ABSTRACT
A rigid-ion lattice dynamical model is developed for calculating phase and group velocities in dispersive sc, bcc, and fcc crystals. The model is easy to understand, allows non-central symmetric forces and requires no explicit use of group theory. Results are given for the sc lattice up to and including third nearest-neighbor interactions, and agree with Born-von Karman theory. This model allows, however, a maximum of 3 force constants per site whereas the general Born-von Karman model specifies, for example, 4 constants for fourth nearest-neighbors in bcc, and 4 constants each for third and fifth nearest-neighbors in fcc crystals. This model thus constrains one of the 4 force constants to be linearly dependent upon two of the other force constants for such neighbors. The model in its present form results in a symmetric force matrix and thus is not applicable for the diamond lattice. The model, however, provides a straightforward method for calculating phonon-focusing effects in sc, bcc and fcc crystals.
