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1、CHAPTER1PrinciplesofPowderDiffractionabROBERTE.DINNEBIERANDSIMONJ.L.BILLINGEaMax-Planck-InstituteforSolidStateResearch,Heisenbergstrasse1,bD-70569Stuttgart,Germany;DepartmentofPhysicsandAstronomy,4268Biomed.Phys.Sci.Building,MichiganStateUniversity,EastLansing,MI48824,USA1.1INTRODUCTIONThischapterpr
2、esentssomeverybasicresultsaboutthegeometryofdiffractionfromcrystals.Thisisdevelopedinmuchgreaterdetailinmanytextbooksbutaconcisestatementofthebasicconceptsgreatlyfacilitatestheunderstandingoftheadvancedlaterchapterssowereproduceitherefortheconvenienceofthereader.Sincetheresultsaresobasic,wedonotmake
3、anyattempttoreferencetheoriginalsources.Thebibliographyattheendofthechapterlistsaselectionofsomeofourfavoriteintroductorybooksonpowderdiffraction.1.2FUNDAMENTALSX-raysareelectromagnetic(em)waveswithamuchshorterwavelengththan10visiblelight,typicallyontheorderof1A˚(¼110m).Thephysicsofem-wavesiswellu
4、nderstoodandexcellentintroductionstothesubjectarefoundineverytextbookonoptics.Herewebrieflyreviewtheresultsmostimportantforunderstandingthegeometryofdiffractionfromcrystals.Classicalem-wavescanbedescribedbyasinewavethatrepeatsperiodicallyevery2pradians.Thespatiallengthofeachperiodisthewavelengthl.Ift
5、woidenticalwavesarenotcoincident,theyaresaidtohavea‘‘phaseshift’’withrespecttoeachother(Figure1.1).Thisiseithermeasuredasalinearshift,Donalengthscale,intheunitsofthewavelength,orequivalentlyasaphaseshift,dfonanangularscale,suchthat:Ddj2p¼)dj¼Dð1Þl2pl12Chapter1Figure1.1Graphicalillustrationofthephase
6、shiftbetweentwosinewavesofequalamplitude.Thedetectedintensity,I,isthesquareoftheamplitude,A,ofthesinewave.Withtwowavespresent,theresultingamplitudeisnotjustthesumoftheindividualamplitudesbutdependsonthephaseshiftdj.Thetwoextremes2occurwhendj¼0(constructiveinterference),whereI¼(A1+A2),and2dj¼p(destru
7、ctiveinterference),whereI¼(A1A2).Ingeneral,2I¼[A1+A2exp(idj)].Whenmorethantwowavesarepresent,thisequationbecomes:"#2XI¼AjexpðijjÞ;ð2Þjwherethesumisoverallthesine-wavespresentandthephases,fjaremeasure
