Phonons in Solid Hydrogen and Deuterium Studied by Inelastic Coherent Neutron Scattering

Abstract

Phonon dispersion relations have been measured by coherent neutron scattering in solid para-hydrogen and ortho-deuterium. The phonon energies are found to be nearly equal in the two solids, the highest energy in each case lying close to 10 meV. The pressure and temperature dependence of the phonon energies have been measured in ortho-deuterium and the lattice change determined by neutron diffraction. When a pressure of 275 bar is applied, the phonon energies are increased by about 10%, and heating the crystal to near the melting point decreases them by about 7%. The densities of states, the specific heats, and the Debye temperatures have been deduced and found to be in agreement with the published experimental results. The Debye temperatures are 118 K for hydrogen and 114 K for deuterium. For hydrogen the Debye-Waller factor has been measured by incoherent neutron scattering and it corresponds to a mean-square displacement of the hydrogen molecules of 0.48 ${\mathrm{\AA }}^2$.