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 a bosonic quantum of a crystal's normal modes. Because phonon number is not conserved in thermal equilibrium, its chemical potential is zero.