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1、2.2.4ScatteredWaveAmplitudeandStructureFactor(p.39)?????????'????(18)F??dVn(r)expik?k?r??dVn(r)exp?i?k?rcrystalWhenthediffractionconditionissatisfied,??i.e.?k?G(21)Eq.(18)canbewrittenas???F???dVn(r)exp??iG?r?Gcrystal????N?dVn(r)exp??iG?r??NS?(39)GcellNcellsr=0atavertexofthecell???S???dVn(r)exp??iG
2、?r?GcellStructureFactorRevisionSupposingjatomsinthecell,?totalelectronconcentrationatduetoallatomsinthesinglecell:r???n(r)??nj(r?rj)(40)j???S???dVn(r)exp??iG?r?Gcell?????????dVnj(r?rj)exp?iG?rj?????????exp??iG?rj??dVnj(r?rj)exp??iG?(r?rj)?(41)jatomPhasefactorbetweenatomsWedefinetheatomicformfactor
3、???????f?dVn(r?r)exp?iG?(r?r)j?jjj(42)atom??SothatSG???fjexp??iG?rj?(43)jStructureFactorRevisionScatteringintensity????Atomsinacellrj?xja1?yja2?zja3(44)????Foragivenscatteringn1,n2,n3:G??1b1??2b2??3b3??S???fexp??iG?r?Gjjj(46)S?(???)??fexp??i2?(?x??y??z)?G123j1j2j3jjIntensityofthescatteringforG22*I
4、??F??S??S??S?GGGGGFromknownf,obtainatomarrangementinacrystalcelljAccordingtotheknowncrystalstructure,deducetheintensityforacertaindiffractionExample:structurefactorofabcclattice(p.40)-Twoatomsinthecrystalcellwithcoordinates(000)and(?,?,?)-Thetypeofatomsisthesame,andtheatomicformfactorisf????-Forac
5、ertaindiffractionvectorG??b??b??b112233StructurefactorS(???)??fexp??i2?(?x??y??z)?123j1j2j3jj?f?f?exp??i?(?????)?123?f?1?exp??i?(?????)??123When=oddinteger,?1??2??3S(?1?2?3)?0?????=eveninteger,S(???)?2f123123Inadiffractionpatternofabcccrystal,-(100),(300),(111),(221)etc.donotappear.-(200),(110),(2
6、22),etc.arepresent.Figure2-16Explanationoftheabsenceofa(100)reflectionfromabcclattice.MITOpenCourseWareStructurefactorinCsClstructure-Twoatomsinthecrystalcellwithcoordinates(000)and(?,?,?)-Twotypesofatomswiththeatomicformfactorsfandfrespectively1222I??F??S?GGG??f?fexp??i?(?????)???f?fexp?i?(?????)
7、??121231212322?f?f?2ffcos?(?????)1212123Iff~f,when=oddinteger,?????I~012123Fig.2-17ComparisonofX-rayreflectionsfromKClandKBrpowders2.2.5AtomicScatteringFactor(p.41)Wedefinetheatomicformfactor???????f?dVn(r?r)exp?
