The Solid State

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Unutilized or vacant spaces left after packing:
Tetrahedral void: A void between four touching spheres. Smaller in size.

Octahedral void: A void between six touching spheres. Bigger than tetrahedral voids.

Let the number of closed packed spheres be N, then:

The number of octahedral voids generated = N
The number of tetrahedral voids generated = 2N

Packing Efficiency:

1. In a face- Centred cubic (HCP and CCP) structures: 74%
2. In a Body-Centred cubic structure: 68%
3. In a simple cubic lattice: 52.38%

Calculation of pacing efficiency in bcc (body-centered cubic) structure:
The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell.

Since, there are 2 atoms present in the unit cell of bcc structure,
therefore, packing efficiency of bcc structure.

Calculation of pacing efficiency in hcp and ccp structure:
The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell.

Since, there are 4 atoms present in the unit cell of hcp and ccp structure,
therefore, packing efficiency of hcp or ccp structure.

Calculation of pacing efficiency in simple cubic structure:
The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell.

Since, there are 1 atoms present in the unit cell of simple cubic structure,
therefore, packing efficiency of simple cubic structure.