Debye θ and compressibility. III. Cubic metals

Abstract

It has been shown that for crystal belonging to the cubic class, general relations can be obtained connecting the Debye characteristic temperature, θ, and the compressibility, χ , and that they do not depend on the nature of the potential energy of the crystal. An error in the literature has been pointed out in connection with a θ, χ relation for the ionic crystals of the CsC1 type. The following formulas are obtained for the metals belonging to the cubic class: θ=h/k 1/2π(6a/mχ)^1/2 for the body centered cubic structure and θh/k 1/2π(4.5a/mχ)^1/2 for the face centered cubic structure, where h and k are Planck's and Boltzman's constants, a, the lattice constant and m, the atomic mass. θ's calculated from these relations compare well with their 'experimental' values.