 |
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 
To index