材料表征教学资料 diffraction

1、dr. di wu, nanjing university1dr. di wu, nanjing university2dr. di wu, nanjing university3n从衍射谱我们可以得到如下信息：从衍射谱我们可以得到如下信息： 晶体中原子层的面间距；晶体中原子层的面间距； 确定单晶或者晶粒的取向；确定单晶或者晶粒的取向； 确定未知材料的晶体结构；确定未知材料的晶体结构； 测量晶粒的大小、形状和内应力。测量晶粒的大小、形状和内应力。dr. di wu, nanjing university4dr. di wu, nanjing university5dr. di wu, nanj

2、ing university6sin2ddrtieee01sin202ditieeeeplane wavedr. di wu, nanjing university721eee)1 (sin20ditieee)(sinsinsin0diddiditieeeee)sincos(2)sin(0deetdi)sin2cos(1 (2)sin(cos4020didii2sin2 ndndsindr. di wu, nanjing university8rdneeeee.321).1 ()1(20niiitieeeee)11(0iintieeee)()(2222220iiiininintieeeeeee

3、e2sin2sin)21(0neetnisin2dplane wavedr. di wu, nanjing university920sinsinsinsinddniinn0sinsinnnnsinsinndsin02maxini, whenndsindr. di wu, nanjing university10-1.0-0.50.00.51.0-10010203040506070n=8d=100 nm=500 nmintensity (a. u.)20sinsinsinsinddniimdnsin0minihnmdsinm and h are integers.-1.0-0.50.00.51

4、.0-10010203040506070n=4d=100 nm=500 nmintensity (a. u.)dr. di wu, nanjing university11hnmdsinnmdsinm=1, 2, 3, , n-1ndsinand ndsin-0.2-0.10.00.10.2-10010203040506070n=8d=100 nm=500 nmintensity (a. u.)dr. di wu, nanjing university12nndsinndsinndnddn22dr. di wu, nanjing university13plane waveoydysuppos

5、e the slit of in width as a combination of slits of dy in widthtieee0sin20yitiyeeeedr. di wu, nanjing university14yyitiyyeeeeesin202222sin20dydyeeeyiti22sin20sin21yitieieesin0tieeesin220sinii dr. di wu, nanjing university15220sinii sin = 0, or = 0i = imaxthe diffraction peak width 2/. = n, or sin =

6、ni = imindr. di wu, nanjing university16220sinii sindd is the diameter.dr. di wu, nanjing university17dr. di wu, nanjing university18op20ssrop r2s0sdr. di wu, nanjing university19op2tieee0)(02stieree)(022stierefes0sdr. di wu, nanjing university20op2222ei s2202)(rref022if2rs0sdr. di wu, nanjing unive

7、rsity21o2o1oi0r2r1s0s)(02)(02221sstitiereferefe)(21011srsr)(22022srsrdr. di wu, nanjing university220ssh)(2122)(022rhirhitieeerefes)(21011srsr)(22022srsr112rh 222rh dr. di wu, nanjing university23)(11222rhirhieeff02ifi 0sshs/s0 /h)(02stierefedr. di wu, nanjing university24njrhijeff122dr. di wu, nanj

8、ing university25njrhijjeff122)(dr. di wu, nanjing university26dr. di wu, nanjing university27as0snjajhieff122202sinsinahahnifidr. di wu, nanjing university28hahn1lchkbhhahdr. di wu, nanjing university290sshs0 s hc lbkahhdr. di wu, nanjing university302g (hkl)o (000)h (hkl)ls/s0 /0sshhkkh0skh00sk dr.

9、 di wu, nanjing university31o (000)h (hkl)ls/s0 /2dh1sin2d21sin1ddr. di wu, nanjing university32nacbandsin2acb1122ddr. di wu, nanjing university33ndhklsin2sin2ndhklsin2)(hklnddr. di wu, nanjing university34s0 /o (000)s0 /lhdr. di wu, nanjing university35animationdr. di wu, nanjing university362/dr.

10、di wu, nanjing university37dr. di wu, nanjing university38dr. di wu, nanjing university39dr. di wu, nanjing university40dr. di wu, nanjing university41dr. di wu, nanjing university42dr. di wu, nanjing university43dr. di wu, nanjing university44dr. di wu, nanjing university45dr. di wu, nanjing univer

11、sity46dr. di wu, nanjing university47dr. di wu, nanjing university48dr. di wu, nanjing university49dr. di wu, nanjing university50dr. di wu, nanjing university51ws21or)1 (22wsdr. di wu, nanjing university52222lkhadhklndsin2)(4sin222222lkhadr. di wu, nanjing university53dr. di wu, nanjing university5

12、4dr. di wu, nanjing university55dr. di wu, nanjing university56x-ray sourcedetectoramplifiercomputersamplesourcesampledetector2dr. di wu, nanjing university57010203040506070020004000600080001000012000intensity (a.u.)2 (degrees)dr. di wu, nanjing university58dr. di wu, nanjing university59dxexffxfxi2

13、)()()(defxffxi21)()()(dr. di wu, nanjing university60)()()()(xgbxfaxbgxaf)()(fxf)(1)(afaaxfaiefaxf2)()(dr. di wu, nanjing university61dxxxgxfxgxf)()()()()()(fxf)()(gxg)()()()(gfxgxf)()()()(gfxgxfdr. di wu, nanjing university62dr. di wu, nanjing university630)(axax ax1)(dxaxdr. di wu, nanjing univers

14、ity6422)(xaeaxg)(xa)(1)(22222)(xbebabeabxaxabaxbadr. di wu, nanjing university65dexxi2)()(1)()(2dxexxidexxi2)(dr. di wu, nanjing university66)(r)()(nnrrrlcnbnanrn321dr. di wu, nanjing university67)()()(axxfxhdxxaxxf)()()(axf *=dr. di wu, nanjing university68)()()()(nnnnrrfrrrfrh)(rf)(rf)(rhdr. di wu

15、, nanjing university69)(x点散射体1)()(x一维晶格)(nax)()(naxfnaienax2)()(点散射体2ff 一维晶格jrhijeff22nnhinanahiefef2222*dr. di wu, nanjing university7011111)(222aiainaieeefha ha h is an integer.)(1)()(ahahaf01)1)(1 (11)(2222aiaiaiaieeeef)(fdr. di wu, nanjing university71hahaf)(1)(hhvf)(1)(hdr. di wu, nanjing unive

16、rsity72)(rdvdvr)(rrie2vridverf2)()(unit: the scattering amplitude of a single scattering centerdr. di wu, nanjing university73scattering center distribution function in a single cell, )()(rr stands for the cell in an ideal infinite crystallattice function of a infinite crystal)()(nnrrrlfor the latti

17、ce of finite crystal)()(rrl01)(rinside in the crystaloutside in the crystaldr. di wu, nanjing university74)()()(rrlrthe relative diffraction amplitude is therefore, )()()(rrlrfc)()()(rrlr)(rfhdr. di wu, nanjing university75hrihdverf2)(is the diffraction amplitude of a single cell, called the structu

18、re factor)()()()()(rrlrrlrhhv)()(1hhv)(1is the fourier transform of the size factor)()(rdr. di wu, nanjing university76dverfrhih2)(jlzkyhxijjrhijjjjjefef)(22)()()(jjjjrrrrdverjrhij2)(jrrrdverjrrhijj)(2)(jrhijjedvr2)(hdr. di wu, nanjing university77)1 ()(lkhihklefflkhevenff2lkhodd0f(110) (200) (220)

19、(121) (100) (111) (102) (300) dr. di wu, nanjing university78)()(lkhialnihkleffflkhevenalniffflkhoddalnifffdr. di wu, nanjing university79)1 ()()()(hlilkikhihkleeeffff40fh, k, l: all even or all oddh, k, l: mixed even and odddr. di wu, nanjing university80)1)()()()()(hlilkikhilkhiclnahkleeeefff)(4cl

20、nafff0fh, k, l: all evenh, k, l: mixed even and oddh, k, l: all odd)(4clnafffdr. di wu, nanjing university81)1)(1 ()()()()(2hlilkikhilkhihkleeeeff0f0fh, k, l: all evenh, k, l: mixed even and oddh, k, l: all odd)1 (4iffnlkh2n: oddn: evenff8dr. di wu, nanjing university82)1)()()()()(2hlilkikhilkhiasga

21、hkleeeefff)(4asgafff0fh, k, l: all evenh, k, l: mixed even and oddh, k, l: all odd)(4asgaifffnlkh2n: oddn: even)(4asgafffdr. di wu, nanjing university83)()()()(hlilkikhinialhkleeefffnialfff3h, k, l: all even or all oddh, k, l: mixed even and oddnialfffdr. di wu, nanjing university84h, k, l: mixed ev

22、en and odd0fdisordered structurenialfffordered structuredr. di wu, nanjing university85ra: the percentage of a atoms occupation on a sitesca: the percentage of a atoms in the crystalaaaccrs1dr. di wu, nanjing university86ordered structure: ra=1, s=1disordered structure: ra=ca, s=0aaaccrs1in ni3al st

23、ructure, if h, k, and l are mixed with even and odd integers)(nialhklffsfdr. di wu, nanjing university87dvedverriri22)()(cba321cczbbyaaxrthe 3 dimensions of the crystal is n1a, n2b, and n3c. dxdydzdzccdybbdxaadv)()(dr. di wu, nanjing university88dveri2)(dzedyedxecnczibnbyianaxi332211020202anaxianaxi

24、eiadxe111102102211121sin) 1(21111neaeianinidr. di wu, nanjing university89dzedyedxecnczibnbyianaxi332211020202)()(333222111332211sinsinsinnnniennnabciiiinvsinsin)(at the vicinity of the origin in the reciprocal lattice, i is small, thereforedr. di wu, nanjing university90iiiihnfi222sinsiniiiink22sin

25、sin111n221n331ndr. di wu, nanjing university91dr. di wu, nanjing university92real spacereciprocal spacedr. di wu, nanjing university93dr. di wu, nanjing university94ls/s0 /hls/s0 /hdr. di wu, nanjing university95iiiihiiiihnfnfi222222sinsinsinsindr. di wu, nanjing university96222iinien共同点： 它们在 时取最大值

26、。 当 时， 它们都表现出函数的特性 曲线下的面积相同，均为 。iiin22sinsin2in0iinindr. di wu, nanjing university97inihiiiihiienfnfi2222222sinsin2)(22nahenfcnbnanan3212)(22thenfidr. di wu, nanjing university982)2(cos(22thenf)2(cos)sin2(h2)(22thenfi22nfihm2)2(cos(222thmenfii2)2(cos(21tecoscos2ln2)2(221tktdr. di wu, nanjing univers

27、ity99miid)2(mi02dr. di wu, nanjing university100if the angle slightly deviated from the braggs angle, the phase difference of adjacent planes changes accordingly.acb1122db2bdsin22)(2b)sin(22bddr. di wu, nanjing university101)cossincos(sin22)sin(22bbbdd)cos2sin2(2bbddbd cos222cosbddr. di wu, nanjing

28、university102if scattering amplitude of a single plane is a, m layers scattering amplitude a should be10mkikaeathe intensity is 222221022sin2sin11maeeaaeaiiimmkikdr. di wu, nanjing university103222222sin)(2sin2sinmmmamai02 02)(maiim)cos()2(2sin)()2(222bddmmmaid2cosbddr. di wu, nanjing university104d

29、mdiddmmmaidbmb22222sincos2)cos()2(2sin)()2(bmmdkicosbmtkiidcos)2(89. 0kpractically, 1kdr. di wu, nanjing university105d0d buniform distortionununiform distortiondr. di wu, nanjing university106sin2d0)cos(sin2ddtgdd)( bdifferent values from different part of the crystal, due to ununiform lattice distortion, results in the widened diffraction lines.dr. di wu