Umbrella stoichiometry: A guide to the solid state chemistry of copper-rich oxides

Umbrella stoichiometries are relatively unstable compositions that can be leveraged to promote the formation of unconventional solid state structures. La^III and Cu^II in a one to one ratio is such a stoichiometry. The addition of a third metal such as W^VI, V^V, or Ru^V generates a complex set of potential products. Nonetheless, La₄Cu₃MoO₁₂ forms a single phase because no low energy multiphase alternatives exist for a stoichiometry so close to an umbrella stoichiometry. The cations in the structure are severely under-coordinated, yet oxygen can be removed from the structure by substituting Cu^II for Mo^VI. La₄Cu_3+xMo_1-xO_12-2-x forms a single phase for 0.0 ≤ x ≤ 0.12 before La₂Cu₂O₅ appears. This structurally unfavorable substitution is tolerated because it moves the composition even closer to the umbrella stoichiometry.