Phonon Totally Explained

ť For KDE4's multimedia framework, see Phonon (KDE).

In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. 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 conductivities. In particular, the properties of long-wavelength phonons give rise to sound in solids -- hence the name phonon from the Greek φονή (phonē) = voice. In insulating solids, phonons are also the primary mechanism by which heat conduction takes place.
Phonons are a quantum mechanical version of a special type of vibrational motion, known as normal modes in classical mechanics, in which each part of a lattice oscillates with the same frequency. These normal modes are important because, according to a well-known result in classical mechanics, any arbitrary vibrational motion of a lattice can be considered as a superposition of normal modes with various frequencies; in this sense, the normal modes are the elementary vibrations of the lattice. Although normal modes are wave-like phenomena in classical mechanics, they acquire certain particle-like properties when the lattice is analysed using quantum mechanics (see wave-particle duality.) They are then known as phonons. Phonons are bosons possessing integer spin.

Repeating derivation of normal modes

The equations in this subsection either don't use axioms of quantum mechanics or use relations for which there exists a direct correspondence in classical mechanics.

Mechanics of particles on a lattice

Consider a rigid regular (or "crystalline") lattice composed of N particles. (We will refer to these particles as "atoms", though in a real solid they may actually be ions.) N is some large number, say around 10²³ (on the order of Avogadro's number) for a typical piece of solid. If the lattice is rigid, the atoms must be exerting forces on one another, so as to keep each atom near its equilibrium position. In real solids, these forces include Van der Waals forces, covalent bonds, and so forth, all of which are ultimately due to the electric force; magnetic and gravitational forces are generally negligible. The forces between each pair of atoms may be characterized by some potential energy function V, depending on the separation of the atoms. The potential energy of the entire lattice is the sum of all the pairwise potential energies:

,sum_

is the frequency of the phonons (or photons) in the state,

, k_B

is Boltzmann's constant, and

, T

is the temperature.

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