Two-phonon density of states and anharmonic decay of large-wave-vector LA phonons

Effects of the lattice dispersion upon anharmonic decay of near-zone-boundary LA phonons in Ge are studied by making reference to the two-phonon density of states in the [100] and [111] directions. As the wave vector approaches Brillouin-zone boundaries, the two-phonon density of states increases more rapidly than ω², implying the spontaneous decay rates of the large-wave-vector LA phonons become more frequent as compared to ω⁵ dependence predicted in the continuum elasticity theory.