Heat capacity of hexagonal tungsten bronzes

The heat capacity of four hexagonal tungsten bronzes (KₓWO₃, RbₓWO₃, CsₓWO₃, and TlₓWO₃), WO₃, and cubic NaₓWO₃ have been measured from 1 to 55 K. The excess heat capacity reported by King et al. for RbₓWO₃ and attributed to an Einstein mode is also present in KₓWO₃, CsₓWO₃, and TlₓWO₃. The values of x determined from the excess heat capacity agree reasonably well with the nominal composition having $x=0.33$. The Einstein temperatures ΘE for the metal ions vibrating in the channels formed by the six-membered rings of WO₆ octahedra were found to be 58 K for Rb, 70 K for Cs, and 38 K for Tl. Two unexplained peaks in the heat capacity of KₓWO₃ near 20 K precluded an accurate determination of ΘE for this tungsten bronze, but ΘE is estimated to be between 60 and 90 K. The magnitudes of the Einstein temperatures can be understood in terms of the masses and ionic radii of the metal ions. All four hexagonal tungsten bronzes are superconductors. Measurements of the heat capacity with a magnetic field showed RbₓWO₃ to be a type-I superconductor, but KₓWO₃ to be a type-II superconductor.