A series of [Ba
x
Cs
y
][(Ti, Al)
3+
2
x
+
y
Ti
4+
8-2
x
-
y
]O
16
hollandites, synthesized at 1250°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 ≼
x
≼ 1.14, whilst for caesium endmember hollandites (
x
= 0) 1.32 ≼
y
≼ 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 hoilandite, 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 5
c
supercell for hollandite. Superlattice ordering in [Ba
x
Cs
y
][(Ti, Al)
3+
2
x
+
y
Ti
4+
8-2
x
-
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
+
≼ 0.33 and tunnel-site occupancies of 1.03‒1.15 display 4.5 ≼
m
≼ 5.0. Intermediate hollandites with 0.40 ≼ Cs
+
≼ 0.70 and tunnel-site occupancies ranging from 1.14 to 1.23 possess superstructures with 5.5 ≼
m
≼ 5.7, whereas caesium endmembers and caesium-rich hollandites have tunnel-site occupancies between 1.12 and 1.51 and 5.9 ≼
m
≼ 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 more than about one Al
3+
per formula unit, one-dimensional (uncorrelated) ordering is suppressed, and three-dimensional order occurs almost exclusively. Hollandite superstructures, and thus their stoichiometries, are determined both by mutual repulsion between large cations within individual tunnels, and intertunnel interaction between large cations. The ceramic high-level nuclear wasteform, Synroc, contains a titanate hollandite belonging to the above series. It has been suggested that the capacity of Synroc to immobilize caesium may be impaired if caesium and barium are not incorporated solely in hollandite, but are partitioned between hollandite and additional titanate phases or hollandite-related structures. No such phase has been encountered in the synthesis of the above hollandite series or in Synroc, prepared according to current specifications, because the trivalent species are present in sufficient abundance to allow the incorporation of all barium and caesium in hollandite. Consequently two-component titanates (for example Cs
2
Ti
6
O
13
or Ba
2
Ti
9
O
20
), do not appear in the phase assemblage. Moreover, the trivalent species do not comprise Al
3+
alone but also include some Ti
3+
, which promotes more favourable structural modifications and kinetics. Furthermore, the phase assemblage includes ‘reduced’ rutile, which effectively prohibits crystallization of two-component titanates with [Ba, Cs]/[Ti] ratios higher than that in hollandite, and also three-component [Ba, Cs] [Ti, Al]
3+
-titanates other than hollandite. When these three criteria are satisfied, the appearance of additional, potentially undesirable phases in the Synroc mineralogy is suppressed, and all barium, caesium (and rubidium) may be successfully immobilized in hollandite.
Drop Size Distribution Broadening Mechanisms in a Bin Microphysics Eulerian Model
