Molecular simulations of interfacial and thermodynamic mixing properties of grossular–andradite garnets

 Experimental observations using transmission electron microscopy (TEM) indicate that Fe3+-rich grossular–andradite solid solutions with oscillatory zoning tend to occur as separate lamellae of andradite and intermediate compositions (Hirai and Nakazawa 1986; Pollok et al. 2001). From one lamella to the next, the Fe3+ concentration can change significantly within a few nm. In order to understand the Fe3+ and Al content of each phase and the thermodynamics, chemistry, structure, and stability at the interfaces, Monte Carlo simulations were performed. According to our calculations, there is an ordered structure with a 1:1 ratio of Al and Fe3+ with alternating Al and Fe octahedra along the main cubic crystallographic axes. Even though this ordered grandite is more energetically favorable than a 1:1 mixture of the end members grossular and andradite [by ≈1.6 kJ (mol exchangeable cations)−1], this structure is stable only at temperatures below ≈500 K. Enthalpies, free energies, configurational and vibrational entropies of mixing, and the long-range order parameter are influenced by the formation of ordered grandite below 500 K. These data also explain why interfaces are stable only between grossular and grandite or between andradite and grandite but not between the end members. The interface energies between the end members and ordered grandite are comparably low [0.16 meV Å−2∥(1 0 0), 0.55 meV Å−2∥(1 1 0), 0.63 meV Å−2∥(1 1 1)] and, therefore, do not hinder the formation of lamellae. Our calculations on the free energies of mixing indicate that there are miscibility gaps between grossular and grandite and between grandite and andradite only below ≈430 K. Since most of these solid solutions are formed at higher temperatures for which we did not find evidence of a miscibility gap, the formation of compositional oscillations is probably due to kinetic hindering of thermodynamically stable complete solid solutions.  A new methodological aspect is the incorporation of zero-point energies of vibrations and the vibrational entropies into the calculation of the free energy of mixing. In case of the grossular–andradite solid solution, these vibrational effects change the free energy of mixing by only a few percent.