BAYES ESTIMATION - A NOVEL-APPROACH TO DERIVATION OF INTERNALLY CONSISTENT THERMODYNAMIC DATA FOR MINERALS, THEIR UNCERTAINTIES, AND CORRELATIONS .2. APPLICATION

Internally consistent thermodynamic data, including their uncertaintie s and correlations, are reported for 22 phases of the quaternary syste m CaO-Al2O3 - SiO2 - H2O. These data have been derived by simultaneous evaluation of the-appropriate phase properties (PP) and reaction prop erties (RP) by the novel technique of Bayes estimation (BE). The therm odynamic model used and the theory of BE was expounded in Part I of th is paper. Part II is the follow-up study illustrating an application o f BE. The input for BE comprised, among others, the a priori values fo r standard enthalpy of formation of the i-th phase, DELTA(f) H(i)0, an d its standard entropy, S(i)0, in addition to the reaction reversal co nstraints for 33 equilibria involving the relevant phases. A total of 269 RP restrictions have been processed, of which 107 turned out to be non-redundant. The refined values for DELTA(f) H(i)0 and S(i)0 obtain ed by BE, including their 2 sigma-uncertainties, appear in Table 4; th e Appendix reproduces the corresponding correlation matrix. These data permit generation of computed phase diagrams with 2 sigma-uncertainty envelopes based on conventional error propagation; Fig. 3 depicts suc h a phase diagram for the system CaO-Al2O3-SiO2. It shows that the ref ined dataset is capable of yielding phase diagrams with uncertainty en velopes narrow enough to be geologically useful. The results in Table 4 demonstrate that the uncertainties of the prior values for DELTA(f)H (i)0, given in Table 1, have decreased by up to an order of magnitude, while those for S(i)0 improved by a factor of up to two. For comparis on, Table 4 also lists the refined DELTA(f)H(i)0 and S(i)0 data obtain ed by mathematical programming (MAP), minimizing a quadratic objective function used earlier by Berman (1988). Examples of calculated phase diagrams are given to demonstrate the advantages of BE for deriving in ternally consistent thermodynamic data. Although P - T curves generate d from both MAP and BE databases will pass through the reversal restri ctions, BE datasets appear to be better suited for extrapolations beyo nd the P - T range explored experimentally and for predicting equilibr ia not constrained by reversals.