Electrical Properties of Sodium Tungsten Bronze

With the addition of sodium atoms the ferroelectric insulator W${\mathrm{O}}_3$ acquires metallic properties. We have grown single crystals of ${\mathrm{Na}}_x{\mathrm{WO}}_3$ using a method developed at the Linde Air Products Company. Chemical analyses for sodium concentration showed $x=0.66\mathrm{}$. The electrical resistivity was found to have a value of (1.9±0.2)×${10}^{-4\mathrm{}}$ ohm-cm at 0°C and to decrease approximately linearly with decreasing temperature in the range 20°C to -160°C. The Hall coefficient was found to have a value of (-5.1±0.2)×${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^3$/coulomb at 20°C and to decrease slightly with decreasing temperature. This value for the Hall coefficient indicates one electron carrier for each sodium atom added to the crystal. Using Pauli's theory of paramagnetism for free electrons in simple metals the calculated magnetic susceptibility is 0.53×${10}^{-6\mathrm{}}$. The value observed by Stubbin and Mellor for a sodium concentration corresponding to $x=0.9\mathrm{}$ was 0.45×${10}^{-6\mathrm{}}$. Using the free electron theory of metals, the following properties have been calculated: electron mobility and mean free path, energy at the surface of the Fermi distribution, thermal conductivity, and electronic specific heat.