Elasticity of hydrogen to 24 GPa from single-crystal Brillouin scattering and synchrotron x-ray diffraction

We have developed a technique for studying the elasticity of single crystals of solid hydrogen and related materials at very high pressures and used the method to determine the second-order elastic moduli of single-crystal n-type hydrogen to 24 GPa at 295 K. The method involves the measurement of acoustic velocities as a function of crystallographic direction by Brillouin scattering in a diamond anvil cell with the orientation of the single crystals determined by synchrotron x-ray diffraction. Between 6 and 24 GPa, the adiabatic bulk modulus of ${\mathrm{H}}_2$ increases by more than a factor of 3 and the shear modulus increases by more than a factor of 4. The acoustic anisotropy of hydrogen decreases from 11% to 6% for compressional waves and from 23% to 14% for shear waves. The data are also used to calculate thermodynamic properties of hydrogen at high pressures. By including the observed velocity anisotropy, the equation of state of ${\mathrm{H}}_2$ derived from Brillouin data is in agreement with previous results derived solely from x-ray diffraction.