Computing ternary liquid phase diagrams: Fe-Cu-Ni

We compute the phase separation of the immiscible liquid alloy Fe-Cu-Ni. Our computational approach uses a virtual semigrand canonical Widom approach to determine differences in excess chemical potentials between different species. Using an embedded atom potential for Fe-Cu-Ni, we simulate liquid states over a range of compositions and temperatures. This raw data is then fit to Redlich-Kister polynomials for the Gibbs free energy with a simple temperature dependence. Using the analytic form, we can determine the phase diagram for the ternary liquid, compute the miscibility gap and spinodal decomposition as a function of temperature for this EAM potential. In addition, we compute density as a function of composition and temperature, and predict pair correlation functions. We use static structure factors to estimate the second derivative of the Gibbs free energy (the $S^0$ method) and compare with our fit Gibbs free energy. Finally, using a nonequilibrium Hamiltonian integration method, we separately compute absolute Gibbs free energies for the pure liquid states; this shows that our endpoints are accurate to within 1 meV for our ternary Gibbs free energy, as well as the absolute Gibbs free energy for the ternary liquid.