材料表征教学资料-diffraction

Dr.DiWu,NanjingUniversity1衍射Dr.DiWu,NanjingUniversity2衍射是什么衍射技术考察大量散射体对电磁辐射的散射。我们主要考虑晶体材料中原子、原子团和分子对电磁辐射的散射。各种衍射技术最后都会给出一个衍射谱图，所谓的衍射pattern。这些衍射谱记录了晶体对射线衍射的角度和强度。Dr.DiWu,NanjingUniversity3衍射能干什么从衍射谱我们可以得到如下信息：•晶体中原子层的面间距；•确定单晶或者晶粒的取向；•确定未知材料的晶体结构；•测量晶粒的大小、形状和内应力。Dr.DiWu,NanjingUniversity4可见光的衍射Fraunhofer衍射：远场衍射，即平面波和散射体的相互作用；Fresnel衍射：近场衍射，除了Fraunhofer衍射以外的衍射；电子衍射在大多数情况下属于Fraunhofer衍射，但是在某些特殊的场合属于Fresnel衍射。Dr.DiWu,NanjingUniversity5波前Huygens:波前上的每一个点都是一个球面波源，这些球面波相互干射形成新的波前。Everypointonthewavefrontisasourceforsphericalwaves.Thesesphericalwavesinterferencewitheachothertoformthenewwavefront.Dr.DiWu,NanjingUniversity6双缝衍射从两个狭缝出射的波之间有光程差，因而有位相差，在距离r,位相差为。sin2ddrtieEE01sin202ditieeEEplanewaveDr.DiWu,NanjingUniversity7Doubleslitdiffractionmaximumintensityator21EEE)1(sin20ditieeE)(sinsinsin0diddiditieeeeE)sincos(2)sin(0deEtdi))sin2cos(1(2)sin(cos4020dIdII2sin2ndndsinDr.DiWu,NanjingUniversity8MultislitdiffractionrdNEEEEE...321)...1()1(20NiiitieeeeE)11(0iiNtieeeE)()(2222220iiiiNiNiNtieeeeeeeE2sin2sin)21(0NeEtNisin2dplanewaveDr.DiWu,NanjingUniversity9Multislitdiffraction20sinsinsinsinddNIINN0sinsinNNnsinsinndsin02maxINI,whenndsinDr.DiWu,NanjingUniversity10-1.0-0.50.00.51.0-10010203040506070N=8d=100nm=500nmIntensity(a.u.)Multislitdiffraction20sinsinsinsinddNIImdNsin0minIhNmdsinmandhareintegers.-1.0-0.50.00.51.0-10010203040506070N=4d=100nm=500nmIntensity(a.u.)Dr.DiWu,NanjingUniversity11MultislitdiffractionThereareN-1diffractionminimumsbetweentwodiffractionmaximums.hNmdsinNmdsinm=1,2,3,…,N-1NdsinandNdsincorrespondtotwointensityminimumsaroundadiffractionmaximum.-0.2-0.10.00.10.2-10010203040506070N=8d=100nm=500nmIntensity(a.u.)Dr.DiWu,NanjingUniversity12MultislitdiffractionThewidthofthediffractionpeakis.LargerNgeneratessharperpeaks.ToX-raydiffraction,Nisdirectlyassociatedwiththesizeofcrystallitesunderdetection.NNdsinNdsinNdNddN22Dr.DiWu,NanjingUniversity13TotheslitattheoriginO,,whiletotheslitaty,.DiffractionfromslitwithfinitewidthplanewaveOydysupposetheslitofinwidthasacombinationofslitsofdyinwidthtieEE0sin20yitiyeeEEDr.DiWu,NanjingUniversity14DiffractionfromslitwithfinitewidthyyitiyyeeEEEsin202222sin20dydyeeEyiti22sin20sin21yitieieEsin0tieEEsin220sinIIDr.DiWu,NanjingUniversity15Diffractionfromslitwithfinitewidth220sinIIsin=0,or=0I=Imaxthediffractionpeakwidth~2/.=n,orsin=nI=IminDr.DiWu,NanjingUniversity16Diffractionfromasmallhole(aperture)Thepeakwidthis1.22/D.Anyapertureinanymicroscopewouldputlimitationsontheresolution(R).220sinIIsinDDisthediameter.RDRDr.DiWu,NanjingUniversity17GeometricofDiffractionThegeometrictheoryofdiffractionisessentiallythesameforX-rays,electronsandneutrons.Followingassumptionshasbeenmade,Theintensityofthescatteredbeamismuchlowerthanthatoftheincidentbeam.Theinteractionofthescatteredbeamandtheincidentbeamisomitted.Thescatteringofthescatteredbeamisnotconsidered.Thesourceisadequatelyfarfromthescatteringsystemsothattheincidentbeamisregardedasaplanewave.Thesizeofthescatteringsystemissufficientlysmall.Dr.DiWu,NanjingUniversity18点散射体的散射OP2putthescatteringcenterattheoriginOandconsiderthescatteredbeamatPSandSareunitvectorinthedirectionofincidentandscatteredbeam0SSROPcomparedwiththephaseatO,thephaseatPisretardedbyR2obviously,thebeamisscatteredinalldirections.Thescatteredbeamisspherical.S0SDr.DiWu,NanjingUniversity19点散射体的散射OP2tieEE0Iftheelectriccomponentoftheincidentbeamisrepresentedas)(02stieREEtheamplitudeofthescatteredbeamatP,E2shouldbesisthephaseretardinducedbythescatteringcenteritselfwewriteE2as)(022stieREfEf2isthescatteringcoefficientS0SDr.DiWu,NanjingUniversity20点散射体的散射ThebeamintensityIinacertaindirectionisdefinedastheenergyscatteredintounitsolidangleinthisdirectioninunittime.OP2222EIThebeamintensityinthedirectionofisS2202)(RREf022If2RTheintroductionofbeamintensityI2ismuchconvenientbecauseR,whichisrelatedtodistanceisavoided.S0SDr.DiWu,NanjingUniversity21随机分布的点散射体的散射O2O1OI0WefirstconsiderasystemwithtwoscatteringcentersatO1andO2.r2r1S0SInthedirectionS,theamplitudeofvibrationE2is)(02)(02221sstitieREfeREfE)(21011SrSr)(22022SrSrDr.DiWu,NanjingUniversity22随机分布的点散射体的散射definethescatteringvector0SSHE2canbewrittenas)(2122)(022rHirHitieeeREfEs)(21011SrSr)(22022SrSr112rH222rHDr.DiWu,NanjingUniversity23随机分布的点散射体的散射Thescatteringcoefficientofthesystemcanbewrittenas)(11222rHirHieeffThebeamintensitycanstillbeexpressedas02IfI0SSHS/S0/H)(02stieREfEDr.DiWu,NanjingUniversity24随机分布的点散射体的散射Theaboveresultscanbegeneralizedtoasystemofnrandomlydistributedidenticalpointscatteringcenters.Thescatteringcoefficientofasy