Vectors, components, and minerals

Ionic substitutions in minerals are directed chemical displacements and may be treated as vector quantities. This approach, pioneered by J.V.Smith and J.B.Thompson Jr, has many advantages over the barycentric coordinates (such as Gibbs triangles). Planar vector diagrams for a given mineral group can have chemical limits, generally dictated by ionic charge and bounded by lines representing zero contents of individual ions, as well as narrower crystal-chemical limits, generally dictated by ionic radii and bounded by lines representing constraints such as all Si as tetrahedral and Mg as octahedral. A given vector does not necessarily imply that a given mineral will be correspondingly zoned chemically, unless the mineral's composition is very close to a chemical or crystal-chemical limit. -from Author