Cell theory simulations on hard sphere crystals

Abstract

In this thesis we explore a method which approximates the free energy of binary hard-sphere crystals. This method is called cell theory, which is an example of a mean field approximation. We use Monte Carlo integration to approximate the Helmholtz free energy per particle. We combine this with Monte Carlo simulations for the equation of state, to approximate the Gibbs free energy. When we compare the Gibbs free energy for the MgCu\textsubscript{2} to an FCC mixture, we find that MgCu\textsubscript{2} has a stability region starting from $\beta P \sigma_L^3 =30$. When taking into account that our method structurally overestimates the free energy, this result corresponds to literature. From this we find that our method can be an improvement to predictions based on packing arguments alone.