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An internally consistent thermodynamic dataset with uncertainties and correlations: 1. Methods and a worked example
Author(s) -
POWELL ROGER,
HOLLAND T. J. B.
Publication year - 1985
Publication title -
journal of metamorphic geology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.639
H-Index - 114
eISSN - 1525-1314
pISSN - 0263-4929
DOI - 10.1111/j.1525-1314.1985.tb00324.x
Subject(s) - set (abstract data type) , least squares function approximation , thermodynamics , mathematics , computer science , chemistry , statistics , physics , estimator , programming language
This, the first two papers, sets out the philosophy and methods of determining an internally consistent thermodynamic dataset for minerals using the least squares method. The applicability of the least squares method is discussed, and it is applied to a small set of experimental equilibria in the system Na 2 O–Al 2 O 3 –SiO 2 –H 2 O. The importance is stressed of defining not only the enthalpies of formation of minerals, but also the uncertainties and the correlations among them. The system which has been used as an illustration for this paper serves as a visual guide to the method, as it is small enough to represent graphically in two dimensions. In the paper which follows, we extend the method to a system of 60 equations (experimentally determined equilibria) involving 34 unknowns (enthalpies of formation of mineral end‐members).