Well again i'm very new to the field of solid state physics. I understand that phonons are the lattice vibrations which are transferred from one atom to another. In case of harmonic vibration, the phonons are similar to the elastic spring and the atoms are considered like the balls attached to the spring that are vibrating. However i would like to know 1. under what case can we consider the phonons as harmonic vibrations and why? 2. what is the basis of the assumption that phonons are harmonic vibration (because in elastic springs, the force constant varies linearly with respect to the displacement, while the interatomic potential varies non linearly with respect to the displacement).