Lattice Dynamics of Cubic Lattices with Long-Range Interactions

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Abstract
An analytic study is made of the dispersion relations and frequency spectra of unbounded cubic lattices in which there exist long‐range pair potentials of the form r−p, where r is the distance between particles. This paper is an extension of work by Davies and Yedinak in which simple cubic lattices are studied. Cubic lattices having two particles per unit cell are now considered. The analytic behavior of the optical branches near the origin of the first Brillouin zone is determined for the case of 1 ≤ p ≤ 3 and the resulting contribution of the longitudinal optical branch to the frequency spectrum is obtained. A special case of such lattices is Kellermann's model for NaCl. This model is studied in detail.

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