The Bayesian approach to an internally consistent thermodynamic database: theory, database, and generation of phase diagrams

• Published in: Contributions to mineralogy and petrology 1998-10, Vol.133 (1-2), p.149-168
• Main Authors: Chatterjee, Niranjan D., Krüger, Ralf, Haller, Gerd, Olbricht, Walter
• Format: Article
• Language: English
• ISSN: 0010-7999; 1432-0967
• DOI: 10.1007/s004100050444

An internally consistent thermodynamic dataset has been derived for 148 endmember phases (145 solids and 3 fluids) comprising the elements Li, Na, K, Be, Mg, Ca, Ti, Cr, Mn, Fe, Zn, Al, Si, C, H, and O. This has been achieved by simultaneous treatment of phase property (like standard enthalpy of formation, standard entropy, molar heat capacity, molar volume, thermal expansivity, bulk modulus etc.) and reaction reversal data by the Bayesian method. The theory underlying the approach, and the computational methods involved, are briefly outlined. (For the benefit of readers unfamiliar with inference statistics, the basic concepts of the Bayes method are also presented in such a way that they can be grasped intuitively.) Although not yet addressed, this method can be extended to refine the thermodynamic mixing properties of crystalline solutions. The sources of the input data, culled from the literature, are summarized in the Appendix. The resulting database is succinctly documented in this paper. It includes the enthalpies of formation and entropies, their uncertainties, and the correlation among them. The database allows calculation of P-T, T-X sub(CO2), P-X sub(CO2), and T-f sub(O2) sections, with error propagation into the computed phase diagrams on a routine basis. A user-friendly computer program has been written to generate such phase diagrams. It is public domain software. The software and the thermodynamic database (which includes a complete documentation of the thermodynamic data above and beyond those listed (Table 2, here) may be downloaded from the web site http://homepage.ruhr-uni-bochum.de/niranjan.chatterjee/Index.htm. Examples of computed phase diagrams are given to illustrate the quality of the data and the capabilities of the software.