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 H2 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 H2 derived from Brillouin data is in agreement with previous results derived solely from x-ray diffraction.