  In order to identify and quantitatively analyze the anharmonicity of phonons
relevant to the anomalous thermal expansion in the Ih phase of ice, we
performed neutron inelastic scattering measurements of the phonon spectrum as a
function of pressure up to 1 kbar at 225 K in deuterated ice (D2O), and as a
function of temperature over 10-225 K at ambient pressure in both H2O and D2O
ice. We also performed density functional theory calculations of the lattice
dynamics. The anomalous expansion is quantitatively reproduced from the
analysis of the neutron data as well as from the ab-initio calculations.
Further, the ab-initio calculations are used to visualize the nature of
anharmonic phonons across a large part of the Brillouin zone. We find that the
negative thermal expansion below 60 K in the hexagonal plane is due to
anharmonic librational motion of the hexagonal rings of the ice molecules, and
that along the hexagonal axis originates from the transverse vibrations of the
hexagonal layers.
