The Crystal Lattice
Most solids have periodic arrays of atoms which form what we call a crystal lattice. Amorphous solids and glasses are exceptions. The existence of the crystal lattice implies a degree of symmetry in the arrangement of the lattice, and the existing symmetries have been studied extensively.
One of the implications of the symmetric lattice of atoms is that it can support resonant lattice vibration modes. These vibrations transport energy and are important in the thermal conductivity of non-metals, and in the heat capacity of all solids.
The existence of a periodic crystal lattice in solid materials provides a medium for characteristice lattice vibrations.
On the scale of the lattice spacing, these vibrational modes are quantized, with the quantum of lattice vibration being called a phonon. Treating the lattice vibrations quantum mechanically led to the Einstein model and the Debye model of specific heat.
In the BCS Theory of superconductivity, electron pairs in the low-temperature material couple by means of phonons to produce Cooper pairs. The phonon coupling produces a bound state which cannot be excited by the available thermal energy and therefore move without resistance through the crystal lattice.
Lattice vibrations can also interact with light to produce scattering called Brillouin scattering, which is used in laser spectroscopy.