ABSTRACT
Phonon group velocites have been calculated for symmetry planes in fcc crystals using a lattice dynamical model utilizing 16 force constants and sixth nearest-neighbor interactions. Calculations are presented for one metal, copper, for which experimental dispersion curves can be matched with a Born-von Karman analysis. Group velocities are predicted to vanish at zone boundaries along (100) and 〈111〉 axes. Furthermore, the group velocity along 〈110〉 axes becomes negative inside the first Brillouin zone for larger values of the wave vector. Polar plots of phase and group velocities for the (010) and (110) planes are given for several different magnitudes of the wave vector. The pronounced cuspidal features in the group velocity of copper undergo remarkable changes and spread to other modes as the magnitude of the wave vector is increased. Since energy carried by phonons is parallel to the group velocity such cuspidal behavior gives rise to strong phonon-focusing effects. Such strong focusing is predicted to dramatically change the phonon transport properties of these crystals and thus the phonon contribution to the thermal conductivity.
