Packing efficiency of hcp and ccp structures

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We have discussed earlier that in both type of close packing (hcp and ccp) approximately amount of the available volume is occupied by spheres (atoms).

1. Let us calculate the efficiency of packing in ccp structure

(FCC arrangement)

We have found that for a ccp arrangement

 

 

We also know that, per unit cell in ccp arrangement has effectively 4 spheres.

Therefore,

Percentage efficiency

 

 

2. Efficiency of body centered cubic structures

We know, for a bcc structure

In bcc structure, the total number of atoms per unit cell is 2.

Volume of the cube = a³

Therefore,

Percentage efficiency

= 68%

Therefore,

• Relation between atomic radius r (which is d/2 for pure elements) and a the edge unit cell of a cubic crystal.