calculate the radius of the largeset interstitial void in th

calculate the radius of the largeset interstitial void in the FCC iron lattice, and the largest interstiitial voids occur at the (1/2,0,0), (0,1/2,0) and (0,0,1/2) type positions

Solution

Let the radius of an Fe atom be R and that of the interstitial atom at the position (0, ½, 0)be r.Then we see that

2R + 2r = a

In addition, from geometry we see that

(2R)²= (½ a)²+(½ a)²=½ a²

Solving for a gives

2R = (1/2)a

or   a = 22R

Hence,2 R+ 2r=22R

Or r=(2- 1) R=0.414R=0.414 (0.129nm) =0.053nm