Electrical Resistivity and Hall Coefficient of Sodium Tungsten Bronze

The electrical resistivity and Hall coefficient of single crystals of sodium tungsten bronze (${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$) have been measured as a function of temperature and as a function of sodium concentration. The resistivity decreased linearly with decreasing temperature from 300°K to 125°K and was very nearly constant below 30°K. The resistivity at 26°C exhibited a minimum value of (3.20±0.14) (${10}^{-5\mathrm{}}$) ohm-cm at $x\cong 0.75$. The residual resistivity at 0°K also exhibited a minimum at $x\cong 0.75$ and had a value of (1.25±0.10) (${10}^{-5\mathrm{}}$) ohm-cm. The variation of the Hall coefficient with temperature was less than 2 percent over the temperature range 78°K to 370°K. The Hall coefficient varied inversely with the sodium concentration from $x=0.584\mathrm{}$ to $x=0.897\mathrm{}$, and over this entire concentration range the Hall coefficient corresponded to one free electron for each sodium atom in the crystal. Hence, the anomalous minimum in the resistivity at $x\cong 0.75$ must be attributed solely to an anomalous maximum in the electron mobility. An adequate explanation of the minimum in resistivity does not seem possible in terms of thermal scattering alone.