The Evolution of Multicomponent Systems at High Pressures: II. The   Alder-Wainwright, High-Density, Gas-Solid Phase Transition of the Hard-Sphere   Fluid
  The thermodynamic stability of the hard-sphere gas has been examined, using the formalism of scaled particle theory [SPT], and by applying explicitly the conditions of stability required by both the second and third laws of thermodynamics. The temperature and volume limits to the validity of SPT have also been examined. It is demonstrated that scaled particle theory predicts absolute limits to the stability of the fluid phase of the hard-sphere system, at all temperatures within its range of validity. Because scaled particle theory describes fluids equally well as dilute gases or dense liquids, the limits set upon the system stability by SPT must represent limits for the existence of the fluid phase and transition to the solid. The reduced density at the stability limits determined by SPT is shown to agree exactly with those of that estimated for the Alder-Wainwright, supercritical, high-density gas-solid phase transition in a hard-sphere system, at a specific temperature, and closely over a range of more than 1,000K. The temperature dependence of the gas-solid phase stability limits has been examined over the range 0.01K-10,000K. It is further shown that SPT describes correctly the variation of the entropy of a hard-core fluid at low temperatures, requiring its entropy to vanish as T goes to zero by undergoing a gas-solid phase transition at finite temperature and all pressures. 
J. F. Kenney