Statistical Mechanics of Hard Spheres: Application of the Improved Scaled Particle Theory to the Hard Sphere Crystal

In a previous article (Baeyens and Verschelde in J. Math. Phys. 36:201, 1995), an improved approach to the scaled particle theory of Reiss et al. was presented. We used a generalized series expansion of the contact correlation function G(y,r). Truncating it after the third term, we obtained a Pad,-like expression for the compressibility factor of the system. That expression contains two parameters which we were able to calculate, not only for the fluid state, but also for the known glassy states (Baeyens and Verschelde in Z. Phys. B 102:255, 1997). The resulting equations of state are in good agreement with the simulation data. Yet in the case of the hard sphere crystal our improved scaled particle theory fails, which is one of the reasons why an extension of it is desirable. In this paper the above mentioned expansion of G(y,r) will once more be generalized. Truncation after the sixth term leads to a simple but acceptable equation of state for the hard sphere fcc-crystal. It reproduces the free energies, the compressibility factors and the pressure of freezing and melting to within 0.3, 5, and 0.6 percent respectively.