Doping Rare-earth (RE) elements to ZrO2 helps stabilize the cubic and tetragonal phases and improves resistance to thermal shock and sintering at high temperatures. Since a RE ion has a lower valency (3+) than Zr ion (4+), oxygen vacancies are formed to preserve electroneutrality. We have studied the crystal structure of La0.1Zro.9O1.95 and Nd0.1Zr0.9O1.95 by neutron diffraction and examined the associated oxygen defects by a Fourier transform of the filtered residual diffuse scattering. The hydration process was investigated by inelastic neutron-scattering measurements of the hydrogen vibrational density of states of the surface hydroxyl groups and physisorbed water on these fine powders. We compare the O-H stretch vibrations from samples with only surface hydroxyl groups to multilayer coverage of water molecules. The decreasing energies and increasing widths of the O-H stretch bands with increasing H2O coverage indicate the influence of hydrogen bonding on the motion of water molecules. Similar elastic and inelastic experiments were also performed on a high surface-area pure ZrO2 powder.