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1、X-Raydiffraction-EriceCrystallography2011ITSupportX射線衍射晶體學(xué)2011支持-艾瑞克TheThomsonscatteringmodelAX-rayplanewavepropagatesalongthexdirection,thescattererisinO.Qistheobservationpoint,intheplane(x,y).F=eE;a=F/mIeth=Iisin2?[e4/(m2r2c4)]?istheanglebetweentheaccelerationdirectionoftheelect
2、ronandtheobservationdirection.Ifthebeamisnon-polarised,wecandividetheoverallincidentbeamintotwocomponentswiththesameintensity(=0.5Ii),thefirstpolarizedalongtheyaxis,thesecondalongthezaxis.Forthefirstcomponentφ=(π/2-2θ)andIey=0.5Ii[e4/(m2r2c4)]cos22?.Forthesecondcomponentφ=π/2andIe
3、z=0.5Ii[e4/(m2r2c4)]ThereforeIeTh=Ii[e4/(m2r2c4)][(1+cos22?)/2]4AO=-r.so;BO=r.s;AO+BO=r.(s-so)(AO+BO)/?=r.(s-so)/?=r.r*wherer*=(s-so)/??=2?r*.rr*=2sin?/?F(r*)=Ao+Ao’exp(2?ir*.r)F(r*)=?jAjexp(2?ir*.rj)=?jfjexp(2?ir*.rj)wheref2=I/IethIfthescattererdistributionisacontinuoumthenYoucan
4、easilyrecognizethattheamplitydeF(r*)istheFouriertransformoftheelectrondensity.ViceversaTheaboveformulasarequitegeneral:theywillbeappliedtothecasesinwhich?(r)representstheelectrondensityofanelectron,ofanatom,ofamolecule,oftheunitcell,ofthefullcrystal.Thescatteringamplitudeofanelect
5、ronAnexample:theatomC(2x1s;2x2s;2x2p)(?e)1s=(c13/?)exp(-2c1r);(?e)2s=c25/(96?)r2exp(-c2r)Icoe+Iincoe=IeTh?Iincoe=IeTh-Icoe=IeTh-IeThfe2=IeTh(1-fe2)6Icoe=IeThfa2=IeTh(Σj=1,..,Zfei)2Iincoe=IeTh(Σj=1,..,Z[1-fej2])Theatomicthermalfactor?a(r)istheelectrondensityforanatomisolated,locate
6、dattheorigin.Owingtothethermalagitation,thenucleusmovesattheinstanttintor’:thentheelectrondensitywillbe?a(r-r’).Letp(r’)theprobabilityofthatmovement:thenScatteringamplitudeofamoleculeLet?j(r)betheelectrondensityforanatomisolated,thermicallyagitatedandlocatedattheorigin.Then?(r-rj)
7、willbetheelectrondensityofthesameatomwhenitsnucleusisinrj.Let?M(r)betheelectrondensityofamolecule:.ScatteringamplitudeofaninfinitecrystalAsweknowtheelectrondensityofacrystalmaybeexpressedasaconvolution:ScatteringamplitudeofafinitecrystalAfinitecrystalmayberepresentedastheproduct
8、where?(r)isthefunctionformwhichis
