Unlike static lattice model , which deals with average positions of atoms in a crystal, lattice dynamics extends the concept of crystal lattice to an array of atoms with finite masses that are capable of motion. This motion is not random but is a superposition of vibrations of atoms around their equilibrium sites due to the interaction with neighbor atoms. A collective vibration of atoms in the crystal forms a wave of allowed wavelength and amplitude.Just as light is a wave motion that is considered as composed of particles called photons, we can think of the normal modes of vibration in a solid as being particle-like. Quantum of lattice vibration is called the phonon.
The problem of lattice dynamics (LD) is to find the normal modes of vibration of a crystal. In other words, LD seeks to calculate the energies (or frequencies ) of the phonons as a function of their wave vector's k . The relationship between and k is called phonon dispersion .
LD offers two different ways of finding the dispersion relation: