Semi-empirical Gibbs free energy formulations for minerals and fluids for use in thermodynamic databases of petrological interest

The P–T partition function in statistical thermodynamics can be used to derive semi-empirical formulations of the Gibbs free energy G for minerals and fluids. Parameterization of these equations includes simultaneous regression of experimental heat capacity and molar volume data, allowing fitting, appraisal and optimization of various data sources, as required in the construction of internally consistent petrological data bases. This approach can also be extended to minerals with -transitions and to fluids by considering the Gibbs free energy as a function of pressure P, temperature T and an ordering parameter X, so that accurate modelled representation and extrapolation of the thermodynamic properties of large numbers of petrologically significant minerals and coexisting fluids can be attained. The ordering parameter is chosen to denote the equilibrium mole fraction (thermodynamic probability) of ordered clusters (structural units) in a substance when G(T,P, X)=min. The procedure is tested on existing experimental data for the system MgO–SiO₂–H₂O. The proposed Gibbs free energy formulation permits thermodynamic properties of minerals, fluids and phase equilibria to be described and extrapolated over a wide range of pressure (0–800 kbar) and temperature (20–3000 K), thus allowing effective use in thermodynamic data bases of petrological interest.