Elasticity and Poisson's ratio of hexagonal close-packed hydrogen at high pressures

The elasticity at high pressure of solid hydrogen in hexagonal close-packed (hcp) phase I has been examined experimentally by laser acoustics technique in a diamond anvil cell, up to 55 GPa at 296 K, and theoretically using pair and three-body semiempirical potentials, up to 160 GPa. In the experiments on ${\mathrm{H}}₂$ and ${\mathrm{D}}₂$, the compressional sound velocity has been measured; the Poisson's ratio has been determined by combining these data with the previously reported equation of state. At room temperature, the difference between the adiabatic and isothermal processes vanishes above 25 GPa but cannot be neglected at lower pressure. Theoretically, all five elastic constants of hcp hydrogen have been calculated, and various derived elastic quantities are presented. The elastic anisotropy of hcp hydrogen was found to be significant, with $\mathrm{\ensuremath{\Delta}}P\ensuremath{\approx}1.2,\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}{S}₁\ensuremath{\approx}1.7$, and $\mathrm{\ensuremath{\Delta}}{S}₂\ensuremath{\approx}1$. Calculations suggest the Poisson's ratio to decrease with pressure reaching a minimum value of 0.28 at 145 GPa. In the experiment, the Poisson's ratio is also found to decrease with pressure. Theoretical calculations show that the inclusion of zero-point vibrations on the elastic properties of ${\mathrm{H}}₂$ does not result in any drastic changes of the behavior of the elastic quantities.