The equation of state for a fluid described by the Weeks-Chandler-Andersen (WCA) potential
was solved to determine at what pressures and temperatures the fluid will theoretically freeze. A
Monte Carlo (MC) algorithm was used to sample a system of 256 spheres for a set of thermodynamic
averages to locate and confirm a phase transition. A thorough discussion of the basics of the
Metropolis MC algorithm and the derivation of thermodynamic averages for WCA are developed.
The phase transitions over varying densities and temperatures were found and used to plot a pair
of phase diagrams which describe the equation of state. The WCA potential is a modification of
the Lennard-Jones potential and it treats intermolecular potentials as fully repulsive which means
there is no liquid state. Its implementation into density functional theory (DFT) has been of
interest to the Roundy research group for some time, and to determine whether or not the DFT is
accurate the group needs to compare results with the MC. The WCA potential is used as a model
for crystal growth kinetics and dendrimers, so simulations that better model the properties of those
categories of materials can provide greater insight into their behavior.