Chapter/Index: Introduction | A |
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D |
E |
F |
G |
H |
I |
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T |
U |
V |
W |
X |
Y |
Z |
Appendix
Tables of Burgers Vectors of Defects in FCC Structures
& Determination of Burgers Vector of FCC Lattice Defects
| Table 1815a. Burgers vectors (b) of perfect and partial dislocations in fcc structure.
| Type |
Burgers vector |
Note |
| Crystallographic notation |
Thompson's notation |
| Perfect |
1/2<1 1 0> |
AB |
See Table 1815b |
| Partial |
1/3<1 1 1> |
Aα |
Frank partial |
| 1/6<1 1 2> |
Aβ
|
Shockley partial |
| 1/6<110> |
αβ |
Stair-rod partial |
| 1/3<1 0 0> |
δα/CB |
Stair-rod partial |
| 1/3<1 1 0> |
δD/Cγ |
Stair-rod partial |
| 1/6<0 1 3> |
δγ/BD |
Stair-rod partial |
| 1/6<1 2 3> |
δB/Dγ |
Stair-rod partial |
Table 1815b. Standard analysis of g·b for relevant reflections in the fcc crystal structure for perfect dislocations.
| Plane of dislocation |
(1-1 1) or (1-1-1) |
(1-1-1) or (11-1) |
(1-1 1) or (1 1-1) |
(1 1 1) or (1 1-1) |
(1 1 1) or (1-1 1) |
(111) or (-111) |
| g |
b (×1/2) |
[1 1 0] |
[1 0 1] |
[0 1 1] |
[1 -1 0] |
[1 0 -1] |
[0 -1 1] |
| 1 -1 1 |
g·b |
0 |
2 |
0 |
2 |
0 |
2 |
| -1 1 1 |
0 |
0 |
2 |
-2 |
-2 |
0 |
| 1 -1 -1 |
0 |
0 |
-2 |
2 |
2 |
0 |
| 1 1 -1 |
2 |
0 |
0 |
0 |
2 |
-2 |
| 0 0 2 |
0 |
2 |
2 |
0 |
-2 |
2 |
| 0 -2 0 |
-2 |
0 |
-2 |
2 |
0 |
2 |
| 2 -2 0 |
0 |
2 |
-2 |
4 |
2 |
2 |
| 1 -1 3 |
0 |
4 |
2 |
2 |
-2 |
4 |
Table 1815c. Values of g·b for Frank partial dislocations in fcc structures. [1]
| |
Fault plane
|
(111) |
(11-1) |
(1-11) |
(-111) |
| b (×1/3) |
[111] |
[11-1] |
[1-11] |
[-111] |
| g |
2 0 0 |
g·b |
2 |
2 |
2 |
-2 |
| 0 -2 0 |
-2 |
-2 |
2 |
-2 |
| 2 -2 0 |
0 |
0 |
4 |
-4 |
| 2 2 0 |
4 |
4 |
0 |
0 |
| 1 1 1 |
3 |
1 |
1 |
1 |
| 1 -1 -1 |
-1 |
-1 |
1 |
-3 |
| 4 -2 -2 |
0 |
4 |
4 |
-8 |
| 3 1 1 |
5 |
1 |
3 |
-1 |
Table 1815d. Values of g·b for Stair-rod partial dislocations in fcc structures. [1]
| |
Fault plane
|
(1 1 1) |
(1 -1 1) |
(1 1 -1) |
(-1 1 1) |
| b (×1/6) |
[1 -1 0] |
[0 1 -1] |
[1 0 -1] |
[-1 0 1] |
[1 1 0] |
[0 1 1] |
[1 0 1] |
[1 -1 0] |
[0 1 1] |
[1 1 0] |
[0 -1 1] |
[1 0 1] |
| g |
2 0 0 |
g·b |
2 |
0 |
2 |
-2 |
2 |
0 |
2 |
2 |
0 |
2 |
0 |
2 |
| 0 -2 0 |
2 |
-2 |
0 |
0 |
-2 |
-2 |
0 |
2 |
-2 |
-2 |
2 |
0 |
| 2 -2 0 |
4 |
-2 |
2 |
-2 |
0 |
-2 |
2 |
4 |
-2 |
0 |
2 |
2 |
| 2 2 0 |
0 |
-2 |
2 |
-2 |
4 |
2 |
2 |
0 |
2 |
4 |
-2 |
2 |
| 1 1 1 |
0 |
0 |
0 |
0 |
2 |
2 |
2 |
0 |
2 |
2 |
0 |
2 |
| 1 -1 -1 |
2 |
0 |
2 |
2 |
0 |
-2 |
0 |
2 |
-2 |
0 |
0 |
0 |
| 4 -2 -2 |
6 |
0 |
6 |
-6 |
2 |
-4 |
2 |
6 |
-4 |
2 |
0 |
2 |
| 3 1 1 |
2 |
0 |
2 |
2 |
4 |
2 |
4 |
2 |
2 |
4 |
0 |
4 |
Table 1815e. Values of g·b for Shockley partial dislocations in fcc structures. [1]
| |
Fault plane
|
(1 1 1) |
(1 1 -1) |
(1 -1 1) |
(-1 1 1) |
| b (×1/6) |
[-1 -1 2] |
[2 -1 -1] |
[-1 2 -1] |
[2 -1 1] |
[-1-1-2] |
[-1 2 1] |
[-1-2-1] |
[-1 1 2] |
[2 1-1] |
[-2-1-1] |
[1 -1 2] |
[1 2-1] |
| g |
2 0 0 |
g·b |
-2 |
4 |
-2 |
4 |
-2 |
-2 |
-2 |
-2 |
4 |
-4 |
2 |
2 |
| 0 -2 0 |
2 |
2 |
-4 |
2 |
2 |
-4 |
4 |
-2 |
-2 |
2 |
2 |
-4 |
| 2 -2 0 |
0 |
6 |
-6 |
6 |
0 |
-2 |
2 |
-4 |
2 |
-2 |
4 |
-2 |
| 2 2 0 |
-4 |
2 |
2 |
2 |
-4 |
2 |
-6 |
0 |
6 |
-6 |
0 |
6 |
| 1 1 1 |
0 |
0 |
0 |
2 |
-4 |
2 |
-4 |
2 |
2 |
-4 |
2 |
2 |
| 1 -1 -1 |
-2 |
4 |
-2 |
2 |
2 |
-4 |
2 |
-4 |
0 |
0 |
0 |
0 |
| 4 -2 -2 |
-6 |
12 |
-6 |
8 |
2 |
-10 |
2 |
-10 |
8 |
-4 |
2 |
2 |
| 3 1 1 |
-2 |
4 |
-2 |
6 |
-6 |
0 |
-6 |
0 |
6 |
-8 |
4 |
4 |
Similar to the determination of Burgers vectors of lattice dislocations as discussed in page3463, for an fcc structure, zone axes like [110] (see page3915) are especially useful because the accessible g vectors include (002), (1-11), (1-1-1), (2-20), (1-13) and their opposites, and the defects usually lie on {111} planes. As an example, if we found g1·b = 0 at g1 = [1 1 -1] and g2·b = 0 at g2 = [0 0 2], and then we can determine b = 1/2[1 -1 0] as indicated in the tables above.
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