# 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), the *activity coefficient*, so that
where substitution of cation j occurs on n sites per formula unit,
e.g. (Ca,Mg,Fe)CO_{3}, the activity of the j-rich end
member i will be

*a*_{i} = (*X*_{jj})^{n}

where X is the mole fraction of cation i on the site and _{} 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

- Spear (1993)
- Thermodynamics of mixtures, Ch 6 pp. 153-163 (Entropy of mixing, G-X diagrams)
- Ideal solutions
- Non-ideal activity models, Chapter 7

- Andrew Putnis (1992) Introduction to Mineral Sciences. Cambridge University Press
- Roger Powell (1978) Equilibrium Thermodynamics in Petrology
- Wood, B.J. and Fraser D.G. (1977) Elementary Thermodynamic for Geologists. Oxford University Press.

[ 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.

This page last modified 12 October 2004