The number of octahedral voids per lattice site in a lattice is _________. (Rounded off to the nearest integer)

Solution

Chemistry ma’am · 4 steps

In a close-packed lattice, every sphere gets exactly one octahedral void and two tetrahedral voids.

1. Pick a close packing. Voids are counted in a close-packed arrangement (ccp or hcp). Take ccp, which is the fcc unit cell, and count lattice sites and octahedral voids in one cell.
2. Count lattice sites. There are 8 corners shared by 8 cells each, and 6 face centres shared by 2 cells each. That gives 8 × 1/8 + 6 × 1/2 = 4 sites per cell.
3. Count octahedral voids. There is 1 void at the body centre, owned fully by the cell. There are 12 more at the edge centres, each shared by 4 cells. That gives 1 + 12 × 1/4 = 4 voids per cell.

   (octahedral voids)/(lattice sites) = 4/4 = 1

4. So. There is 1 octahedral void per lattice site. The tetrahedral voids, 8 per cell, would give 2 per site.

The common slip: 2. Counting tetrahedral voids instead of octahedral ones gives 2, not 1. There are 8 tetrahedral voids in an fcc cell, which is 2 per site.

The idea to keep. For N spheres in close packing, there are N octahedral voids and 2N tetrahedral voids. Remember the 1 : 1 : 2 ratio and you never need to redraw the cell.

Answer from the NTA final answer key. Solution by PrepWiser.