Question

Give the number of lattice points in one unit cell of the crystal structures.

i. Simple cubic

ii. Face-centred cubic

iii. Body-centred cubic

iv. Face-centred tetragonal

Answer 1

i. Lattice points in simple cubic unit cell = 8 (at corners)

\(\therefore\) Lattice points per unit cell = 8 \(\times\cfrac{1}{8}\) = 1.

ii. Lattice points in face-centred cubic unit cell = 8 (at corners) + 6 (at centre of a face) = 14.

\(\therefore\)Lattice points per unit cell = 8 \(\times\cfrac{1}{8}\) + 6\(\times\cfrac{1}{2}\) = 4.

iii. Lattice points in body-centred cubic unit cell = 8 (at corners) + 1 (at centre of the body)

\(\therefore\) Lattice points per unit cell = 8 \(\times\cfrac{1}{8}\) + 1 = 2

iv. Lattice points in face-centred tetragonal crystal (unit cell) = 8 (at corners) + 6 (at centre of the face)

\(\therefore\)Lattice points per unit cell = 8\(\times\cfrac{1}{8}\)+ 6 \(\times\cfrac{1}{2}\) = 4