Question

The distance between an octahedral and tetrahedral void in bcc lattice will be
(1)sqr root 3 a
(2)sqr root 3a/2
(3)sqr root3a/3
(4)sqr root 3a/ 4

Answer 1

For CCP (I prefer to call the crystal of atoms CCP, preserving FCC for the corresponding lattice of points) the octahedral voids (i.e. their centroids) are located at the centre of the cube and the mid points of the edges. The tetrahedral voids are located at 1/4 distance from the corners on each body diagonal.

Now the octahedral void at the centre of the cube is crystallographically equivalent to those at the mid points of the edges. So whatever result we find for the centre of the cube will also be true for the voids at the mid points of the edges.

Now consider the the void at the centre f the cube. It is surrounded by 8 tetrahedral voids, all at a distance of √3a/4 within the same unit cell. These have to be the nearest voids, because any tetrahedral void in a neighbouring cell has to be at a larger distance (nearest point in a neighbouring cell is at a/2).

Thus the minimum distance between an octahedral and a tetrahedral void in CCP is √3a/4