An internally consistent thermodynamic dataset with uncertainties and correlations: 2. Data and results

Abstract This, the second of two papers, represents the application of a least squares approach, discussed in the previous paper, to the generation of an internally consistent thermodynamic dataset involving 60 reactions among 43 phases, in the system K₂O–Na₂O–CaO–MgO–Al₂O₃–SiO₂–H₂O–CO₂. We make the assumption that all the thermodynamic data, with the exception of enthalpies of formation of the phases, are well known, and solve for an internally consistent set of enthalpies which reproduces the 60, experimentally determined, phase equilibrium reactions. An important difference between our dataset and that of previous alternatives in the literature is that we are able to determine the uncertainties on, and correlations between, the enthalpies of formation for all phases in the set, and hence are able to apply simple error propagation techniques to determine the uncertainties in any phase equilibrium calculations performed using this dataset. Selection of reactions, for geothermometry and geobarometry, may be more readily made by choosing equilibria with small uncertainties in their thermodynamics. Our data are in reasonably close agreement with the high temperature molten oxide calorimetry results on silicate minerals where available, a fact which lends a degree of confidence to the results.