Lattice static Green function for an hcp lattice

Two different techniques for calculating the lattice distortion under a unitary force, the lattice Green function (GF) at zero frequency, are discussed. One is based on the classical Fourier inversion procedure for a finite number of points within the first Brillouin zone, i.e., periodic boundary conditions are assumed. Explicit formulas which take full profit of the hcp lattice symmetry and allow for a fast and relatively simple calculation of the GF are deduced. An extrapolation procedure is proposed in order to evaluate the GF for a lattice with infinite boundaries. This procedure allows one to differentiate the lattice dispersive contributions to the GF from the continuum ones. A second calculation technique, called semidiscrete, is proposed. This is based on assuming that the atoms located beyond a given distance from the lattice point where a force is applied are displaced like points of an infinite elastic medium under that force. Both techniques are applied to calculate the GF for some points of an hcp lattice held by two different interatomic potentials adjusted to some Mg parameters. The dispersive contribution to the GF values is found to be potential dependent and relatively small.