# Practical Aspects of Mineral Thermobarometry

### Phase components and composition space

This section introduces briefly the concepts of end members,
additive and exchange components, and substitution vectors. It is
also described in Spear's *Metamorphic Phase Equilibria* Ch 4,
pp 75-79.

For many purposes it is convenient to think of mineral composition
variation in terms of a multidimensional space. The number of
dimensions you need is one less than the smallest number of end
members (*phase components*) you need to describe the full range
of possible compositions. For example, olivines
(Mg,Fe)_{2}SiO_{4} need one dimension (a line joining
the end members forsterite and fayalite). You can describe the
composition of any olivine by choosing one end member composition as
an **additive component** and expressing all the possible
substitutions in the form of **exchange components**.

For simple olivines the only exchange component needed is
FeMg_{-1}. It can be thought of as a vector which points from
forsterite towards fayalite, and whose magnitude tells us how far in
this direction the mineral composition lies.

- Adding 1 unit of this exchange component to forsterite takes
us to [FeMg]SiO
_{4}, or Fo_{50}. - Adding 2 units of this exchange component to forsterite takes us all the way to the Fe end member fayalite.
- Adding 0.5 units of this exchange component takes us to
Fo
_{75}, etc....

Aluminosilicate garnets
(Fe,Mn,Mg,Ca)_{3}Al_{2}Si_{3} need a
three-dimensional composition space. If we choose pyrope to be the
origin of this space (the additive component), the composition of any
garnet is described by three vectors - an amount and a "direction"
given by the exchange component. For garnet the logical choices of
exchange component vectors are FeMg_{-1}, MnMg_{-1},
and CaMg_{-1}.

To describe coupled substitutions we can define a coupled exchange vector, as for example in the plagioclase series, where the vector relating albite to anorthite is

NaSiCa_{-1}Al_{-1}

or in the *tschermak substitution*, which occurs in a wide
range of silicates, for which the exchange vector can be written

Al^{vi}Al^{iv}Mg_{-1}Si_{-1}

Spear gives a table of common exchange vectors encountered in rock-forming minerals (Table 4.2, p.77).

This page last modified 12 October 2004