Garnet and spinel lherzolite assemblages in MgO–Al₂O₃–SiO₂ and CaO–MgO–Al₂O₃–SiO₂: thermodynamic models and an experimental conflict

Abstract

The recent publication of an updated thermodynamic dataset for petrological calculations provides an opportunity to illustrate the relationship between experimental data and the dataset, in the context of a new set of activity–composition models for several key minerals. These models represent orthopyroxene, clinopyroxene and garnet in the system CaO–MgO–Al2O3–SiO2 (CMAS), and are valid up to 50 kbar and at least 1800 °C; they are the first high‐temperature models for these phases to be developed for the Holland & Powell dataset. The models are calibrated with reference to phase‐relation data in the subsystems CaO–MgO–SiO2 (CMS) and MgO–Al2O3–SiO2 (MAS), and will themselves form the basis of models in larger systems, suitable for calculating phase equilibria in the crust and mantle. In the course of calibrating the models, it was necessary to consider the reaction orthopyroxene + clinopyroxene + spinel = garnet + forsterite in CMAS, representing a univariant transition between simple spinel and garnet lherzolite assemblages. The high‐temperature segment of this reaction has been much disputed. We offer a powerful thermodynamic argument relating this reaction to the equivalent reaction in MAS, that forces us to choose between good model fits to the data in MAS or to the more recent data in CMAS. We favour the fit to the MAS data, preserving conformity with a large body of experimental and thermodynamic data that are incorporated as constraints on the activity–composition modelling via the internally consistent thermodynamic dataset.

The elastic solid solution model for minerals at high pressures and temperatures

“…Figure 4 shows the elastic model predictions for the py 50 gr 50 composition at high pressures and temperatures. At 1000-1500 K, the excess Gibbs free energy predicted by the model is in remarkably good agreement with the empirical fit proposed by Green et al (2012) on the basis of phase equilibria. The non-configurational excess entropy results in systematic deviations from Green et al (2012) at lower and higher temperatures.…”

A thermodynamic model for silicate melt in CaO–MgO–Al2O3–SiO2 to 50 kbar and 1800 °C

“… Pure model phases are all end‐members from the Holland & Powell (2011) data set. For a – x models, HP = Holland & Powell (2011); G = Green et al. (2012). …”

“…Consequently, we have neglected protoenstatite and high‐ T Pbca orthoenstatite; we have assumed that the liquidus orthopyroxene phase is the same in all of the CMAS experiments modelled, and that it is appropriate to model it using the Mg 2 Si 2 O 6 end‐member ‘en’ from the Holland & Powell (2011) data set, where en represents the polymorph of enstatite known to be stable in the range ∼600–1000 °C at 1 bar (Atlas, 1952; Boyd & England, 1965). Green et al. (2012) discussed the importance of this assumption for the solid models used in this study.…”

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

“…Different bulk compositions differ in the Na/Ca bulk ratio and bulk X Cr (X Cr ¼ Cr/(Cr þ Al): Presnall et al (1979) investigated Cr-free system, with the lowest bulk Na 2 O/CaO ratio. This may seem insignificant here, but as the Gasparik experiments were used to calibrate the thermodynamic model employed by Powell (1998, 2011), thermodynamic calculations with the thermocalc model Powell, 1998, 2011) are expected to yield unreliable results in mantle compositions involving spinels and garnets (Green et al, 2012). Depleted lherzolite has the same Na 2 O/CaO ratio of FLZ, but higher X Cr .…”