Lattice dynamics,third order elastic constants and low temperature lattice thermal expansion of zirconium

The lattice dynamics and the anharmonic properties of the hexagonal Zirconium are worked out using Keating's approach. The dispersion curves are fitted using twelve second order parameters and the six second order elastic constants are evaluated. The ten third order elastic constants are calculated using five third order parameters. The experimental measurements on the pressure derivatives of the second order elastic constants in Zirconium are in good agreement with the calculated values. The low-temperature limit of the lattice thermal expansion is calculated which agrees well with the value obtained from thermal expansion data. The variation of the generalised GPs of the elastic modes with the direction of propagation is illustrated by polar diagram.