Three‐body interaction and lattice dynamics of metals

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Abstract
Pseudopotential theory demonstrates that the total energy of a metal consists of an effective two‐body central interaction and a purely volume dependent part. Starting from this basis, a model expression for the energy in a metal is developed. A three parameter expression for the volume energy is used of which only two are necessary for the lattice dynamical properties. It is shown that the interpretation of the volume strain as the local strain, as demanded by the adiabatic hypothesis, leads at once to an effective three‐body ion‐ion interaction which is essential in order to demonstrate the equality of the static and dynamic elastic constants. The present model has no difficulty either with the equilibrium condition or with the symmetry properties of the dynamical matrix as in other phenomenological models. The model is applied to calculate the phonon frequencies of the b.c.c. metal W and the f.c.c. metals Cu, Ag, and Ni. With a suitable expression for the two‐body central interaction the model can be easily extended to calculate a fairly large number of both static and dynamic properties of metals.