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