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Uncertainties on elastic parameters and occupancy factors: how do they affect the accuracy of the calculated Gibbs energy of minerals at (P,T) conditions? The case of 3T- versus 2M 1-phengite

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Abstract

The present paper reports a study about how the uncertainties on some fundamental thermodynamic and structural quantities (formation enthalpy, specific heat, thermo-elastic properties, occupancy factors) propagate and affect the Gibbs energy calculated at given pressure and temperature conditions [G(P,T)] for mineral phases. A particular attention is paid to the role played by the uncertainties on the bulk modulus, its first derivative versus pressure, molar volume at a reference condition, i.e. V 0, and occupancy factors. The calculations in question are carried out for three phases: 2M 1-phengite, olivine and MgAl-spinel, in order to provide coverage for thermo-elastic parameters values common in a variety of natural processes. Above a few GPa, the uncertainty due to the deformation energy, i.e. σ[ΔG deform], and dependent on the parameters governing the equation of state, grows the dominant contribution to the total uncertainty on G(P,T), i.e. σ[G(P,T)]. σ[ΔG deform] is very sensitive to V 0, but the comparatively small σ(V 0)/V 0 value makes the V 0-contribution to σ[ΔG deform] less relevant than those due to the elastic parameters. The stability curve of 3T- versus 2M 1-phengite as a function of pressure (Curetti et al. in Phys Chem Mineral 32:670–678, 2006) is here revised in the light of the uncertainty on G(P,T): an improvement of accuracy such as to reduce the uncertainty on bulk modulus and its first derivative versus pressure by a 0.05 factor is, in principle, required to guarantee a fully unambiguous description of the relative stability between these two phases.

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Acknowledgments

Italian Ministry for University and Research (M.U.R.S.T) and Italian National Research Council (C.N.R) are kindly acknowledged for contributing to fund the investigations in question. The authors are grateful to the reviewers for comments to improve the quality of the manuscript.

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Authors and Affiliations

  1. Dipartimento di Scienze della Terra, Università di Milano, Via Botticelli 23, 20133, Milano, Italy

    Alessandro Pavese

  2. National Research Council (CNR), IDPA, Section of Milan, Via Botticelli 23, 20133, Milano, Italy

    Alessandro Pavese & Valeria Diella

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  1. Alessandro Pavese
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  2. Valeria Diella
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Correspondence to Alessandro Pavese.

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Pavese, A., Diella, V. Uncertainties on elastic parameters and occupancy factors: how do they affect the accuracy of the calculated Gibbs energy of minerals at (P,T) conditions? The case of 3T- versus 2M 1-phengite. Phys Chem Minerals 34, 637–645 (2007). https://doi.org/10.1007/s00269-007-0179-1

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