The accuracy of standard enthalpies and entropies for phases of petrological interest derived from density-functional calculations

Abstract

The internal energies and entropies of 21 well-known minerals were calculated using the density functional theory (DFT), viz. kyanite, sillimanite, andalusite, albite, microcline, forsterite, fayalite, diopside, jadeite, hedenbergite, pyrope, grossular, talc, pyrophyllite, phlogopite, annite, muscovite, brucite, portlandite, tremolite, and CaTiO3–perovskite. These thermodynamic quantities were then transformed into standard enthalpies of formation from the elements and standard entropies enabling a direct comparison with tabulated values. The deviations from reference enthalpy and entropy values are in the order of several kJ/mol and several J/mol/K, respectively, from which the former is more relevant. In the case of phase transitions, the DFT-computed thermodynamic data of involved phases turned out to be accurate and using them in phase diagram calculations yields reasonable results. This is shown for the Al2SiO5 polymorphs. The DFT-based phase boundaries are comparable to those derived from internally consistent thermodynamic data sets. They even suggest an improvement, because they agree with petrological observations concerning the coexistence of kyanite + quartz + corundum in high-grade metamorphic rocks, which are not reproduced correctly using internally consistent data sets. The DFT-derived thermodynamic data are also accurate enough for computing the P–T positions of reactions that are characterized by relatively large reaction enthalpies (> 100 kJ/mol), i.e., dehydration reactions. For reactions with small reaction enthalpies (a few kJ/mol), the DFT errors are too large. They, however, are still far better than enthalpy and entropy values obtained from estimation methods.