Resonant Ultrasound Studies of Quasi-2D Na$_{x}$CoO$_{2}$ (0.7 $\le $ x $\le $ 0.77)

Cobalt-based oxides have been shown to represent a new paradigm for a good thermoelectric material. These materials violate all of the traditional guidelines to help identify a potentially good thermoelectric material. In order to obtain a better understanding of its physical properties, we have initiated the synthesis of layered Na$_{x}$CoO$_{2}$, and started a study of the elastic properties of these materials using Resonant Ultrasound Spectroscopy (RUS). In this work, we discuss our results for sodium cobaltate compounds with 0.7 $\le $ x $\le $ 0.77. Single crystals were successfully grown in a floating-zone furnace, and the elastic constants have been measured as a function of temperature (5-300K) and in magnetic fields up to 5 Tesla. The resulting plots of elasticity vs. temperature clearly reflect a transition below 50 K, which is believed to be associated with rearrangement of the Na-atoms between the CoO$_{2}$ planes.