Energetics of brannerite-type solid solutions: The system MnV₂O₆LiMoVO₆Mo₂O₆

Brannerite-type solid solutions in the system MnV₂O₆LiMoVO₆Mo₂O₆ (MnLif{cyrillic}) were studied by high-temperature drop-solution calorimetry and X-ray diffraction. Enthalpies of mixing, referred to brannerite standard states, are ΔH_mix = y(1 - y)(24.8 - 51.7y) kJ/mole for (1 - y)MnV₂O₆ - yLiMnVO₆ (MnLi) and ΔH_mix = 23.4x(1 - x) for (1 - x)MnV₂O₆ - xMo₂O₆ (Mnf{cyrillic}). A fit to all the data simultaneously (the two joins above, three ternary points, and one point along Lif{cyrillic}) gives values similar to those above for ΔH_mix(MnLi) and ΔH_mix(Mnf{cyrillic}) while suggesting a negative heat of mixing along the Lif{cyrillic} binary and negligible ternary excess terms. Parameters for the transformation of Mo₂O₆ from the MoO₃ structure to the hypothetical brannerite structure are estimated to be: ΔH = 10.0 kJ/mole Mo₂O₆, ΔV° = 7.65 cm³/mole. Both the MnV₂O₆LiMoVO₆ system studied here and the MgV₂O₆LiMoVO₆ system studied previously show positive heats of mixing at MnV₂O₆- or MgV₂O₆-rich compositions and negative heats of mixing at LiMoVO₆-rich compositions. In each case, a linear correlation of the enthalpy interaction parameter, λ_H, and the volume interaction parameter, λ_V, is observed. Both systems show that positive heats of mixing correlate with negative volumes of mixing and negative heats of mixing correlate with positive volumes of mixing, but the MgLi correlation has a steeper slope than that for MnLi. This rather unusual but systematic behavior thus persists in several systems with brannerite structure.