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

Abstract

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 k-transitions and to fluids by considering the Gibbs free energy as a function of pressure P, temperature T and an ordering parameter X a , 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 a ) ¼ min. The procedure is tested on existing experimental data for the system MgO-SiO 2 -H 2 O. 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.

Thermodynamic modeling of solubility and speciation of silica in H2O-SiO2 fluid up to 1300C and 20 kbar based on the chain reaction formalism

“…Our calculations have also shown a similar strong positive correlation between isothermal silica solubility and the degree of association or clustering of H 2 O molecules in pure H 2 O ( Fig. 1c), which increases with increasing density (e.g., Gorbaty & Kalinichev, 1995;Luck, 1980;Gerya & Perchuk, 1997;Gerya et al, 2004). This strongly suggests that the dissolution of silica is directly related to the actual proportion of associated (i.e., clustered, "liquid-like") H 2 O molecules in the aqueous fluid, and offers the possibility of deriving a general thermodynamic description for silica solubility in water.…”

“…This strongly suggests that the dissolution of silica is directly related to the actual proportion of associated (i.e., clustered, "liquid-like") H 2 O molecules in the aqueous fluid, and offers the possibility of deriving a general thermodynamic description for silica solubility in water. It has been shown recently (Gerya & Perchuk, 1997;Gerya et al, 2004) that from the viewpoint of thermodynamics pure H 2 O fluid (and many other gases) can be effectively treated as a mixture of molecules in two distinct states:…”

“…However, at present no precise, generally applicable thermodynamic treatment describing both the bulk solubility and the speciation of silica in aqueous silica-rich fluid has been developed. In the present paper we derive and test such a formalism for the SiO 2 -H 2 O system using a combination of the chain reaction approach and a new Gibbs free energy equation of water based on a homogeneous reaction formalism (Gerya & Perchuk, 1997;Gerya et al, 2004).…”

Goldschmidt Abstracts 2007- E and F

“…5 -1.0 GPa. An alternative approach is to treat H 2 O in terms of a statistical thermodynamic model involving a dynamic equilibrium between "gas-like" disordered and "liquid-like" clustered molecules (Gerya and Perchuk, 1997;Gerya et al, 2004), where X(liq) is the mole fraction of the latter. Gerya et al (2005) successfully tested this approach for SiO 2 -H 2 O solutions to 1300°C and 2 GPa.…”

Goldschmidt Conference Abstracts 2005

“…X H 2 O has been calculated assuming all salts are fully associated under all conditions. Gerya & Perchuk (1997) and Gerya et al (2004) have shown that pure H 2 O can be treated as a solution of molecules in (1) "liquid-like" (clustered) state, and (2) "gas-like" (free) state. Quartz solubility in H 2 O -CO 2 fluids is almost as ideal, with a solvation number of 3.5.…”