An element crystallises in a face-centred cubic (fcc) lattice with unit cell edge length a . The shortest distance between the centre of an octahedral void and the centre of a tetrahedral void in this crystal lattice is:

Step-by-step solution

In an fcc unit cell, an octahedral void is located at the body centre, which has coordinates ( a 2 , a 2 , a 2 ) . Tetrahedral voids are located on the body diagonals at a distance of one-fourth of the body diagonal from each corner. The coordinates of a nearest tetrahedral void from the origin are ( a 4 , a 4 , a 4 ) . The shortest distance d between the centre of an octahedral void and a tetrahedral void is the distance between these two points: d = ( a 2 - a 4 )^2 + ( a 2 - a 4 )^2 + ( a 2 - a 4 )^2 d = ( a 4 )^