On the calculation of certain crystal potential constants, and on the cubic crystal of least potential energy

Abstract

Mathematical investigations of the physical properties of a crystal usually proceed in term s of its potential energy, and applications of the general formulae obtained are impossible without a knowledge in explicit term s of this function. Its evaluation requires, of course, a knowledge of the interatomic forces in the crystal, but, even when this information is available, the calculation of the potential energy presents a further problem, for which there is no general solution. The present paper is designed to supply certain necessary steps in the elucidation of the latter problem in the case of the cubic crystals, when the law of force between atom s is expressed as a series of inverse powers of the distance—probably the most general form in which the force is ever likely to be expressed.