Static and Dynamical Elastic Constants of Simple Metals

Abstract

The compressibility problem of Brovman and Kagan is discussed and examined numerically. The issue of the problem is that the two methods of the calculation of the elastic constants in terms of the second order perturbation based on the same pseudopotential do not give the identical result. One is the method of the static homogeneous deformation. The other is the dynamical long-wave phonon method within the two body central potential approximation. Although the conventional dynamical method, which adopts the zero pressure from the static method, yields the required violation of the Cauchy relation, the difference between the elastic constants obtained from the two methods still persists. The compressibility problem is shown to be important for alkali metals and significant for A 1 and Pb.