Higher-order elasticity of cubic metals in the embedded-atom method

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Abstract
The higher-order elasticity of cubic metals in the framework of the embedded-atom method (EAM) is investigated. Proper groupings of the second- and third-order elastic moduli are shown to yield expressions that depend solely on either the electron density function or the pair potential and which therefore facilitate the construction of EAM models. This formulation also makes evident some important restrictions on the EAM functions and lattice summations. In order for the EAM to model the anharmonic properties accurately, (a) at least the third-nearest-neighbor interactions must be included in the expressions for the cohesive energies of both the body-centered-cubic and face-centered-cubic metals and (b) an electron density function of an inverse power form, as has been employed previously, generally is not valid. Specific EAM models are constructed for a diverse selection of metals (i.e., aluminum, copper, sodium, and molybdenum). These models identically reproduce the respective second- and third-order elastic moduli, as well as the binding energy, atomic volume, unrelaxed vacancy formation energy, and Rose's universal equation of state. They also provide reasonable phonon frequency spectra and structural energy differences