Phonons and anomalous thermal expansion behavior of H2O and D2O ice Ih

In order to identify and quantitatively analyze the anharmonicity of phonons relevant to the anomalous thermal expansion in the $\mathrm{I}h$ phase of ice, we performed neutron inelastic scattering measurements to study the phonon spectrum as a function of pressure up to 1 kbar at 225 K in deuterated ice (${\mathrm{D}}₂\mathrm{O}$), and as a function of temperature over 10--225 K at ambient pressure in both ${\mathrm{H}}₂\mathrm{O}$ and ${\mathrm{D}}₂\mathrm{O}$ 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.