Hard spheres systems equilibrium phase diagram

The application of this approach to the hard-sphere system was presented by Ree and Hoover in a footnote to their paper on the hard-sphere phase diagram. They made a calculation where they used Eq. (2.27) for the solid phase and an accurate equation of state for the fluid phase to obtain results that are in very close agreement with their results from MC simulations. The LJD theory in combination with perturbation theory for the liquid state free energy has been applied to the calculation of solid-fluid equilibrium for the Lennard-Jones 12-6 potential by Henderson and Barker [138] and by Mansoori and Canfield [139]. Ross has applied a similar approch to the exp-6 potential. A similar approach was used for square well potentials by Young [140]. More recent applications have been made to nonspherical molecules [100,141] and mixtures [101,108,109,142]. 

Fig. 9. Two-parameter ordering phase diagram for a system of 500 identical hard spheres (Truskett et ai, 2000 Torquato et ai, 2000). Shown are the coordinates in structural order parameter space (r, ) for the equilibrium fluid (dot-dashed), the equilibrium FCC crystal (dashed), and a set of glasses (circles) produced with varying compression rates. Here, r is the translational order parameter from (26) and is the bond-orientational order parameter Q( from (25) normalized by its value in the perfect FCC crystal ( = Each circle...

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