Three-body interaction in h.c.p. metals

The consideration of two-body central forces cannot explain the correct ordering of dispersion branches in the GAMMAKM direction in many h.c.p. metals. The importance of three-body forces in these metals is also indicated by the fact that for these metals the sum rule of Waren is not satisfied. 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 of a metal is developed. It is shown that the interpretation of the volume strain as the local strain, as demanded by the adiabatic hypothesis, leads to an effective three-body interaction between the ions. The model is applied to study the lattice dynamics of Mg and Be. It is found that the model predicts the correct ordering of the dispersion branches and fairly good agreement is obtained in the case of phonon frequencies and elastic data. (author)