电子衍射花样标定

4.4 电子衍射谱标定 Indexing: the zone axis [uvw] (plane normal) and at least one low index spot (hkl) (normally two spots), with hu+kv+lw=0. 4.4 电子衍射谱标定 图3.9 Al3Ni 型正交相Al74.8Fe1.5Ni23.7的选区电子衍射花样 Indexing of 2D patterns Æ3D reciprocal lattice Æ3D real lattice Æorientation/phase identification 4.4.1 The size of diffraction patterns (1/λ)/ghkl＝L/Rhkl’ R’d = λL When is θ small (electron diffraction), Rd=λL=diffraction constant S0/λ= k0 S/λ= k ghkl (hkl) 000 (hkl) L=相机 长度 θ Rhkl ’ Rhkl 4.4.2 Indexing a pattern of a known substance A table of interplanar spacings d is needed. a) Choose three spots such as h3k3l3, h1k1l1, h2k2l2. b) Measure the d values, and thus determine the indices. c) By trial and error a consistent set of indices is chosen such that h3k3l3= h1k1l1 + h2k2l2. d) [uvw], the zone axis, is obtained by any two vectors (e.g. R1×R2) S0/λ= k0 S/λ= k ghkl (hkl) 000 相机长度 Rhkl h1k1l1h2k2l2 h3k3l3 [uvw] R1R2 4.4.2 Indexing a pattern of a known substance Example: an fcc crystal with a = 0.58nm. d=a/(h2 +k2 +l2)1/2. A diffraction pattern is shown below with R1=R2=8.96mm, R1^R2=109.5º. Lλ=3.0 nm.mm. a) Choose three spots R1, R2, R3 (R3 = R1 + R2 ) b) d1= d2= Lλ/R1= 0.335nm, Æ {111}. c) A consistent set of indices is 002= 111 + 111. d) R1×R2=[110], the zone axis晶带轴. R1R2 109.5º 111111 002 [110] R3 a) 直接利用已知d值标定 已知物质的d值计算 1、使用公式：立方系 d=a/(h2 +k2 +l2)1/2 2、使用软件：Carine 3、查XRD 标准 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 粉末卡 Standard powder XRD data; b) 查表标定法 利用软件计算出某种物质所有可能的衍射谱(R1+ R2=R3) 与实验谱比较 reci.exe fi2.dat reci.exe PARAMETERS A= 5.8000 B= 5.8000 C= 5.8000 Å AF= 90.000 BT= 90.000 GM= 90.000 NUVW= 3 NSY= 1 NL= 1 SY: 1-CUBIC; 2-TETRA; 3-ORTH; 4-HEX; 5-MONO; 6-TRIC LT: 1-F; 2-I; 3-C; 4-B; 5-A; 6-P; 7-R; K U V W H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI d1 d2 1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 2.051 2.051 2 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 3.349 3.349 3 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 2.900 2.900 4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 2.051 1.749 5 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 2.051 1.297 6 2 1 1 1 -1 -1 0 2 -2 1.633 1.915 90.00 3.349 2.051 7 3 1 0 0 0 -2 -1 3 -1 1.658 1.658 72.45 2.900 1.749 8 3 1 1 0 -2 2 2 -4 -2 1.732 1.732 73.22 2.051 1.184 9 3 2 2 0 2 -2 -4 2 4 2.121 2.121 103.63 2.051 .967 10 3 3 1 2 -2 0 2 0 -6 2.236 2.236 77.08 2.051 .917 11 2 1 0 0 0 -2 -2 4 0 2.236 2.449 90.00 2.900 1.297 12 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 3.349 1.331 13 3 2 0 0 0 -2 -4 6 0 3.606 3.742 90.00 2.900 .804 R2 R1 109.5º 111 111 002 [110] R3 220 fi2.dat 例：γ-Fe, R1R2 109.5º 111111 002 [110] R3 γ-Fe, a = 0.36nm. R1= R2=14.4mm, R3=16.7mm, R1^R2=109.5º. Lλ=3.0 nm.mm. dhkl (hkl) Teta I% 0.2078 (111) 21.75 100 0.1800 (002) 25.34 46 0.1273 (022) 37.24 26 0.1085 (113) 45.21 31 0.1039 (222) 47.83 9 0.0900 (004) 58.86 6 0.0826 (313) 68.85 33 0.0805 (024) 73.11 41 例：γ-Fe, R1R2 109.5º R3 γ-Fe, a = 0.36nm. R1= R2=14.4mm, R3=16.7mm, R1^R2=109.5º. Lλ=3.0 nm.mm. 例：γ-Fe, R1R2 109.5º R3 γ-Fe, a = 0.36nm. R2/R1 =1 R1= R2=14.4mm, R3=16.7mm, R1^R2=109.5º. Lλ=3.0 nm.mm. PARAMETERS A= 3.6000 B= 3.6000 C= 3.6000 AF= 90.000 BT= 90.000 GM= 90.000 NUVW= 3 NSY= 1 NL= 1 SY: 1-CUBIC; 2-TETRA; 3-ORTH; 4-HEX; 5-MONO; 6-TRIC LT: 1-F; 2-I; 3-C; 4-B; 5-A; 6-P; 7-R; K U V W H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2 1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.273 2 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 2.078 2.078 3 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 1.800 1.800 4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.085 5 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 1.273 .805 111111 002 [110] 例：γ-Fe, a = 0.36nm. R1=16.7mm R2=37.3mm, R1^R2=90º. Lλ=3.0 nm.mm. 2,-4,42,-4,22,-4,02,-4,-22,-4,-4 0,0,40,0,20,0,-20,0,-4 -2,4,4-2,4,2-2,4,0-2,4,-2-2,4,-4 Zone axis : [210] R1 R2 dhkl (hkl) Teta I% 2.078 (111) 21.75 100 1.800 (002) 25.34 46 1.273 (022) 37.24 26 1.085 (113) 45.21 31 1.039 (222) 47.83 9 0.900 (004) 58.86 6 0.826 (313) 68.85 33 0.805 (024) 73.11 41 K U V W H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2 1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.273 2 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 2.078 2.078 3 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 1.800 1.800 4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.085 5 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 1.273 .805 6 2 1 1 1 -1 -1 0 2 -2 1.633 1.915 90.00 2.078 1.273 7 3 1 0 0 0 -2 -1 3 1 1.658 1.658 107.55 1.800 1.085 8 3 1 1 0 -2 2 2 -4 -2 1.732 1.732 73.22 1.273 .735 9 3 2 2 0 2 -2 -4 2 4 2.121 2.121 103.63 1.273 .600 10 3 3 1 2 -2 0 0 2 -6 2.236 2.236 102.92 1.273 .569 11 2 1 0 0 0 -2 -2 4 0 2.236 2.449 90.00 1.800 .805 12 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 2.078 .826 13 3 2 0 0 0 -2 -4 6 0 3.606 3.742 90.00 1.800 .499 例：γ-Fe, a = 0.36nm. R1=16.7mm, R2=37.3mm, R2/ R1=2.2335 R1^R2=90º. Lλ=3.0 nm.mm. 2,-4,22,-4,0 0,0,2 Zone axis : [2,1,0] R1 R2 例：γ-Fe, a = 0.36nm. R1=14.4mm, R2=23.6mm R1^R2=90º. Lλ=3.0 nm.mm. dhkl (hkl) Teta I% 2.078 (111) 21.75 100 1.800 (002) 25.34 46 1.273 (022) 37.24 26 1.085 (113) 45.21 31 1.039 (222) 47.83 9 0.900 (004) 58.86 6 0.826 (313) 68.85 33 0.805 (024) 73.11 41 2,0,-4 2,-2,-2 2,-4,0 1,1,-3 1,-1,-1 1,-3,1 0,2,-2 0,-2,2 -1,3,-1 -1,1,1 -1,-1,3 -2,4,0 -2,2,2 -2,0,4 Zone axis : [211] R1 R2 K U V W H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2 1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.273 2 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 2.078 2.078 3 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 1.800 1.800 4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.085 5 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 1.273 .805 6 2 1 1 1 -1 -1 0 2 -2 1.633 1.915 90.00 2.078 1.273 7 3 1 0 0 0 -2 -1 3 1 1.658 1.658 107.55 1.800 1.085 8 3 1 1 0 -2 2 2 -4 -2 1.732 1.732 73.22 1.273 .735 9 3 2 2 0 2 -2 -4 2 4 2.121 2.121 103.63 1.273 .600 10 3 3 1 2 -2 0 0 2 -6 2.236 2.236 102.92 1.273 .569 11 2 1 0 0 0 -2 -2 4 0 2.236 2.449 90.00 1.800 .805 12 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 2.078 .826 13 3 2 0 0 0 -2 -4 6 0 3.606 3.742 90.00 1.800 .499 例：γ-Fe, a = 0.36nm. R1=14.4mm R2=23.6mm, R2/ R1=1.639 R1^R2=90º. Lλ=3.0 nm.mm. 0,-2,2 -1,1,1 -1,-1,3 Zone axis : [2,1,1] R1 R2 Fe3C, Cementite, Pnma, 5.0890, 6.7433, 4.5235 a b c x y z 002 0-11 0-20 0-40 Zone axis : [100] Fe3C, Cementite, Pnma, 5.0890, 6.7433, 4.5235 注意：滑移面消光！ Fe3C, Cementite, Pnma, 5.0890, 6.7433, 4.5235 注意：滑移面消光！ 2-20 1-121-11 002 Zone axis : [110] dhkl (hkl) Teta I% 3.757 (011) 11.83 1 3.372 (020) 13.21 2 3.022 (1-11) 14.77 1 2.545 (200) 17.62 3 2.387 (-12-1) 18.82 29 2.381 (2-10) 18.88 27 2.262 (002) 19.91 21 2.218 (20-1) 20.32 15 2.107 (21-1) 21.45 54 2.067 (102) 21.88 61 2.031 (-220) 22.29 58 2.013 (031) 22.50 100 Fe3C, Cementite, Pnma, 5.0890, 6.7433, 4.5235 注意：滑移面消光！ Zone axis : [010] 002 200 4.4.3 Indexing of single crystal spot patterns from an unknown phase Procedure a) Survey the literature to collect information of possible phases. b) Three possible routes to reach its full indexing a) Calculate d spacings and compare them with the standard powder XRD data; b) Measure R2/R1, R2^R1, and compare them with tables in archives; c) Try a cubic phase; d) Use double tilting to determine directly the 3D reciprocal lattice. c) In general three independent patterns are necessary to determine a reciprocal structure. d) Obtain the real lattice type and parameters. R1R2 109.5º R3 A diffraction pattern is shown on the right: R1=R2=14.4mm, R1^R2=109.5º. Lλ=3.0 nm*mm. Standard powder XRD data; d1=d2 0.208 d3= 0.180 d4= 0.127 做表 R1R2 109.5º R3 R1=R2=14.4mm, R3/R1= 1.155 R1^R2=109.5º. Lλ=3.0 nm*mm. PARAMETERS A= 3.6000 B= 3.6000 C= 3.6000 AF= 90.000 BT= 90.000 GM= 90.000 NUVW= 3 NSY= 1 NL= 1 SY: 1-CUBIC; 2-TETRA; 3-ORTH; 4-HEX; 5-MONO; 6-TRIC LT: 1-F; 2-I; 3-C; 4-B; 5-A; 6-P; 7-R; K U V W H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2 1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.273 2 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 2.078 2.078 3 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 1.800 1.800 4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.085 5 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 1.273 .805 6 2 1 1 1 -1 -1 0 2 -2 1.633 1.915 90.00 2.078 1.273 7 3 1 0 0 0 -2 -1 3 1 1.658 1.658 107.55 1.800 1.085 8 3 1 1 0 -2 2 2 -4 -2 1 732 1 732 73 22 1 273 735 [1 1 0] -11-1 -111 -220 -200 Cubic indexing Cubic indexing a) Choose three shortest reciprocal vectors R1, R2, R3, R3=R1+R2, measure the angle R1^R2. b) Calculate d1, d2, (R2/R1)2, (R3/R1)2. c) self-consistent combinations of hkls so that R3=R1+R2. d) In general three independent patterns are necessary to determine the reciprocal structure. R1R2 109.5º R3 A diffraction pattern is shown on the right: R1=R2=14.4mm, R1^R2=109.5º. Lλ=3.0 nm*mm. d1 d2 (R2/R1)2 (R3/R1)2 0.208 0.208 1 (1.155)2=4/3 Cubic indexing R1R2 109.5º R3 R1=R2=14.4mm, R1^R2=109.5º. Lλ=3.0 nm*mm. h2+k2+l2 （hkl） 简单立方 体心立方 面心立方 1 100 100 2 110 110 110 3 111 111 111 4 200 200 200 200 5 210 210 6 211 211 211 8 220 220 220 220 d1 d2 (R2/R1)2 (R3/R1)2 0.208 0.208 1 (1.155)2=4/3=8/6 111 111 111/111 002/111 d=a/√(h2+k2+l2 )=a/√N=Lλ/R (R2/R1)2=N2/N1 整数之比！ Cubic indexing R1R2 109.5º 111111 002 [110] R3 R1=R2=14.4mm, R1^R2=109.5º. Lλ=3.0 nm*mm. d1 d2 (R2/R1)2 (R3/R1)2 0.208 0.208 1 (1.155)2=4/3 111 -1-11 -1-11/111 002/111 Self-consistency of indices: (111)+ (-1-11)=(002) Angle check: (111)^(-1-11)=109.5º Lattice type:fcc Lattice constant : a=d111*√3=0.360 nm Phase identification: γ-Fe 奥氏体铁 Two more patterns are necessary to assure the phase identification Exercises: index the following patterns in cubic schemes. Note that there may be more than one possibilities for each pattern. Give the corresponding lattice types and constants. R1R2 R3 R1= R2= R3= 23.6mm, R1^R2=120º. Lλ=3.0 nm*mm. d1 d2 (R2/R1)2 (R3/R1)2 lattice constant 0.127 0.127 1 1 [111] 110 -101 -101/110 011/110 cP, cI 0.18 nm 220 -202 -202/220 022/220 cF 0.36 nm N hkl c bcc fcc 1 100 100 2 110 110 110 3 111 111 111 4 200 200 200 200 5 210 210 6 211 211 211 8 220 220 220 220 Exercises: index the following patterns in cubic schemes. Note that there may be more than one possibilities for each patterns. Give the corresponding lattice types and constants. R1 R2 R3 R1= R2= 16.7mm, R1^R2=90º. Lλ=3.0 nm*mm. d1 d2 (R2/R1)2 (R3/R1)2 lattice constant 0.180 0.180 1 2 [001] 100 010 010/100 110/100 0.180 nm 1-10 110 110/1-10 200/1-10 0.255 nm 200 020 020/200 220/200 0.360 nm N hkl c bcc fcc 1 100 100 2 110 110 110 3 111 111 111 4 200 200 200 200 5 210 210 6 211 211 211 8 220 220 220 220 Exercises: index the following patterns in cubic schemes. Note that there may be more than one possibilities for each patterns. Give the corresponding lattice types and constant. R1 R2 R3 R1= 16.7 mm, R2 = R3= 27.5 mm, R1^R2=107.5º. Lλ=3.0 nm*mm. d1 d2 (R2/R1)2 (R3/R1)2 0.180 0.109 11/4 11/4 [130] N hkl c bcc fcc 1 100 100 2 110 110 110 3 111 111 111 4 200 200 200 200 5 210 210 6 211 211 211 8 220 220 220 220 002 -31-1 -31-1/002 -311/002 cF, 0.36 nm Exercises: index the following patterns in cubic schemes. Note that there may be more than one possibilities for each patterns. Give the corresponding lattice types and constants. R1 R2 R3 R1= 16.7mm, R2=23.6 mm, R1^R2=90º. Lλ=3.0 nm*mm. d1 d2 (R2/R1)2 (R3/R1)2 a 0.180 0.127 2 3 [110] N hkl c bcc fcc 1 100 100 2 110 110 110 3 111 111 111 4 200 200 200 200 5 210 210 6 211 211 211 8 220 220 220 220 1-10 002 002/1-10 1-12/1-10 cI 0.255 nm 002 -220 -220/002 -222/002 × 001 -110 -110/001 -111 /001 cP 0.18 nm Use double tilting to determine directly a 3D reciprocal lattice 000 α1 α2α3 000 α1 α2 α3 α1 α2α3 000 100 010 [001]010 001 [100] α1=26.56 120 110 [210] 120 001 α2=18.43 [110] 110 001 111 α3=18.43 [010] 000 001 100 101 Use double tilting to determine directly a 3D reciprocal lattice 图3.4 六角相Al5FeNi的选区电子衍射花样 Figure 3.4 SAED patterns arranged in a stereo manner of the hexagonal Al5FeNi phase. 4.4.4 Ring patterns For randomly orientated aggregates of polycrystals, the reciprocal lattice becomes a series of spheres. The radii Ri = Lλ/di. The number of points contributing to each sphere is known as the multiplicity. 7.4 Ring patterns 7.4 Ring patterns 典型非晶电子衍射 7.5 Powder patterns 图3.5 铸态合金Al71Fe5Ni24的X 射线(λCuK　= 0.15406 nm)衍射谱 Figure 3.5 X-ray diffraction pattern of the as-cast Al71Fe5Ni24 alloy. 7.4 Ring patterns How to index a known powder pattern 1. Calculate the d list 2. Find out the indices for each peak How to index an unknown powder pattern 1. Survey the literature 2. Calculate the d list 3. Compare with XRD cards