Microscopic Theory of Dielectric Screening and Lattice Dynamics in the Wannier Representation. II. Model Application to the Transition Metals Pd and Ni

The unified theory of lattice dynamics in the Wannier representation, presented in a previous paper, is here used to calculate the phonon dispersion of the transition metals Pd and paramagnetic Ni. This application represents the first microscopic phonon calculation in transition metals which takes into account the local field effects in the $d$-electron response. Using a tight-binding model for the $d$ electrons and a nearly-free-electron description for the $s$ electrons it is shown that these effects give contributions to the longitudinal-phonon branches and to the elastic constants $C_{11}$ and $C_{12}$ of the same order of magnitude as the Hubbard-exchange corrections (10-20%).