Question

Consider a one-dimensional Bravais lattice with two ions per primitive
cell, with N primitive cells in total. How many phonon types are there in the lattice

Answer 1

Solution:
There two types of phonons in crystal system

1. Optical phonons : These types of phonons exist in crystals whic has two or more than two atoms/ions per primitive cell.In optical phonos out of phase movement/vibrations of atoms/ions takes place.

2.Acoustic phonons: These types of phonons exist in all crystals irrespective of number of atoms/ions per primitive cell.

Atoms/ions movements or vibrations are in phase in acoustic phonon.

Given: In one dimensional bravais lattice number of ions per primitive cell = 2

Total number of primitive cell = N

Then,

Total number of Acoustic phonons = N

Total number of Optical phonons = N