3. Summary

To summarize, in this chapter we have introduced the concept that the most stable phase, at constant temperature and pressure, has the most negative value of the Gibbs free energy. Also, we have recalled that at equilibrium any system, at constant temperature and pressure, has its lowest possible value for the Gibbs free energy. We have found it possible to partition the various thermodynamic potentials into various categories according to their origin. For example, the entropy can be partitioned into thermal and configurational contributions. We have found that the vibrational entropy of an ordered array of hard spheres can be larger than that for a random array. Also, at equilibrium, a system constrained to a constant composition proceeds, from low to high temperature (from low to high pressure), through a sequence of phases in such a way that the entropy (volume) continually increases (decreases). If the increase in entropy (decrease in volume) is discontinuous at distinct temperatures (pressures) corresponding to transitions from the regime of stable equilibrium of one phase to that of another, the transitions are of first order. For first-order transitions, it is possible to represent the regimes of phase stability in a P T phase diagram. The Clapeyron equation yields the dependence of the transition temperature on pressure for polymorphic transitions. We have also defined the state of thermodynamic equilibrium and have been introduced to the concepts of long- and short-range order, the equilibrium values of which are determined by minimizing the free energy with respect...