The formation of many oxides with unpredictable structures can be attributed to a balance between stable and unstable compositions. A surprising number of the members of the Ln4Cu3MoO12 and Ln'2Ln''2-Cu3MoO12 (Ln = La - Nd, Sm - Lu) families form, all crystallizing in a hexagonal structure similar to that of YMnO3. Some do not form because either the average lanthanide size is too small (rβ(Ln) <105 pm, where r(Ln) ≡ 9-coordinate trivalent lanthanide radii) or the difference between the size of Ln' and Ln'' is too large (Δr(Ln) > 14 pm). Furthermore, even if Ln'4Cu3MoO12 and Ln''4Cu3MoO12 form single phases, attempts to synthesize the corresponding solution phase, Ln'2Ln''2Cu3MoO12, may result in a mixture of simpler metal oxides. The explanation illuminates the importance of unstable 'umbrella' stoichiometries for the formation of unconventional structures in multication systems.
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