How many lattice points are there in one unit cell of each of the following lattice?
a. Face-centred cubic
b. Face-centred tetragonal
c. Body-centred

Explanation

In face centred cubic arrangement,
Lattice point located at the corners of the cube = 8
Lattice point located at the corners of each face = 6
Total no. of lattice points = 8 + 6 = 14
(b) In face centred tetragonal, the number of lattice points is also the same i.e., 8 + 6 = 14.
(In both the cases, particles per unit cell `=8xx1//8+6xx1//2=4)`
(c) In body centred cubic arrangement,
Lattice point located at the corners of the cube = 8
Lattice points located in the centre of the body = 1
Total no. of lattice points = `8+1=9`
(the total number of particles per unit cell `=8xx1//8+1=2`)