Towards a molecular theory of freezing: The equation of state and free energy from the first BBGKY equation
We determine crystalline solutions of a closed BBGKY equation for the local density in a classical hard sphere system. The inhomogeneous solutions, which bifurcate from the fluid phase, are applied to calculate the equation of state and free energy. A first order phase change is found in two and three dimensions and its existence is shown to depend on the direction of bifurcation and on global properties of the solutions. The results are discussed in terms of the closure.