Elastic constants in density-functional theory

Abstract

A formalism for computing the elastic constants of a macroscopically uniformly strained solid within canonical density functional theory is developed, using a rather general characterization of the strained state as a constrained minimum of the density functional. This permits microscopic parameters characterizing the solid density to respond freely to the strain. Interesting extremal properties of some elastic constants are found. In particular it is shown that the exact value of any of the diagonal elastic constants is a lower bound to any variational approximation of them. The role of defects in the solid and the effects of the choice of the variational class of solid densities is discussed in some detail. The method is applied to a calculation of the three independent elastic constants of a hard sphere solid using the Ramakrishnan-Yussouf density functional. Numerical results are given and discussed.