefulforIRF=4. Note:IfJVIEW=11andJBT=2theparametersRM2andRM3areusedtocontrol whethertwoconsecutivereflectionsbelongstoasamecluster. ThisisonlyforIRFdifferentfrom4/-4. Theruleisthefollowing: Thereflectionsiandi+1belongtothesameclusterif a)TwTh(i+1)-TwTh(i)<(Fwhm(i)+Fwhm(i+1))*RM2/2 OR b)TwTh(i+1)-TwTh(i)<(Fwhm(i)+Fwhm(i+1))/2andI(i+1)
thehexagonaldescription. Warning:don'tforgetblanksbetweensymmetryoperators; itisadvisabletochecktheLauesymmetryand symmetryoperatorsintheoutputfileespeciallyfor thosespacegroupsforwhichalternativeoriginsare shown(i.e.usethesettingwith-1attheorigin). Upperand/orlowercasecharacterscanbeused. Somespacegroupsarenotcorrectlygenerated,forthose casesyouhavetochangethesettingorgiveyourown symmetryoperators(seeaboveISYM). Forcubicspacegroupusetheoldnotation,e.g.Fd3m insteadofFd-3m. Thespacegroupsymbolmustbegiveneveninthecasethat youaregivingyourownsymmetryoperators.Thereflections (iftheyarenotreadfromfile)willbegeneratedaccording tothespacegroupsymbol. Acommentcanbeputaftercolumn20.Ifthiscommentstarts withthekeyword"Mag"(withoutquotes)thenthefollowing lineisreadifJBT=10 ---------------------------------------------------------------------------Line11-3-0*:Time_rev(i)(i=1,NS+1)(OnlyifJBT=+10/-10andComment=Mag) (upto25integers) --------------Commentline: !TimeReversalOperationsonCrystalSpaceGroup ---------------------------NSisthenumberofindependentsymmetryoperatorsgiven infileCODFIL.OUTforthecrystallographicspacegroup. Time_rev(i)=-1iftimereversalisassociatedtooperator "i"formagneticsymmetry,otherwiseisequalto1. TheorderofoperatorsisthesameasinCODFIL.OUT,so afirstrunisneededforknowingthelistof crystallographicsymmetryoperators. ForcentrosymmetricgroupsTime_rev(NS+1)tellstheprogram iftimereversalisassociated(-1)ornot(1)tothe inversionoperator.Thislastitemshouldbegivenonly forcentrosymmetricspacegroups. Thisapproachassumesthatthemagneticsymmetrybelongs tothefamilyofthecrystallographicspacegroup.However theusercantreattheproblemusingsubgroupsofthespace group(makingtheappropriateconstraintsintheatomic positions)whenneeded. Exoflines11-3/11-3-0*: P6/mmmMagneticsymmetrybelow !TimeReversalOperationsonCrystalSpaceGroup 111111-1-1-1-1-1-11 ---------------------------------------------------------------------------Line11-3-1*:MULT,ICENT,NLAUE,NMAGR(OnlyifISYM><0) (4integers) --------------Commentline: !NsymCenLaueMagMat ---------------------------MULT=Numberorsymmetryoperatorsgivenbelow. ICENT=1Noncentrosymmetricstructure
2Centrosymmetricstructure NLAUE=Integercorrespondingtothefollowinglaueclasses: 1:(-1),2:(2/m),3:(mmm),4:(4/m),5:(4/mmm),6:(-3,R),7:(-3m,R), 8:(-3),9:(-3m1),10:(-31m),11:(6/m),12:(6/mmm),13:(m3),14:(m3m) Thisnumberisonlyusedforcheckingthesymmetryoperators givenbyusers.Foraphasedescribedinahexagonalbasis oneshouldputNLAUE=6,7...12,evenifthespacegroupsymbol usedforgeneratingthereflectionsisofdifferentsymmetry. NMAGR=Numberofmagneticrotationmatricesforeach symmetryoperator. -------------------------------------------------------------------------Line11-3-2*:MULT(1+NMAGR)linesoftheform: =>IfISYM=1thesymmetryoperatorsaregiveninnumericform: --------------Commentline: !S11S12S13T1S21S22S23T2S31S32S33T3 !M11M12M13M21M22M23M31M32M33Ph ---------------------------.S11S12S13T1S21S22S23T2S31S32S33T3(3(3Int,1real)) .R11R12R13R21R22R23R31R32R33.Phase(9Int,1real) MULT. .NMAGRlines blocks.. . =>IfISYM=-1thesymmetryoperatorsaregiveninalpha-numericform: e.g. ! SYMMX,Y,Z MSYMU,V,W,0.0 ! SYMMX+1/2,-y,Z MSYM-U,V,-W,0.0 ! SYMM-x,-y,-Z MSYMU,V,W,0.0 ThesymbolsU,V,WareusedfortheFouriercomponentsofthe magneticmomentsalongX,Y,Z.Thenumericalvaluefollowing theMSYMoperatoristhemagneticphaseinunitsof2pi. ---------------------------------------------------------------------------Line11-4:4or2linesforeachoftheNatoms ForX-rayornuclearNeutronscattering:----------> ---------------------------------------------------------------------Line11-4-1:LABEL,NTYP,X,Y,Z,B,N,IOPIN,IOPFIN,N_Type (2A4,5realsand3integers) --------------Commentline: !AtomTypXYZBisoOccInFinN_t/Codes ----------------------------
IfJBT=4,-4(structuralmodelsuppliedbyuser):--> Line11-4-1:LABEL,NTYP,P1,P2,P3,P4,P5,P6,P7,P8 (2A4,8reals){parametersdefinedbyuserinSTRMOD} --------------Commentline: !AtomTypp1p2p3p4p5p6p7p8 !p9p10p11p12p13p14p15p16 -------------------------------------------------------------------------------------------------
FormagneticNeutronscattering:------------------> ---------------------------------------------------------------------Line11-4-1:LABEL,NTYP,IMAGR,IK,X,Y,Z,B,N,Mx,My,Mz (2A4,2integersand8reals) --------------Commentline: !AtomTypMagVekXYZBisoOccRxRyRz !IxIyIzbeta11beta22beta33MagPh ---------------------------IfJBT=5,-5(magneticmodelsuppliedbyuser):--> Line11-4-1:LABEL,NTYP,IMAGR,IK,P1,P2,P3,P4,P5,P6,P7,P8 (2A4,2integersand8reals){parametersdefinedbyuserinMAGMOD} --------------Commentline:(defaultJBT=5) !AtomTypMagVekXYZBisoOccMombetaPhase !Phi&ThetaofCone-axis+unusedparams ------------------------------------------------------------------------------------------------Thevariablesdefinedeitherfornuclearormagneticscatteringhave thefollowingmeaning: LABEL=Identificationcharactersforatomorobject. NTYP=Linktoscatteringdataforatom:eitherNAMfrom8.1 orchemicalsymbolandvalencetoaccessinternal table(useonlyuppercaseletters).Seenoteabove inline8. Alsoaseriesofspecialformfactors(undertest!)are availablewithrefinableparameters.Forusingthis optionNTYPshouldbeequaltooneofthefollowing words:SPHS(available),SPHE,ELLI,DISK,TORE SASH(notavailableyet),FUD1,FUD2,FUD3,FUD4(tobe suppliedbyuserinFdum1.for(seeForm_Factorsubroutine). Seemathematicalsectionfordetails. IMAGR=Ordinalnumberofthemagneticrotationmatrices appliedtothemagneticmomentoftheatom.Tobe givenonlyinthecaseofamagneticphase IK=Numberofthepropagationvectortowhichtheatom
contributes.IfIK=0theatomisusedforallthe propagationvectorsinthecalculationofstructurefactor. IfIK<0theatomcontributestoVK(abs(IK))andtothe vectorVK(abs(IK)+NVK/2) X,Y,Z=fractionalatomiccoordinates B=isotropicdisplacement(temperature)parameterin angstroms**2 N=occupationnumberi.e.chemicaloccupancyxsite multiplicity(canbenormalizedtothemultiplicity ofthegeneralpositionofthegroup). IOPIN,IOPFIN=Ordinalnumberoffirstandlastsymmetryoperator appliedtotheatom,apartfromtheidentitywhichmust alwaysbethefirstone. Usefultodescribepseudosymmetries. Thisoptionisnormallyusedwhentheusersupplytheir ownlistofsymmetryoperators(ISYM=1).Becarefulwith multiplicityofreflections!.Itissuggestedthatthe userssupplyalsotheirlistofreflections. IfIOPIN=IOPFIN=0allthesymmetryoperatorsareapplied. Onlyusedforcrystallographicstructures. N_Type=0->Isotropicatom (noanisotropictemperaturefactorsaregiven) 2->Anisotropicatom.Thetemperaturefactorsshould begivenbelow. 4->Theform-factorofthisatomiscalculatedusing aspecialsubroutineandrefinableparameters shouldbegivenbelow(undertest!) Mx,My,Mz=Componentsalongthecrystallographicaxisofthe magneticmoments(Bohrmagnetons),ifJBT=1. InthecaseJBT=-1thesethreeparameterscorrespondtothe sphericalcomponentsofthemagneticmoment,inthefollowing order:M,PhiandTheta.M:magnitudeofthemagneticmoment PhiandThetaaresphericalanglesofvectorM(seenoteon JBT=-1) Ifthemagneticphaseisincommensurateordescribedinthe crystallographiccellwiththehelpofapropagationvector, thesecomponentareactuallytherealpartoftheFourier componentsofthemagneticmomentoftheatom. ---------------------------------------------------------------------------Line11-4-2:CX,CY,CZ,CB,CN,CMx,CMy,CMz (8reals) CX,CY,CZ=codewordsforfractionalatomiccoordinates (seebelow) CB=codewordforisotropicdisplacement(temperature) parameter CN=codewordforoccupationnumber CMx,CMy,CMz=codewordsformagneticmomentcomponents
IfJBT=4,-4/5,-5CP1,CP2,CP3,CP4,CP5,CP6,CP7,CP8 ForX-rayornuclearNeutronscattering:----------> ---------------------------------------------------------------------------STANDARD: Line11-4-3:b11,b22,b33,b12,b13,b23(ForN_typ=2) (7reals) --------------Commentline: !beta11beta22beta33beta12beta13beta23/Codes ---------------------------bij=anisotropicdisplacement(temperature)parameters(betas) OR(ForN_typ=4)(ANDifN_typ=5,butnotavailable) --------------Commentline: !Form-factorrefinableparameters ---------------------------Line11-4-3:f1f2f3f4f5f6f7 (7reals) Line11-4-4:Cf1Cf2Cf3Cf4Cf5Cf6Cf7 Line11-4-5:f8f9f10f11f12f13f14 (7reals) Line11-4-6:Cf8Cf9Cf10Cf11Cf12Cf13Cf14 (7reals) Theparametersf1tof14areusedfordescribingtheform-factor ofthecurrentobject RIGIDBODYORNON-STANDARD: IfJBT=4,-4--->P9,P10,P11,P12,P13,P14,P15 {parametersdefinedbyuserinSTRMOD} ---------------------------------------------------------------------FormagneticNeutronscattering:------------------> ---------------------------------------------------------------------------Line11-4-3:Mxi,Myi,Mzi,b11,b22,b33,MPhas (7reals) IfJBT=5,-5--->P9,P10,P11,P13,P14,P15,P12 {parametersdefinedbyuserinMAGMOD} ---------------------------------------------------------------------Mxi,..=ImaginarycomponentsoftheFouriercoefficientin Bohrmagnetons(IfJBT<0,sphericalcomponentsas forrealcomponentsMx,My,Mz,seeline11-4-1) bii=diagonalpartofanisotropictemperaturefactors MPhas=Magneticphaseoftheatom(seemathematicalsection) IfJHELIX=1(seeline11-2-1)thethirdcomponentMzis calculatedbytheprograminordertohaveanimaginary vectororthogonaltotherealvector. IfJBT<0,thenthephi-angleoftheimaginarypart iscalculatedbytheprogramforkeepingtheorthogonal constraint.
---------------------------------------------------------------------------Line11-4-4:CB11,CB22,CB33,CB12,CB13,CB23,CMPhas (7reals) CBIJ=codewordforanisotropicdisplacement(temperature) parameters,orforimaginarycomponentsofthemagnetic Fouriercoefficient. CMPhas=codewordformagneticphase. IfJBT=4,-4CP9,CP10,CP11,CP12,CP13,CP14,CP15 ************************************************************************ Newinputformatforatomparameters Thelines11-4-1to11-4-4shouldbechangedforthecaseJBT=10,-10 ************************************************************************ ForXraysornuclear+magneticNeutronscattering:----------> ---------------------------------------------------------------------Line11-4-1:LABEL,NTYP,IMAGR,IK,X,Y,Z,B,NN_type(a) (2a4,2int,5real,1int) Line11-4-2:CX,CY,CZ,CB,CN(b) (5reals) Line11-4-3:MxMyMzMxiMyiMziMPhas(c) (7reals) Line11-4-4:CMxCMyCMzCMxiCMyiCMziCMPhas(d) (7reals) Line11-4-5:b11b22b33b12b13b23(e) (6reals) Line11-4-6:Cb11Cb22Cb33Cb12Cb13Cb23(f) (6reals) Line11-4-7:f1f2f3f4f5f6f7(g) (7reals) Line11-4-8:Cf1Cf2Cf3Cf4Cf5Cf6Cf7(h) (7reals) Line11-4-9:f8f9f10f11f12f13f14(i) (7reals) Line11-4-10:Cf8Cf9Cf10Cf11Cf12Cf13Cf14(j) (7reals) IfN_type=0Onlylines(a)and(b)needtobegiven IfN_type=1givethelines(a),(b),(c)and(d) IfN_type=2givethelines(a),(b),(e)and(f) IfN_type=3givethelines(a)->(f) ifN_type=4givethelines(a),(b)and(g)->(j)(specialform-factor) --------------Commentlines: !AtomTypMagVekXYZBisoOccN_type !Linebelow:Codes !RxRyRzIxIyIzMagPh !Linebelow:Codesor... !beta11beta22beta33beta12beta13beta23/Linebelow:Codes ---------------------------ThisinputcouldbealsousedforXrays,insuchcaseIMAGRand IKshouldbezeroforalltheatomsandJobtyporJtyp(n)=0.In suchcasethespacegroupsymbolcanbeusedforgenerationof reflectionsandsymmetryoperators.
ForaphasewithmagneticcontributionsNTYPshouldbeequalto themagneticformfactorsymbol.Theprogramextractsinternallythe fermilengthsymbolfromNTYP.Iftherearemagneticcontributions thesymmetryshouldbecontrolledbytheuser(ISYM=1)andthe magneticpartshouldbedescribedwiththeformalismofpropagation vectors,themagneticcontributioniscalculatedonlyforthesatellite reflections.Iffundamentalreflectionshavemagneticcontribution thepropagationvectork=(0,0,0)mustbeincludedexplicitelyif thereareotherpropagationvectors.Ifthemagneticcellisthe sameasthechemicalcellpropagationvectorsarenotneeded. Forthemoment,thesymmetryoperatorsmustbelongtothegroup ofthepropagationvectorGk,sosomeatomsneed,ingeneral,tobe repeatedfortherestofpositionsnotgeneratedbyGk. ------------------------------------------------------------------------------------------------------------------------------------------------====>Foriabs(IRF)<>4(nointegratedintensitydata)andConstWavelength ---------------------------------------------------------------------------Line11-5-1:S,GAM1,Bov,STR1,STR2,STR3,IstrainModel (6realsand1integer) --------------Commentline: !ScaleShape1BovStr1Str2Str3Strain-Model ---------------------------S=scalefactor GAM1=profileshapeparameter,e.g.: eta0forNPROF=4,5butnotforNPROF=7(seeline11-6-1) m0forNPROF=6 Bov=overallisotropicdisplacement(temperature)factor inangstroms**2 STR1,STR2,STR3=strainparameters,definedthroughthesubroutine STRAIN(seeadditionalinformation) IfISTR=1setthesevaluesto0.0 IstrainModel=Integertoselectaparticularmodelforstrains insubroutineSTRAIN. ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-5-2:CS,FLGAM1,CBov,CSTR1,CSTR2,CSTR3 (6reals) CS=codewordforscalefactor FLGAM1=codewordforGAM1 CBov=codewordforoverallisotropicdisplacement (temperature)factor CSTR1,CSTR2,CSTR3=codewordforstrainparameters IfISTR=1setthesevaluesto0.0 -----------------------------------------------------------------------------------------------------------------------------------------------------====>Foriabs(IRF)=4(integratedintensitydata) ---------------------------------------------------------------------------Line11-5-1:Sc1,Sc2,Sc3,Sc4,Sc5,Sc6 (6reals)
--------------Commentline: !ScaleFactors !Sc1Sc2Sc3Sc4Sc5Sc6 ---------------------------Line11-5-2:CSc1,CSc2,CSc3,CSc4,CSc5,CSc6 (6reals) Sci=scalefactorfordomain(i) CSci=codeofthescalefactorfordomain(i) Forpowderdataonlythefirstscalefactorisused -------------------------------------------------------------------------===>Endiabs(IRF)=4 ---------------------------------------------------------------------------====>Foriabs(IRF)<>4(nointegratedintensitydata)andConstWavelength ---------------------------------------------------------------------------Line11-6-1U,V,W,X,Y,IG,SZ,IsizeModel FWHM(orshape)parameters: --------------Commentline: !UVWXYGauSizLorSizSize-Model orforNPRO=11(splitpseudo-Voigt) !UlVlWlXlYGauSizLorSizSize-Model ---------------------------(7realsand1integer) Forprofiles0to6and12: FWHM^2=(U+DST^2)*Tan^2(Theta)+V*Tan(Theta)+W+IG/cos^2(Theta) =====>ForNPROF=4(tripledpseudo-Voigt),thethree componentsareassumedtohavethesameeta0andFWHM, sotheeffectivetotalwidthdependsontheadditional shapeparameterShp1(seeline11-8-3). Theprofilefunctionisgivenbytheformula: p4(x)=X*pV(x-D)+(1-X-Y)*pV(x)+Y*pV(x+D) where D=Shp1/d.costheta pV(x)=Eta0*L(x)+(1-Eta0)*G(x) So,apartfromtheFWHMthatiscalculatedfromU,V,W DSTandIGparametersforasinglecomponent,theprofile functionhasFOURshapeparametersEta0,X,YandShp1. Thisfunctionisadaptedformediumresolutionneutron powderdiffractomershavingdefectsonthemonochromator and/ortheguidespacialspectraldistributiongiving risetoanon-gaussiandistributionofwavelengths. =====>ForNPROF=5and12(pseudo-Voigt)theetaparameter canbedependentonXthroughtheformula: pV(x)=Eta*L(x)+(1-Eta)*G(x) Eta=Eta0+X*2Theta
=====>ForNPROF=11(splitpseudo-Voigt)DSTandIGarecommon totheleftandrightpartsoftheprofile.Moreoveradditional FWHMparametersareusedasnewshapeparameters,sothe expressionoftheleftFWHM(L)forNPROF=11is FWHM^2(L)=(Ul+DST^2)*Tan^2(Theta)+Vl*Tan(Theta) +Wl+IG/cos^2(Theta)+Shp1/tan^2(2Theta) Shp1isappliedonlyfor2Theta<=90.ThevalueofETAfortheleft partisgivenby:Etal=Etal0+Xl*2Theta Theexpressionoftherightpartis: FWHM^2(R)=(Ur+DST^2)*Tan^2(Theta)+Vr*Tan(Theta) +Wr+IG/cos^2(Theta)+Shp2/tan^2(2Theta) Shp2isappliedonlyfor2Theta>90.ThevalueofETAfortheright partisgivenby:Etar=Etar0+Xr*2Theta TheFWHMandshapeparametersfortherightpartarereadinnextlines =====>ForNPROF=6(Pearson-VII)themparameter canbedependentonXandYthroughtheformula: m=m0+100*X/2Theta+10000*Y/(2Theta)**2 =====>ForNPROF=7,theFWHMofthetwocomponentsiscalculatedas FWHM^2(gaussian)=(U+DST^2)*Tan^2(Theta)+V*Tan(Theta)+W+IG/cos^2(The ta) FWHM(lorentzian)=Xtan(Theta)+(Y+F(SZ))/cos(Theta) Allexpressionsarein(degrees2Theta)^2 U,V,W=Half-widthparameters(normallycharacterizingtheinstrumental resolutionfunction). X=Lorentzianisotropicstrainparameter. DST(STR)=Anisotropicgaussiancontributionofmicrostrain.Itis calculatedinsubroutineSTRAINasafunctionofIstrainModel orISTR.IfIstrainModel<>0thenISTRmustbezero.DSTdepends onSTR1,STR2,...parametersandhkl. IG=Isotropicsizeparameterofgaussiancharacter F(SZ)=anisotropiclorentziancontributionofparticlesize.Itis calculatedinsubroutineSIZEanddependonparameterSZandhkl. IsizeModel=IntegertoselectaparticularmodelforF(SZ) insubroutineSIZE. ---------------------------------------------------------------------------Line11-6-2:CU,CV,CW,CX,CYCIGCSZ:codewordsfortheFWHM (orshape)parameters (7reals) ---------------------------------------------------------------------------Line11-6-3:Ur,Vr,Wr,Etar0,Xr (5reals)ReadonlyifNPRO=11(splitpseudo-Voigt)
--------------Commentline: !UrVrWrEtar0Xr ---------------------------FWHMandshapeparametersfortherightpartofthesplitpseudo-Voigt function.ThisfunctionissimilartoNPROF=5buttheleft(x<0)and right(x>0)partsoftheprofilehavedifferentU,V,W,eta0andX parameters.Additionalshapeparametersarealsoread. Line11-6-4*:CUr,CVr,CWr,CEtar0,CXr:codewordsfortheFWHM andshapeparameters (5reals)ReadonlyifNPRO=11 ---------------------------------------------------------------------------===>Endiabs(IRF)<>4 ---------------------------------------------------------------------------====>Foriabs(IRF)=4(integratedintensitydata) ---------------------------------------------------------------------------Line11-6-1:Ext1,Ext2,Ext3,Ext4,Ext5,Ext6,Ext7 (7reals) --------------Commentline: !ExtinctionParameters !Ext1Ext2Ext3Ext4Ext5Ext6Ext7 ---------------------------Line11-6-2:CExt1,CExt2,CExt3,CExt4,CExt5,CExt6,CExt7 (7reals) Exti=Extinctionparameter(i) CExti=Codeoftheextinctionparameter(i) Atpresentonlythefirstextinctionparameterisused. ===>Endiabs(IRF)=4 ---------------------------------------------------------------------------Line11-7-1:a,b,c,a,b,gcellparametersinAanddegrees (6reals) --------------Commentline: !abcalphabetagamma ------------------------------------------------------------------------------------------------------Line11-7-2:CA,CB,CC,CD,CE,CF: (6reals) codewordsforcellconstantsA,B,C,D,E&Fdefined by: 1/d2=Ah2+Bk2+Cl2+Dkl+Ehl+Fhk Notethatthesecodewordsdonotreferdirectlyto thecellparameters;forinstance,inthehexagonal system,thelastcodewordCFmustbethesameasCA andCB. ---------------------------------------------------------------------------Line11-8-1:G1,G2,Pas1,Pas2,Pas3,Pas4 (6reals) --------------Commentline:
!Pref1Pref2Asy1Asy2Asy3Asy4 ---------------------------G1,G2=preferredorientationparameters(seeMath.section) whenNORI=0,G1=0meansnopreferredorientation whenNORI=1,G1=1meansnopreferredorientation Pa1,..Pas4=asymmetryparametersappliedtoanglesbelowRLIM (givenonline4:seeMathematicalsection) IfNPHASEisnegativeonlythefirstparameterisrelevant. ---------------------------------------------------------------------------Line11-8-2:CG1,CG2,CPas1,CPas2,CPas3,CPas4 (6reals) CG1,CG2=codewordsforpreferredorientationparameters CPas1,...CPas4=codewordsforasymmetryparameters ---------------------------------------------------------------------------Line11-8-3*:Shp1,CShp1,Shp2,CShp2 (4reals) --------------Commentline: !AdditionalShapeparameters ---------------------------Additionalshapeparametersandcorrespondingcodewords. ReadonlyifNPRO=4orifNPRO>8 ForNPRO=11(splitpseudo-Voigt)theycorrespondtotheadditional contributiontotheFWHMfortheLeft(L)andRight(R)partof theprofilefor2Theta<90and2Theta>90respectively. addFWHM^2(L)=Shp1/tan^2(2Theta),addFWHM^2(R)=Shp2/tan^2(2Thet a) ForNPRO=12(Convolutedpseudo-Voigtwithaxialdivergenceasymmetry) Shp1=S_Lissourcewidth/detectordistance Shp2=D_Lisdetectorwidth/detectordistance Theseparametersplaytheroleofasymmetryparameters,theyareused onlyforreflectionsbelow2Theta=RLIM. ---------------------------------------------------------------------------Line11-8-4*:U2,V2,W2 (3reals)U,V,Wparametersforthesecondwavelength presentinthediffractionpattern. ReadonlyifRATIOisnegative. --------------Commentline: !AdditionalU,V,WparametersforLambda2 ------------------------------------------------------------------------------------------------------Line11-8-5*:CU2,CV2,CW2 (3reals)CodewordsoftheadditionalU,V,Wparameters ReadonlyifRATIOisnegative. ---------------------------------------------------------------------------TIMEOFFLIGHTDATA =============================================================================== ====>LINES11-5-1to11-8-5aresubstitutedbythefollowinglinesfor TIMEOFFLIGHTDATA
============================================= ===================== ================================================= ================================== ========= Line11-5-1:S,Ext,Bov,STR1,STR2,STR3, IstrainModel (6reals+1integer) --------------Commentline: !ScaleExtincBovStr1 !ScaleExt incBovStr1Str2Str3Strain Str2Str3Strain-Model -Model -------------------------------------------------------------------------------------------------------------------------------------------------Sameparametersasin11-5-1forCW,exceptthatGAM1isre Sameparametersasin11-5-1forC W,exceptthatGAM1isreplaced placed bytheextinctionparameterEXT. Line11-5-2:CS,FLEXT,CBov,CSTR1,CSTR2,CSTR3 (6reals) Codewordsoftheaboveparameters ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-6-1:Sig2,Sig1,Sig0,Xt,Yt,Z1,Z0,IsizeModel (7realsand1integer) --------------Commentline: !Sig-2Sig-1Sig-0Xt !Sig-2Sig-1 Sig-0XtYtZ1Z0 YtZ1Z0Size-Mode Size-Mode l ---------------------------------------------------------------------------------------------------------------------------------------------------------GaussianFWHMparameters: (d2=d*d,d4=d2*d2,d:d-spacing) Sigma^2=(sig2+GSIZ)d4+(sig Sigma^2= (sig2+GSIZ)d4+(sig1+DST)*d2+sig0 1+DST)*d2+sig0 Xt,Yt:Notusedatpresent Z1=GSIZ:Gaussianisotropicsizecomponent Z0:Notusedatpresent Units::sig2,GSIZ:(microsecs/Angstrom^2)^2 sig1,DST:(microsecs/Angstrom)^2 sig0:(microsecs)^2 DSTdependsonSTR1,STR2,...throughtheselectedstrainm DSTdependsonSTR1,STR2,...thro ughtheselectedstrainmodel. odel. TheGaussianFWHMisSigma*sqrt(8Ln2) Line11-6-2CSig2,CSig1,CSig0,CXt,CYt,CZ1,CZ0 (7reals) Codewordsoftheaboveparameters ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-6-3:Gam2,Gam1,Gam0,LStr,LSiz (5reals) --------------Commentline: !Gam-2Gam-1Gam-0LStrLSiz ---------------------------------------------------LorentzianFWHMparameters: gamma=(gam2+DSIZ)d2+(gam1 gamma=( gam2+DSIZ)d2+(gam1+LStr)*d+gam0 +LStr)*d+gam0 gamma:LorentzianFWHM LStr:Lorentzianisotropicstrain LSiz:Lorentzianisotropicstrain
DSIZ=F(LSiz):FdependsonLSiz(andeventuallyonmoresiz DSIZ=F(LSiz):FdependsonLSiz(a ndeventuallyonmoresize e parameters)through parameters)throughtheselectedsizemodel theselectedsizemodel Units::gam2,DSIZ:microsecs/Angstrom^2 gam1,LStr:microsecs/Angstrom gam0:microsecs Line11-6-4CGam2,CGam1,CGam0,CLStr,CLSiz (5reals) Codewordsoftheaboveparameters ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-7-1:a,b,c,alpha,beta,gamma (6reals) --------------Commentline: !abcalph !a bcalphabetagamma abetagamma --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Line11-7-2:CA,CB,CC,CD,CE,CF: (6reals) Cellparametersandcodewordsasabove. ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-8-1:G1,G2,alph0,beta0,alph1,beta1 (6reals) --------------Commentline: !Pref1Pref2alph0beta0alph1beta1 -------------------------------------------------G1,G2:Preferredorientationparameters(asabove) G1,G2:Preferredorientationpar ameters(asabove) alph0,beta0,alph1,beta1:Parameter alph0,beta0,a lph1,beta1:Parametersdefiningthevariation sdefiningthevariation oftheexponentialdecay constantswithd-spacing. Fastdecay:alpha=alpha0+alpha1/d Slowdecay:beta=beta0+beta1/d4 alphaandbetaareinreciprocalmicro alphaandbeta areinreciprocalmicrosecondsanddinangstrom secondsanddinangstroms. s. Line11-8-2:CG1,CG2,Calph0,Cbeta0,Calph1,Cbeta1 (6reals) Codewordsoftheaboveparameters ---------------------------------------------------------------------------------------------------------------------------------------------------Line11-8-3:Abs1,CAbs1,Abs2,CAbs2 (4reals) --------------Commentline: !Absorptioncorrectionparameters ---------------------------------Abs1,Abs2:Absorptioncorrectionparameters CAbs1,CAbs2:Codewords Thephysicalmeaning Thephysicalmeaningoftheseparametersdepe oftheseparametersdependon ndon thefunctionselecte thefunctionselectedbyIABSCOR(seeLine4) dbyIABSCOR(seeLine4) ----------------------------------------------------------------------------------------------------------------------------------------------------
=====================END=OF=SPECIFIC=INPUT=FOR =====================E ND=OF=SPECIFIC=INPUT=FOR=T.O.F.================== =T.O.F.=========================== ========= Line11-8-6*:Ahkl,Shf1,Shf2,IASV,ISHIF (3realsand2integers) --------------Commentline: !AsyPShift1Shift2ModAModS ---------------------------ReadonlyifJSOL=1 Ahkl=HKL-dependentasymmetryparameter. Shf1,Shf2=HKL-dependentshiftparameters. Thethreelastparametersar The threelastparametersaredefinedbytheuserthr edefinedbytheuserthrough ough thesubroutinesASYMHKL&SH the subroutinesASYMHKL&SHIFHKL,whereaparticular IFHKL,whereaparticularmodel model fordisplacementandasymmet for displacementandasymmetryofBraggreflectionsi ryofBraggreflectionsisbuilt. sbuilt. IASV=Modelforasymmetry. ISHIF=Modelforshifts. ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-8-7*:CAhkl,CShf1,CShf2 ReadonlyifJSOL=1 (3reals) CAhkl=codewordforhkl-depend CAhkl= codewordforhkl-dependentasymmetryparameter entasymmetryparameter CShf1,CShf2=codewordsforhkl-depen CShf1,CShf2= codewordsforhkl-dependentshiftparameters. dentshiftparameters. ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-8-8*:Sh1,Sh2,Sh3 --------------Commentline: 'Shift-cos(1)orShift-sin(-1)axis'in 'Shift-cos(1)or Shift-sin(-1)axis'inthesamelineasthenum thesamelineasthenumbers bers ---------------------------(3reals)IfIshift=+/-1,[Sh1,Sh2,S (3reals)IfI shift=+/-1,[Sh1,Sh2,Sh3]isthevectordefinin h3]isthevectordefining g theaxial"shift-platelets". ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-9*:Sz1,Sz2,Sz3 (3reals)IfIsizeModel=+/-1,[Sz1,S (3reals)IfI sizeModel=+/-1,[Sz1,Sz2,Sz3]isthevectordef z2,Sz3]isthevectordefiningthe iningthe platelets. ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-10-1*:St1,St2,St3 (3reals)IfIstrainModel=7,[St1,St2, (3reals)IfI strainModel=7,[St1,St2,St3]isthevectordefini St3]isthevectordefiningthe ngthe axialmicrostrain. ----------------------------------------------------------------------------------------------------------------------------------------------------Line11-10-2*:Str4,Str5,Str6,Str7,Str8 (5reals/5reals) :CStr4,CStr5,CStr6,CStr7,CStr8 IfIstrainModel>8,5a I fIstrainModel>8,5additionalstrainparamete dditionalstrainparameters rs andcodes. --------------Commentline: !5additionalstrainparameters(IstrainModel>8) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Line11-11*:NVKpairoflineswith propagationvectorsandcodes ComponentsofKinrecipro Co mponentsofKinreciprocallatticeunits. callatticeunits. (3reals)Kx,Ky,Kz (3reals)CKx,CKy,CKz --------------Commentline:
!Propagationvectors: ------------------------------------------------------------------------------------------------------Line11-12*:IFURTlineswithfurtherparametersintroducedby users,eachlinecontains: (A4,2reals):NAMEPARVALUEPARCODEPAR --------------Commentline: !Furtherparameters: ------------------------------------------------------------------------------------------------------Line11-13*:Generalizedstrain parametersandcodewords (5reals/5reals)IfISTR=1,3 (STR(j),j=1,5),(CODSTR(j),j=1,5) (STR(j),j=6,10),(CODSTR(j),j=6,10) --------------Commentline: !Additionalstrainparameters: ---------------------------Twosetsoffivestrainparametersandtheircodes Eg. STR1STR2...STR5 CSTR1CSTR2...CSTR5 STR6STR7...STR10 CSTR6CSTR7...CSTR10 ---------------------------------------------------------------------------Line11-14*:Generalizedsizeparametersandcodewords (6reals/6reals)IfISTR=2,3 --------------Commentline: !Generalizedstrainparameters: ---------------------------(Siz(j),j=1,6),(CODSiz(j),j=1,6) Asetofsixsizeparametersandtheircodes Eg. Siz1Siz2...Siz6 CSiz1CSiz2...CSiz6 ---------------------------------------------------------------------------Line11-15*:NDISTnumberoflinesofdistanceconstraints CATOD1,CATOD2,ITnum,T1,T2,T3,Dist,Sigma (2A4,1integerand5reals) --------------Commentline: !Softdistanceconstraints: ---------------------------CATOD1andCATOD2:Namesoftheatomstobeconstrained Theymustcoincidewithlabelsinthe asymmetricunit. ITnum:Integerforselectingtherotationpartofthe symmetryoperatortobeappliedtothecoordinates oftheatomCATOD2.
(T1,T2,T3):Translationpartoftheabovesymmetryoperator Dist:Valueoftherequireddistance. Sigma:Standarddeviationofthedistance. Thenumberingofsymmetryoperatorstobegivenindistanceconstraints conditions.TheintegernumbertobegivenisITnum.Ifcombination withacenterofsymmetryisneededthevaluemustbeenteredasnegative. Non-hexagonalframes ITnumSymmetrysymbolRotationmatrix (1)1-->(x,y,z) (2)2(0,0,z)-->(-x,-y,z) (3)2(0,y,0)-->(-x,y,-z) (4)2(x,0,0)-->(x,-y,-z) (5)3+(x,x,x)-->(z,x,y) (6)3+(-x,x,-x)-->(z,-x,-y) (7)3+(x,-x,-x)-->(-z,-x,y) (8)3+(-x,-x,x)-->(-z,x,-y) (9)3-(x,x,x)-->(y,z,x) (10)3-(x,-x,-x)-->(-y,z,-x) (11)3-(-x,-x,x)-->(y,-z,-x) (12)3-(-x,x,-x)-->(-y,-z,x) (13)2(x,x,0)-->(y,x,-z) (14)2(x,-x,0)-->(-y,-x,-z) (15)4-(0,0,z)-->(y,-x,z) (16)4+(0,0,z)-->(-y,x,z) (17)4-(x,0,0)-->(x,z,-y) (18)2(0,y,y)-->(-x,z,y) (19)2(0,y,-y)-->(-x,-z,-y) (20)4+(x,0,0)-->(x,-z,y) (21)4+(0,y,0)-->(z,y,-x) (22)2(x,0,x)-->(z,-y,x) (23)4-(0,y,0)-->(-z,y,x) (24)2(-x,0,x)-->(-z,-y,-x) Hexagonalframes ITnumSymmetrysymbolRotationmatrix (25)1-->(x,y,z) (26)3+(0,0,z)-->(-y,x-y,z) (27)3-(0,0,z)-->(-x+y,-x,z) (28)2(0,0,z)-->(-x,-y,z) (29)6-(0,0,z)-->(y,-x+y,z) (30)6+(0,0,z)-->(x-y,x,z) (31)2(x,x,0)-->(y,x,-z) (32)2(x,0,0)-->(x-y,-y,-z) (33)2(0,y,0)-->(-x,-x+y,-z) (34)2(x,-x,0)-->(-y,-x,-z) (35)2(x,2x,0)-->(-x+y,y,-z) (36)2(2x,x,0)-->(x,x-y,-z) ---------------------------------------------------------------------------Line11-16*:NMAGCnumberoflinesofmagneticmomentconstraints --------------Commentline: !Softmomentconstraints:
---------------------------(A2,2reals):CATOM,Moment,Sigma CATOM:Twolettersequaltothetwofirstcharacterofthe labelofatomsinasymmetricunitwhichareconstrained. Moment:Valueoftherequiredmagneticmoment. Sigma:StandarddeviationofMoment. (Itdoesn'tworkwithincommensuratemagneticstructures) ---------------------------------------------------------------------------LINE12*:NRELLlinescontainingthefollowingitems (1integerand2reals) --------------Commentline: !Hardlimitsforselectedparameters: ---------------------------NUMPAR,LowLIMIT,HighLIMIT WhereNUMPARisthe"number"oftheparameter(asgiven bytheparametercode)tobeconstrainedwithinthelimits specifiedbytheinterval[LowLIMIT,HighLIMIT] Foraproperuseofthisoptiononehastoputlimits tothevariableappearingforthefirsttimewiththe wishedparametercode.Thisshouldhaveapositivesign andaunitmultiplier. ---------------------------------------------------------------------------Line12-1*:NCONFG,NSOLU,NREFLEX,NSCALEF (3integers) --------------Commentline: !NconfgNsoluNum_RefNscalef -----------------------------------ReadonlyifICRYG=2.TheprogramtriesNCONFGconfigurations andselectthebestNSOLUsolutions(lowerR-factors)using thefirstNREFLEXreflectionsofthefileCODFILn.HKL. IfNSCALEFisdifferentfromzero,thenthescalefactorused intheprogramisobtainedfromtherelation: Sum{Iobs}=Scale*Sum{Icalc} AconfigurationmeansasetofNRELLvaluesoftheselected parameterswithintheboxdefinedinLINE12. Theconstraintsestablishedwiththecodingofparameters havenothesamemeaningaswithleast-squares(LS).InLS refinementfortwovariableshavingcodesxx1.00andxx0.5 theshiftappliedtothesecondvariableishalftheshift appliedtothefirstoneirrespectiveoftheirinitialvalues. InMontecarlosearch,thevalueofthesecondvariableis justhalfthevalueofthefirstvariable.Onlyoneparameter, numberedhereas"xx",controlsthevalueofthetwovariables eitherinLSorinMontecarlosearh.
---------------------------------------------------------------------------LINE13*:ISCALE,IDIFusedonlyifIPL.ne.0(line3) (2integers) --------------Commentline: !IscaleIdif ----------------------------
ISCALE=countspercharacterpositionforobservedand calculatedcurvesonlineprintplot IDIF=countspercharacterfordifferencecurve ---------------------------------------------------------------------------LINE14*:THET1,THET2 (2reals)Thereflectionlistbetweentheseanglesis savedinthefileCODFILHKL.SAV --------------Commentline: !2Th12Th2 ---------------------------==================ENDOFCODFIL.PCR'SDESCRIPTION=============================
3.-MATHEMATICALINFORMATION
--------------------------------------------3.1:Calculatedprofile.Structurefactors. --------------------------------------------Calculatedcountsyciattheithsteparedeterminedby summingthecontributionfromneighbouringBraggreflections plusthebackground: yci=SSUM(Lh.Fh^2.Omeg(Ti-Th).Ah.Th.Ph+ybi whereSisthescalefactor LhcontainstheLorentz,polarizationand multiplicityfactors Fhisthestructurefactor.Theratioofthe intensitiesforthetwowavelengthsisabsorbed inthecalculationofFh^2,sothatonlya singlescalefactorisrequired. Ahistheasymmetryfunction Thisthetransmissionfactor(line4) Phdescribesthepreferredorientationofthe sample Omegisthereflectionprofilefunctionwhich approximatestheeffectsofbothinstrumental and,possibly,specimenparameters. ybiisthebackgroundintensity -----------------------------------------Form-factorcalculationsandRefinements -----------------------------------------Apartfromthestandardscatteringfactorforindivualatomsexistingin aninternallibraryofFullProf.Theversion3.2andhighercanhandlecomple
x form-factorsasastandardoption.Inthegeneralexpressionofthenuclear structurefactor: F(H)=Sum(s){ns.f(H)s.Sum(j)[Tjs.exp(2pi(HGjrs+tj)]} theformfactorf(H)isnormallydependentonthemoduleofH.Formolecular plasticcrystalsthetreatmentofrotatingmoleculescannotbedoneusing anatomicdescription.Theapproachofamolecularform-factorthattakes intoaccounttheparticulardynamicsoftheobjectismorereliable. f(H)dependsonaseriesofparametersfordifferenttypesofobjects. CoefficientsofSymmetryAdaptedSphericalHarmonics,geometricalparameters (radiusofasphere,lengthandradiusofacylinderordisk,etc),scatterin g density,etccouldservefordescribingthescatteringfactorofacomplex object. IntheFullProfversion3.2orhighertheavailable(orprojected)objects arethefollowing: Sphere: Elipsoidal: Cylinderofellipticalsection: ---------------------------------------Magneticscatteringcalculations ---------------------------------------ForamagneticphaseF(Q)^2iscalculatedusingthegeneral expresionofHalpernandJohnson: F(Q)^2={Fm(Q)^2-(e.Fm(Q)^2} whereFm(Q)isthemagneticstructurefactor,Q=H+kandeistheunit vectoralongthescatteringvectorQ. ThemagneticmomentisconsideredasaFouriersuperpositionoftype: m(l,j)=Sum(k){S(k,j)exp[-2.pi.i.k.R(l)]} Insuchacasethemagneticstructurefactorisgivenby: Fm(H+k)=Sum(j){S(k,j)fj(H+k)exp[2.pi.i.(H+k).r(j)]}
TheSum(j)isoveralltheatomsinthecrystallographiccell Ifsymmetryrelationsareestablishedforcouplingthedifferent FouriercomponentsS(k,j),phasefactorsareaddedtotheexponential andthesumisonlyfortheasymmetricunit: Fm(Q=H+k)=0.2695Sum(s){ns.f(Q)s. Sum(j)[(Rj(s).S(k,s)Tjs.exp(2pi(QMjrs-Psik(j,s))]} Thesumover(s)concernsthemagneticatomsoftheasymmetricunitfor thewavevectork(theFouriercomponentkcontributesonlytok-satellite),
nsistheoccupationfactorandf(Q)sistheformfactorofatoms. Thesumover(j)concernsthedifferentsymmetryoperatorsofthecrystal spacegroupMj={g,t}j(gandtaretherotationalandtranslationalpartof Mj.ThematrixRj(s)transformthecomponentsoftheFouriertermS(k,s)of thestartingatomstothatnumberedas"j"intheorbitofs. Tjsisthetemperaturefactor.ThephasefactorPsik(j,s)hastwocomponents: Psik(j,s)=Mphas(s)+Phase(j) Mphas(s)isaphasefactorwhichisnotdeterminedbysymmetry.Itisa refinableparameteranditissignificantonlyforanindependentsetof magneticatomswhichrespecttoanotherone. Phase(j)isaphasefactordeterminedbysymmetry.TheFouriercomponentk ofthemagneticmomentofatoms,S(k,s)istransformedto S(k,sj)=Rj(s)S(k,s)exp{-2piiPhase(j)} ThesignofPsik(j,s)changesfor-k.ThereflectionH+khasthe"negative" signindicatedintheaboveformulasandthereflectionH-khasthe positivesign. InthegeneralcaseS(k,s)isacomplexvector(ingeneralthereare sixcomponents.InoldversionsofFullProfonecouldsimulatethis complexvectorbysplittingtheatomcontributingtopropagationvector kintwopartsbyputtinga"magneticphase"ofpi/2withrespecttothe realpartofS(k,s).Themagneticphasesaregiveninfractionsof2pi, thenfortheabovepurposeonecanuseafixedPhase=0.25. Inthenewversiontheabovesplittingisnotneeded.Theimaginary componentsarereadintheplacewhichwasreservedforanisotropic temperaturefactors(seelines11-4-3).ForthescatteringvectorH-k theFouriercomponentisthecomplexconjugateoftheFouriercomponent usedforcalculatingthestructurefactorforH+k.Theprogramtakes intoaccountautomaticallythisfact.Ifkisattheinteriorofthe BrillouinZoneafactor1/2isappliedtotheFouriercoefficient. Letusconsiderasingleindex"j"forthesublatticejofthesite"s". TheFouriercoefficientforthesublatticeisgivenby: S(k,j)={1/2[MRxje1+MRyje2+MRzje3]+ 1/2i[MIxje1+MIyje2+MIzje3]}exp(-2.pi.i.Psik(j)) Thevector-kmustalsobegiveneitherexplicitlyorimplicitlyby givingNVK<0(seeNVKonline11-2).IfNVK<0theprogramapplies thefactor1/2becauseitissupposedthatkisnonequivalentto-k evenifkbelongtothesurfaceoftheBrillouinzone. IftheoptionJHELIX=1isused,thenumberoffreeparameterspermagnetic atomisreduced.TheFouriercoefficientsareconsideredoftheform: S(k,j)=1/2[m1suj+im2jvj]exp(-2.pi.i.Psik(j)) whereujandvjareorthogonalunitvectors.Ifm1j=m2j=m0themagnetic structureforthesublatticejcorrespondstoaclassicalhelix (orspiral)ofcylindricalenvelope.Alljatomshaveamagneticmoment equaltom0.Ifm1j/=m2jthehelixhasanellipticalenvelopeandthe momentshavevaluesbetweenmin(m1j,m2j)andmax(m1j,m2j).Ifm2j=0 themagneticstructurecorrespondstoamodulatedsinusoidofamplitude A=m1j. Ingeneral,theuserhastocalculatetherealmagneticmomentsfromthe
refinedvaluesoftheFouriercomponents:thephrase"MagneticMoment"in theoutputfilemeansthemodulusofthecorrespondingFouriercomponent. TheprogramMOMENThasbeenwritteninordertohelptheuserwiththese calculations.Inanycasethecalculationofthemagneticmomentofthe atom"j"intheunitcellofindex"l"shouldbedonebyusingthe formula: m(l,j)=Sum(k){S(k,j)exp[-2.pi.i.k.R(l)]}= =Sum[k]{[MRxje1+MRyje2+MRzje3]cos2pi[k.R(l)+Psik(j)]+ [MIxje1+MIyje2+MIzje3]sin2pi[k.R(l)+Psik(j)]} whereSum[k]isthesumextendedforhalfthenumberofpropagation vectors,i.e.overthenumberofpairs(k,-k). Ifthepropagationvectorkiscommensurate(rationalcomponents) onecanusethemagneticunitcellandm(k,j)canbeidentifiedwith themagneticmomentatsitej.Inthiscaseonecandescribethemagnetic structurewithPsik(j)=0andQ=H,beingHanintegervectorofthe reciprocallatticeofthemagneticcell. Ifk=1/2H,onecanusethechemicalunitcellandrealmagneticmoments. Insuchacaseonlyonepropagationvectorisneeded:ifNVKisgiven asnegativethegenerationofmagneticreflectionscouldbeinerror. Forcenteredcrystallographicunitcellsonecanuseonlythecontentof aprimitivecellandgeneratethesatellitesfromthesymbolofthe centeringfollowedby-1(e.g.I-1foraI-centeredcell).Inorder totaketheadvantageofthecrystallographicconventions(propagation vectorgivenwithrespecttothereciprocalbasisoftheconventional cell)onecanusethedimensionsandthemetricsoftheconvencional cellprovidedthat,puttingthecontentofaprimitivecellinthe conventionalcellframe,theocupationfactorsaremultipliedbythe numberofcenteringvectors.SeethetwofilesHOBK1.PCRandHOBK2.PCR intheanonymousFTParea. -----------------3.2:Background -----------------Backgroundintensityybiattheithstepisobtained(line2 and6*or10-2*)eitherfromanuser-suppliedtableof backgroundintensities(optionallines6*),orfromarefinable backgroundfunction ybi=SUM(Bm.(Ti/BKPOS-1)^m)+SUM(Bcjsin[Qidj]/Qidj) with0<=m<=5forNBCKGD=0,or0<=m<=11forNBCKGD=-3. Theoriginofthebackgroundpolynomialisgivenbyaselectable inputparameterBKPOS(line4)andshouldbesuppliedbytheuser. Thesecondsum(sixterms)isusedonlyifNBCKGR=-1.Theparameter toberefinedare: Bo,B1,...B5,Bc1,...Bc6,d1,...d6 QiisgivenbyQi=4pi.sin(Thetai)/Lambda(1) TheparametersdjaredistancesinAngstroms. ThebackgroundcanbealsoreadfromasuppliedfileFILE.BAC. Theactualbackgroundiscalculatedfromthereadbackgroundapplying thefollowingformula: Backg(2theta)=a*BackgRead[(1+c)2theta+d]+b
Thebackgroundparametersandcodes,giveninline10-2*,correspondto thecoefficientsoftheaboveformulainthefollowingorder:a,b,c,d. Ifaisgivenaszero,theprogramputsa=1.Limitsagainstdivergence arefixedbyprogram.Theparametercisallowedtovaryuptoa maximumvalueabs(c)=0.1andabs(d)iskeptbelow3degrees(2theta). Theusercanchektheexcursionofthoseparametersoutofthe allowedrangewhentheyarestrictlyzeroandtheirstandard deviationis(fixedarbitrarilyto)0.99999. Thisoptionisusefulwhencomplicatedbackgroundshapesarepresent duetosampleenvironment. Anewprocedurefortreatingthebackgroundhasbeenintroduced. Thebackgroundisajustediterativelyateachcyclebyusinga Fourierfilteringtechnique.Thestartingbackgroundisreadfrom afile.Atcycle"n"thenewbackgroundiscalculatedfromtheold one,cycle"n-1",withtheformula: Back(n)=Back(n-1)+Filtered[yobs-ycal](n-1) whereFiltered[yobs-ycal]isastronglysmoothedversion ofyobs-ycal.TheparametercontrollingthesmoothingisFWINDOW whichisequivalenttoPSTdescribedinsubroutineSMOOFTdescribed inNumericalRecipes(seeref19).TheimplementationofSMOOFTin FullProfisnotthesameasinref19. Whenusingthismethoditiswisetodrawthefinalbackground toseeifitisreallyasmoothcurve.Thisoptionisonly justifiableincasesofaverywavybackground.Thestarting backgroundshouldbeclosetotherealone. ---------------------------3.3:Peak-shapefunctions ---------------------------TheprofilefunctionisselectedbythecontrolvariableNPROF(line2). Thecurrentlyavailablefunctionsaregivenaboveandtheirparticular definitionscanbefoundintheliterature. --------------------------------------------------------3.4:Monochromator,Lorentzandgeometricalcorrections --------------------------------------------------------Monochromatorpolarizationcorrection(CTHMandKinline4); theLorentzpolarizationfactorLPiscalculatedas: LP=[1-K+K.CTHM.cos(2Theta)^2]/2(sinTheta)^2.cosTheta withCTHM=cos(2Thetam)^2.ForinstancewithaGraphite monochromator,CTHM=0.8351and0.7998forCuKbandCuKa respectively. NotethatKisusedonlyforsynchrotrondata(INSTRM=4, orILOR=3)anddoesnothavetobeinputforotherkindof data: -forneutrons,LP=1/2sin2Theta.cosThetai.e.Kisignored -forcharacteristicX-Rayradiation(unpolarizedbeam) theformulausedis: LP=[1+CTHM.cos(2Theta)^2]/2(sinTheta)^2.cosTheta thatcorrespondstothegeneralformulaaboveforK=0.5 multipliedby2.
-forsynchrotronradiation:Kmustbegiven(K~0.1) Inthetransmissiongeometry,flatplatewiththescatteringvector withintheplate(StoegeometryforX-rays,ILOR=2) thelorentzfactoris: L=1/sin2Theta andthepolarizationcorrectionisgivenby: P=K(1+c1cos2Theta^2)/(1+c1)+(1-K)(1+c2cos2Theta^2)/(1+c2) wherec1=sqrt(CTHM)=abs(cos(2Thetam)) c2=CTHM=(cos(2Thetam))**2 K=fractionofperfectcrystalcontribution Notethattheprogram,internally,calculatestheLorentzfactorcombined withtheabsortioncorrection.Anon-zeroabsorptioncoefficient(mt) mustbegiventogetcorrectresults(seesection3.7toknowthetotal correctionforthiscase). ----------------3.5:Asymmetry ----------------Asymmetrycorrection(RLIMinline4):theshapeofthe peaksbelowRLIMiscorrectedusingthesemi-empiricalfunction: A=1-P.sign(2Thetai-2Thetah).(2Thetai-2Thetah)2/tan2Thetak wherePisarefinableparameter. Theaboveformulaforasymmetrycorrectionhasbeenremovedfrom theprogram.Itwasreallyverybad!.Theexpressiongivenby Berar&Baldinozzi(J.Appl.Cryst,26,128(1993))hasbeenintroduced Theasymmetrycorrectionadoptsnowtheform: A=1+{P1Fa(z)+P2Fb(z)}/tanTheta+{P3Fa(z)+P4Fb(z)}/tan2Theta Wherez=(2Thetai-2Theta-shift)/FWHM, (Shiftincludesthezero-pointandothershiftingterms) Fa(z)=2zexp(-z^2),Fb(z)=2(2z^2-3)Fa(z) andhasfourindependentparameters,whicharereadatthesame placeasbefore. IfNPHASE<0themethodproposedbyC.J.Howard,inJ.Appl.Cryst.15 615-620(1982),isused.Theapproximationoftheconvolution integralisperformedusingtheBode'srule(Simpsonformulafor fivepoints).Theprofileiscalculatedasasuperpositionoffive profilefunctions(onlypseudo-Voigt#5and#7areimplementedfor thiscorrection)calculatedatdisplacedpoints: Omega(x)={7g(x)+32g(x+c2.P)+12g(x+c3.P)+32g(x+c4.P)+7g(x+c5.P)}/90 Wherex=2Thetai-2Theta-shift,Pistheasymmetryparameterand cotan(2Theta)=16.c2=4.c3=16/9.c4=c5
---------------------------3.6:Preferredorientation ---------------------------Twofunctionsarecurrentlyimplementedintheprogram: NORI=0-->TheusualRietveldfunction: Ph=(G2+(1-G2)*exp(G1*a^2)) whereG1andG2arerefinableparametersand aistheacuteanglebetweenthescattering vectorandthenormaltothecrystallites (plateyhabit). NotethatsettingG1toanynumber>99.0for aphasecausestheprogramtogeneratefor thatphaseonlythosereflectionsforwhich d*isparalleltothepreferredorientation vectorPREFspecifiedinline11.2. NORI=1-->March'sfunction Ph=G2+(1-G2)*((G1cosa)^2+(sina)^2/G1)^-1.5 whereG1isarefinableparameter.Thisexpressionis adaptedbothtofiberandplateyhabits: G1<1plateyhabit(aistheacuteanglebetween thescatteringvectorandthenormaltothe crystallites) G1=1nopreferredorientation G1>1needle-likehabit(aistheacuteanglebetween thescatteringvectorandthefiberaxis direction) NotethatthesevaluesofG1correspondtothe BragggeometryofusualX-raypowder diffractometer,fortheDebye-Scherrergeometry ofmostneutronpowderdiffractometersthe oppositeholds. TheparameterG2representsthefractionofthesamplethat isnottextured.Theprogramputitsvaluebetween0and1 incaseofdivergence. ---------------------------------------3.7:Absorption(andmicroabsoprtion) ---------------------------------------Absorptioncorrection:forDebye-Scherrerdata,intensitiesmaybe correctedfortheeffectsofsampleabsorptionbyapplyingthe followingtransmissionfactor: Th=exp[-(1.7133-0.0368sinTheta^2)mR+(0.0927+0.375sinTheta^2)(mR)^2] wheremisthelinearabsorptioncoefficientandRtheradius ofthecylindricalsample. ForaflatplateintransmissiongeometryforX-rays(ILOR=2) theabsorptioncorrectionisimplementedas:
Th=exp(-mt/cosTheta)/cosTheta wheretisthe"effective"thicknessofthesample.Theproductmt isgiveninthesameplaceasmR. ForBragg-BrentanogeometryinX-raysanangular-dependent microabsorptioncorrectionhasbeenintroducedfollowingreference20. ThefactorThbecomes: Th--->ThSr=Th(1-P) whereSrisgivenbytheformula6ofthefirstreference20(or Pisgivenbyformula17ofthesecondreference20). P=P0*Cp*(Tau/sinTheta)*(1-Tau/sinTheta) Thelimitationsanddegreeofapplicabilityoftheaboveformulaare explainedinreference20. ----------------------------3.8:Systematiclineshifts ----------------------------SystematiclinepositionerrorsD2Theta:powderdiffractiondataare sometimesaffectedbysystematicaberrationsarisingeitherfromthe sampleitselforfromanimpropersettingofthesampleor diffractometer.FullProfgivesthepossibilitytocorrectfortwoof themostcommonlyoccurringerrorsbyrefiningtheparameterscalled SYCOSandSYSIN(line10-1).Theseparametersrelatetoerrorshaving acosThetaandsin2Thetadependency,respectively.Thecorrespondingerrors originatefromadifferentphysicalor/andgeometricalproblem dependingonthediffractiongeometry.Theyaresummarizedbelow: a)Bragg-Brentanoparafocusingarrangement:thetwolargestsystematic aberrationsofTheta-2Thetapowderdiffractometersoperatinginthisgeometr y arisefromspecimendisplacementandtransparency;thesample displacementerrorisoneofthelargestsystematicerroraffecting linepositionsinthisgeometry.Itisgivenby: D2Theta=-2s/RcosTheta[inradians] wheresisthedisplacementofthesamplesurfacewithrespecttothe axisofthegoniometerandRtheradiusofthegoniometercircle. Thenegativesignmeansthatadisplacementawayfromthecenterof thefocusingcirclemovesthediffractionlinestolower2Thetaangle. TherefinableparameterisSYCOS=-2s/R.Thisisbyfarthelargest systematicaberrationinthisgeometry.Astheanglesareexpressed indegreesinFullProf,thesampleoffsetcanbecalculatedas: s=pi.R.SYCOS/180 Thetransparencycorrectionisgivenbytherelation: D2Theta=1/(2mR)sin2Theta[inradians] wheremisthelinearabsorptioncoefficientofthesample. Thisrelationholdsinthecaseofthickabsorbingsamplesandthe refinableparameterisSYSIN=1/(2mR).Forthintransparentsamples, thecorrectionwouldwrite:
D2Theta=t/RcosTheta[inradians] wheretisthesamplethickness;this(lessusual)correctionisnot explicitlyincludedinthecodebutcanbeaccountedforbythe displacementcorrectionwhichturnsouttoshowthesame2Thetadependency. Notehoweverthatsamplesrequiringthatkindofcorrectionwouldalso givebiasedintegratedintensities;correctionforthiseffectisnot implementedinFullProf.Forfurtherdetailsonsystematicaberrations inBragg-Brentanogeometry,see[13]. b)Debye-Scherrer:thelargestshiftsofDebye-Scherrerringsresultfrom sampleoff-centeringandabsorption.Eccentricityperpendiculartothe incidentbeamdirectionisnormallyasecondordereffectifbothsides oftheDebye-Scherrerringaremeasured. Ifonlyonesideoftheconeismeasured,thelineshifttakestheform: D2Theta=e/RcosTheta[inradians] whereedenotestheeccentricity,thatistherefinedparameteris SYCOS=e/R. Eccentricityintheincidentbeamdirectionisobservedinbothcases andtakestheform: D2Theta=e/Rsin2Theta[inradians] i.e.,therefinedparameterisSYSIN=e/R.Thecorrectionisnegative forashiftalongthebeamdirectiontowardsthedetector. Forhighlyabsorbingspecimenwithradiusr,diffractionislimitedto acylindricalsurfacelayerresultinginamaximumpeakshift: D2Theta=r/RcosTheta[inradians] i.e.,inthiscase,SYCOS=r/R.Thelattereffectalsoleadsto disymmetricallineprofiles. c)Curvedpositionsensitivedetectorwithflatplatesample:forthe asymmetricgeometryofdiffractometersusingacurvedpositionsensitive detector(CPSD)withaflat-platesample,thedisplacementcorrection takestheform: D2Theta=-s/(R.sina)sin2Theta[inradians] whereRistheradiusoftheCPSandatheincidentbeamangle (indegrees)atsamplesurface.Thus,theparameterrefinedbyFullProf isSYSIN=-s/(R.sina).Thenegativesignmeans,asinthecaseof Bragg-Brentanogeometry,thatadisplacementawayfromthecenterof thefocusingcirclemovesthediffractionlinestolower2Thetaangle;the valueofthesampleoffsetisgivenby: s=pi.R.SYSIN.sina/180 -----------------3.9:Codewords ------------------
CodewordsCxtheyareenteredforeachrefinedparameter. Azerocodewordmeansthattheparameterisnotbeingrefined. Foreachrefinedparameter,thecodewordisformedas: Cx=sign(a).(10p+|a|) wherepspecifiestheordinalnumberoftheparameterx (i.e.prunsfrom1toMAXS)anda(multiplier)isthefactorbywhich thecomputedshiftwillbemultipliedbeforeuse. Thecalculatedshiftsarealsomultipliedbyarelaxationfactor (line5)beforebeingappliedtotheparameters. ---------------------------3.10:Standarddeviations ---------------------------Standarddeviationsareestimatedfromtheformula: si=|a|.[Chi2*Mii]1/2 whereaisthecoefficientofthecodewordfortheparameter Miiisthecorrespondingdiagonalelementintheinvertedmatrix TheChi2indexusedintheaboveformulaisalwayscalculatedfor thepointsinthepatternhavingBraggcontributions,thussicould begreaterthanthecorrespondingvaluecalculatedwithotherprograms. AsChi2iscalculatedintwoways(seebelow)theusercaneasily calculatetheothervalue. ---------------------------3.11:Methodofrefinement ---------------------------Leastsquaresrefinement(thestandardmethod): Mp=Sum(i){wi(yoi-yic)^2} theweightsoftheobservationsarecalculatedas: wi=1/variance(obs)i Maximumlikelihoodrefinement:theweightsoftheobservations arecalculatedateachcycleas: wi=1/variance(calc)i -------------------------3.12:Agreementfactors -------------------------Thequalityoftheagreementbetweenobservedandcalculatedprofiles ismeasuredbyasetofnowadaysconventionalfactors.InFullProf twosetsofindicesarecalculated,accordingtothemeaningofthe integerN.InthefirstsetNisthetotalnumberofpointsusedin therefinement(N=NPTS-NEXC=totalnumberofpointsinthepatterntotalnumberofexcludedpoints).Inthesecondsetonlythosepoints wherethereareBraggcontributionsaretakenintoaccount.The definitionoftheindicesisasfollows: TheprofileRp=100Si|yoi-yci|/Si|yoi|
TheweightedprofileRwp=100[Siw|yoi-yci|2/Siw|yoi|2]1/2 TheBraggRB=100Sk|Ik-Ick|/Sk|Ik| TheexpectedRexpected=100[(N-P+C)/Si(wiyoi2)]1/2 ThegoodnessoffitChi2=[Rwp/Rexpected]^2 whereN-P+Cisthenumberofdegreesoffreedom (ThemeaningofNhasbeengivenabove,Pthenumberofrefined parametersandCthenumberofstrictconstraintfunctions). Excludedregionsarealwaysexcludedfromthecalculationof allagreementfactors. ConventionalRietveldR-Factors:cRp,cRwparecalculatedasabove butusingbackgroundcorrectedcounts. ThemagneticR-factorisdefinedastheBraggRB-factorbutisapplied tomagneticintensities. The"observed"integratedintensityIkisinfactcalculatedfromthe Rietveldformula: Ik=IckSi{Omeg(Ti-Tk)(yoi-Bi)/(yci-Bi)} Thisformulaisequivalenttoa"proportionalsharing"ofthe integratedintensityofaclusterbetweenitscomponentsaccording totheactualmodel.Then,ifthemodelcontainsastrictlyzero integratedintensityforthecomponent"k"(Ick=0),theobserved integratedintensityisalsozero:Ik=0,evenifitisobviousthat Ikisnotzerofromtheexperimentalpattern.Thishasasaconsequence thatthereflectionswithIc=0donotcontributetotheBraggR-factor. Althoughcommonlyusedincrystallography,theRp,Rw,RBagreementfactors arenotsatisfactoryfromastatisticalpointofview.Therefore,anumberof statisticallymoresignificantparametersarecalculatedbyFullProf: a)thedeviance[15]definedas: D=2Sum(i){yioln(yio/yic)-(yio-yic)} b)fromthedeviance,onecanderivetwoothermeasuresofdiscrepancywhich areusefulasmodelselectioncriteria(somewhatanalogoustoHamilton's criterion).Thesecriteriatakeaccountofboththegoodnessoffitofa modelandofthenumberofparametersusedtoachievethatfit.Theytake theform: Q=D+a.maxs wheremaxsisthenumberofrefinedparametersandarepresentsthe"cost" offittinganadditionalparameter.Akaike'sinformationcriterionuses a=2whileSchwarz'scriterionhasa=ln(maxs). c)theDurbin-Watsonstatisticparameters:dandQ.Theuseofthesetwo quantitiestoassessthequalityoftherefinementhasbeadvocatedby HillandFlack[16].Thisstatisticwhichmeasuresthecorrelationbetween adjacentresiduals(serialcorrelation)isdefinedas: d=Sum(i=2toN){[wi(yi-yic)-w(i-1)(y(i-1)-y(i-1)c)]^2}/Sum(i){[wi(yi-yic)]^2} Serialcorrelationistested(atthe99.9%confidencelevel)bycomparing
thevalueofdtothatofQwhichisgivenbytherelation: Q=2{(N-1)/(N-P)-3.0902/Sqrt(N+2)} Threecasesmayoccur: -ifd<Q,thereispositiveserialcorrelation:successivevaluesof theresidualstendtohavethesamesign.Thisisthemostcommon situationinprofilerefinement. -ifQ<d<4-Q,thereisnocorrelation -ifd>4-Q,thereisnegativeserialcorrelation:successivevaluesof theresidualstendtohaveoppositesign. --------------------------------3.13:Analysisoftherefinement --------------------------------Anempricalanalysisoftherefinementhasbeenintroducedattheendof thefileCODFIL.SUM.Apartfromsomesubjectivecommentsthatcouldappear inthatanalysistherearesomeimportantquantitiesthathavetobeknown bytheusersbecausetheyhavenotbeenpublishedyet. -ExpectedRpfactorsarecalculatedsupposingthebestpossiblemodel. Rp=Sumabs(Yiobs-Yical)/Sum(Yiobs),whereYicaliscalculatedwith thehelpofaPoissonianfunction,Genpoi(x),fromYiobs.Theargument ofGenpoiisanintegervaluerepresentinganobservationwhichis equaltotheirvariance,Genpoireturnsanotherpossiblevaluecompatible withthedeterministicvaluexofvariancex.Thevalueofxis calculatedformYiobsandVariance(Yiobs)asfollows: c1=Yiobs/Var(Yiobs) x=Yiobs*c1 Yical=Genpoi(x)/c1 -Thepercentageofthecontributiontothetotalintegratedintensity (Sum(Iobs)forallphases)ofeachphaseisnowwritten. -Thenumberofrefinedparametersdistributedinthreeclassesare written: Nglb:Numberofglobalparameters(notdependingofthephaseindex) Nprofp:Numberofprofileparameters. Nintdp:Numberofintensity-dependentparameters(x,y,z,B,occ,Mx...) Thepreferredorientantionparametersareincludedinthis class. -Aneffectivenumberofreflectionsiscalculatedinordertogetthe ratioRefni=(EffectiveNumberofReflections)/Nintdp=Enref/Nintdp. -Theconceptofeffectivenumberofreflectionsisintroducedinorder totakeintoaccounttheeffectoftheresolutionintherefinement. Itisclearthatwellseparatedindependentreflectionsgivebetter resultsthatwhenthereflectionsareoverlaped.Aglobaleffective numberofreflectionsiscalculatedbytheprogram.Foreachphase, asimilarindicatoriswritten. Areflectioncontributesasx/(x+nearest),where"x"isthe fractionofthetotalareaofthecurrentphaseand"nearest"is thenumberofadjacentreflectionsverifyingtheformula:',
2theta-p*FWHM<=2theta(adjacent)<=2theta+p*FWHM "nearest"isweightedbythecorresponding"x(s)",andpis aparameterlowerthanunity. Thegeneralformulaforcalculatingtheglobaleffectivenumber ofreflectionsis: Enref=Sum(i){x[ph:i]/Sum(ni){x[ph:ni]}} whereSum(i)isasumoverallthereflectionscontributingtothe allowedareasofthediffractogram.Sum(ni)isthesumextendedto thereflectionsneartothereflection"i"(includingthisreflection). Thesymbolx[ph:i]isthe"x"-valueofthephasetowhichthereflection "i"belongs. Thesameformularestrictedtoreflectionsofasinglephaseisapplied tocalculateEnref(Iphase):Effectivenumberofreflectionsofthe phaseIphase. Theprogramcalculatesthesenumbers(Enref's)andtheratios(Refni's) forthreevaluesoftheparameterp(1,1/2and1/4).
4.-ADDITIONALNOTES
--------------------------4.1:MagneticRefinements --------------------------Foraconmensuratestructuretwodescriptionsofthemagnetic structurearepossible:thegeneralformalismusingfourier componentsofmagneticmomentsthroughthepropagationvectorsor acrystallographic-likedescriptionusingthemagneticunitcell. Themostsimpleone,foranon-expertuser,istodescribethe magneticstructureinthemagneticunitcell.Inthatcasetwo importantpointsmustbetakenintoaccount: a)Formagneticstructuresdescribedinamagneticunitcelllarger thanthecrystallographiccell,thecoordinatesofatomsmustbe changedconsequently,aswellastheunitcellparameters. Thecodesforcommon(orrelated)parameterwiththecrystallographic counterpart,mustbechangedapplyingathecorrectmultiplicative factor.Itisworthstressingthatcodesforcellparametersare actuallyappliedtothe"cellconstants"definedby: 1/d2=Ah2+Bk2+Cl2+Dkl+Ehl+Fhk Therefore,ifyouaredealingwithanorthorhombicstructure whichhasamagneticstructurewithpropagationvectork=[1/200] youhavetousethemagneticunitcell2xa,b,candifthecodes ofthecrystallographicunitcella,b,careforexample: Cellabc909090 CodeCell81.0091.00101.00000 thecorrespondingvaluesforthemagneticcounterpartare:
Cell2abc909090 CodeCell80.2591.00101.00000 thereasonisthatthecrystallographiccellconstantAis inthiscase:Ac=1/a**2andthemagneticcellconstantis Am=1/(2a)**2=0.25*Ac.Asexplainedabove,themultiplicative factorisappliedtoshiftsofparameters. b)Thescalefactorsofthecrystallographicandmagneticparts havetoberelatedinsomewayinordertogetgoodvalues ofmagneticmoments.Thisrelationdependsonthewaythe usersdescribesthemagneticstructure,howeverseveralrules canbeusefultoavoidbulkerrors: i)Usethecorrectoccupationnumbersinthecrystallographic part(=multiplicityofspecialposition/generalmultiplicity) ii)Thenumberofmagneticatomsinthechemicalunitcellmust coincidewiththedescriptionabove,thereforetheoccupation numbersinthemagneticpartarerelatedtothenumberof symmetryoperatorsgiven,thecentrosymmetry(ornot)ofthe magneticstructure. Iftheserequirementsaresatisfiedandthemagneticunitcell isthesameasthechemicalone,thescalefactorsarestrictly thesamenumbers;and,thereforerepresentsthesameparameter withashiftequaltounity. Ifthemagneticunitcellisamultipleone,andtheabove requirementsaresatisfied,therelationbetweenthescale factorsisamultiplicativefactorgivenby: Sc:crystallographicscalefactor Sm:magneticscalefactor Sm=1.0/(Volm/Volc)**2Sc Inthecaseoflargemagneticcellsitcanbemoreconvenienttomodify theoccupationnumbersofmagneticatomsinsuchawaythatthetwoscale factorscoincide. Forincommensuratemagneticstructuresthegeneralformalismmustbeapplied. Whenthemagneticstructureisdescribedusingtheformalismofpropagation vectors,thecomponentsMx,My,Mznolongerrepresenttruemagneticmoments. Theusershouldbecautiousininterpretingtheoutputfiles.Themodulusof the"magneticmoment"representtheFouriercomponentmodulusofanatomic magneticmomentwhichhavetobecalculatedexternally.Thecalculationof theintensityisbasedontheexpressionofmagneticstructurefactorgiven inmathematicalsection,thereforetheuserknowshowtoplaywithhisinput itemsinordertoobtainphysicallysoundresults. Forsphericaldescriptionofthemagneticmomentsthefollowingmustbe takenintoaccount: Theorthonormalsystemwithrespecttowhicharedefinedthe sphericalanglesverifies: XaxiscoincideswiththecrystallographicA YaxisbelongstotheplaneA,B ZaxisisperpendiculartotheplaneA,B
Theparticularimplementationofsphericalcomponentsinmagnetic structurerefinementsisthatZaxismustcoincidewithC.That worksinallcrystallographicsystemsexceptfortriclinic.The monoclinicsettingmustbechangedto->112/mtosatisfythe aboveprescription. -------------------------4.2:Propagationvectors -------------------------Acompletelistofreflectionscanbegeneratedwhenpropagationvectors ofanincommensuratestructurearepresent.Toeachfundamentalreflection itisaddedthecorrespondingsatellites.Fornpropagationvectorsk1, k2,...kn,therearensatellitesobtainedfromeachfundamentalreciprocal latticevectorh: Fundamentalreflection:h=[h,k,l] Satellitesh1=h+k1,h2=h+k2,...hn=h+kn Inthepresentversionoftheprogramnosymmetryanalysisisperformed. WerecommendtousethetriclinicspacegroupL-1(whereL=P,A,B,C,F,I,R) inordertohaveafullsetofreflectionswiththepropermultiplicity whenthetruemagneticsymmetryisnotknown. Theprogramgeneratesfirstalistofuniquereflectionscorresponding totherequiredspacegroupandthenaddsthesatellites.Thismethod hadtobemodifiedforreflectionsbelongingtotheboundaryplanes andlinesoftheasymmetricregionofthereciprocalspaceinorder toobtainthecorrectnumberofreflectionsandnotmiss(orrepeat) someofthem.Becarefulwithpropagationvectorskequivalentto-k!. Twovectorsk1andk2are"equivalent"ifk1-k2isavectorofthe reciprocallattice.So,fork2=-k1,ifK=2*k1belongstothereciprocal lattice,k1is"single"andbelongstoapointofhighsymmetryofthe BrillouinZone. InsuchcasesonlyONEpropagationvectorsshouldbeintroducedNVK=1, iftheuserputsNVK=-1,thesatellitereflectionsarenotcorrectly generated. Forcenteredcellsapropagationvectorkhavingcomponents+-1/2, verifiesthat2khasintegercomponents,butthatdoesnotmean thatkand-kareequivalent,because2kcouldnotbelongtothe reciprocallattice.ForaClatticethepropagationvector k1=(1/200)isnotequivalenttok2=(-1/200)becauseK=2*k1=(k1-k2) K=(100)doesnotbelongtothereciprocallattice:h+k=2nisthe latticeCconditionforcomponents(hkl).Onthecontrary,the vector(001/2)is"single"because(001)isareciprocallatticepoint oftheClattice. ------------------------------------------------------------------------------4.3:Microstrainsanddomainsizeeffects.HKL-dependentshiftsandasymmetry. ------------------------------------------------------------------------------Inrealmaterialsitisfrequenttofindmoreorlessstrongmicrostructure effectsintheshapeandwidthofBraggreflections.Thecapabilities oftheprograminordertohandletheseeffectsisreflectedintwo subroutines(STRAINandSIZE)whichcalculatethebroadeningofBragg reflectionsasafunctionofhklandasetofmicrostructuralparameters dependingdefiningamodel. Ingeneralthebroadeningofreflectionsduetomicrostrainshasanangular
dependenceoftheform:DFWst=etan(Theta).Thecorrespondingdependencefor the sizeeffectisgivenbytheScherrerformulaDFWsi=c/cos(Theta).Thereaderi s referredtotheliteratureforfurtherdetails. AnincreaseoftheUhalfwidth-parameterwithrespecttotheinstrumental valueisindicativeofthepresenceofmicrostrains.Thevalue(U-Uins)is anestimateoftheisotropicbroadening.TheparameterIG(line11-6-1)is ameasureoftheisotropicsizeeffect. strain(gaussian)=(pi/1.8).Sqrt(U-Uins)(in%) size(gaussian)=180KLambda/(pi.sqrt(IG))(Lambda&sizeinA) whereKdenotestheScherrercrystalshapeconstantneartounity. Iftheusertriestoobtainthemaximumphysicallysignificantinformation onthemicrostructureofhis(her)sample,theprofilefunctionNPROF=7must beused.Onlyinthatcasecanbeperformedacorrectconvolutionofthe instrumentalfunctionwiththeintrinsicprofilefunction(consideredboth asVoigtians).InthecaseNPROF=7,isotropiclorentzianandgaussiancontributionsofsizeandmicrostrainsarerepresentedbythefollowingparameters: GaussiancomponentLorentziancomponent Size:sqrt(IG)Y Strainsqrt(U)X TheFWHMofthegaussianandlorentziancomponentsoftheVoigtfunction forNPROF=7iscalculatedusingtheexpressions: FWHM^2(gaussian)=[U+c.DST(STR)^2]*Tan^2(Theta)+V*Tan(Theta) +W+IG/cos^2(Theta) FWHM(lorentzian)=Xtan(Theta)+(Y+F(SZ))/cos(Theta) TheisotropicparticlesizebroadeningYprovidesasizevaluegivenby: size(lorentzian)=180KLambda/(pi.Y)(Lambda&sizeinA) K=FWHM/Integral-Breadth=2/piforalorentzian (withsuchvalueforK,sizerepresentthevolumeaverageddiameter ofcrystallitesinalldirections) Foranisotropiccontributions{DST(STR)andF(SZ)}theactualversionof FullProfhasthefollowingsetofmicrostructuralmodels: Sizeeffect:{onlylorentziancomponentistakenintoaccountforanisotropic broadeningofsizeoriginthroughF(SZ)} ISTR=0andIsizeModel/=0{IntegertoselectaparticularmodelforF(SZ) insubroutineSIZE} IsizeModel=1Plateletcoherentdomains.F(SZ)isassumedto beoftheformF(SZ)=SZ*cos(phi),whereSZistherefined parameterandphiistheacuteanglebetweenthescattering vector(h,k,l)andthevectordefiningtheplatelet shapeofdomains{[Sz1,Sz2,Sz3]inline11-9*} IsizeModel=-1Needle-likecoherentdomains.F(SZ)isassumedto beoftheformF(SZ)=SZ*sin(phi),whereSZistherefined parameterandphiistheacuteanglebetweenthescattering
vector(h,k,l)andthevectordefiningtheneedle shapeofdomains{[Sz1,Sz2,Sz3]inline11-9*} IsizeModel=2to7,inthesecasesthebroadeningisconsideredonly forreflectionsoftheform:(00l),(0k0),(h00),(hk0), (h0l)and(0kl).Thefunctionis:F(SZ)=SZ. IsizeModel=8Onlysatellitesreflectionsareconsideredtobebroadened. InthiscasealsoF(SZ)=SZ. IsizeModel=9Reflections(HKL)withH=2n+1andK=2m+1arebroadened. InthiscasealsoF(SZ)=SZ. IsizeModel=10Reflections(H0L)withH+L=2narebroadened. InthiscasealsoF(SZ)=SZ. IsizeModel=11Reflections(HKL)except(HHL)arebroadened. InthiscasealsoF(SZ)=SZ. IsizeModel=12Reflections(HKL)withH=2n+1arebroadened. InthiscasealsoF(SZ)=SZ. IsizeModel=13Reflections(HKL)withH=2nandK=2m+1arebroadened. InthiscasealsoF(SZ)=SZ. ISTR>1:Ageneralizedformulationofthesizeeffectisappliedandthe sizeparameters(uptosix)aregiveninline11-14*. InthatcasetheF(SZ)functionisgivenby: F(p1...p6)=180Lambda/(pi^2)*d(hkl)^2*Quad(p1...p6) Quad=p1h^2+p2k^2+p3l^2+2(p4hk+p5hl+p6kl) wherethesizeparametersarep1,p2,...p6. Thisformulationassumesthattheaveragediametercanbe expressedasanellipsoidofrefinableparametersp1..p6.Therefore =d(hkl)*Quad Straineffects:{onlygaussiancomponentistakenintoaccountforanisotropic broadeningduetostrainsthroughDST(STR)} ISTR=0andIstrainModel/=0{IntegertoselectaparticularmodelforDST(STR ) insubroutineSTRAIN} FWHM(strain)=DSTtanTheta=cSigma(1/d^2)/(1/d^2)tanTheta theconstantcisequalto2sqrt(Ln2)(180/pi).Intheprogramthe effectivevalueusedisc*10e-3,thereforeitisnecessarytodivide therefinedstrainparametersby1000.Theusercanconsultthemodules FDUM's.FORfordetailsandreference17. IstrainModel=1Orthorhombicstraininatetragonallattice. RefinedparameterSTR1. IstrainModel=2Strainalong"a"inanorthorhombiclattice. RefinedparameterSTR1. IstrainModel=3Strainalongadiagonaloftheabplaneinanorthorhombic latticeforwhichanequivalentmonoclinicdoublecellhas
beenused. RefinedparameterSTR1. IstrainModel=4Sameas3butstrainsalongthetwodiagonals. RefinedparametersSTR1,STR2. IstrainModel=5Straininanorthorhombiclatticewithfluctuationsalong "a"and"b"andcorrelationbetween"a"and"b". RefinedparametersSTR1,STR2,STR3. IstrainModel=6Straininanorthorhombiclatticewithfluctuationsalong "a","b"and"c"andcorr(a,b)=-1,corr(a,c)=1,and corr(b,c)=0. RefinedparametersSTR1,STR2,STR3. IstrainModel=7Uniaxialmicrostrain.DST(STR)isassumedtobeofthe formDST(STR)=STR1*cos(phi),whereSTR1istherefined parameterandphiistheanglebetweenthescattering vector(h,k,l)andthevectordefiningtheaxialdirection ofstrains{[St1,St2,St3]inline11-10*} IstrainModel=8Generalanisotropicstrainofhexagonalsymmetry. (Seeref.17) STR1=Saa=Sigma(A),STR2=Scc=Sigma(C)STR3=Cac=Correl(A,C) 1/d^2=SQ=A(h^2+k^2+hk)+Cl^2=Am^2+Cl^2 Var(SQ)=Saa^2m^2+Scc^2l^4+2SaaSccCacml^2 FWHM^2(strain)=Var(SQ)(P/SQ)^2 {P=180/pi*sqrt(8Ln2)1.E-03tan(theta)} IstrainModel=9StrainadaptedforcompoundsLaNi5-like.Formulaby: P.Thompsonetal,J.LessCommMet129,105-114(1987) Fourparam.:GaussianFWHM=Sqrt(Sumj[S(j)])tan(theta) STR1->S(1)=xPar(1) STR2->S(2)=l^4/(h^2+k^2+l^2)xPar(2) STR3->S(3)=(h^2k^2+k^2l^2)/(h^2+k^2+l^2)xPar(3) STR4->S(4)=h^2k^2/(h^2+k^2+l^2)xPar(4) IstrainModel=10Generalanisotropicstrainfororthorhombicsymmetry. (Seeref.17) 6strainparameterscorrespondingto: STR1=Saa=Sigma(A),STR2=Sbb=Sigma(B),STR3=Scc=Sigma(C), STR4=Cab=Corr(A,B),STR5=Cac=Corr(A,C),STR6=Cbc=Corr(B,C) Where: SQ=Ah^2+Bk^2+Cl^2 Var(SQ)=Saa^2h^4+Sbb^2k^4+Scc^2l^4+ 2SaaSbbCabh^2k^2+ 2SaaSccCach^2l^2+
2SbbSccCbck^2l^2 FWHM^2=Var(SQ)(P/SQ)^2 {P=180/pi*sqrt(8Ln2)1.E-03tan(theta)} IstrainModel=11Generalanisotropicstrainformonoclinicsymmetrybeing thesettinggamma/=0(2-foldaxisalong001) (Seeref.17) {limitedto8parameterbyputtingarbitrarilyzero twocorrelationvalues(Cad=Cbd=0)} 8strainparameterscorrespondingto: STR1=Saa=Sigma(A),STR2=Sbb=Sigma(B),STR3=Scc=Sigma(C),STR4=Sdd=Sigma(D), STR5=Cab=Corr(A,B),STR6=Cac=Corr(A,C),STR7=Cbc=Corr(B,C),STR8=Ccd=Corr(C,D) Where: SQ=Ah^2+Bk^2+Cl^2+Dhk {Saa^2SaaSbbCabSaaSccCac0}(h^2) {SaaSbbCabSbb^2SbbSccCbc0}(k^2) Var(SQ)=(h^2,k^2,l^2,hk){} {SaaSccCacSbbSccCbcScc^2SccSddCcd}(l^2) {00SccSddCcdSdd^2}(hk) FWHM^2=Var(SQ)(P/SQ)^2 {P=180/pi*sqrt(8Ln2)1.E-03tan(theta)} ISTR=1,3Thegeneralizedformulationofthestrainbroadeningisused and10parameterarereadinline11-13*.Theformalismis thatdescribedinreference17.Thestrainparameterscorrespond tothefluctuationsandcorrelationsofdirectcellparameters. Thelowersymmetryismonoclinicwiththeconventionalsetting. Thehexagonallatticeistreatedasaspecialcase. Strainparameters:Px=sigma(x),x,y=a,b,c,beta corr(x,y)=sin(Pxy) TheparameterPxyisanangleindegrees.Thisparticulardescription isfortakingintoaccountthatcorr(x,y)=covar(x,y)/(sigma(x).sigma(y)) andmustbelongtotheinterval[-1,1].Thestrainparametersareread inthefollowingorder: Pa,Pb,Pc,Pbeta,Pab Pac,Pabeta,Pbc,Pbbeta,Pcbeta Note: ----Insomecasestheuseofsize-strainoptionsoftheprogram,thecomputing timeisgreatlyincreased.Thisisrelatedtothefactthatthenumber ofreflectionscontributingtoeachparticularpointofthediagram increasesbecausethebroadeningisquiteimportant.Anexcessive computingtimemayindicateadivergenceoftherefinementthathas attributedatoomuchlargeFWHMtosomereflections.
-----------------------------------HKL-dependentshiftsandasymmetry. -----------------------------------Asapartofmicrostructuraleffects,theprogramcanhandlesomecases ofpeak-shiftsandasymmetryeffects.Nohkl-dependentasymmetrymodelis currentlyavailable.Twomodelsareavailableforpeak-shifts: ISHIF=1/-1 Uniaxialshiftsalongadirection[S1,S2,S3] ShiftofBraggreflectionsoftheform: Shift(hkl)=Shift1*cos(Phi(hkl))(Ishif=1) orShift(hkl)=Shift1*sin(Phi(hkl))(Ishif=-1) WherePhiistheangle:between[hkl]and[S1,S2,S3] ISHIF=2 Shift(hkl)=Shift1*Coeff(hkl)*tan(Theta(hkl)) TheparameterCoeff(hkl)mustbegivenbyuserinthefilefromwhich Braggreflectionindicesandmultiplicitiesareread. ThisoptioncannotbeusedsimultaneouslywiththeoutputofaFourier file,soJFOUissettozeroytheprogram. -----------------------------------4.4:Quantitativephaseanalysis -----------------------------------Forquantitativeanalysisitisessentialthattwoconditionsarefulfilled: -samplemustbecarefullypreparedtocomplytothedefinitionofapowder: homogeneity,sufficientnumberofparticleswithrandomorientation -structurefactorsmustbecorrectlycalculated AccordingtoBrindley,itisconvenienttoclassifymixedpowdersaccordingto thevalueoftheproductmDwheremisthelinearabsorptioncoefficientandD ameasureofthelinearsizeofaparticle.Fourcasesmustbeconsidered: -finepowders:mD<0.01 Theindividualparticlesofthepowderhavenegligibleabsorptionandno correctionhastobeappliedtothedata -mediumpowders:0.01<mD<0.1 -coarsepowders:0.1<mD<1 -verycoarsepowders:mD>1 InamixtureofNcrystallinephasestheweightfractionWjofphasejisgiven by: Wj={SjZjMjVj/tj}/Sum(i)[SiZiMiVi/ti] whereSjisthescalefactorofphasej Zjisthenumberofformulaunitsperunitcellforphasej Mjisthemassoftheformulaunit Vjistheunitcellvolume tjistheBrindleyparticleabsorptioncontrastfactorforphasej definedas:
tj=(1/Vj)Integ[exp{-(mj-mu)x}dVj] whereVjisthevolumeofaparticleofphasej mjistheparticlelinearabsorptioncoefficient muisthemeanlinearabsorptioncoefficientofthesolidmaterial ofthepowder xisthepathoftheradiationintheparticleofphasejwhen reflectedbythevolumeelementdVj Thelatterparameteraccountsformicroabsorptioneffectsthatbecomeimportant whenthecompoundsofthepowderhaveratherdifferentlinearabsorption coefficients.Itscalculationrequiresonlytheknowledgeoftheparticle radiusRandlinearabsorptioncoefficientm.Valuesoftasafunctionofthe product(mj-mu)RhavebeentabulatedbyBrindleyandarereproducedbelow: RtttRttt (mj-mu)(2Th=0)(2Th=90)(2Th=180)(mj-mu)(2Th=0)(2Th=90)(2Th=180) -----------------------------------------------------------------------------0.502.0682.0362.029-0.401.8131.8071.827 -0.301.5081.5731.585-0.201.3521.3531.362 -0.101.1591.1621.163-0.091.1421.1431.144 -0.081.1241.1251.125-0.071.1071.1081.108 -0.061.0901.0911.091-0.051.0741.0731.074 -0.041.0591.0581.059-0.031.0431.0421.042 -0.021.0281.0271.027-0.011.0141.0141.014 0.001.0001.0001.0000.010.9860.9860.986 0.020.9720.9730.9730.030.9590.9600.960 0.040.9450.9460.9470.050.9320.9330.934 0.060.9180.9190.9210.070.9050.9060.908 0.080.8920.8930.8950.090.8780.8790.882 0.100.8650.8660.8700.200.7420.7530.760 0.300.6400.6530.6710.400.5450.5690.587 0.500.4680.4960.529 R.J.Hill&C.J.Howard,J.Appl.Cryst.20,467-476(1987) G.W.Brindley,Phil.Mag.36,347-369(1945) ------------------------------------------------------------------------------4.5:User-suppliedparameters&subroutinesfor structure-factorcalculation. ------------------------------------------------------------------------------Somepowderdiffractionapplicationsneeduser-suppliedparametersand subroutinescalculatingthestructurefactors.Examplesofthiskindof applicationsarethefollowing: -Formfactordetermination. -Rigidbody-generalizedcoordinatesrefinements. -TLSrefinements. -Descriptionofincommensuratephasesinrealspace(notFourier components)bysomesimpleparameters. -Anharmonicdisplacementparameters. Todothat,theusercanpreparehis(her)ownsubroutinesandlinkthe objectFDUM1,FDUM2,FDUM3,...withtherestofthemodulesandtheFullProf library. Forcrystalstructuresthesubroutinetocalculatethestructurefactor
squaredforareflection(hkl)mustbecalledSTRMOD.Foramagnetic phasethenameisMAGMOD.Examplesofthesearecontainedinthepublic sourcecodeFDUM's.FOR. Theusercanalsomodifyorintroducenewmodelsforstrainsandsize effectsinthesubroutinesSIZEandSTRAINwhicharealsoincludedin FDUM's.FOR Usefulinformationforusersconcerningtheinternalparameters: Theparameters(refinablevariables)usedinFullProfaredividedinthree categories:Globalparameters,AtomparametersandPhaseparameters.For eachcategorythereisanarraytostorethevalues:GLB,XLandPAR. Theglobalparametersarethefollowing: GLB(J):J=1,2....40 J=1:T0Zero J=2,...7:b1,b2,...b6Backgroundparameters J=8,9:SYCOS,SYSINSystematic2Theta-shifts/DTT1,DTT2forTOF J=10..15:Bc1,.....Bc6BackgroundcoefficientsforDebyelikefunction:DBback J=16..21:d1,.....d6distancesinAngstromsinDBback J=22,23,24,25:a,b,c,dBackgroundtransformingcoefficients J=26:FlambdaWavelength(forCWneutron)/2SinThetaforT OF J=27,28,29:P0,Cp,TauMicroabsorptioncoefficients J=30..35:Additionalbackgroundparameters J=35..40:Notusedatpresent XL(I,J):Atomparameters,theindexIrunsoveratoms I=1,2,..N1,N1+1,N1+2,....N1+N2,N1+N2+1,....N1+N2+N3....N N1:numberofatomsofphase1 N2:numberofatomsofphase2 ............................................... N:totalnumberofatoms:N1+N2+N3+...+NNPHASE TheindexJrepresentsdifferentatomparameters J=1,2,3:(x,y,z)fractionalcoordinates J=4:Bisotropictemperaturefactor J=5:Occ.Occupationfactor. J=6....8:(Mx,My,Mz)Magneticmomentcomponents 9...11:(Mxi,Myi,Mzi)ImaginaryMagneticmomentcomponents J=12:MPhasMagneticphaseoftheatom J=13..18:(betas11,22..)Anisotropicthermalfactors J=19..32:Coefficientsofgeneralizedform-factors TheseatomicparameterscanbeusedbythesubroutinesSTRMODandMAGMOD forotherpurposes. Moreover,thereareothernon-atomicparameterswhichcanbeusedalsofor defininggeneralizedcoordinates.Theyareinternallystoredinthearray PAR(K,J)wheretheindexKrunoverthephasesandJrepresentsdifferent parameters: PAR(K,J):K=1,2,....NPHASE
J=1:SScalefactor J=2:BovOveralltemperaturefactor J=3,4,5:U,V,WHalfwidthparameters J=6,..11:A,B,C,D,E,FCellconstants J=12,13:G1,G2Preferredorientationparameters J=14:As1FirstAsymmetryparameter J=15,16:X,YShapeparameters(dependonNPROF) J=17:eta(m)Shapeparameterofp-Voigt(Pearson) J=18..27:Str1...Str10Strainparameters J=28:IGIsotropicgaussiansizeparameter J=29..34:Siz1...Siz6Anisotropicsizeparameters J=35,36,37:As2,As3,As4Additionalasymmetryparameters J=38:AsymhklHKL-dependentasymmetryparameter J=39,40:Shf1,Shf2HKL-dependentshiftparameters J=41,42:Shap1,Shap2Additionalshapeparameters J=43,44,45:U2,V2,W2..U,V,Wparametersforlambda(2) J=46,47,48:Ud,Vd,WdU,V,WforrightpartofSpV(x) J=49,50:Eta0d,XdEtaandXforrightpartofSpV(x) J=51,..59:CYiCoeffs.ofSphericalHarmonics(sizebr oad.) J=60..MPAR:P1,P2,....User-suppliedparameters LASTMPAR=59NumberoftheLastparameterused internally.Tobeusedasoffset foruser-suppliedsubroutines. ---------------------------------------------------------------------------4.6:Examplesofuser-suppliedsubroutinesforstructure-factorcalculation ---------------------------------------------------------------------------CRYSTALSTRUCTUREREFINEMENTS InFullProfthedefaultJBT=4optionisanupdatedsubroutinewritten byV.Rodriguezwhichhandlesrigidbodyobjects.
Guideforthe GeneralRigid-Body-Constraints/TLSSubroutine forRietveldRefinements ********************** V1.4(January1997) DrV.Rodriguez LaboratoiredeSpectroscopieMoleculaireetcristalline* (U.A.124CNRS) UniversitedeBordeauxI,351coursdelaLiberation F-33405TALENCECedex Tel:(33)56.84.63.61 Fax:(33)56.84.84.02 *UMRPhysico-ChimieMoleculairesinceJanuary1st1997 Forfurtherdetailssee "Aroutineforcrystal-structurerefinementsbasedonrigid-body modelwithconstrainedgeneralizedcoordinatesandmeanthermal
displacements" RodriguezV.andRodriguez-CarvajalJ., J.AppliedCryst.,(tobepublished) ********************* InthepresentversionofFullprofthedefaultJBT=4optionreferstoa subroutinewhichhandlesrigidbodyobjects.Herewegiveashortguidein ordertofacilitatetheuseofthissubroutine.Thisroutineshouldbeused withcautionandtheusershouldbefamiliarenoughwith"conventional" Rietveldrefinements.Thesubroutineisstillunderimprovement.Atthis time,alltheoptionshavebeenwelltestedexceptoptionNr4(seebelow). Iacknowledgeallsuggestionsandnotificationsofpossiblebugsfoundin theprogram. ItshouldbepointedoutthatoptionJBT=4isnotrestrictedto "perfect"rigid-body-groups.InthestandarddefinitionofRietveldatomic positions,reducedcoordinatesareused.Withinthissubroutine,molecules oratomicgroupsaredefinedbysphericalinternalcoordinatesandsix additionnalparameters,whichdefinethegroupspositionandorientation inthecrystal. Inaddition,thisextendedversionofRietveldrefinementallowstodistort groupsinafinalrefinementstepifrequired. Note:Eachparameterreferingtotheorthonormalcrystalsystemis recognizedbytheappended"c". Eachparameterreferingtotheorthonormalmolecularsystemis recognizedbytheappended"m". A-Descriptionoftheparameters ******************************* -Anykindofrigidbodygroupsbuiltfromatomscanbegenerated. -Allparametersdescribedbelowarerefinableexceptoptional parametersP6(alwaystrue)andP16(specificto"satellite"rigidbody groups). -Eachgroupofatoms(rigidbodygroup,RBG)isidentifiedby1or2 lettersandanumberfrom1to99(bothcompatiblewiththestandardDBWS formatandthefreeformatofFullprof).ThenumberindicatesthataRBGis defined.Thelabel(twolettersmax.)andthenumberoftheatommustnotbe separated. -RepresentationofRBGisperformedasfollow: 1)Definitionoftheisolatedgroupinanorthonormalmolecular system.Eachatomicposition(xm,ym,zm)isdefinedthrough sphericalcoordinates(dm=distance,thetam,phim).Thecentre ofthismolecularsystemmayormaynotcoincidewithanatom. 2)Definitionoftheabsoluteposition(Xc,Yc,Zc)andorientation (anglesTHETAc,PHIcandCHIc)ofthemolecularorthonormal systeminthecrystallographicorthonormalsystem.Theseare standardEULERanglesdefinitions. Inthisway,eachgroupisentirelydefinedwithinacrystal. -Anti-clockwiserotationsarealwaysappliedtosphericalangles. Thesestandardsphericalanglesaredefinedasfollow: THETAc/thetam:inclinationwithrespecttotheZc/zmaxisofthe
correspondingorthonormalsystem[-Pi,Pi]. PHIc/CHIcandphim:rotationaroundtheZc/zmaxisofthecorresponding orthonormalsystem[0,2*Pi]. -Theorthonormalcrystallographicsystem,withrespecttowhichthe sphericalanglesTHETAc,PHIcandCHIcofanyRBGaredefined,fulfills thefollowingconditions: Xcaxiscoincideswiththecrystallographicdirectiona Ycaxisbelongstotheplane(a,b) Zcaxisisperpendiculartotheplane(a,b)(paralleltoc*) Onecanimaginehowtoplacearigidmoleculeinthecorrectpositioninthe unitcellbymakingthefollowingoperations: -TheRBGhasbeencompletelydefinedbythesphericalcoordinates (dm,thetam,phim)ofeachatomintheinternalorthogonalsystem,that coincidesatthebeginningwiththeorthogonalcrystallographicsystem. -PerformarotationCHIcofthewholeRBGaroundthezmaxisofmatrix: (COS(CHIc)-SIN(CHIc)0) M1=(SIN(CHIc)COS(CHIc)0) (001) -PerformarotationofthewoleRBGincliningtheirz-axisto theanglesTHETAcandPHIcofmatrix: (COS(THETAc)*COS(PHIc)-SIN(PHIc)SIN(THETAc)*COS(PHIc)) M2=(COS(THETAc)*SIN(PHIc)COS(PHIc)SIN(THETAc)*SIN(PHIc)) (-SIN(THETAc)0COS(THETAc)) -TranslatetheoriginoftheRBGtotheposition(Xc,Yc,Zc)whichare transformedinreducedcoordinates(xo,yo,zo)withxo=Xc/a,yo=Yc/b, zo=Zc/c -"Freeatoms"(unconstrainedorisolated)canbeaddedwithnumber0 orwithoutnumber.Eachisolatedatomhasthesamedefinitionof parametersasdescribedintheFullprofmanual(seelines11.4.1and 11.4.3oftheFullprofguide).Currentinformationabout"freeatoms" isprintedtothescreenwhenparameterP6(seebelow)issettoany negativevalue.Notethatthefollowingparameters:P6,P7,P8,P15 andP16,areobsoleteinthiscase. -Rigidbodysatellitegroups(RBSG)canbealsoincludedinthis version,forexampleamethylgroupwithinarigidgroupsuchas [N(CH3)4]+(tetramethylammonium).Thedefinitionandthestructure oftheparametersarealmostthesameasthoseforamainRBG.The coordinatesofthecentreofthesatellitegroupshouldnotbespecified sincetheyarespecifiedthroughtheknowledgeofitsabsoluteposition intheinputfile"x.pcr".TheorientationTHETAc,PHIcofsatellites groupsisalsodefinedfollowingthevalueofparameterP16ofthe1st satelliteatom(seebelow,optionabs(P6)=2). OneeasyexternaldegreeoffreedomoftheRBSGistherotationaround thez-molecularaxisi.e.theN-Cbond.Thisdegreeoffreedomis accesiblethroughtheEULERanglePHIcthatcanberefined. -Alloutputisidenticalforisolatedand/orconstrainedatoms.
-Everyatomhas16itemsstoredin(X(Iphase,j),j=1,16)andeach parameterisdenotedhereasP1,P2,...P16.Thereadingofthese parametersisdescribedinlines11-4-1and11-4-3oftheFullprof guide. Example: P1P2P3P4P5P6P7-THETAc P8-PHIc TD1N.38900.54090.287964.000000.166671.000-.290.142 .00.00.00.00.00.0071.0061.00 1.493001.57080-.95532.33333.66667.250001.041000 .00.00.00.00.00.0051.00 P9-dmP10-thetamP11-phimP12-xoP13-yoP14-zoP15-CHIcP16 xyz TD2C.47744.84054.287964.000000.16667.000.000.000 .00.00.00.00.00.00.00.00 .750001.570801.57080.00000.00000.00000.00000 .00.00.00.00.00.00.00 P9-dmP10-thetamP11-phim xyz OO.28146-.04125.41456.000001.00000-1.000.000.000 .00.00.00.00.00.00.00.00 .03957.07078.09069.00314.01571-.015010 .00.00.00.00.00.00 beta11beta22beta33beta12beta13beta23 ->InaRBG(here,thegenericnameisTD)eachatom(TD1andTD2) hasitsinternalcoordinatesstoredinthefollowingitems: distancetothecentredm:P9 Sphericalanglethetam:P10 Sphericalanglephim:P11 Theatomicreducedcordinatesareonlyforinformationwithoption1 (RBG),seebelowfordetails. Reducedcoordinatex:P1 Reducedcoordinatey:P2 Reducedcoordinatez:P3 TheparametersP4andP5havetheirusualmeaningforeachatom: Isotropictemperaturefactor:P4 Ocupationnumber:P5 ->ThefirstatomofeachRBG(atomNo1,hereTD1)containsthefractional coordinates(xo,yo,zo)ofthecentreoftheRBG(P12,P13,P14)and thethreeEULERorientationanglesTHETAc,PHIcandCHIc(inradians, respectivelyP7=-.290,P8=.142andP15=1.041)ofthewholegroup. Here,thecentreoftheRBGdoesnotcoincidewithanatom(NorCin thisexample)sincethefirstatomhasanonzerovaluedm=P9=1.493. Ofcourse,itispossibletobuildaRBGwithanatomcoincidingwith thecentreoftheRBG. ->Thethirdatom(oxygen,Number0(ornonewhichisequivalentto0))is
unconstrained("freeatom")anditsitemsarethestandardones:here, reducedcoordinates(x,y,z)+atomictemperatureparameters(betaij). ->NoterminaloutputisrequiredforthewholeRBGTD(P6>0). Terminaloutputateachcycleisrequiredfor"freeatom"oxygen (P6<0). B-Practicaldetails ******************* 1-Theitemabs(P6)ofthefirstatomindicatestheoptionselected. IfP6<0,thecurrentinformationisprintedonthescreen andinthefileCODFIL.OUT. (filex.out).IfthevalueofP6is0foraRBG,theparameter defaultsto"1",correspondingtothestandardRBGoption. 2-Thedistanceareexpressedinthesameunitaswavelengthandcell parameters(usuallyinangstroms)andtheanglesarealways expressedinradians: 3-Thelistingofthedifferentoptionsisafunctionofthemain optionalparameterP6.Inthefollowing,thetemperatureparameters areexclusivelyBoveralorBiso(isotropicDebye-Wallerfactors) exceptforTLSoptionwithabs(P6)=5. abs(P6)=1.0x:Normalrigidbodyoption. Ifx=1thefractionalcoordinatesofthecenter ofmassisoutput.Thatsupposesthateveryatom oftheMoleculehasbeengivenexplicitelyinthe asymmetricunit. 2.xx:Satellitegroup(RBSG)option(Int(abs(P6))=2). Theintegervaluexx=100*(int(abs(P6))-2)givesthe absolutenumberofthereferencegroup(asthey appearfollowingthewritingorder,whateverthe numberofphase). -->TheparameterP15isassignedtotherotationCHIc ofRBSGasforRBG. -->TheparameterP16ofthefirstatomoftheRBSGis definedasfollows:P16=N1.N2with N1=Int(P16):Nrofthefirstreferenceatom ofthereferenceRBG. N2=100*(P16-Int(P16)):Nrofthesecondreferenceatom ofthereferenceRBG. N1:CentreoftheRBSG N2:Optional(ifN2isgiventhenN1-N2defines theinternalz-axis) Example:3.021streferenceatom=Nr3 2ndreferenceatom=Nr2 AtomNr3isthecentreoftheRBSGandthe zaxisoftheRBSGisorientedinthe direction:atomNr2->atomNr3. Ofcourse,the(xo,yo,zo)fractionalcoordinatesofthe RBSGarenotneeded.Theprogramcalculatesautomatically thecorrespondingvalues.
a)Ifthesecondatomisdefined(N2#0),the sphericalanglesoftheRBSGarecalculatedfrom thesetworeferenceatoms. b)Ifthesecondatomisnotdefined(N2=0),the centreofthemainRBGistakenasthesecond referenceatomoftheRBSG. c)IfN2=N1,thesphericalorientationanglesofthe RBSGarethoseofthemainreferenceRBG. Apartfromtheseconstraints,aRBSGistreatedas anormalRBGwithasmanyatomsasdesired.The refinementofthecentreoftheRBSGaswellasthe orientationanglesTHETAcandPHIcareperformedin themainRBG. 3.0x:Thesphericalcoordinates(parametersP9,P10and P11)aregeneratedfromthereducedcoordinates(P1, P2andP3)atthefirstcycle.Thentheparameter P6isautomaticallysetto1andthesignofthe optioniskepti.e.thenextoptionisRBG. Forselectingtheinternalorthogonalsystemthe userhastogiveintheparameters(P12,P13,P14) theoriginoftheintenalorthogonalframeandin (P9,P10,P11)thecoordinatesofanatom(thatmay befictitious)fordefiningtheplane"xz". The(P1,P2,P3)coordinatesofthefirstatomdefines thez-axisoftheinternalframe,whichisinthe directionV3=(P1-P12,P2-P13,P3-P14)inthe conventionalcrystalframe(fractionalcomponents). the"y"axisinperpendiculartotheplane"xz" definedbythevectors: V3=(P1,P2,P3)-(P12,P13,P14)->z-axis V1=(P9,P10,P11)-(P12,P13,P14)->withinthexzplane y-axisisinthedirectionV3xV1 Thisoptionisveryusefullasitfacilitates theuseofstandardinputfilewithJBT#4,the conversionofpublishedstructuresintospherical internalcoordinatesystems,etc... Ifx=1thefractionalcoordinatesofthecenterof massisoutputasinoption1. 4.xx:Optiontogenerateanidealizedmoleculelike aliphaticchains,planarorhelicoidalmolecules..., wherexxisthenumberofatomicplanesalongthe RBGZcaxiswhichisthereferenceaxis. Thesphericalcoordinatesarecalculatedfromthree parametersP9,P10andP11.Theseparametersare lostafterprocessing.Theyaredefinedas: P9-distanceofoneatomtothecenteroftheaxis P10-anglebetweentwoatomslyinginconsecutive planesandthecorrespondingmid-pointlying alongtheZc-axis. P11-orderofthegeneratingaxis(integer) Examples:1-ForanaliphaticchainCnalongZcinthe
(Xc,Zc)plane(conformationalltrans). distance=1.54/2.(angstroms) angle=114.*pi/180.(radians) axisorder=2 2-Forbenzenelyingintheplane(Xc,Yc) distance#1.40*2.(angstroms) angle=0.*pi/180.(radians) axisorder=6 TheparameterP15isassignedtoCHIzasintheRBG optionandtheparameterabs(P6)issetto1inthe 1stcycle,thesignoftheoptioniskept. Therefore,thegeneratedgroupistreatedasa normalRBGinthenextcycles. Remark:Furtherimprovementsareschedduledforthis optionwhichisnotverytrustlyatthepresent time. 5.0x:TLSoptionforRBGincludingsatellitegroups,if any.ThisTLSversionisbasedontheformalism ofV.SchomakerandK.N.Trueblood,ActaCryst.(1968), B24,p-63.Inthiscase,therefinementisperformed withthesocalledonestepprocessi.e.atomic positionsandtemperaturefactorsTLSarerefined together. TheoriginofthemainRBGMUSTbethecentreof massoftheentiregroupconcerned!!!The subroutinecalculatesthecentreofmassofthe moleculeifx=1.ThisoptionMUSTbesetwhenthe centreofthegroupdoesnotcoincidewiththe centreofmass.Inthiscase,makesurethatall atomsconstitutingtheRBGaredefinedintheinput filesincetheRBGoptiondoesnotgenerateatomic positions.Suchasituationcanoccurinnon-centrosymmetricspacegroup,asinureaSPG:P-421M, sincethemoleculeislocatedonaC2vsite(mm.). Here,onemustentertheentiremoleculeinthe asymmetricunit. TheelementsoftheT(6),L(6)andS(9)matrices arereadin"furtherparametersIFURT"(see Fullprofguide,line11.12)followingtheusual orderie.1122331213and23forTandL.As theSmatrixisnotsymmetric,9elementscanbe requiredinthegeneralcase.Thesixfirstelements areasdefinedpreviously,andthethreelastones arerespectivelyS21,S31andS32. Similarlytotheatomictemperatureparameters betaij,thecomponentsoftheTLSmatriceshave symmetryconstraints,whichareimposedbythe symmetryofthecrystallographicsite(notthe molecularsymmetry!).Thesesymmetryrelations canbefoundinthepaperbySchomakerand Trueblood(1968). TheTelementsareexpressedinangstroms^2,theL componentsinradians^2andtheSonesinangstroms* radians.Forconvenience,theoutputtothescreen
andtounit7(x.out)oftheTLScomponentsare expressedinthefollowingunits:angstroms^2forT, indegrees^2forLanddegrees*angstromsforS. Remark:Whenusingthisoption,onerefinesthe observedstructurefactorsbyassumingthatthe atomictemperaturefactorsareconstrainedabinitio tosatisfytherigid-bodyhypothesis.ItiswellknownthattheRBG/TLScangreatlyreducethe numberofatomicandthermalparameters,especially whenthemoleculeislocatedatasiteofhigh symmetry,buttheusershouldbefamiliarenough withtheTLShypothesisnottoperforminconsistent refinements. 4-Itisadvisedtousespecificrigidbodyrefinementcodesasdamping parameters,especiallyfortherotationalparameterwhichneedtobe currentlythreetimehigherthantheotherones.Itishighly recommendedtousetheoptionswithscreenoutput(P6withanegative value)tocontroleachRBGrefinementstepssincegoodconstrained refinementsarenotsoeasytoperform. 5-Concerningtherefinements:whenamainRBGhassatellitesgroups, thederivativesofthegeneralRBGparameters,i.e.the3orientation anglesTHETAc,PHIcandCHIcandthecoordinates(xo,yo,zo)ofthe centreofthegroup,containthecontributionsofthesatellitesgroups. Incontrast,thederivativesoftheinternalsphericparametersdonot accountforthesecontributions. 6-Whenthissubroutineisused,threeadditionnalfilesoffixednames arecreatedattheend:x#.m,x#.bsandx#.ortep(where#standsforthe numberofthephase),containingatomicparametersinaformat suitabletobeusedwithwell-knownsoftwarepackages(Molview,Balls &SticksandORTEP).NotethatfilesforMolviewaredirectely executable.Theoutputforthetwoothersoftwareareincompletein thesensethattheycontaineithercartesiancoordinates(Balls& Sticks)orreducedcoordinates+atomictemperatureparameters (ORTEP)ofatomslocatedintheasymmetricunit. MAGNETICSTRUCTUREREFINEMENTS InthepresentversionofFullProfthedefaultJBT=5optioncorresponds tothecalculationofthemagneticstructurefactorforaconicalmagnetic structure.Themagneticintensitiesarecalculatedfollowingstandard formulaasgiven,forinstance,inthepaperbyJ.M.Hasting&L.M.Corliss publishedisPhysRev126(2),556(1962).Nosymmetryoperationcanbe introduced:allthemagneticatomswithinaprimitiveunitcellmust begiven(constraintshavetobeintroducedthroughthecodesofthe parameters).ThesubroutineMAGMOD,inthiscase,doesnottakeinto accountsymmetryforcalculations(seethemodulesFDUM's.FORfordetails). HoweverISYMmustbesetto1,thevalueofthefourparameters MULT,ICENT,NLAUE,NMAGRshouldbe:0110. Theatomparameterscorrespondtothefollowingvariables: ->P1,P2,P3,P4andP5correspondtox,y,z,B,occoftheatom ->P6isthemagneticmomentoftheatom(inBohrmagnetons) ->P7isthehalf-angleconeoftheatom(degrees)
->P8isthemagneticphaseoftheatom(infractionsof2pi) ->P9ofthefirstatomcorrespondtoPhi(degrees) ->P10ofthefirstatomcorrespondtoTheta(degrees) (Phi,Theta)arethesphericalangles(degrees)oftheconeaxis Theorthonormalsystemwithrespecttowhicharedefinedthe sphericalanglesverifies: XaxiscoincideswiththecrystallographicA YaxisbelongstotheplaneA,B ZaxisisperpendiculartotheplaneA,B Theparticularimplementationofsphericalcomponentsinmagnetic structurerefinementsisthatZaxismustcoincidewithC.That worksinallcrystallographicsystemsexceptfortriclinic.The monoclinicsettingmustbechangedto->112/m ItisrecommendedtogeneratethereflectionsusingP-1as Spacegroupsymbolanduseforconicalstructuresthevalue IRF=0(Generatessatellites+fundamentals).Forapurehelix IRF=-1(onlysatellitesaregenerated).Thenumberofpropagations vectorsmustbesetto-1(togenerate+and-satellites). Forcalculatingthemagneticmomentsindifferentcellsthefollowing formulashouldbeused: Themagneticintensityisgivenbythefollowingformula: Fm**2=(p.sinw)**2.Sum(j){m(j)f(H,j)cos(bj)exp(2pii.Hrj)} Fm**2=p**2.(1+cosw**2)/4.Sum(j){m(j)f(H+-k,j)sin(bj)exp(2pii.Hrj-+fj)} ThecorrespondencewiththeparametersP1,..P10isthefollowing: rj=(P1,P2,P3)j f(H+-k,j)=P5j.FormFactor(H+-k,j)exp(-P4j(sintheta/lamda)**2) m(j)=P6j bj=P7j fj=P8j Theunitaryvectordefiningtheaxisoftheconeisgivenby: n=(cosP9sinP10,sinP9sinP10,cosP10) cosw=n.Q/mod(Q),whereQisthescatteringvector ------------------------------------------------------------------5.-SINCLECRYSTALANDINTEGRATEDINTENSITY REFINEMENTS 5.1:Generalcomments. Theversion3.0.0(orhigher)ofFullProfpermitstherefinementof integratedintensitydata.Singlecrystaland/orpowderintegratedintensities canbeincluded(orusedalone)asobservationsforrefiningastructural model.ThispossibilityincreasesthecapabilitiesofFullProfforhandling otherkindofdata,butitcannotcompete(orsubstitute)moreelaborated programsspecializedinsinglecrystalwork.
Thestructurefactorcalculationisexactlythesameasinpowder diffraction,soalltheavailablefeaturescanbedirectlyusedwith integratedintensitydata. TheR-factorsinsinglecrystalworkarecalculatedaccordingto thefollowingformulae: Optimizedfunction: M=Sum{n}[w(n)(F2obs(n)-Sum{k}[F2cal(k)])^2] Theindex"n"runsovertheobservations(1,..Nobs) Theindex"k"runsoverthereflectionscontributingtotheobservation"n" F2isthesquareofthestructurefactor(intensitycorrectedforLp-factor) RF2-factor=100*Sum{n}[|F2obs(n)-Sum{k}[F2cal(k)]|]/Sum{n}[F2obs(n)] RF2w-factor=100*Sqrt(M/Sum{n}[w(n)F2obs(n)^2]) RF-factor=100*Sum{n}[|Fobs(n)-sqrt(Sum{k}[F2cal(k)])|]/Sum{n}[Fobs(n)] Fobs=Sqrt(F2obs) Chi2(Intens)=M/(Nobs-Npar) NoticethatRF2wforw(n)=1.0isnotthesamevalueasRF2. Forintegratedintensitypowderdata,F2obsisinfactSum{k}[jLpF2(k)]. WhentheoptionIWGT=2(unitweights)isused. Theinverseofthenormal matrixisnotmultipliedbyChi2asisusualinweightedrefinements. 5.2:Theextinctioncorrection. Atpresentonlythe"empiricalcorrection"(asingleparameter),asused inSHELX,hasbeenimplemented.Ihopetohavetimeforputtingthe anisotropicBecker-Coppensextinctioncoefficientsintotheprogram. 5.3:Mixedrefinements. Thisoptionisstillinanexploringstage.Forthemomentonlya singlepowderdiffractionprofilecanbeusedwithdifferentsetsof integratedintensitydatathatarerelatedtoeachphase. Aglobalpowderdiffractionpatterncanbegivenasprimaryinformation, andsome"phases"canbegiveninadditionwiththeirownintegrated intensitydata.FormixingX-rayandneutronrefinement,thebestthing todoistoprovidea"powder"neutrondiffractionpatternastheglobal datainformationandasetofintegratedintensitiesforthe crystallographicphasetoberefined.Apresentitisnecessaryto "repeat"thesamephase,asinthatmodellingtheneutronpattern, usingtheappropriateconstraintsintherefinedparameters(using thesamecodeforphysicallyidenticalparameters). ------------------------------------------------------------------6.-REFERENCES
1.-H.M.Rietveld,ActaCryst.22,151-1152(1967) 2.-H.M.Rietveld,J.AppliedCryst.2,65-71(1969) 3.-A.W.Hewat,HarwellReportNo.73/239,ILLReportNo.74/H62S
4.-G.Malmros&J.O.Thomas,J.AppliedCryst.10,7-11(1977) 5.-C.P.Khattak&D.E.Cox,J.AppliedCryst.10,405-411(1977) 6.-D.B.Wiles&R.A.Young,J.AppliedCryst.14,149-151(1981)/ 15,430-438(1982) 7.-G.S.Pawley,J.AppliedCryst.14,357-361(1981) 8.-HalpernandJohnson 9.-E.Prince,J.Appl.Cryst.16,508(1983) 10.-W.A.Dollase,J.AppliedCryst.19,267-(1986) 11.-K.D.Rouse,M.J.Cooper,E.J.York&A.Chakera,ActaCrystA26, 682(1970) 12.-A.W.Hewat,ActaCryst.A35,248(1979) 13.-A.J.C.Wilson,MathematicaltheoryofX-raypowderdiffraction PhilipsTechnicalLibrary,Eindhoven(1963) 14.-J.F.Berar&*.Lelann,J.Appl.Cryst.24,1-5(1991) 15.-A.Antoniadis,J.Berruyer&A.Filhol,ActaCryst.A46,692-711(1990) 16.-R.J.Hill&H.D.Flack,J.AppliedCryst.20,356-361(1987) 17.-J.Rodriguez-Carvajal,M.T.Fernandez-DiazandJ.L.Martinez, JournalofPhysics:CondensedMatter3,3215-3234(1991) 18.-J.Rodriguez-Carvajal,PhysicaB192,55-69(1993) 19.-NumericalRecipes,byW.H.Press,B.P.Flanery,S.A.Teukolskyand W.T.Vetterling(Fortranversion),CambridgeUniversityPress,1990. 20.-W.Pitschke,N.MatternandH.Hermann,PowderDiffraction8(4), 223-228(1993). (Inthispapertheauthorsrefinesimultaneouslyalloccupation numbers.Thispracticeshouldbeavoided.Ifthecalculationwere exactthatgivesrisetoasingularmatrixwhenthescalefactor isalsorefined) Seealso W.Pitschke,H.HermannandN.Mattern,PowderDiffraction8(2), 74-83(1993).
7.-DIMENSIONSOFARRAYSOFTHESTANDARDVERSION
Dimensionscanbeadaptedtotheavailablememorybychanging thevaluesinPARAMETERstatements IDSZ:Maximumnumberofpointsinthediffractionpattern IRS:Maximumnumberofreflections NATS:Maximumnumberofatomsinasymmetricunit(allphasesincluded)