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透射电镜样品的制备: ( 1 )分散晶体(粉末样) 干粉法 液体法 ( 2 )萃取复型:用于观察断口形貌,第二相大小分布,点阵类型 ( 3 )薄膜 平面膜 截面膜 方法: 超薄切片 减薄 人工 + 电化学减薄或离子减薄 聚焦离子束. 选区电子衍射:. 阿贝衍射原理. 220. 010. 110. g 110. b*. a*. 000. 100. 倒易点阵与正点阵. g 110. r 110. b. a. d 110. S / l = k. - PowerPoint PPT Presentation
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透射电镜样品的制备:
( 1 )分散晶体(粉末样) 干粉法
液体法
( 2 )萃取复型:用于观察断口形貌,第二相大小分布,点阵类型
( 3 )薄膜 平面膜
截面膜
方法:超薄切片
减薄 人工 + 电化学减薄或离子减薄
聚焦离子束
选区电子衍射:
阿贝衍射原理
倒易点阵与正点阵
d110
g110
b
a b*
a*000 100
010 110
g110
220
r110
衍射几何条件:厄瓦球面
S0/= k0
S/= k
ghkl
The size of diffraction patterns(1/)/ghkl = L/Rhkl’
R’d = L
When is small (electron diffraction),
Rd=L=diffraction constant
S0/= k0
S/= k
ghkl
(hkl)
000
(hkl)L= 相机长度
Rhkl ’
Rhkl
Plotting and indexing of single crystal spot patterns
When is small (electron diffraction), the reflection sphere cuts a 2D reciprocal plane.
S0/= k0
S/= k
ghkl
(hkl)
000
相机长度
Rhkl
图 3.9 Al3Ni 型正交相 Al74.8Fe1.5Ni23.7 的选区电子衍射花样
Plotting and indexing of single crystal spot patterns
Indexing: the plane normal [uvw] and at least one low index spot (hkl) (normally two spots), with hu+kv+lw=0.
S0/= k0
S/= k
ghkl
(hkl)
000
相机长度
Rhkl
Plotting and indexing of single crystal spot patterns
For a known substance but unknown orientation, a table of interplanar spacings d is needed.
a) Choose three spots such as h3k3l
3, 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 h3
k3l3= h1k1l1 + h2k2l2.
d) [uvw], the zone axis, is obtained by any two vectors (e.g. R1×R2)
S0/= k0
S/= k
ghkl
(hkl)
000
相机长度
Rhkl
h1k1l1h2k2l2
h3k3l3
[uvw]
R1R2
Plotting and indexing of single crystal spot patterns
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. L=3.0 nm.mm.
a) Choose three spots R1, R2, R3 (R3 = R1 + R2 )
b) d1= d2= L/R1= 0.335nm, {111}.
c) A consistent set of indices is 002= 111 + -1-11.
d) R1×R2=[1-10], the zone axis 晶带轴 .
R1R2 109.5º
111111
002
[110]
R3
也可以直接查表
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 .96710 3 3 1 2 -2 0 2 0 -6 2.236 2.236 77.08 2.051 .91711 2 1 0 0 0 -2 -2 4 0 2.236 2.449 90.00 2.900 1.29712 3 2 1 1 -1 -1 -1 3 -3 2.517 2.582 97.61 3.349 1.33113 3 2 0 0 0 -2 -4 6 0 3.606 3.742 90.00 2.900 .804
R2
R1109.5º
111
111
002
[110]
R3
220
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 indexinga) Calculate d spacings and compare with standard powder XRD data;
b) Measure R2/R1, R2^R1, and compare 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.
R1R2 109.5º
R3
A diffraction pattern is shown on the right: R1=R2=14.4mm, R1^R2=109.5º. L=3.0 nm*mm.
Standard powder XRD data;
d1=d20.208
d3=0.180
d4=0.127
Cubic indexingCubic 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) Judge possible combinations of hkl.
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. L=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. L=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
Cubic indexing
R1R2 109.5º
111111
002
[110]
R3
R1=R2=14.4mm, R1^R2=109.5º. L=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
cF, a = 0.36 nm. 奥氏体铁
Self-consistency of indices: (111)+ (-1-11)=(002)Angle check: (111)^(-1-11)=109.5ºLattice constant check: a=d111*3=0.360 nmTwo 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 patterns. Give the
corresponding lattice types and constants.
R1R2
R3
R1= R2= R3= 23.6mm, R1^R2=120º. L=3.0 nm*mm.
d1 d2 (R2/R1)2 (R3/R1)2 lattice constant0.127 0.127 1 1 110 -101 -101/110 011/110 cP, cI 0.18 nm 220 -202 -202/220 022/220 cF 0.36 nm
[111]
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. L=3.0 nm*mm.
d1 d2 (R2/R1)2 (R3/R1)2 lattice constant0.180 0.180 1 1100 010 010/100 110/100 0.180 nm1-10 110 110/1-10 200/1-10 0.255 nm200 020 020/200 220/200 0.360 nm
[001]
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. L=3.0 nm*mm.
d1 d2 (R2/R1)2 (R3/R1)2
0.180 0.109 11/4 11/4 002 -31-1 -31-1/002 -311/002 cF, 0.36 nm
[130]
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. L=3.0 nm*mm.
d1 d2 (R2/R1)2 (R3/R1)2 a0.180 0.127 2 3001 -110 -110/001 -111 /001 cP 0.18 nm1-10 002 002/1-10 1-12/1-10 cI 0.255 nm 002 -220 -220/002 -222/002 ×
[110]
Use double tilting to determine directly a 3D reciprocal lattice
000 1
23
000
12
3
1
23
000
100
010
[001]010
001
[100]
1=26.56
120
110
[210]
120
001
2=18.43
[110]
110
001111
3=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.
Ring patterns
For randomly orientated aggregates of polycrystals, the reciprocal lattice becomes a series of spheres.
The radii Ri = L/di.
The number of points contributing to each sphere is known as the multiplicity.
Ring patterns
Ring patterns
典型非晶电子衍射
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.
Ring patterns
How to index a known powder pattern1. Calculate the d list2. Find out the indices for each peak
How to index an unknown powder pattern1. Survey the literature2. Calculate the d list3. Compare with XRD cards
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