Vibrational dynamics and phonon dispersion of polycrystalline ice XII and of high-density amorphous ice

Abstract

The dynamics of high-density polycrystalline ice XII have been studied with neutron and x-ray scattering techniques in the range of translational and librational modes. Depending on the energy range of interest, different neutron spectrometers have been utilized. This way, accurate information on mode energies, sound velocities $(\overline{v}=2350\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$, and the Debye temperature $({T}_{D}=240\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ have been obtained. Having applied protonated $({\mathrm{H}}_{2}\mathrm{O})$ and deuterated $({\mathrm{D}}_{2}\mathrm{O})$ sample material, we were as well able to study the effects of coherence on the inelastic response and to follow the dispersion of acoustic phonons in the second Brillouin zone. The purely coherent scattering character and the kinematics of x rays were exploited to follow the dispersion of phonons in the first Brillouin zone, to discriminate between modes of longitudinal and transverse polarizations, and to determine the longitudinal velocity of sound $({v}_{\mathrm{l}}=4060\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$. In addition, the inelastic properties of ice XII are compared to the responses of polycrystalline cubic ice ${I}_{c}$ and the high-density amorphous structure.