In mathematics, a vector of one component has a direction and magnitude, and defines a line (actually, a family of lines unless we define a starting point), two vectors define a plane, three a space, and so on. In chemical petrology, on the other hand, a one component system is a point, two components are needed for defining a line, three for a plane, and four for a space. Mathematicians and chemical petrologists appear to use the word ‘component’ somewhat differently. In this paper I shall attempt to show how these differences can be resolved, using the lithium micas as an example.
Isomorphic substitutions in minerals have both a direction (or sense) and a magnitude, and thus can be thought of as vector quantities. The analytical and graphical representation of such substitutions is facilitated by the use of exchange operators, or components that contain negative quantities of certain elements and that perform the operation of exchange (if added to a mineral formula: Burt, 1974, 1976, 1979; these are sometimes also called ‘exchange components’). Simple examples of exchange operators (isomorphic substitutions) that are important in micas include NaK−1, MgFe2+−1, MnFe−1, Fe3+ Al−1, and Fe(OH)−1.
If we simultaneously considered all of such possible exchanges in the mica group, a graphical representation would become impossible. Inasmuch as we are mainly interested in complicated coupled substitutions, especially those involving lithium, we can simplify our task considerably by ‘condensing’ down vectors that involve simple substitution, such as those listed above.