High-pressure thermal expansion, bulk modulus, and phonon structure of diamond

Abstract

The thermodynamic properties of diamond at high pressures (up to 1000 GPa) have been investigated using the ab initio pseudopotential plane wave method and the density-functional perturbation theory. The $P\ensuremath{-}V\ensuremath{-}T$ equation of states has been calculated from the Helmholtz free energy of the crystal in the quasiharmonic approximation. The pressure dependence of the equilibrium lattice constant, bulk modulus, mode Gr\"uneisen parameters, and phonon structures has been presented. Some interesting dynamical features of diamond have been found at high pressures: (a) The thermal expansion coefficient decreases with the increase of pressure. At ultrahigh pressure $(>~700 \mathrm{GPa}),$ diamond exhibits a negative thermal expansion coefficient at low temperatures. (b) The phonon frequency at ${X}_{4}$ and ${L}_{3}^{\ensuremath{'}}$ gradually goes higher than that of ${X}_{1}$ and ${L}_{2}^{\ensuremath{'}},$ respectively. (c) The unusual overbending of the uppermost phonon dispersion curves near ${\ensuremath{\Gamma}}_{25}^{\ensuremath{'}}$ decreases with the increase of pressure. Such overbending results in a maximum in the phonon density of states, which has been invoked in the previous study [Phys. Rev. B 48, 3164 (1993)] to explain the famous sharp peak in the two-phonon Raman spectrum of diamond. Our present results predict that this sharp peak near the high-frequency cutoff will decrease with the pressure.