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Main Sections

1. Microprobe analyses

2. Mineral groups

3. Solid solutions

Energy of mixing

Mixing on sites

Non-ideal solutions

Reciprocal solutions

Simple models, DQF

Activity calculations

4. Thermobarometers

5. Uncertainties

6. P-T calculations

7. Phase diagrams



Docs and downloads

Activity coding



Bugs and quirks

Bulk compositions

Modal proportions

Spreadsheet tools

Practical Aspects of Mineral Thermobarometry

Non-ideal mixing

Activity coefficient (one-site substitution)

If the mixing is non-ideal, we can introduce a factor gamma(gamma), the activity coefficient, so that where substitution of cation j occurs on n sites per formula unit, e.g. (Ca,Mg,Fe)CO3, the activity of the j-rich end member i will be

ai = (Xjgammaj)n

where X is the mole fraction of cation i on the site and gamma is the activity coefficient.

Ideal and non-ideal solutions

In an ideal solution, the activity coefficient is 1, and so a = X. In non-ideal solutions, the activity coefficient will have some value greater or smaller than one, which will be a function of composition, temperature, and perhaps other variables. Careful experimental work is needed to determine its values. Solid solution series which show miscibility gaps at lower temperatures are clearly non-ideal.

More reading for this section can be found in

[ Notes for further content in these sections ... ]

Energetics of ideal solutions

Free energy of an ideal solution. Figure (G-X)

Configurational entropy of mixing only, no enthalpy of mixing, volumes are linear across range.

Real Solutions

Follow Spear, Ch 7, , pp. 191-

Raoult's and Henry's Laws [diagram]

Gibbs energy: ideal and excess parts

Series expansion of excess free energy, giving symmetrical or asymmetrical properties

Symmetrical (truncated at quadratic term) sometimes called regular solutions

Mixing parameters

Excess free energy, mixing parameters. Figure(s) (G-X)

Spear fig 7-9 helps to define WG (Margules parameter or mixing parameter), showing its relationship to Henry's Law coefficient.

Show relationship between activity coefficient and WG

Figures and expressions for A-X relations for non-ideal binary system. Most relevant example might be muscovite-paragonite.

Formulations for ternary and quaternary solutions

Generalised 1-site asymmetric (Spear 1993, p. 204) [no space for full expansions]

Typical application is to Fe-Mn-Mg-Ca garnets

Many parameters, poorly constrained by data; commonly assume many are zero or negligible.


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This page last modified 12 October 2004