In this paper, we will consider a variety of different approximations the cluster expansion of the excess free energy, which will be added on to the ideal free energy expression given in Equation . The total free energy density βf ν 0 = βf id ν 0 + βf exc ν 0 can then be compared against previous models in the literature, such that we can establish relationships between these models via their inclusion or neglect of various terms in the cluster expansion.