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*.

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: