Crystallography and Interfaces

1
Crystallography and Interfaces

• Crystals and their structure
• Indexing
• Reciprocal lattice
• Interfaces

2
(No Transcript)
3
(Birmingham University)
4
(H. Jones, 1982)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(DoITPOMS micrograph library, R. F. Cochrane)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
(No Transcript)
41
(No Transcript)
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
lattice motif structure
primitive cubic lattice motif Cu at 0,0,0
Zn at 1/2, 1/2, 1/2
46
Lattice face-centred cubic Motif C at 0,0,0
C at 1/4,1/4,1/4
47
(No Transcript)
48
(No Transcript)
49
1/4
3/4
1/4
3/4
Lattice face-centred cubic Motif Zn at 0,0,0
S at 1/4,1/4,1/4
50
(No Transcript)
51
(No Transcript)
52
fluorite
53
(No Transcript)
54
(No Transcript)
55
Interfaces
Grain boundary is a region over which the lattice
orientation changes. A general interface is a
discontinuity which separates different crystal
structures or chemical compositions.
56
Creation of a bi-crystal
cut and rotate by angle q about axis normal to
diagram
q
57
(No Transcript)
58
(No Transcript)
59
Dislocation energy per unit length
60
Interface energy per unit area
61
(No Transcript)
62
(No Transcript)
63
Degrees of freedom
crystal 1
crystal 2
interface
64
Five degrees of freedom
Two specify unit vector normal to interface. Two
specify axis of rotation. One specifies
right-handed angle of rotation.
65
body-centred cubic
cubic close-packed
66
b
a
3
3
a
2
b
b
2
1
a
1
(a)
(b)
BAIN
STRAIN
(d)
(c)
Body-centered
Body-centered
cubic martensite
tetragonal
austenite
67
(No Transcript)
68
001
b
b'
100
o
a'
a
b
(a)
o
b'
(b)
a,a'
69
Coherency
Stress-free coherent interface only possible if
one crystal can be converted into another by a
strain which is an invariant-plane strain.
70
(No Transcript)
71
hexagonal close-packed
cubic close-packed