Transport, magnetic, thermoelectric, and structural properties of hollandite titanates BaxTi8 O16+δ

We studied hollandite titanates ${\mathrm{Ba}}_{x}{\mathrm{Ti}}_{8}{\mathrm{O}}_{16+\ensuremath{\delta}}$, which have double chains of edge-sharing ${\mathrm{TiO}}_{6}$ octahedra with various numbers of $d$ electrons per Ti $n=(x\ensuremath{-}\ensuremath{\delta})/4$. Anomalies at $\ensuremath{\sim}200\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ were observed in the temperature dependence of various quantities over a wide range of $n$, which were caused by the charge ordering of the $d$ electrons. It was found that charge ordering is stable when $d$ electrons exist at every fifth site along the Ti chain. A structural phase transition from tetragonal to monoclinic occurs as a secondary effect of the charge ordering. When $n$ is close to 0.4, the anomalies at $\ensuremath{\sim}200\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ disappear, and the crystal structure remains monoclinic from 300 K down to the lowest temperatures. It was also found that this series of compounds exhibits negative Seebeck coefficients with large absolute values at room temperature and that the figure of merit for thermoelectric materials ($ZT$) was maximized at $n\ensuremath{\sim}0.22$ (0.05 at room temperature).