**phonon**(rus. фонон) — (from Greek

*phone*meaning "a sound") a quantum of crystalline lattice atoms vibration.

### Description

In crystalline materials, atoms and molecules are actively interacting with each other, and it is not easy to discuss such thermodynamic phenomena as individual atom vibrations in them, as we come up with huge systems of trillions of interconnected linear differential equations with no feasible analytical solution. It is much more convenient to consider the concerted atomic vibrations of a crystal as sound-wave propagation in it, with phonons being the quanta. A term was coined by analogy with photon, the electromagnetic field quantum.

Phonon spin is zero. Phonon belongs to the bosons, and is described by the Bose-Einstein statistics.

The phonon concept allows one to describe the thermal and other properties of a crystal using kinetic gas theory methods. In most cases, phonons are the main heat reservoir of solids. The heat capacity of a crystalline solid is almost identical with the heat capacity of the phonon gas. The thermal conductivity of a crystal can be described as the thermal conductivity of the phonon gas, with the thermal resistance being due to the transfer processes.

The scattering of conduction electrons when interacting with phonons is the basic mechanism of electrical resistivity of metals and semiconductors. Since conduction electrons can emit and absorb phonons, the electrons attract to each other making some metals superconduct at low temperatures. Phonons emitting excited atoms and molecules ensure nonradiative electronic transitions. In relaxation processes in solids, phonons typically serve to drain the energy stored by the other degrees of freedom of a crystal, such as electronic ones.

Acoustic and optical phonons are distinguished.

At low wave vectors, acoustic phonons are described by the linear dispersion law and a parallel shift of all the atoms in the unit cell. This dispersion law describes the sound vibrations of the lattice, so the phonon is termed as acoustic.

Optical phonons exist only in crystals whose unit cells contain two or more types of atoms. At low wave vectors, those phonons have such atomic vibrations that the centre of gravity of the unit cell remains stable.

Phonon spin is zero. Phonon belongs to the bosons, and is described by the Bose-Einstein statistics.

The phonon concept allows one to describe the thermal and other properties of a crystal using kinetic gas theory methods. In most cases, phonons are the main heat reservoir of solids. The heat capacity of a crystalline solid is almost identical with the heat capacity of the phonon gas. The thermal conductivity of a crystal can be described as the thermal conductivity of the phonon gas, with the thermal resistance being due to the transfer processes.

The scattering of conduction electrons when interacting with phonons is the basic mechanism of electrical resistivity of metals and semiconductors. Since conduction electrons can emit and absorb phonons, the electrons attract to each other making some metals superconduct at low temperatures. Phonons emitting excited atoms and molecules ensure nonradiative electronic transitions. In relaxation processes in solids, phonons typically serve to drain the energy stored by the other degrees of freedom of a crystal, such as electronic ones.

Acoustic and optical phonons are distinguished.

At low wave vectors, acoustic phonons are described by the linear dispersion law and a parallel shift of all the atoms in the unit cell. This dispersion law describes the sound vibrations of the lattice, so the phonon is termed as acoustic.

Optical phonons exist only in crystals whose unit cells contain two or more types of atoms. At low wave vectors, those phonons have such atomic vibrations that the centre of gravity of the unit cell remains stable.

#### Author

- Naymushina Daria A.

#### Sources

- The Great Soviet Encyclopedia (in Russian), 3rd. Edition // Moscow: Sovetskaja ehnciklopedija, 1969–1978. — http://bse.sci-lib.com/article116912.html (reference date: 12.12.2011).
- Physical Encyclopedic Dictionary (in Russian) // Moscow: The Great Soviet Encyclopedia, 1995. — 928 pp.