In this chapter a number of models for the thermodynamic properties of various phases will be described. The integral Gibbs energy will be used as the modeled thermodynamic property. The reason to model the Gibbs energy rather than any other thermodynamic function is that most experiments are done at constant temperature and pressure. From the Gibbs energy all other important quantities can be obtained according to Eqs. (2.12). Using the Gibbs energy means that the modeling is limited to a “mean-field” approximation. Thermodynamic calculations using “Monte Carlo” methods or “molecular dynamics” are outside the scope of this presentation, but these techniques can provide important information about the type of mean-field model to be selected.

A phase may sometimes have a particular physical or chemical feature that requires a special model in order for it to be described accurately. It is not uncommon that the mathematical expression for such a model may be identical to the expression derived to describe another physical feature. That simply means that the mathematical expression is more general than the physical model. Whenever such a generalized expression can be obtained, it will be called a formalism. A general formalism should be able to handle cases when various constituents added to a phase behave differently, for example some may dissolve interstitially or cause chemical ordering. Most of the models used in this book are special cases of the compound-energy formalism (CEF).