Calculating phase diagrams involving solid solutions via non‐linear equations, with examples using THERMOCALC

Abstract

Phase diagrams involving solid solutions are calculated by solving sets of non‐linear equations. In calculating P–T  projections and compatibility diagrams, the equations used for each equilibrium are the equilibrium relationships for an independent set of reactions between the end‐members of the phases in the equilibrium. Invariant points and univariant lines in P–T  projections can be calculated directly, as can coordinates in compatibility diagrams. In calculating P–T  and T–x / P–x pseudosections – diagrams drawn for particular bulk compositions – the equilibrium relationship equations are augmented by mass balance equations. Lines in pseudosections, where the mode of one phase in the lower variance equilibrium is zero, and points, where the modes of two phases are zero, can then be calculated directly. The software, THERMOCALC, allows the calculation of these and a range of other types of phase diagram. Examples of phase diagrams and phase diagram movies, with instructions for their production, along with the THERMOCALC input and output files, and the Mathematica TM functions for assembling them, are presented in this paper, partly in hard copy and partly on the JMG web sites (http://www.gly.bris.ac.uk/www/jmg/jmg.html, or equivalent Australian or USA sites).