Phase relations and Gibbs energies of spinel phases and solid solutions in the system Mg–Rh–O

Abstract

Pure stoichiometric MgRh₂O₄ could not be prepared by solid state reaction from an equimolar mixture of MgO and Rh₂O₃ in air. The spinel phase formed always contained excess of Mg and traces of Rh or Rh₂O₃. The spinel phase can be considered as a solid solution of Mg₂RhO₄ in MgRh₂O₄. The compositions of the spinel solid solution in equilibrium with different phases in the ternary system Mg–Rh–O were determined by electron probe microanalysis. The oxygen potential established by the equilibrium between Rh + MgO + Mg_1+xRh_2−xO₄ was measured as a function of temperature using a solid-state cell incorporating yttria-stabilized zirconia as an electrolyte and pure oxygen at 0.1 MPa as the reference electrode. To avoid polarization of the working electrode during the measurements, an improved design of the cell with a buffer electrode was used. The standard Gibbs energies of formation of MgRh₂O₄ and Mg₂RhO₄ were deduced from the measured electromotive force (e.m.f.) by invoking a model for the spinel solid solution. The parameters of the model were optimized using the measured composition of the spinel solid solution in different phase fields and imposed oxygen partial pressures. The results can be summarized by the equations: MgO + β–Rh₂O₃→MgRh₂O₄; ΔG∘(± 1010)/J mol⁻¹ = − 32239 + 7.534T; 2MgO + RhO₂→Mg₂RhO₄; ΔG∘(± 1270)/J mol⁻¹ = 36427 − 4.163T; ΔGM/J mol⁻¹ = 2RT(x In x + (1 − x)In(1 − x)) + 4650x(1 − x), where ΔG° is the standard Gibbs free energy change for the reaction and ΔG_M is the free energy of mixing of the spinel solid solution Mg_1+xRh_2−xO₄.