Structural incompatibilities and liquid-liquid phase separation in molten binary silicates: A computer simulation

We have carried out a series of ion dynamics simulations on binary silicate systems ranging from MnO-SiO₂, which shows a large liquid-liquid miscibility gap, to K₂O-SiO₂, which does not unmix even below the stable liquidus. We have used Coulomb attractions plus Born-Mayer-Huggins repulsive pairwise-additive potentials, evaluating the energies with a full Ewald summation. Energies of the systems were determined at a constant pressure using the Andersen algorithm. In the simulated systems (which are too small to permit phase separation) results show that in the MnO-SiO₂ system the heats of mixing are indeed positive, and greater than any conceivable T·ΔS value, in the composition range 0.5 < X_SiO2 < 1.0 in which phase separation occurs in practice. In K₂O-SiO₂, by contrast, ΔH_m is always negative. Analysis of angular correlations as a function of temperature using new "circular distribution functions," allows the origin of the unfavorable mixing energy to be determined in terms of structural/geometrical incompatibilities. At high silica contents the incorporation of smaller divalent cations, which seek four coordination, can only be realized by distorting the network from its lowest energy topology to provide the requisite nonbridging oxygens. On cooling, the divalent cations are seen to move out of these unfavorable sites as a first step towards phase separation on a macroscopic scale. In the case of large low-charge-density cations, a greater degree of bridging is retained by forming large gaps which can easily host the cations and even allow them to diffuse freely.