The energy of a lattice vibration is quantized. The quantum energy is called a phonon in analogy with the photon of the electromagnetic wave. Elastic waves in crystals are made up of phonons. Thermal vibrations in crystals are thermally excited phonons, like the thermally excited photons of black-body electromagnetic radiation in a cavity. The energy of an elastic mode of angular frequency ω is ε=(n+1/2)ℏω when the mode is occupied by n phonons.
Solid state physics is a lot more interesting than I'd thought! (Then they go on to talk about plasmons, magnons, polarons, and excitons...) Even planck's constant shows up!