最新x-ray diffraction - erice crystallography it supportx射线衍射晶体学支持-艾瑞克幻灯片.ppt

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1、X-Raydiffraction-EriceCrystallography2011ITSupportX射线衍射晶体学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