ABSTRACT
Phonon group velocities have been calculated for symmetry planes in bcc monotomic crystals using a rigid-ion lattice dynamical model utilizing 12 force constants and fifth nearest-neighbor interactions. Calculations are presented for two metals: sodium and tungsten for which experimental dispersion curves are available, and which reasonably agree with Born-von Karman predictions. Group velocities along all 3 principal axes are predicted to vanish at zone boundaries. Furthermore, group velocities along the (111) axes in both metals become negative for larger values of the wave vector within the first Brillouin zone. Polar plots of phase and group velocities for the (010) and (110) planes are given for several different magnitudes of the wave vector in both sodium and tungsten. The large cuspidal features in the group velocity of sodium undergo remarkable changes and spread to other modes as the magnitude of the wave vector is increased. Tungsten, although elastically isotropic for small values of the wave vector, exhibits pronounced cuspidal features in the group velocity for larger values of the wave vector. Since energy carried by phonons is in the direction of the group velocity such cuspidal features gives rise to strong focusing of phonons along cuspidal edges. These phonon-focusing effects arise because dispersion can be quite different along different crystallographic directions. Strong phonon focusing is predicted to dramatically change the phonon transport properties of these crystals and thus the phonon contribution to the thermal conductivity.
