Influence of cation vacancy concentrations on ultra-low thermal conductivity in $(1-x)$BiVO$_4$-$x$Bi$_{2/3}$MoO$_4$ scheelite solid solutions

Bismuth vanadate - bismuth molybdate solid-solution was prepared to elaborate ceramics with different amounts of cation vacancies. Dense ceramics with similar microstructures were obtained and the evolution of their melting point, specific heat, thermal diffusivity, and conductivity as a function of the amount of vacancy was evaluated. At room temperature, the thermal conductivity decreases from 1.74 W m$^{-1}$ K$^{-1}$ for BiVO$_{4}$ (x=0) to 1.12 W m$^{-1}$ K$^{-1}$ for Bi$_{0.867}$$\square$$_{0.133}$Mo$_{0.4}$V$_{0.6}$O$_{4}$ (x=0.4). Moreover, we show that a very small amount of vacancy (1.7%, x=0.05) is enough to provide a large decrease in thermal conductivity by more than 15%, in agreement with a mass fluctuation scattering model. However, the temperature of the melting point also decreases with increasing amount of vacancy. Our results suggest adding only a very small amount of vacancy as the best strategy to obtain superior materials for thermal barriers and thermoelectric devices, with ultra-low thermal conductivity and high-temperature stability.