In the first Brillouin zone, their allowed frequencies have an optical and 
In the first Brillouin zone, their allowed frequencies have an optical and an acoustical branch, and one way of determining their dispersion relation is through inelastic neutron scattering. They behave as though they have a momentum equal to h-bar times their wavenumber, but actually don't carry any momentum at all. The application of Planck statistics to them allows the derivation of the Debye model of heat capacity, and effects involving three of these, such as the umklapp process, result from third-order anisotropies in the lattice geometry. FTP, identify these particles which represent the quantization of elastic waves in solids.
In the first Brillouin zone, their allowed frequencies have an optical and an acoustical branch, and one way of determining their dispersion relation is through inelastic neutron scattering.
phonons