Solution to Exercise 3.1-1: "Calculate Geometry Factors"

The geometry factor (always for a single vacancy) was defined as
g  =  ½ · Si æ ç è ö ÷ ø
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 · æ ç è ö ÷ ø
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 · æ ç è ö ÷ ø
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 · æ ç è ö ÷ ø

Lattice and Crystal

Ionic Crystals

Exercise 3.1-1: Calculate the Geometry Factor

Exercise 3.3-1 Quick Questions

© H. Föll (Defects - Script)