the formula $t=\frac{r_{M}
+r_{O}}{\sqrt{2}(r_{W} + R_{O})}$ [@gs], where $r_{j}$ are the ionic radii. For a perovskite structure to be stable, $t$ must be less than unity. The tolerance factors for NaWO$_3$ and KWO$_3$ are 0.909 and 1.056 respectively, indicating that the potassium atom is slightly too large to form a stable structure. Potassium bronzes have been formed with high $x$ contents, but only under high-pressure synthesis conditions [@chamb]. Rubidium and caesium cubic bronzes with high $x$ content cannot be formed. The hexagonal structure, having larger tunnels, is able to accommodate larger ions than observed in the cubic system. In the experimental system the stability of hydrogen is notoriously difficult to maintain, as it is quite mobile due to its small size. Both hydrogen and lithium are small enough ions to be able to occupy the small triangular sites between the hexagonal tunnels [@90]. Thus reported experimental results for H$^+$- and Li$^+$-hexagonal bronzes may show differing behaviour from larger atoms because the occupied sites may be different in each case. In the experimental hexagonal system, the $a$ parameter is observed to increase as ions are intercalated while the $c$ parameter decreases. The final values are relatively consistent across the series, as 