
The geometry factor (always for a single vacancy) was defined as 
 
g 
= ½ · S_{i} 
æ ç è 
Dx_{i} a 
ö ÷ ø 
2 




With Dx_{i} = component of the jump in xdirection. 

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 Dx_{i} = 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 Dx_{i}
= a/2 in xdirection, 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 Dx_{i}
= a/4 in xdirection, and we obtain 


g _{diamond}  = ½ · 
4 ·  æ ç è
 1 4 
ö ÷ ø  2 
= 1/8 


 
