Ab initiocalculation of elastic properties of solid He under pressure

Abstract

The high-pressure equation of state and elastic properties of solid He $(^{4}\mathrm{He})$ have been calculated using density functional theory formulated in the framework of the exact muffin-tin orbitals method. The theoretical results, obtained within the generalized gradient approximation for the exchange-correlation functional, are in good agreement with the experimental data available for pressures between $13\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and $32\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. We predict that at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the hexagonal phase of He remains mechanically and thermodynamically stable up to the highest pressure considered in the present study $(\ensuremath{\sim}150\phantom{\rule{0.3em}{0ex}}\mathrm{GPa})$. The calculated anisotropy ratios of He are similar to those observed in the case of hexagonal metals with $c∕a\ensuremath{\sim}1.63$. On the other hand, we find that hydrostatic pressure has negligible effect on the anisotropy of He. This indicates that He can be used as a quasihydrostatic medium in high-pressure experiments up to at least $150\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$.