1、电子衍射分析及应用电子衍射分析及应用?电子衍射物相鉴定-CuSn(相)?从复合电子衍射图确定取向关系-相与Cu6Sn5 相?从复合电子衍射图推定未知结构-Cu17Sn14电子波在晶体中的弹性散射电子波在晶体中的弹性散射电子波受晶体点阵平面散射,其弹性散射部分在一定方位会相互干涉加强,称为衍射衍射。正空间点阵与倒易点阵正空间点阵与倒易点阵正空间-面心立方倒易空间-体心立方倒易点阵的数学描述倒易点阵的数学描述?正空间与倒易空间的对偶关系衍射的物理光学描述衍射的物理光学描述?电子源-kV?晶体点阵平面(d)?倒易点阵矢(g)g=1/d,g-nhkl?衍射条件:Ewald球与倒易阵点交截衍射的数学描述
2、衍射的数学描述-Bragg反射反射?2dsin=n衍射的数学描述衍射的数学描述-反射球构图反射球构图?(1/)2=g单晶电子衍射图与倒易点阵平面的对应单晶电子衍射图与倒易点阵平面的对应-1倒易点阵平面与晶带的对应关系倒易点阵平面与晶带的对应关系单晶电子衍射图与倒易点阵平面的对应单晶电子衍射图与倒易点阵平面的对应-2(引自吴秀玲等,1996,电子显微学报,252)电子衍射图标定的晶体学数据准备电子衍射图标定的晶体学数据准备?点阵常数-a,b,c;,?点阵平面间距dhkl(ghkl)?点阵平面夹角-(h1k1l1h2k2l2)?原子坐标-x,y,z?空间群对称要素晶体点阵的度量张量晶体点阵的度量张
3、量()()=*ccbcaccbbbabcabaaacbacbaccbcaccbbbabcabaaacbacba?tt-1晶体点阵正倒空间矢量晶体点阵正倒空间矢量=wvulkhtlkhwvuthkltuvwabccbahklabccbauvwcbahklcbauvw1*001010100)()()()()()()()(倒易点阵基矢倒易点阵基矢=cbatcbacbatcbacbatuvwcbahklcbauvw1*)()()(倒易点阵平面构造倒易点阵平面构造uvw=851G1=(0w-v)G2=(w0-u)00001-510-81-1-31-220-151-3-1电子衍射强度与结构因子电子衍射强度
4、与结构因子(1)Cu3Au001衍射图电子衍射强度与结构因子电子衍射强度与结构因子(2)CsCl001 zone电子衍射强度与结构因子电子衍射强度与结构因子(3)CsCl110 zone影响衍射强度的诸因子影响衍射强度的诸因子?原子散射因子 f()?结构因子 F(hkl)=jfjexp(2ihxj+kyj+lzj)?尺寸因子点阵消光与结构消光点阵消光与结构消光?面心立方金属与金刚石结构的硅?六角密堆结构的(001)衍射电子衍射相分析(电子衍射相分析(1)?测量单晶斑点衍射图的基本参数?二边长一夹角?三边长?应用相机长度转换到倒易点阵平面?L=Rd?g1,g2,?验证此倒易点阵平面参数可能与某一
5、相的某一倒易平面相符?允许分析误差-3-5%电子衍射相分析(电子衍射相分析(2)?构成欲对比相的倒易点阵平面(在计算范围内)?与实验图对比?输出结果(1)?换另一个欲对比相?输出结果(n)两相取向关系的电子衍射分析两相取向关系的电子衍射分析两相点阵基矢取向关系的电子衍射分析两相点阵基矢取向关系的电子衍射分析uvw/UVW;(h1k1l1)/(H1K1L1);(h2k2l2)/(H2K2L2)=cbasssssssssCBA333231232221131211两相正倒空间基矢关系两相正倒空间基矢关系1*)()()()(=skksIkcbacbasCBACBAkcbaCBAcbakCBAcbasC
6、BA设则右乘两相点阵的指数变换两相点阵的指数变换(1)如两相有点阵平面(hkl)与(HKL)平行,并将其面间距归一化。则有=LKHslkhlkhsLKHCBAHKLCBAshklCBAHKLcbahkl1*)()()()(两相点阵的指数变换两相点阵的指数变换(2)对于ruvw=RUVW=wvusWVUWVUswvu1利用度量张量矩阵及取向变换矩阵联系两相正、倒空间点阵利用度量张量矩阵及取向变换矩阵联系两相正、倒空间点阵aAa*A*s-1st-1tsTsT-1T-1TrRhHsTsT-1TT-1s-1stt-1正空间倒空间基矢矢量从一张两相重叠的电子衍射斑点图中求从一张两相重叠的电子衍射斑点图中
7、求s矩阵矩阵(1)?(1)u1v1w1/U1V1W1;(2)(h2k2l2)/(H2K2L2)(3)(h3k3l3)/(H3K3L3)?把关系(1)转到倒空间(h1k1l1)/(H1K1L1)?进一步列等式gh1k1l1/|g1|=GH1K1L1/|G1|g2/|g2|=G2/|G2|g3/|g3|=G3/|G3|从一张两相重叠的电子衍射斑点图中求从一张两相重叠的电子衍射斑点图中求s矩阵矩阵(2)(;)(3332221113/30002/20001/13332221113332221113/30002/20001/1333222111111*1*1*sHhshHcbascbalkhlkhlkh
8、DdDdDdLKHLKHLKHCBAcbalkhlkhlkhDdDdDdCBALKHLKHLKHT=无铅焊料无铅焊料CuSn中的物相中的物相(from L.L.Ye et al.,2002)Cu-Sn相图相图?Cu-Sna=4.19A;c=5.086A.?Cu6Sn5a=20.95Ac=25.43A5次调制相的衍射图次调制相的衍射图(from L.L.Ye et al.,2002)六角六角CuSn相的数据相的数据?HKLDAF?0 0 1 5.0860 0.0000?0 1 0 3.6286 3.6117?0 1 1 2.9539 71.9021?0 0 2 2.5430 32.5960?1
9、1 0 2.0950 100.0000?0 1 2 2.0825 67.9954?1 1 1 1.9371 0.0000?0 2 0 1.8143 5.1095?0 2 1 1.7088 45.3492?0 0 3 1.6953 0.0000?1 1 2 1.6170 19.6694?0 1 3 1.5360 40.7461有关物相资料有关物相资料?相,六角NiAs型Cu:(000)(001/2)多余(1/3,2/3,3/4)(2/3,1/3,1/4)?相,单斜晶系a=11.022A,b=7.282Ac=9.827A,b=98.84o(from A.N.Larsson et al.,Acta
10、Cryst.,B50(1994)636)从从-1-11取向衍射图求取向衍射图求s矩阵矩阵-11-102-110000111010010051-101-12-1-11-1-10从从-1-11取向衍射图求取向衍射图求s矩阵矩阵-2=1061.0000145.000189.0000145.0000843.0,59.960645.160275.530645.160484.121039.0000076.0038.00038.0076.0,867.25000556.17778.80778.8556.1711mmhhTTtt从从-1-11取向衍射图求取向衍射图求s矩阵矩阵-3?准备好了三对平行且相等的倒易矢
11、量?(1-10)-(1-12)?(2-11)-(005)?(8.78,-8.78,25.87)-(-9.24,-4.03,1.27)从从-1-11取向衍射图求取向衍射图求s矩阵矩阵-4?列出等式后实施矩阵乘法TTHhHh)(102021201000612.10006118.0999388.1005259.0005259.2005259.1007856.2007856.0007856.1)(11=的含义相当于s从从-1-11取向衍射图求取向衍射图求s矩阵矩阵-5?复核相的基矢?A=a-2c11.044 A,0.2%?B=a+2b7.276 A,0.08%?C=2a+c9.803 A,0.24%?
12、=98.88oCu有序位置的确定有序位置的确定求两相基矢对应矩阵的另一方法求两相基矢对应矩阵的另一方法u2v2w2h2k2l2U2V2W2H2K2L2h1k1l1u1v1w1H1K1L1U1V1W1h3k3l3H3K3L3从两正空间矢叉乘得第三倒易矢从两正空间矢叉乘得第三倒易矢?已知u2v2w2/U2V2W2;h1k1l1/H1K1L1?转换r2-g2,R2-G2;g1-r1,G1-R1?r1Xr2=g3,R1XR2=G3u1w2-v2w1=h3,w1u2-u1w2=k3,u1v2-v1u2=l3?将所有三对倒易矢归一化程序输入数据程序输入数据?Hexagonal-CuSn 4.1900 4.
13、1900 5.0860 90.0000 90.0000 120.0000 5 1?Monoclinic-Cu6Sn5 11.022 7.2820 9.8270 90.0000 98.8400 90.0000 2 1?0-1 1-1-1 0?1 0 0 1-1 2输出结果输出结果?matrixh3=0.0380-0.0759-0.0759?h3Length=0.0235?spH3=0.0227-0.0227-0.0302?H3Length=0.0047?transform matrix=1.0028 1.0007 -2.0038-1.0028 1.0040 -0.0009 2.0056 2.00
14、56 1.0016 相倒易空间构图相倒易空间构图-1-11取向的孪晶畴取向的孪晶畴(from L.L.Ye et al.,2002)CuSn201-Cu6Sn5001取向衍射图取向衍射图010-112000-132020-550-200 001三重调制的衍射图三重调制的衍射图-1(from L.L.Ye et al.,2002)三重调制的衍射图三重调制的衍射图-2100h衍射图衍射图00001001100112354201h衍射图衍射图000010-102-11267从倒空间推出未知结构的倒易基矢从倒空间推出未知结构的倒易基矢(6)-(1)=(11)(3)-(11)=(12)(1)=(0,1/
15、3,1/3),(11)=(-1/3,0,1/3),(12)=(1/3,-1/3,1/3)从倒易基矢反推实空间基矢从倒易基矢反推实空间基矢=1111121213/13/13/13/103/13/13/10*1*scbacbasCBA三倍周期新结构的正空间基矢三倍周期新结构的正空间基矢A=a+2b+c,B=-2a-b+c,C=a-b+cA=B=C=8.862 A=90.34o三重调制三重调制CuxSny的有序畴结构的有序畴结构Index of Fig.(b)?001?111100110-120-2103-3030-303-3000图(图(e)的指标化)的指标化?2-11h?0-14011-102-
16、1-11000300141-241?-1-22h?011图(图(f)的指标化)的指标化011-221-21030033-303-3000图(图(h)的指标化)的指标化?2-2-1h?11-1000-1-10-10-201-23030-3-3-330推定单胞内原子位置推定单胞内原子位置-Cu?The 0 th kind and 0 th atoms posit.=0.0000 0.0000 0.0000?The 0 th kind and 1 th atoms posit.=0.1667 0.1667 0.1667?The 0 th kind and 2 th atoms posit.=0.66
17、67 0.0000 0.3333?The 0 th kind and 3 th atoms posit.=0.8333 0.1667 0.5000?The 0 th kind and 4 th atoms posit.=0.6667 0.3333 0.0000?The 0 th kind and 5 th atoms posit.=0.8333 0.5000 0.1667?The 0 th kind and 6 th atoms posit.=0.3333 0.0000 0.6667?The 0 th kind and 7 th atoms posit.=0.5000 0.1667 0.833
18、3?The 0 th kind and 8 th atoms posit.=0.6667 0.6667 0.6667?The 0 th kind and 9 th atoms posit.=0.8333 0.8333 0.8333?The 0 th kind and 10 th atoms posit.=0.3333 0.6667 0.0000?The 0 th kind and 11 th atoms posit.=0.5000 0.8333 0.1667?The 0 th kind and 12 th atoms posit.=0.0000 0.6667 0.3333?The 0 th k
19、ind and 13 th atoms posit.=0.1667 0.8333 0.5000?The 0 th kind and 14 th atoms posit.=0.0000 0.3333 0.6667?The 0 th kind and 15 th atoms posit.=0.1667 0.5000 0.8333?The 0 th kind and 16 th atoms posit.=0.1945 0.8611 0.1945The 1 th kind and 0 th atoms posit.=0.3611 0.0278 0.3611The 1 th kind and 1 th
20、atoms posit.=0.6944 0.0278 0.0278The 1 th kind and 2 th atoms posit.=0.9722 0.6389 0.6389The 1 th kind and 3 th atoms posit.=0.3611 0.3611 0.0278The 1 th kind and 4 th atoms posit.=0.6944 0.6944 0.3611The 1 th kind and 5 th atoms posit.=0.9722 0.9722 0.3055The 1 th kind and 6 th atoms posit.=0.3055
21、0.6389 0.3055The 1 th kind and 7 th atoms posit.=0.3611 0.6944 0.6944The 1 th kind and 8 th atoms posit.=0.3056 0.3056 0.6389The 1 th kind and 9 th atoms posit.=0.0278 0.6944 0.0278The 1 th kind and 10 th atoms posit.=0.0278 0.0278 0.6945The 1 th kind and 11 th atoms posit.=0.6389 0.6389 0.9722The 1
22、 th kind and 12 th atoms posit.=0.6389 0.9722 0.6389The 1 th kind and 13 th atoms posit.=0.0278 0.3611 0.3611Cu17Sn14相中相中Sn原子位置原子位置从结构因子数据分析新相不是三角系从结构因子数据分析新相不是三角系?HKLDAF?-1 0 0 8.8617 13.6673?0-1 0 8.8617 30.4738?0 0 1 8.8617 4.2702?0 1 0 8.8617 30.4738?1 0 0 8.8617 13.6673?-1 1 0 6.2849 11.4301?-1
23、 0 1 6.2849 18.0917?1-1 0 6.2849 11.4301?0-1 1 6.2849 18.4344?-1-1 0 6.2476 14.6413?0 1 1 6.2476 6.0022?1 0 1 6.2476 12.6029?1 1 0 6.2476 14.6413新相倒易平面基本数码新相倒易平面基本数码?Zone axis uvw=-1 1 1?No H K L d(A)g(1/A)Fg/g1 phi HL pg 1/R?0 0 -1 1 6.2849 0.1591 18.4344 1.0000 0.0000 -1-0.3320 0.0000?1 -1 -1 0 6.
24、2476 0.1601 14.6413 1.0060 60.1959 0 0.6640 0.0000?2 1 0 1 6.2476 0.1601 12.6029 1.0060 60.1959 01.0000 0.0650?Zone axis uvw=2 0 1?No H K Ld(A)g(1/A)Fg/g1 phi HL pg 1/R?0 0 -1 0 8.8617 0.1128 30.4738 1.0000 0.0000 0-0.0036 0.0000?1 -1 0 2 3.9725 0.2517 13.7625 2.2307 90.1528 0 0.4007 0.0000?2 -1 -1 2 3.6286 0.2756 16.1102 2.4422 65.9814 1 1.0000 0.0506总结总结?电子波长短使单晶电子衍射图与倒易点阵的对应显得直观,有利于物相鉴定?两相复合电子衍射图可以提供两相晶体点阵基矢对应性的重要信息?在一些特定条件下,两相复合电子衍射图也可以确定未知有序结构