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

Our plain-English summary of The accuracy of standard enthalpies and entropies for phases of petrological interest derived from density-functional calculations, by A. Benisek, E. Dachs (Contributions to Mineralogy and Petrology. Beiträge Zur Mineralogie und Petrologie, 2018).

The study

• Authors: A. Benisek, E. Dachs
• Journal: Contributions to Mineralogy and Petrology. Beiträge Zur Mineralogie und Petrologie
• Published: 2018;173(11):90
• Cited by: 7 articles, as counted by NIH iCite
• Read it: PubMed · Publisher · Free full text

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.

In plain English

This was a computer-calculation study in mineral chemistry. It was not a study of health, disease, or asbestos exposure. The authors used a quantum-mechanical method called density functional theory (DFT) to calculate two heat-related properties, standard enthalpies and entropies, for 21 well-known minerals. One of the 21 was tremolite. The article does not discuss asbestos, fibers, or the fibrous form of tremolite. They compared the results with values in a published reference data set. On average, the calculated enthalpies differed from the reference values by about 7 kJ/mol. Pyrope was an outlier at 55.83 kJ/mol, for reasons the authors said are unknown. For tremolite, the calculated enthalpy differed by -9.23 kJ/mol and the entropy by 0.18 J/mol/K. The calculations worked well for reactions where one mineral changes into another form and for dehydration reactions with large energy changes. They failed for a reaction with a small energy change, the breakdown of kyanite to quartz and corundum. The authors concluded that DFT data are far better than estimation methods and should be used together with experimental data.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Computational study: quantum-mechanical density functional theory (DFT) calculations, with results compared to a published reference thermodynamic data set and used in phase-diagram calculations
• Who was studied: 21 well-known minerals (no people or animals): kyanite, sillimanite, andalusite, albite, microcline, forsterite, fayalite, diopside, jadeite, hedenbergite, pyrope, grossular, talc, pyrophyllite, phlogopite, annite, muscovite, brucite, portlandite, tremolite and CaTiO3-perovskite, plus one less-known pyroxene end member, Al-buffonite
• Exposure: Not applicable. No human or animal exposure was studied. Tremolite appears only as one mineral whose thermodynamic properties were calculated; the article does not mention asbestos or fibers.
• Main results:
  • Calculated enthalpies were mostly slightly more negative than the reference values. The average deviation was about 7 kJ/mol, and pyrope was an outlier at 55.83 kJ/mol.
  • Calculated entropies deviated by no more than 4.25 J/mol/K from the reference values, except for two outliers: pyrope (-8.31 J/mol/K) and talc (7.37 J/mol/K).
  • For tremolite, the calculated standard enthalpy was -12313.8 kJ/mol against a reference value of -12304.56 kJ/mol, a deviation of -9.23 kJ/mol. The calculated entropy was 553.18 J/mol/K against 553.00 J/mol/K, a deviation of 0.18 J/mol/K.
  • For the transitions between andalusite, kyanite and sillimanite, the calculated enthalpy changes differed by no more than 1.8 kJ/mol from the reference data set.
  • For the reaction kyanite = quartz + corundum, the calculated enthalpy change of 18.75 kJ/mol differed by more than 100% from the reference value of 6.98 kJ/mol. This shifted the calculated breakdown of kyanite to temperatures as high as 2000 °C, which the authors called far from realistic.
  • For the dehydration of pyrophyllite (enthalpy change about 73 kJ/mol), the calculated reaction position shifted by about 200 °C, which the authors judged still too large.
  • For three mica dehydration reactions with enthalpy changes larger than 100 kJ/mol, the effect of the calculation errors on reaction temperatures was small.
  • The DFT-calculated enthalpies deviated by no more than 1.3% from the reference values, compared with deviations of more than 10% for an estimation method.
• The authors' conclusion: The authors concluded that DFT-based data are suitable for calculating phase transitions and reactions with large enthalpy changes (more than 100 kJ/mol), but not accurate enough for other reactions. They put the uncertainties at about 10 kJ/mol, said the data are far better than estimation methods, and recommended combining them with calorimetry and phase-equilibrium experiments.
• Limitations the authors state:
  • The calculation errors are too large for reactions with small enthalpy changes.
  • The reasons for the large deviation for pyrope are unknown.
  • Magnetic entropy cannot be determined directly with DFT, so iron-containing minerals needed a different, approximate procedure.

Topics

Medical terms in this study, explained in our Lexicon: Forsterite, Diopside, Talc, Brucite, Tremolite, Polymorphs.

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