Some Important Relations

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• Relation between nearest neighbor distance (d) and edge length (a) of a unit cell in a cubic crystal.

1. Simple cubic unit cell

Distance between nearest neighbors

(d) = AB = a for pure elements

fig 2.1

2. Face - centred cubic or ccp arrangement

Distance between nearest neighbors

 

 

fig 2.19

In the right angled triangle ABC,

AC² = AB² + BC²

or = a² + a² = 2a²

From (i) and (ii)

3. Body - centre cube

Distance between nearest neighbor

fig 2.20

In the right angled triangle ABD

Now in right angled triangle ACD,