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The concepts of temperature and thermal equilibrium associated with ionic solids are based on individual atoms and molecules in the system possessing vibrational motion. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. These thermal vibrational modes are associated with atomic and molecular displacements, producing both longitudinal and transverse waves of atomic and molecular displacement.
In the longitudinal (or acoustic) mode, the displacement of particles from their positions of equilibrium coincides with the propagation direction of the wave. Mechanical longitudinal waves have been also referred to as compression waves. For transverse (or optical) modes, individual particles move perpendicular to the propagation of the wave.
As the rules of quantum mechanics apply to all the different vibrational modes in the solid, the lattice pulsates as a complete assembly in discrete energy steps, or thermal phonons. According to the kinetic theory of solids, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's thermal and electrical conductivity.
The phonon is related to both the frequency of vibration and the temperature. If the temperature is raised, the amplitude of vibration increases. The concept of the phonon is therefore considered as the quantum of lattice vibrational energy onto which is superimposed a complex pattern of standing and/or traveling waves that represent changes in temperature. If the solid is at a uniform temperature, the standing wave concept is adequate as the phonon vibrations are uniformly distributed.