Question

Barium Titanate crystal has a cubic perovskite structure where the Ba2+ ions are at the vertices of a unit cube, O2- ions are at the centres of faces while the Ti 2+is at the center. The number of optical phonon modes of the crystal is ?

Answer 1

Answer:

Barium Titanate (BaTiO₃) crystal has a cubic perovskite structure where the Ba2+ ions are at the vertices of a unit cube, O2- ions are at the centres of faces while the Ti 2+is at the center.

So the number of Ba²⁺ ions per unit cell is 8x1/8 = 1

the number of O^2- ions per unit cell is 6 x 1/2 = 3 and

the number of Ti²⁺ ions per unit cell is 1 x 1 = 1.

Therefore, BaTiO₃ has total 1+3+1=5 ions per unit cell. That means N = 5

If N>2 atoms per unit cell then the crystal has 3 acoustic phonon modes and 3N-3 number of optical phonon modes.

BaTiO3 has N = 5, then the number of optical phonon modes is 3N-3 = 3(5) - 3 = 12.