Excess enthalpy of mixing of mineral solid solutions derived from density-functional calculations

Calculations using the density-functional theory (DFT) in combination with the single defect method were carried out to determine the heat of mixing behaviour of mineral solid solution phases. The accuracy of this method was tested on the halite-sylvite (NaCl-KCl) binary, pyrope-grossular garnets (Mg₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂), MgO-CaO (halite structure) binary, and on Al/Si ordered alkali feldspars (NaAlSi₃O₈-KAlSi₃O₈); as members for coupled substitutions, the diopside-jadeite pyroxenes (CaMgSi₂O₆-NaAlSi₂O₆) and diopside-CaTs pyroxenes (CaMgSi₂O₆-CaAlAlSiO₆) were chosen for testing and, as an application, the heat of mixing of the tremolite-glaucophane amphiboles (Ca₂Mg₅Si₈O₂₂(OH)₂-Na₂Mg₃Al₂Si₈O₂₂(OH)₂) was computed. Six of these binaries were selected because of their experimentally well-known thermodynamic mixing behaviours. The comparison of the calculated heat of mixing data with calorimetric data showed good agreement for halite-sylvite, pyrope-grossular, and diopside-jadeite binaries and small differences for the Al/Si ordered alkali feldspar solid solution. In the case of the diopside-CaTs binary, the situation is more complex because CaTs is an endmember with disordered cation distributions. Good agreement with the experimental data could be, however, achieved assuming a reasonable disordered state. The calculated data for the Al/Si ordered alkali feldspars were applied to phase equilibrium calculations, i.e. calculating the Al/Si ordered alkali feldspar solvus. This solvus was then compared to the experimentally determined solvus finding good agreement. The solvus of the MgO-CaO binary was also constructed from DFT-based data and compared to the experimentally determined solvus, and the two were also in good agreement. Another application was the determination of the solvus in tremolite-glaucophane amphiboles (Ca₂Mg₅Si₈O₂₂(OH)₂-Na₂Mg₃Al₂Si₈O₂₂(OH)₂). It was compared to solvi based on coexisting amphiboles found in eclogites and phase equilibrium experiments.