The phonon is a vibration of the atomic lattice.
In normal circumstances, atoms vibrate as a result of their thermal energy. The higher the thermal energy, the greater the vibrational energy.
In a solid lattice, independent vibration of one atom is not possible - vibrations pass from atom to atom.
Such vibrations pass through the whole lattice, which can vibrate as a wave at a single frequency. When this happens, the vibration is called a phonon.
This single-frequency wave has a defined momentum and energy and can be considered to be a quantum unit or a packet of mechanical vibrational energy, just as a photon is considered to be a packet of electromagnetic energy.
Like photons, phonons exist with discrete amounts of energy: they can only accept or lose energy in accordance with the Planck relation:
where ΔE is energy change, h is Planck's constant, and ν is frequency of vibration.
Phonons, like other waves defined quantum mechanically, can be considered as matter waves: therefore, depending on circumstances, phonons can behave like particles or waves, just as electrons can. Interactions between phonons and electrons play significant roles in electrical resistance and, in metals at very low temperatures, superconductivity.
Phonons can carry heat and sound through condensed states of matter - i.e. through solids and (some) liquids. Phonons also play a major role in determining the heat capacities of solids and liquids.