On the Lattice Dynamics of Hexagonal Structure Metals

The lattice dynamics of the hexagonal close‐packed structure (h.c.p.) metals Mg, Zn, and Be are investigated assuming various first principles interionic interaction potentials. It is found that, if the ions interact via a Thomas‐Fermi potential, the Huang condition for the vanishing of the anisotropic stresses is not fulfilled, but only when assuming a c / a ratio corresponding to the ideal h.c.p. structure. One can except the same for Coulomb and Bardeen potentials, too. None of the potentials used gives a satisfactory description of the phonon dispersion relations for the mentioned metals. The need for introducing a nonradially symmetric effective interaction potential is discussed. It is observed that, for the transverse phonon branches Δ 5 and Δ 6 , the Coulomb interaction between the ions leads to better agreement with experiment, than any of the screened Coulomb interactions investigated. The numerical calculations of the lattice sums are carried out with the help of a convergence procedure based on elementary functions.