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# tutorial thermocalc - Calculating phase diagrams involving...

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Calculating phase diagrams involving solid solutions via non-linear equations, with examples using THERMOCALC Roger Powell 1 , Tim Holland 2 and Brenton Worley 1 1 School of Earth Sciences, The University of Melbourne, Victoria 3052, Australia 2 Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK 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 (#####). email address: [email protected] Introduction The advent of large internally-consistent thermodynamic datasets (Helgeson et al. , 1978; Powell & Holland, 1985; Holland & Powell, 1985; Berman, 1988; Holland & Powell, 1990; Gottschalk, 1997) has meant that it has become possible to calculate mineral equilibria involving solid solutions in complex systems (e.g. Spear & Cheney, 1989; Powell & Holland, 1990; Symmes & Ferry, 1992; Mahar et al. , 1997). In principle such calculations allow phase diagrams to be constructed which closely approximate the phase relationships in rocks. Several diﬀerent ways of approaching the calculation of mineral equilibria involving solid solutions have evolved out of those advocated in the chemical and metallurgy literature (e.g. van Zeggeren & Storey, 1970): the Gibbs method (Spear & Cheney, 1989); direct minimisation of Gibbs energy (Connolly, 1990; Wood, 1987, de Capitani and Brown, 1987) and the solution of simultaneous non-linear equations (Powell & Holland 1990). This last approach is the one followed in the software, THERMOCALC, Powell & Holland (1988, and succeeding upgrades), 1

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which uses the internally-consistent thermodynamic dataset of Holland & Powell (1985, 1990, 1998) (e.g. Guiraud et al. , 1990; Baker et al. , 1994; Xu et al. , 1994, Worley & Powell, 1997). The purpose of this paper is to consider the calculation of phase diagrams involving solid solutions by solving sets of non-linear equations. Examples of the application of this approach are calculated with the software THERMOCALC v2.6 using the April 20, 1996 version of the thermodynamic dataset. The version of THERMOCALC, current at acceptance of this paper for
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## This note was uploaded on 03/19/2012 for the course GEOLOGY 6 taught by Professor Rm during the Spring '12 term at UNAM MX.

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tutorial thermocalc - Calculating phase diagrams involving...

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