Pressure dependence of the TO phonon frequency in hcp Zn

Zone-centre transverse optical phonon frequencies νTO(p) of hcp Zn as a function of hydrostatic pressure p have been calculated using the full-potential augmented-plane-wave plus local orbitals first-principles method with the generalized gradient approximation and compared with Raman measurements of frequencies under pressure. The oscillatory behaviour of νTO(p) found in the pressure range of the anomalies of hcp Zn supports our previous work on Zn, where such effects were shown both in the structural parameters and strongly in the elastic constant c44(p). By integrating the equation of motion using the exact potential and the zero-point and temperature excitations of the Raman active modes we show substantial anharmonic effects which make the frequency of one TO mode the order of 5% below the frequency of the other mode; this split is a large part of the observed line widths