# Practical Aspects of Mineral Thermobarometry

## Energy of mixing

#### Chemical potential and Activity

Read about chemical potential and its relationship to other thermodynamic variables in Spear, Ch 6, pp 138-141.

The thermodynamic properties of simple substances, such as the end members of solid solution series, can be measured or estimated. Natural minerals, however, are complex and can vary in composition. We need to bridge this gap, so that we can perform calculations on real phases using thermodynamic data on simple end members.

For most types of thermodynamic calculation it is convenient to
define a standard state, so that thermodynamic quantities such as
chemical potential can be divided into two parts: a standard state
part, and a "real" part. The expression below for the chemical
potential of a component (i) in an impure phase consists of the
chemical potential of the component in its standard state, and a term
which is composition-dependent, containing *a*_{i}, the
activity of component i.

#### Splitting up the chemical potential, and defining activity

µ_{i} =
µ^{°}_{i} + R*T*ln*a*_{i}

The most convenient standard state for solids is the pure end member at the pressure and temperature of interest. The standard state chemical potential will be exactly equal to the molar Gibbs free energy of pure i, and will be a function of temperature and pressure only. The activity of pure i on this basis will be 1; the activity of an end member in an impure phase will be related to its mole fraction, and can be thought of as the composition correction to the free energy.

#### Activity-composition relationships

In what follows we assume* ionic mixing on sites*, i.e. that
cations mix with others over particular crystallographic sites in a
mineral structure.

##### One-site substitution

Where substitution occurs on one site per formula unit, e.g. (Ca,
Mg, Fe) CO_{3}

a_{i} = X_{i}gamma_{i}

where X is the mol fraction of component i 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. Solid solution series which show miscibility gaps at lower temperatures are clearly non-ideal. Non-ideal solutions are treated further in a later section. In practice the assumption of ideal behaviour may be adequate.

This page last modified 12 October 2004