The lattice dynamics of metals using the Shaw model potential

The optimized model potential proposed by Shaw (1968) is used in lattice dynamical theory of simple metals. The general expressions for the dispersion are given and results are presented for examples of simple metals, namely aluminium (fcc) sodium (bcc) magnesium (hcp) and also for thallium (hcp) and indium (bct). All except thallium give satisfactory dispersion curves. The phonon distribution is also given for these metals (omitting thallium). The overall procedure is shown to yield a good description of the lattice mechanical behaviour of metal but breaks down for the larger ions.