Effects of Ordering on the Transport Properties of Sodium Tungsten Bronze

The electrical resistivities, Hall coefficients, and Seebeck coefficients of metallic ${\mathrm{Na}}_x{\mathrm{WO}}_3$ have been measured as functions of the sodium concentration ($x$ value) from $x=0.4\mathrm{}$ to $x=0.9\mathrm{}$ and also a function of the temperature from 4 to 300°K. The resistivity, Hall coefficient, and Seebeck coefficient each showed an anomaly at $x=0.75\mathrm{}$ where the sodium atoms are ordered. These results are the first demonstration of ordering effects in any transport property of any tungsten bronze. A careful selection of crystals that were homogeneous in electrical resistivity was necessary in order to see these ordering effects. For homogeneous crystals, the Hall coefficients were different from those previously reported and do not predict the exact number of free electrons.