# Phonon

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In physics, a phonon is a quasiparticle representing the quantization of the modes of lattice vibrations of periodic, elastic crystal structures of solids.

Phonons play a major role in many of the physical properties of solids, including a material's thermal and electrical conductivities. Thus, the study of phonons is an important part of solid state physics.

A phonon is a quantum mechanical description of a special type of vibrational motion, in which a lattice uniformly oscillates at the same frequency. In classical mechanics these are known as normal modes. These normal modes are important because any arbitrary lattice vibration can be considered as a superposition of these elementary vibrations (cf. Fourier analysis). While normal modes are wave-like phenomena in classical mechanics, they have particle-like properties in the wave–particle duality description of quantum mechanics.

The name phonon comes from the Greek word φωνή (phonē), which translates as sound, voice, as long-wavelength phonons give rise to sound.

The concept of phonons was introduced by Russian physicist Igor Tamm.

## Contents

### Lattice dynamics

The equations in this section either do not use axioms of quantum mechanics or use relations for which there exists a direct correspondence in classical mechanics.

For example, consider a rigid regular, crystalline, i.e. not amorphous, lattice composed of N particles. We will refer to these particles as atoms, although in a real solid these may be molecules. N is some large number, say around 1023 (on the order of Avogadro's number) for a typical sample of solid. If the lattice is rigid, the atoms must be exerting forces on one another to keep each atom near its equilibrium position. These forces may be Van der Waals forces, covalent bonds, electrostatic attractions, and others, all of which are ultimately due to the electric field force. Magnetic and gravitational forces are generally negligible. The forces between each pair of atoms may be characterized by a potential energy function V that depends on the distance of separation of the atoms. The potential energy of the entire lattice is the sum of all pairwise potential energies:[1]

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