How many lattice points are there in one unit cell of each of the following lattice? (i) Face-centred cubic (ii) Face-centred tetragonal (iii) Body-centred
(i) Face-centered cubic Face centered lattice have atoms at corners which is shared by eight atoms and at the centered of face of cube which is shared by two faces. A atom at corner contributes one eight to the unit cell and atom at at face center contribute one half. Total number of lattice points per unit cell: 8×81+6×21=1+3=4 (ii) Face-centered tetragonal Face centered lattice have atoms at corners which is shared by eight atoms and at the centered of face of cube which is shared by two faces. A atom at corner contributes one eight to the unit cell and atom at at face center contribute one half. Total number of lattice points per unit cell: 8×81+6×21=1+3=4 (iii) Body centered Face centered lattice have atoms at corners which is shared by eight atoms and at the centered of cube which is shared by one cube. A atom at corner contributes one eight to the unit cell and atom at center of cube contribute by one. Total number of lattice points per unit cell: 8×81+1×1=1+1=2
