电子衍射谱标定
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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
002 R3
111
111
R2 R1
109.5
[110]
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
[110]
0.1273 (022) 37.24 26
0.1085 (113) 45.21 31
γ-Fe, a = 0.36nm.
0.1039 (222) 47.83 9
R1= R2=14.4mm, R3=16.7mm, 0.0900 (004) 58.86 6 R1^R2=109.5º. Lλ=3.0 nm.mm.
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
1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.27 2 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 2.078 2.0 3 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 1.800 1.80 4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.08
7900R..50230
2.078 1.800
2.07 1.80
4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.08 5 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 0,01,.2273 .80
6 2 1 1 1 -1 -1 0 2 -2 1.633 1.915 90.00 2.078 1.27
(hkl) (111) (002) (022) (113) (222) (004) (313) (024)
Zone axis : [211]
Teta I%
2,-4,0 1,-3,1 0,-2,2 -1,-1,3 -2,0,4
21.75 100
25.34 46 37.24 26
2,-2,-2 1,-1,-1
12 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 3.349 1.331 fi2.dat
例：γ-Fe,
002 R3
dhkl (hkl) Teta I%
111
111
0.2078 (111) 21.75 10
R2 R1
109.5º 0.1800 (002) 25.34 46
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;
13 3 2 0 0 0 -2 -4 6 0 3.606 3.742 90.00 1.800 .49
例：γ-Fe, a = 0.36nm. R1=14.4mm, R2=23.6mm R1^R2=90º. Lλ=3.0 nm.mm.
dhkl 2.078 1.800 1.273 1.085 1.039 0.900 0.826 0.805
4.4.1 The size of diffraction patterns
L= 相 机 长度
(hkl)
S/λ= k
θ
S0/λ= k0 ghkl
000
(hkl)
(1/λ)/ghkl＝L/Rhkl’ R’d = λL When is θ small (electron diffraction),
Rd=λL=diffraction constant
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 UVW
H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2
002 R3
111
R2 R1
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.
PARAMETERS
A= 3.6000 B= 3.6000 C= 3.6000
AF= 90.000 BT= 90.000 GM= 90.000
例：γ-Fe, a = 0.36nm.
R1=16.7mm
R2=37.3mm, R1^R2=90º.
2,-4,-4 2,-4,-2 2,-4,0
Lλ=3.0 nm.mm.
Zone axis : [210]
2,-4,2
2,-4,4
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
10 3 3 1 2 -2 0 0 2 -6 2.236 2.236 102.92 1.273 .56
11 2 1 0 0 0 -2 -2 4 0 2.236 2.449 90.00 1.800 .80
12 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 2.078 .82
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
0,-2,2 -1,-1,3
K UVW
H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2
R2 -1,1,1
1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.27
[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.
K UVW
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 1.27
2 3
1 1
1 0
0 -1 1 -1 -1 0 0 -2 0 0
11 0 -2
1.000 1.000
1.155 1.414
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.
0.0826 (313) 68.85 33
0.0805 (024) 73.11 41
R3 R2 R1
例：γ-Fe,
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,
111 [110]
R2 -1,1,1 -2,2,2
45.21 31 47.83 9 58.86 6
R1
2,0,-4 1,1,-3 0,2,-2 -1,3,-1 -2,4,0
68.85 33
73.11 41
例：γ-Fe, a = 0.36nm.
Zone axis : [2,1,1]
R1=14.4mm R2=23.6mm, R2/ R1=1.639 R1^R2=90º. Lλ=3.0 nm.mm.
ห้องสมุดไป่ตู้
Rhkl ’
Rhkl
4.4.2 Indexing a pattern of a
(hkl)
known substance
相机长度
S/λ= k
S0/λ= k0 ghkl
000
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.
0,0,-4 0,0,-2
R2
0,0,2 0,0,4
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.
Zone axis : [2,1,0] 2,-4,0 2,-4,2
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
002 111
R2
R1 111
220 R3
109.5 [110]
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
7 3 1 0 0 0 -2 -1 3 1 1.658 1.658 107R.515 1.800 1.08
8 3 1 1 0 -2 2 2 -4 -2 1.732 1.732 73.22 1.273 .73
9 3 2 2 0 2 -2 -4 2 4 2.121 2.121 103.63 1.273 .60
Rhkl
h3k3l3
h2k2l2
h1k1l1
R2 R1
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)
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
002 R3
111
111
R2 R1
109.5
[110]
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
[110]
0.1273 (022) 37.24 26
0.1085 (113) 45.21 31
γ-Fe, a = 0.36nm.
0.1039 (222) 47.83 9
R1= R2=14.4mm, R3=16.7mm, 0.0900 (004) 58.86 6 R1^R2=109.5º. Lλ=3.0 nm.mm.
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
1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.27 2 1 1 0 -1 1 -1 -1 1 1 1.000 1.155 70.53 2.078 2.0 3 1 0 0 0 -2 0 0 0 -2 1.000 1.414 90.00 1.800 1.80 4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.08
7900R..50230
2.078 1.800
2.07 1.80
4 3 3 2 2 -2 0 1 1 -3 1.173 1.541 90.00 1.273 1.08 5 2 2 1 2 -2 0 0 2 -4 1.581 1.581 108.43 0,01,.2273 .80
6 2 1 1 1 -1 -1 0 2 -2 1.633 1.915 90.00 2.078 1.27
(hkl) (111) (002) (022) (113) (222) (004) (313) (024)
Zone axis : [211]
Teta I%
2,-4,0 1,-3,1 0,-2,2 -1,-1,3 -2,0,4
21.75 100
25.34 46 37.24 26
2,-2,-2 1,-1,-1
12 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 3.349 1.331 fi2.dat
例：γ-Fe,
002 R3
dhkl (hkl) Teta I%
111
111
0.2078 (111) 21.75 10
R2 R1
109.5º 0.1800 (002) 25.34 46
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;
13 3 2 0 0 0 -2 -4 6 0 3.606 3.742 90.00 1.800 .49
例：γ-Fe, a = 0.36nm. R1=14.4mm, R2=23.6mm R1^R2=90º. Lλ=3.0 nm.mm.
dhkl 2.078 1.800 1.273 1.085 1.039 0.900 0.826 0.805
4.4.1 The size of diffraction patterns
L= 相 机 长度
(hkl)
S/λ= k
θ
S0/λ= k0 ghkl
000
(hkl)
(1/λ)/ghkl＝L/Rhkl’ R’d = λL When is θ small (electron diffraction),
Rd=λL=diffraction constant
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 UVW
H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2
002 R3
111
R2 R1
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.
PARAMETERS
A= 3.6000 B= 3.6000 C= 3.6000
AF= 90.000 BT= 90.000 GM= 90.000
例：γ-Fe, a = 0.36nm.
R1=16.7mm
R2=37.3mm, R1^R2=90º.
2,-4,-4 2,-4,-2 2,-4,0
Lλ=3.0 nm.mm.
Zone axis : [210]
2,-4,2
2,-4,4
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
10 3 3 1 2 -2 0 0 2 -6 2.236 2.236 102.92 1.273 .56
11 2 1 0 0 0 -2 -2 4 0 2.236 2.449 90.00 1.800 .80
12 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 2.078 .82
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
0,-2,2 -1,-1,3
K UVW
H1 K1 L1 H2 K2 L2 R2/R1 R3/R1 FAI D1 D2
R2 -1,1,1
1 1 1 1 0 2 -2 -2 0 2 1.000 1.000 120.00 1.273 1.27
[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.
K UVW
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 1.27
2 3
1 1
1 0
0 -1 1 -1 -1 0 0 -2 0 0
11 0 -2
1.000 1.000
1.155 1.414
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.
0.0826 (313) 68.85 33
0.0805 (024) 73.11 41
R3 R2 R1
例：γ-Fe,
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,
111 [110]
R2 -1,1,1 -2,2,2
45.21 31 47.83 9 58.86 6
R1
2,0,-4 1,1,-3 0,2,-2 -1,3,-1 -2,4,0
68.85 33
73.11 41
例：γ-Fe, a = 0.36nm.
Zone axis : [2,1,1]
R1=14.4mm R2=23.6mm, R2/ R1=1.639 R1^R2=90º. Lλ=3.0 nm.mm.
ห้องสมุดไป่ตู้
Rhkl ’
Rhkl
4.4.2 Indexing a pattern of a
(hkl)
known substance
相机长度
S/λ= k
S0/λ= k0 ghkl
000
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.
0,0,-4 0,0,-2
R2
0,0,2 0,0,4
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.
Zone axis : [2,1,0] 2,-4,0 2,-4,2
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
002 111
R2
R1 111
220 R3
109.5 [110]
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
7 3 1 0 0 0 -2 -1 3 1 1.658 1.658 107R.515 1.800 1.08
8 3 1 1 0 -2 2 2 -4 -2 1.732 1.732 73.22 1.273 .73
9 3 2 2 0 2 -2 -4 2 4 2.121 2.121 103.63 1.273 .60
Rhkl
h3k3l3
h2k2l2
h1k1l1
R2 R1
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)