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

Artur Benisek,Edgar Dachs

doi:10.1007/s00410-018-1514-x

Artur Benisek, Edgar Dachs

Open Access

https://doi.org/10.1007/s00410-018-1514-x

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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.

Highlights

Investigating the standard enthalpy of formation from the elements (ΔfH298.15) and the standard entropy (S298.15) of mineral end members of geological and cosmochemical relevance is a prerequisite for reliable phase diagram calculations and still needed in many aspects: first, because such standard data of some mineral end members are derived from a limited number of experiments and largely missing for chemically more complex systems (e.g., Ti-containing end members of many solid solutions such as pyroxenes, micas, amphiboles) and, second, because there are important
The density functional theory (DFT)-calculated constant volume (CV) of the pyroxenes can be transformed to constant pressure (CP)
The impact of the adopted CV−CP conversion on ΔfH298.15 and S298.15 is in the order of 0.1 kJ/mol and 1 J/mol/K, respectively, and is shown for ΔfH298.15 of low microcline in the chapter

Summary

Introduction

The generation of such end member thermodynamic data is possible in a relatively short time by using the density functional theory (DFT). The uncertainties in ΔfH298.15 given in internally consistent thermodynamic data sets are in the order of a few kJ/mol for well-known phases. The question of the required accuracy of DFT-calculated standard data needed for reliable phase diagram calculations, is, easy to answer. It should not be much larger than the uncertainties of the two calorimetric methods mentioned, allowing incorporating them in the development of internally consistent databases. The quality of DFT-calculated thermodynamic data should be tested by comparison with those from well-known mineral end members with their high accuracy

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Results

Conclusion