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

► Refinement of phase diagram for the system Mg-Rh-O and thermodynamic data for spinel compounds MgRh 2O 4 and Mg 2RhO 4 is presented. ► A solid-state electrochemical cell is used for thermodynamic measurement. ► An advanced design of the solid-state electrochemical cell incorporating buffer electrodes is deployed to minimize polarization of working electrode. ► Regular solution model for the spinel solid solution MgRh 2O 4 – Mg 2RhO 4 based on ideal mixing of cations on the octahedral site is proposed. ► Factors responsible for stabilization of tetravalent rhodium in spinel compounds are identified. Pure stoichiometric MgRh 2O 4 could not be prepared by solid state reaction from an equimolar mixture of MgO and Rh 2O 3 in air. The spinel phase formed always contained excess of Mg and traces of Rh or Rh 2O 3. The spinel phase can be considered as a solid solution of Mg 2RhO 4 in MgRh 2O 4. 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+ x Rh 2− x O 4 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 MgRh 2O 4 and Mg 2RhO 4 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–Rh 2O 3 → MgRh 2O 4; ΔG ∘(± 1010)/J mol −1 = − 32239 + 7.534 T; 2MgO + RhO 2 → Mg 2RhO 4; ΔG ∘(± 1270)/J mol −1 = 36427 − 4.163 T; ΔG M /J mol −1 = 2RT( x In x + (1 − x)In(1 − x)) + 4650 x(1 − x), where Δ G° is the standard Gibbs free energy change for the reaction and Δ G M is the free energy of mixing of the spinel solid solution Mg 1+xRh 2− x O 4.