Subsolidus phase relations in the CaCO3-MgCO3 system predicted from the excess enthalpies of supercell structures with single and double defects

The thermodynamic mixing properties of a binary (A(x)B(1-x)) R solid solution are evaluated from the enthalpies of supercell structures A(m-2)B(2)R(m) and B(m-2)A(2)R(m), where m is the number of the exchangeable sites in the supercell. The excess enthalpies of these structures are converted into concentration-dependent pairwise effective cluster interactions J(n), i.e., the enthalpies of the intracrystalline reactions AA+BB reversible arrow 2AB acting at the n-neighbor distance within the supercell. The pairwise interactions calculated in this way for all possible distances within 3 x 3 x 1 supercells of R (3) over barc calcite and magnesite (m=54) are combined to form an effective Ising-type Hamiltonian from which temperature-dependent enthalpies, entropies, and free energies of mixing are evaluated with the Monte Carlo method. The calculated phase diagram with two miscibility gaps separated by a field of stability of the R (3) over bar dolomite phase is in good agreement with available experimental data, thereby showing that the existence of the intermediate ordered compound can be predicted from the analysis of the supercell structures whose compositions approach the diluted limits.