Thermodynamics of mixing in the ternary rhombohedral carbonate solid solution, (CaxMgy,Mn1−x−y)CO3, from atomistic simulations

The effective pairwise interactions in calcite-magnesite, calcite-rhodochrosite and magnesite-rhodochrosite binary systems were evaluated in the diluted limits from the excess enthalpies of supercell structures of the end-members in which pairs of the incoherent (admixed) atoms were inserted at all distinct distances available in a 3×3×1 supercell. The excess enthalpy of mixing within the ternary calcite-magnesite-rhodochrosite system was evaluated as a function of the pairwise interactions. Thermal averages of the enthalpy of mixing were calculated with the Monte Carlo method, while the free energies of mixing were obtained by thermodynamic integration. The convex-hull construction was used to visualize miscibility gaps within the ternary. The obtained agreement with the experimentally known phase relations shows that the excess mixing properties within the ternary can be successfully predicted from pairwise interactions calculated in the diluted limits. The method is expected to work only for systems in which many-body interactions can be ignored.