1. Thermodynamic Model and Techniques

The core thermodynamic framework that made this book possible is the internally consistent thermodynamic model for the system CaO–MgO–Al₂O₃–SiO₂ (CMAS) published in 2000 [56]. The set of the parameters presented in this book was completed by extending this CMAS model to sodium–bearing systems. A thermodynamic model consists of a set of parameters and an equation of state describing the relationship among them. The parameters can be obtained by a direct measurement of the corresponding thermodynamic properties, or derived by fitting phase equilibrium data. Unfortunately, the equation of state used here and other similar equations currently in use are rather simplistic macroscopic approximations of the microscopic properties, so that even if the microscopic properties were known precisely and completely, there is no guarantee that the resulting model would predict the correct phase relations. Because predicting the correct phase relations is the primary purpose of these models to make them suitable for petrologic applications, it is more important to reproduce phase equilibrium data than to achieve an exact match between the parameters and the measurements. To verify whether a model reproduces the observed phase relations, it has to be sufficiently simple to make the calculation of the corresponding phase diagrams possible. In this book such a thermodynamic model was derived using primarily phase equilibrium data, while the measured thermodynamic properties were used mainly as guiding values to be approached by not necessarily matched.