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

High-resolution transmission electron microscopy and selected-area electron diffraction show that all phases of the general formula [Ba$_x$Cs$_y$] [(Al, Ti)$^{3+}_{2x+y}$ Ti$^{4+}_{8-2x-y}$]O$_{16}$, 1.08 $\leqslant$ x+y $\leqslant$ 1.51 have the hollandite-type substructure. These hollandites display commensurate and incommensurate superlattices owing to the ordered insertion of large cations (Ba$^{2+}$, Cs$^+$) into the (2, 2) tunnel interstices of the octahedral (Al, Ti) O$_6$ framework. Multiplicity (m) of a supercell is defined as d$_{\mathrm{supercell}}$ divided by d$_{002}$ for the subcell. Ordering may be one-dimensional, in which case the cation sequences between (2, 2) channels are independent, three-dimensional with lateral correlation between tunnels, or a combination of both. One-dimensional superstructures yield commensurate multiplicities of 4 in all phases except an aluminous caesium hollandite where m = 6. Three-dimensional superstructures are both incommensurate and commensurate, with 4.5$_0$ $\leqslant m \leqslant$ 6.5$_9$. Multiplicities correlate directly with caesium content per formula unit, establishing a maximum in caesium-rich hollandites. Among barium ($y$ = 0) and caesium endmembers, ($x$ = 0) multiplicities increase modestly with increasing Al$^{3+}$: (Al + Ti)$^{3+}$ content. Superstructure dimensionality is largely determined by the nature and proportions of the trivalent species, rather than the tunnel cations; one-dimensional order is commonplace in hollandites rich in trivalent titanium but rare in aluminous hollandites. High-resolution electron microscopy supports the interpretation of incommensurate superstructures as fine-scale intergrowths of commensurate microdomains with $m$ = 4, 5, 6 or 7. For aluminous hollandites, rare examples of structural modifications involving tunnels of different cross-sectional dimensions may be found, i.e. T(2, $n$), 1 $\leqslant n \leqslant$ 3 intergrowths. As all specimens are sensitive to the electron beam, prolonged irradiation at high electron fluxes can initiate the transformation of single-crystal hollandite to single-crystal rutile. A mechanism for this transformation is proposed, whereby the hollandite crystals initially adjust their multiplicity to six. Growth fronts on {101}$_{\mathrm{holl}}$ subsequently propagate through the crystals consuming hollandite and leaving rutile: the structure of the interface between the phases is believed to contain components of rutile possessing