Lower bound on grain boundary solubility in immiscible alloys

Immiscible alloys are postulated to exhibit increased solubility in non-crystalline regions and specifically in high energy grain boundary (GB) regions. A mean field model describing the lower bound of GB solubility is offered for highly immiscible dilute systems at low temperatures. The results of the model are compared to molecular dynamics simulations of mixing in dilute, highly immiscible, copper alloys with both lattice type and size mismatch. It is shown that solubility limit can be described using an effective nearest neighbor model of the type used to describe solubility in low mismatch, high solubility systems. It is demonstrated that the model can be generalized by using a single parameter set to describe all calculated systems. Variation of the solubility limit and model parameters with properties such as GB energy, temperature and pressure is presented and explained in terms of the simple model. This presents an opportunity for creating a simple transferable model which can allow reliable calibration for realistic systems. The model parameters are shown to offer a low temperature correction to the Fowler-Guggenheim adsorption isotherm.