  Carbon solubility in face-centered cubic Ni-W alloys and the phase diagram of
C-Ni-W are investigated by means of first principle calculations and semi-grand
canonical Monte Carlo simulations. With density functional theory (DFT) total
energies as fitting data, we build a superatom model for efficient simulation.
Multi-histogram analysis is utilized to predict free energies for different
compositions and temperatures. By comparing free energies of competing phases,
we are able to predict carbon solubility and phase diagrams of C-Ni-W at
different temperatures. A simple ideal mixing approximation gives qualitatively
similar predictions.
