 |
The geometry factor (always for a single vacancy) was defined as |
| |
| g |
= ½ · Si |
æ
ç
è |
Dxi
a |
ö
÷
ø |
2 |
|
|
|
 |
With Dxi = component of the jump in x-direction. |
|
Looking at the fcc lattice
we realize that there are 12 possibilities for a jump because there are 12 next neighbors. |
|
|
8 of the possible jumps have a component in x (or –
x ) -direction, and Dxi = a/2 |
|
|
We thus have |
|
|
| g fcc | = ½ · |
8 · | æ
ç
è
| 1
2 |
ö
÷
ø | 2 |
= 1 |
|
|
|
Looking at the bcc lattice
we realize that there are 8 possibilities for a jump because there are 8 next neighbors. |
|
|
All 8 possible jumps have the component Dxi
= a/2 in x-direction, again we have |
|
|
| g bcc | = ½ · |
8 · | æ
ç
è
| 1
2 |
ö
÷
ø | 2 |
= 1 |
|
|
|
Looking at the diamond
lattice we realize, after a bit more thinking (or drawing, or looking at a ball and stick model), that there are 4 possible jumps.
|
|
|
All 4 jumps have the component Dxi
= a/4 in x-direction, and we obtain |
|
|
| g diamond | = ½ · |
4 · | æ
ç
è
| 1
4 |
ö
÷
ø | 2 |
= 1/8 |
|
|
| |
|
© H. Föll (Defects - Script)
Exercise 3.1-1: Calculate the Geometry Factor 
With frame