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

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. sigma[Delta G(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. sigma[G(P,T)]. sigma[Delta G(deform)] is very sensitive to V (0), but the comparatively small sigma(V (0))/V (0) value makes the V (0)-contribution to sigma[Delta G(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