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 3 T - versus 2 M 1-phengite.

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. [ABSTRACT FROM AUTHOR]