A phonon is a quantized mode of vibration that occurs in a rigid crystal lattice, such as those found in solid materials. In other words, it is the quantum mechanical description of lattice vibrations. Phonons play a key role in various physical properties of solids, including thermal conductivity and sound propagation. Phonons can be thought of as discrete packets of vibrational energy, similar to how photons are packets of electromagnetic energy.
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A phonon is one quantum of a lattice-vibration normal mode. In the harmonic approximation, the coupled atomic displacements decompose into oscillators labeled by wavevector and branch, each with excitation energy . Phonons describe a collective motion rather than a separate atom moving through the crystal.
Inelastic neutron or X-ray scattering can transfer momentum and energy to these modes, producing features that map their dispersion and polarization. Their thermal population contributes to heat capacity and transport, while coupling to electrons affects scattering and other material responses. Equilibrium phonon number is not an independently conserved quantity, so its chemical potential is zero in the usual thermal description. Anharmonicity allows phonon interactions and finite lifetimes beyond the independent-oscillator approximation.