Subsolidus phase relations in Ca2Mo2O8–NaEuMo2O8-powellite solid solution predicted from static lattice energy calculations and Monte Carlo simulations

Abstract

Thermodynamic mixing properties and subsolidus phase relations of Ca₂Mo₂O₈–NaEuMo₂O₈ powellites were modelled in the temperature range of 423–1773 K with static lattice energy calculations based on empirically constrained interatomic potentials. Relaxed static lattice energies (SLE) of a large set of randomly varied structures in a 4 × 4 × 2 supercell of I4₁/a powellite (a = 5.226 Å, c = 11.433 Å) containing 128 exchangeable (Ca, Na and Eu) atoms were calculated using the general utility lattice program (GULP). These energies were cluster expanded in the basis set of 69 pair-wise effective interactions and three configuration-independent parameters. Temperature-dependent enthalpies of mixing were calculated using the Monte Carlo method. Free energies of mixing were obtained by thermodynamic integration of the Monte Carlo results. The simulations suggest that the NaEuMo₂O₈ end-member is nearly fully ordered and has I symmetry. The calculated subsolidus temperature-composition phase diagram is dominated by three miscibility gaps which are separated by narrow fields of stability of two ordered phases with the compositions of x = 4/9 and x = 2/3, where x is the mole fraction of the NaEuMo₂O₈ end-member.