Structure and dynamics of superconducting Na x CoO 2 hydrate and its unhydrated analog

Neutron scattering has been used to investigate the crystal structure and lattice dynamics of superconducting ${\mathrm{Na}}_{0.3}{\mathrm{CoO}}_{2}\ensuremath{\cdot}1.4(\mathrm{H}/\mathrm{D}{)}_{2}\mathrm{O},$ and the ``parent'' ${\mathrm{Na}}_{0.3}{\mathrm{CoO}}_{2}$ material. The structure of ${\mathrm{Na}}_{0.3}{\mathrm{CoO}}_{2}$ consists of alternate layers of ${\mathrm{CoO}}_{2}$ and Na and is the same as the structure at higher Na concentrations. For the superconductor, the water forms two additional layers between the Na and ${\mathrm{CoO}}_{2},$ increasing the $c$-axis lattice parameter of the hexagonal ${P6}_{3}/mmc$ space group from 11.16 \AA{} to 19.5 \AA{}. The Na ions are found to occupy a different configuration from the parent compound, while the water forms a structure that replicates the structure of ice. Both types of sites are only partially occupied. The ${\mathrm{CoO}}_{2}$ layer in these structures is robust, on the other hand, and we find a strong inverse correlation between the ${\mathrm{CoO}}_{2}$ layer thickness and the superconducting transition temperature ${(T}_{C}$ increases with decreasing thickness). The phonon density of states for ${\mathrm{Na}}_{0.3}{\mathrm{CoO}}_{2}$ exhibits distinct acoustic and optic bands, with a high-energy cutoff of $\ensuremath{\sim}100\mathrm{meV}.$ The lattice dynamical scattering for the superconductor is dominated by the hydrogen modes, with librational and bending modes that are quite similar to ice, supporting the structural model that the water intercalates and forms ice-like layers in the superconductor.