Nonlocal effects in the lattice dynamics of HCP transition metals

In the present work, consideration is given to the nonlocality of the transition metal model potential (TMMP) of A.D.E. Animalu (Phys.Rev.;B8:3542-54 and 3555-62 (1973) and B10:4964-72 (1974)) and expressions are deduced for the coefficients of linear terms in the expansion of the TMMP form factor in the nonlocal formalism of H. Eschrig and H. Wonn (Phys.Stat.Solidi;40:163-9 (1970)). A complete expression for the energy-wavenumber characteristic G(q) of this theory is used to compute the phonon dispersion curves of Sc, Y and Zr along the GAMMAA, GAMMAM and GAMMAKM symmetry directions. Reasonably good agreement is found between the computed and experimental results for Sc and Y, but relatively poor for Zr. (author)