Dispersion of optical and acoustic phonons in diamond and germanium crystals

The dispersion laws of the optical and acoustic branches in diamond-like crystals have been derived using idealized models of crystal lattices. Two types of analytical expressions have been proposed, whose parameters can be derived from inelastic neutron scattering experiments and the properties of acoustic waves. The calculation results are in satisfactory agreement with experimental data for the crystallographic directions [100], [110], and [111]. The group velocities of optical and acoustic phonons have been determined, and expressions for the effective mass of optical phonons have been derived.