[Ba$_x$Cs$_y$][(Ti,Al)$^{3+}_{2x + y}$Ti$^{4+}_{8 - 2x - y}$]O$_{16}$ Synroc-Type Hollandites. I. Phase Chemistry

A series of [Ba$_x$Cs$_y$][(Ti,Al)$^{3+}_{2x+y}$Ti$^{4+}_{8-2x-y}$]O$_{16}$ hollandites, synthesized at 1250 $^\circ$C and coexisting with 'reduced' rutile, demonstrates complete solid solution between barium and caesium endmembers, and simultaneously between Ti$^{3+}$ and Al$^{3+}$. The presence or absence of rutile has only a minor effect on stoichiometry. For barium endmember hollandites (y = 0) the stoichiometry (i.e. tunnel site occupancy) ranges from 1.08 $\leqslant$ x $\leqslant$ 1.14, whilst for caesium endmember hollandites (x = 0) 1.32 $\leqslant$ y $\leqslant$ 1.51. Neither x nor y correlates with the nature and proportions of trivalent species. An appropriate stoichiometry for the aluminous barium end-member is confirmed as Ba$_{1.14}$Al$_{2.29}$Ti$_{5.71}$O$_{16}$. The composition BaO. Al$_2$O$_3$. 5TiO$_2$ yields this same hollandite, and not the supposed phase 'BaAl$_2$Ti$_5$O$_{14}$'. The phase 'BaAl$_2$Ti$_4$O$_{12}$' does not exist, while the composition BaO. Al$_2$O$_3$.4TiO$_2$ crystallizes to an assemblage containing the hollandite mentioned above. Reinterpretation of published X-ray diffraction data substantiate these conclusions and are consistent with a 5c supercell for hollandite. Superlattice ordering in [Ba$_x$Cs$_y$] [(Ti,Al)$^{3+}_{2x+y}$Ti$^{4+}_{8-2x-y}$]O$_{16}$ hollandites may be commensurate or incommensurate, with typical multiplicity values (m) and tunnel-site occupancies (x+y) correlating with increasing caesium content per formula unit throughout the series. Barium end-members and barium-rich hollandites, with Cs$^+ \leqslant$ 0.33 and tunnel-site occupancies of 1.03-1.15 display 4.5 $\leqslant$ m $\leqslant$ 5.0. Intermediate hollandites with 0.40 $\leqslant$ Cs$^+ \leqslant$ 0.70 and tunnel-site occupancies ranging from 1.14 to 1.23 possess superstructures with 5.5 $\leqslant$ m $\leqslant$ 5.7, whereas caesium endmembers and caesium-rich hollandites have tunnel-site occupancies between 1.12 and 1.51 and 5.9 $\leqslant$ m $\leqslant$ 6.3. For barium or caesium endmembers, multiplicities fail to correlate with tunnel-site occupancies, but do increase with increasing percentages of molar Al$^{3+}$/(Al$^{3+}$ + Ti$^{3+}$) in the structure. Superlattice periodicity is considerably more sensitive to changes in the barium-caesium content of tunnel sites than to variation in the nature of the trivalent species. Long-range superlattice order is determined not so much by the tunnel cations as by the trivalent species. With mo