Derivation of elastic constants from the embedded-atom potential in a lattice model

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Abstract
Empirical N-body potentials, such as the embedded-atom potentials [M.S. Daw, and M. I. Baskes, Phys. Rev. B 29, 6443 (1984)], have recently been used to describe the atomic interactions in hexagonal close-packed (hcp) structures and are in principle suited to describe the interactions in less symmetric structures. But together with the decreasing symmetry in the lattices studied, the relations used to fit the potential parameters to elastic constant data are not valid anymore. In noncentrosymmetric lattices the elastic constants are composed of a homogeneous and an inhomogeneous contribution, but the latter contribution is usually not taken into consideration. In this paper a rigorous derivation of the expressions for elastic constants from the embedded-atom total-energy function is given. These expressions have been applied to potentials previously derived for hcp metals, showing that the inhomogeneous contribution for most of these potentials should not be neglected. Furthermore we will argue that the Raman frequencies can be used as empirical data to fit the relative magnitudes of the homogeneous and inhomogeneous contributions to the elastic constants.