Perturbative theory and tree-body forces in h.c.p. metals

An analysis is presented of the role of the non pair forces in the lattice dynamics of sp bonded hcp metals: Be, Mg and Li. By expanding the total energy up to third order in the electron-ion pseudopotential, a dynamical matrix is derived which contains terms arising from central pairwise interactions between the ions as well as contributions due to sums of three body forces. The phonon dispersion relations are calculated using a local form of the model potential, which allows for a realistic evaluation of the third order contributions. The results show that the three body forces are very important in Be and are responsible for the peculiarities of the spectrum, as is most clearly seen from the analysis of the frequencies at the K point of the Brillouin zone.