电子衍射花样标定

Rhkl ’ Rhkl
(hkl)
4.4.2 Indexing a pattern of a known substance
S/λ= k
相机长度
S0/λ= k0 ghkl 000
Rhkl
h3k3l3 h2k2l2 h1k1l1 R2 R1
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)
Zone axis : [2,1,0] 2,-4,0 2,-4,2
R3/Rຫໍສະໝຸດ Baidu 1.000 1.155 1.414 1.541 1.581 1.915 1.658 1.732 2.121 2.236 2.449 2.582 3.742
FAI
D1
D2
120.00 1.273 70.53 2.078 R2 90.00 1.800 90.00 1.273 0,0,2 108.43 1.273 90.00 2.078 R1 107.55 1.800 73.22 1.273 103.63 1.273 102.92 1.273 90.00 1.800 97.61 2.078 90.00 1.800
(hkl) (111) (002) (022) (113) (222) (004) (313) (024)
Teta 21.75 25.34 37.24 45.21 47.83 58.86 68.85 73.11
I% 100 46 26 31 9 6 33 41
2,-4,0 1,-3,1 0,-2,2 -1,-1,3 -2,0,4
109.5
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
1.27 2.07 1.80 1.08 .80 1.27 1.08 .73 .60 .56 .80 .82 .49
例：γ-Fe, a = 0.36nm. R1=14.4mm, R2=23.6mm R1^R2=90º. Lλ=3.0 nm.mm.
Zone axis : [211]
dhkl 2.078 1.800 1.273 1.085 1.039 0.900 0.826 0.805
[uvw]
4.4.2 Indexing a pattern of a known substance
a) 直接利用已知d值标定 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, {111}. c) A consistent set of indices is 002= 111 + 111. d) R1×R2=[110], the zone axis晶带轴. 002 R3 111 R2 [110] R1 111
I%
10
46
[110]
26
31 9 6
33
41
例：γ-Fe, R3 R2 R1 109.5º γ-Fe, a = 0.36nm. R1= R2=14.4mm, R3=16.7mm, R1^R2=109.5º. Lλ=3.0 nm.mm.
例：γ-Fe, 002 R3 111 R2 R1 111 109.5º γ-Fe, a = 0.36nm. R2/R1 =1 R1= R2=14.4mm, R3=16.7mm, R1^R2=109.5º. Lλ=3.0 nm.mm.
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 3D reciprocal lattice 3D real lattice orientation/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
(hkl)
S/λ= k
θ
L=相机 长度 S0/λ= k0 ghkl 000 (hkl)
002 R2 111 220 R3
R1 111
U V W H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI d1 d2 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 2.051 2.051 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 3.349 3.349 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 2.900 2.900 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 2.051 1.749 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 2.051 1.297 2 1 1 1 -1 -1 0 2 -2 1.633 1.915 90.00 3.349 2.051 3 1 0 0 0 -2 -1 3 -1 1.658 1.658 72.45 2.900 1.749 3 1 1 0 -2 2 2 -4 -2 1.732 1.732 73.22 2.051 1.184 3 2 2 0 2 -2 -4 2 4 2.121 2.121 103.63 2.051 .967 3 3 1 2 -2 0 2 0 -6 2.236 2.236 77.08 2.051 .917 2 1 0 0 0 -2 -2 4 0 2.236 2.449 90.00 2.900 1.297 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 3.349 1.331
R1
-2,4,-4
-2,4,-2
-2,4,0
-2,4,2
-2,4,4
例：γ-Fe, a = 0.36nm. R1=16.7mm, R2=37.3mm, R2/ R1=2.2335 R1^R2=90º. Lλ=3.0 nm.mm.
K 1 2 3 4 5 6 7 8 9 10 11 12 13 1 1 1 3 2 2 3 3 3 3 2 3 3 U V W 1 1 0 3 2 1 1 1 2 3 1 2 2 1 0 0 2 1 1 0 1 2 1 0 1 0 H1 K1 L1 0 -1 0 2 2 1 0 0 0 2 0 1 0 2 1 -2 -2 -2 -1 0 -2 2 -2 0 -1 0 -2 -1 0 0 0 -1 -2 2 -2 0 -2 -1 -2 -2 -1 0 1 0 0 -1 2 -4 0 -2 -1 -4 H2 K2 L2 0 1 0 1 2 2 3 -4 2 2 4 3 6 2 1 -2 -3 -4 -2 1 -2 4 -6 0 -3 0 R2/R1 1.000 1.000 1.000 1.173 1.581 1.633 1.658 1.732 2.121 2.236 2.236 2.517 3.606
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 1 2 3 4 5 6 7 8 9 10 11 12
2,-4,-4 Zone axis : [210] 2,-4,-2 2,-4,0 2,-4,2 2,-4,4
dhkl 2.078 1.800 1.273 1.085 1.039 0.900 0.826 0.805
I% 100 46 26 31 9 6 33 41
R2
0,0,-4 0,0,-2 0,0,2 0,0,4
2,-2,-2 1,-1,-1
R2 -1,1,1 R1
-2,2,2
2,0,-4 1,1,-3 0,2,-2 -1,3,-1 -2,4,0
例：γ-Fe, a = 0.36nm. R1=14.4mm R2=23.6mm, R2/ R1=1.639 R1^R2=90º. Lλ=3.0 nm.mm.
K 1 2 3 4 5 6 7 8 9 10 11 12 13 1 1 1 3 2 2 3 3 3 3 2 3 3 U V W 1 1 0 3 2 1 1 1 2 3 1 2 2 1 0 0 2 1 1 0 1 2 1 0 1 0 H1 K1 L1 0 -1 0 2 2 1 0 0 0 2 0 1 0 2 1 -2 -2 -2 -1 0 -2 2 -2 0 -1 0 -2 -1 0 0 0 -1 -2 2 -2 0 -2 -1 -2 -2 -1 0 1 0 0 -1 2 -4 0 -2 -1 -4 H2 K2 L2 0 1 0 1 2 2 3 -4 2 2 4 3 6 2 1 -2 -3 -4 -2 1 -2 4 -6 0 -3 0 R2/R1 1.000 1.000 1.000 1.173 1.581 1.633 1.658 1.732 2.121 2.236 2.236 2.517 3.606 R3/R1 1.000 1.155 1.414 1.541 1.581 1.915 1.658 1.732 2.121 2.236 2.449 2.582 3.742
例：γ-Fe, a = 0.36nm. R1=16.7mm R2=37.3mm, R1^R2=90º. Lλ=3.0 nm.mm. (hkl) (111) (002) (022) (113) (222) (004) (313) (024) Teta 21.75 25.34 37.24 45.21 47.83 58.86 68.85 73.11
109.5 [110]
fi2.dat
例：γ-Fe, 002 R3 111 R2 R1 111 109.5º dhkl 0.2078 0.1800 0.1273 0.1085 0.1039 γ-Fe, a = 0.36nm. R1= R2=14.4mm, R3=16.7mm, 0.0900 R1^R2=109.5º. Lλ=3.0 nm.mm. 0.0826 0.0805 (hkl) (111) (002) (022) (113) (222) (004) (313) (024) Teta 21.75 25.34 37.24 45.21 47.83 58.86 68.85 73.11
[110]
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 1 2 3 4 U V W 1 1 1 3 1 1 0 3 1 0 0 2 H1 K1 L1 H2 K2 L2 0 2 1 1 0 -2 1 -3 R2/R1 R3/R1 FAI D1 D2
0 2 -2 -2 -1 1 -1 -1 0 -2 0 0 2 -2 0 1
1.000 1.000 120.00 1.273 1.27 1.000 1.155 70.53 2.078 2.0 1.000 1.414 90.00 1.800 1.80 1.173 1.541 90.00 1.273 1.08