
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 




