现代结构分析方法2009-8

现代结构分析方法

(09－10年度第一学期)第8讲倒易点阵、正点阵与衍射

S0/l=k0S/l=kghkl(hkl)000相机长度Rhklba正交点阵沿c轴投影abcabc入射束d100d1107衍射图标定相；取向

7.1单晶衍射图的产生与标定Whenisqsmall(electrondiffraction),Rd=lL=diffractionconstant,thereflectionspherecutsa2Dreciprocalplane.Indexing:theplanenormal[uvw]andatleastonelowindexspot(hkl)(normallytwospots),withhu+kv+lw=0.S0/l=k0S/l=kghkl(hkl)000相机长度Rhkl[-101](101)(010)Plotthefcc[110]diffractionpattern1)Thezoneaxis[uvw]isperpendiculartoalltheplaneindices(hkl)sothathu+kv+lw=0.2)Distinctionsofanfcclattice:allevenorodd(like111,200,311,220,etc.)3)R1+R2=R3,andR1×R2=[UVW],R1andR2beingthetwoshortvectors4)FixR1(ifaandLlaregiventhenR1isaknownvalue)anddrawR2,cosR1^R2=(h1*h2+k1*k2+l1*l2)/(N1N2);R12/R22=N1/N25)Alltheotherspotsaredeterminedbyn1*R1+n2*R2=Rnh1k1l1h2k2l2h3k3l3R1R2h1k1l1=-111Nhklcpbccfcc1100100

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8220220220220109.5ºh2k2l2=1-11h3k3l3=002indexingusingPDFfilesa)ChoosethreespotssuchasR3=h3k3l3,R1=h1k1l1,R2=h2k2l2.b)di=Ll/Ri,d1=Ll/R1=d2=0.208nm{111},R3=Ll/R3=3/16.6=0.180nm{200}.c)h3k3l3=h1k1l1+h2k2l2:{111}+{111}={200}(111)+(1-1-1)=(200),(111)^(1-1-1)=109.5ºd)[uvw]=R1×R2=R1×R3=R3×R2=[01-1]h1k1l1h2k2l2h3k3l3[uvw]R1R2R1=R2=14.4mm,R1^R2=109.5º.Ll=3.0nm*mm.indexingusingPDFfilesa)ChoosethreespotssuchasR3=h3k3l3,R1=h1k1l1,R2=h2k2l2.b)di=Ll/Ri,d1=Ll/R1=0.180nm{200},R2=R3=Ll/R2=0.109nm{311}.c)h3k3l3=h1k1l1+h2k2l2:{200}+{311}={311}(200)+(-113)=(113),(200)^(-113)=107.5ºd)[uvw]=R1×R2=R1×R3=R3×R2=[0-31]R1R2R3R1=16.7mm,R2=R3=27.5mm,R1^R2=107.5º.Ll=3.0nm*mm.PARAMETERSA=5.8000B=5.8000C=5.8000Å

AF=90.000BT=90.000GM=90.000NUVW=3NSY=1NL=1SY:1-CUBIC;2-TETRA;3-ORTH;4-HEX; 5-MONO;6-TRICLT:1-F;2-I;3-C;4-B;5-A;6-P;7-R;

KUVWH1K1L1H2K2L2R2/R1R3/R1FAId1d2111102-2-2021.0001.000120.002.0512.051

2110-11-1-1111.0001.15570.533.3493.34931000-2000-21.0001.41490.002.9002.90043322-2011-31.1731.54190.002.0511.74952212-2002-41.5811.581108.432.0511.29762111-1-102-21.6331.91590.003.3492.051731000-2-13-11.6581.65872.452.9001.74983110-222-4-21.7321.73273.222.0511.184932202-2-4242.1212.121103.632.051.967103312-2020-62.2362.23677.082.051.9171121000-2-2402.2362.44990.002.9001.297123211-1-1-13-32.5172.58297.613.3491.3311332000-2-4603.6063.74290.002.900.804R2R1109.5º111111002[110]R3220R1=R2=14.4mm,R1^R2=109.5º.Ll=48.226A*mm.PARAMETERSA=5.8000B=5.8000C=5.8000Å

AF=90.000BT=90.000GM=90.000NUVW=3NSY=1NL=1SY:1-CUBIC;2-TETRA;3-ORTH;4-HEX; 5-MONO;6-TRICLT:1-F;2-I;3-C;4-B;5-A;6-P;7-R;

KUVWH1K1L1H2K2L2R2/R1R3/R1FAId1d2111102-2-2021.0001.000120.002.0512.0512110-11-1-1111.0001.15570.533.3493.34931000-2000-21.0001.41490.002.9002.90043322-2011-31.1731.54190.002.0511.74952212-2002-41.5811.581108.432.0511.29762111-1-102-21.6331.91590.003.3492.051731000-2-13-11.6581.65872.452.9001.74983110-222-4-21.7321.73273.222.0511.184932202-2-4242.1212.121103.632.051.967103312-2020-62.2362.23677.082.051.9171121000-2-2402.2362.44990.002.9001.297123211-1-1-13-32.5172.58297.613.3491.3311332000-2-4603.6063.74290.002.900.804R1R2R3R1=R2=16.7mm,R1^R2=90º.Ll=48.226

A*mm.PARAMETERSA=5.8000B=5.8000C=5.8000Å

AF=90.000BT=90.000GM=90.000NUVW=3NSY=1NL=1SY:1-CUBIC;2-TETRA;3-ORTH;4-HEX; 5-MONO;6-TRICLT:1-F;2-I;3-C;4-B;5-A;6-P;7-R;

KUVWH1K1L1H2K2L2R2/R1R3/R1FAId1d2111102-2-2021.0001.000120.002.0512.0512110-11-1-1111.0001.15570.533.3493.34931000-2000-21.0001.41490.002.9002.90043322-2011-31.1731.54190.002.0511.74952212-2002-41.5811.581108.432.0511.29762111-1-102-21.6331.91590.003.3492.051731000-2-13-11.6581.65872.452.9001.74983110-222-4-21.7321.73273.222.0511.184932202-2-4242.1212.121103.632.051.967103312-2020-62.2362.23677.082.051.9171121000-2-2402.2362.44990.002.9001.297123211-1-1-13-32.5172.58297.613.3491.3311332000-2-4603.6063.74290.002.900.804R1=16.7mm,R2=R3=27.5mm,R1^R2=107.5º.Ll=48.226A*mm.R1R2R37.1单晶衍射图的绘制与标定ProceduresSurveytheliteraturetocollectinformationofpossiblephases.ThreepossibleroutestoreachitsfullindexingCalculatedspacingsandcomparewithstandardpowderXRDdata;MeasureR2/R1,R2^R1,andcomparewithtablesinarchives;Tryacubicphase;Usedoubletiltingtodeterminedirectlythe3Dreciprocallattice.Ingeneralthreeindependentpatternsarenecessarytodetermineareciprocalstructure.R1R2109.5ºR3Adiffractionpatternisshownontheright:R1=R2=14.4mm,R1^R2=109.5º.Ll=3.0nm*mm.7.2立方点阵标定R.d=Ll,d=a/(h2+k2+l2)R2N=h2+k2+l2ChoosethreeshortestreciprocalvectorsR1,R2,R3,R3=R1+R2,measuretheangleR1^R2.Calculated1,d2,(R2/R1)2=N2/N1,(R3/R1)2=N3/N1Judgepossiblecombinationsofhkl.Ingeneralthreeindependentpatternsarenecessarytodeterminethereciprocalstructure.h2+k2+l2（hkl）简单立方体心立方面心立方1100100

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8220220220220R1R2109.5ºR37.2CubicindexingR.d=Ll,d=a/(h2+k2+l2)R2N=h2+k2+l2ChoosethreeshortestreciprocalvectorsR1,R2,R3,R3=R1+R2,measuretheangleR1^R2.Calculated1,d2,(R2/R1)2,(R3/R1)2.Judgepossiblecombinationsofhkl.Ingeneralthreeindependentpatternsarenecessarytodeterminethereciprocalstructure.R1R2109.5ºR3Adiffractionpatternisshownontheright:R1=R2=14.4mm,R1^R2=109.5º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)20.208 0.208 1 (1.155)2=4/37.2CubicindexingR1R2109.5ºR3R1=R2=14.4mm,R1^R2=109.5º.Ll=3.0nm*mm.h2+k2+l2（hkl）简单立方体心立方面心立方1100100

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8220220220220d1 d2 (R2/R1)2(R3/R1)20.208 0.208 1 (1.155)2=4/3=8/6111 111 111/111002/1117.2CubicindexingR1R2109.5º111111002[110]R3R1=R2=14.4mm,R1^R2=109.5º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)20.208 0.208 1 (1.155)2=4/3111 -1-11 -1-11/111002/111cF,a=d111*N111=0.36nm.奥氏体铁Self-consistencyofindices:(111)+(-1-11)=(002)Anglecheck:(111)^(-1-11)=109.5ºLatticeconstantcheck:a=d111*3=0.360nmTwomorepatternsarenecessarytoassurethephaseidentificationExercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstants.R1R2R3R1=R2=R3=23.6mm,R1^R2=120º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)2 lattice constant0.127 0.127 1 1110 -101 -101/110011/110 cP,cI 0.18nm220 -202 -202/220022/220 cF 0.36nm[111]N（hkl）cPbccfcc1100100

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8220220220220两种可能Exercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstants.R1R2R3R1=R2=R3=23.6mm,R1^R2=120º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)2 lattice constant0.127 0.127 1 1110 -101 -101/110011/110 cP,cI 0.18nm220 -202 -202/220022/220 cF 0.36nm[111]N（hkl）cPbccfcc1100100

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8220220220220两种可能Exercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstants.R1R2R3R1=R2=16.7mm,R1^R2=90º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)2 latticeconstant0.180 0.180 1 2100 010 010/100110/100 0.180nm(=0.18*N100)1-10 110 110/1-10200/1-10 0.255nm(=0.18*N110)200 020 020/200220/200 0.360nm(=0.18*N200)[001]N（hkl）cPbccfcc1100100

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8220220220220三种可能Exercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstants.R1R2R3R1=R2=16.7mm,R1^R2=90º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)2 latticeconstant0.180 0.180 1 2100 010 010/100110/100 0.180nm(=0.18*N100)1-10 110 110/1-10200/1-10 0.255nm(=0.18*N110)200 020 020/200220/200 0.360nm(=0.18*N200)[001]N（hkl）cPbccfcc1100100

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8220220220220三种可能Exercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstant.R1R2R3R1=16.7mm,R2=R3=27.5mm,R1^R2=107.5º.Ll=3.0nm*mm.d1 d2 (R2/R1)2 (R3/R1)20.180 0.109 11/4 11/4002 -31-1 -31-1/002 -311/002 cF,0.36nm

[130]N（hkl）cPbccfcc1100100

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822022022022092213002213001031031021011311311311Exercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstant.R1R2R3R1=16.7mm,R2=R3=27.5mm,R1^R2=107.5º.Ll=3.0nm*mm.d1 d2 (R2/R1)2 (R3/R1)20.180 0.109 11/4 11/4002 -31-1 -31-1/002 -311/002 cF,0.36nm

[130]N（hkl）cPbccfcc1100100

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822022022022092213002213001031031021011311311311Exercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstants.R1R2R3R1=16.7mm,R2=23.6mm,R1^R2=90º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)2 a0.180 0.127 2 3001 -110 -110/001-111/001 cP 0.18nm1-10 002 002/1-101-12/1-10 cI 0.255nm002 -220 -220/002-222/002 ×[110]N（hkl）cPbccfcc1100100

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82202202202209221300221300103103102101131131131112222222222222两种可能Exercises:indexthefollowingpatternsincubicschemes.Notethattheremaybemorethanonepossibilitiesforeachpattern.Givethecorrespondinglatticetypesandconstants.R1R2R3R1=16.7mm,R2=23.6mm,R1^R2=90º.Ll=3.0nm*mm.d1 d2 (R2/R1)2(R3/R1)2 a0.180 0.127 2 3001 -110 -110/001-111/001 cP 0.18nm1-10 002 002/1-101-12/1-10 cI 0.255nm002 -220 -220/002-222/002 ×[110]N（hkl）cPbccfcc1100100

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82202202202209221300221300103103102101131131131112222222222222两种可能7.3三维倒易点阵的直接确定：双倾doubletilting法000a1a2a3000a1a2a3a1a2a3000100010[001]010001[100]a1=26.56120110[210]120001a2=18.43[110]110001111a3=18.43[010]0000011001017.3三维倒易点阵的直接确定：双倾doubletilting法图3.4六角相Al5FeNi的选区电子衍射花样Figure3.4SAEDpatternsarrangedinastereomannerofthehexagonalAl5FeNiphase.7.4多晶衍射与粉末衍射环Forrandomlyorientatedaggregatesofpolycrystals,thereciprocallatticebecomesaseriesofspheres.TheradiiRi=Ll/di.Thenumberofpointscontributingtoeachsphereisknownasthemultiplicity.7.4多晶衍射与粉末衍射环7.4多晶衍射与粉末衍射环典型非晶电子衍射

XRDPowderpattern图3.5铸态合金Al71Fe5Ni24的X射线(λCuK=0.15406nm