Show that in a cubic close packed structure, eight tetrahedral voids are present per unit cell.

Explanation

In a ccp structure of spheres, a tetrahedral void is generated when a sphere in a layer is in contact with a triangular depression formed by three touching spheres in the adjacent layer. Now, in a ccp structure of spheres, each sphere in a layer is in contact with two triangular depression, one of which is in the layer below the layer of the sphere and the other above the layer of the sphere. This results in two tetrahedral voids. Therefore, there are two tetrahedral voids per sphere in a ccp sttructure of spheres. Now, the unit cell in a ccp structure is the face centred cubic unit cell and the number of spheres in this unit cell is four. Since each sphere in a ccp structure of spheres has two tetrahedral voids and the number of spheres per unit cell of this structure is four, the number of octahedral voids per unit cell will be eight.