1.1 Coordination

A critical concept in understanding silicate mineral chemistry (and structure) is that of coordination polyhedra. In order to preserve local electronic neutrality in the silicate structure, the (normally smaller) metal cations are surrounded by oxygen anions. The geometric shape formed by the bounding oxygens defines the various coordination polyhedra. In a hypothetical 2-dimensional structure we can illustrate the notion of the coordination polyhedra using various regular polygons.

In naturally occurring 3-D silicate structures the main coordination polyhedra are tetrahedral or 4-fold (with four bounding oxygens), octahedral or 6-fold (with six bounding oxygens), cubic or 8-fold (with eight bounding oxygens) and 12-fold. The shape of the polyhedra formed by a particular cation is defined the relative size (as reflected in their radii) of the metal cations and the bounding anions (in our 2-D example the hexagon clearly allows a bigger relative central "atom" than the triangle).

The oxygen ion is so large in comparison to most cations that in silicate minerals the structure is dictated by the packing of oxygen ions with cations in the intercies (the figure below shows the relationship between ionic radius and ionic charge for the common rock forming elements). In silicates, which can be considered as ionic structures, each ion tends to surround itself with ions of opposite charge. The number of anions, say of oxygen, that can be grouped around a cation depends on the radius ratio of the two ions (defined as R cation/Ranion) and is termed the coordination number of the cation.

With oxygen as the principal anion, as is the general case for silicates, many cations occur exclusively in one coordination. Cations that have radius ratios near the theoretical boundary between types of coordination may occur in both. Thus Al may occur in either octahedral (6-fold) or tetrahedral coordination (4), while Si occurs almost exclusively in tetrahedral coordination (4) (the only exception being in a few very high pressure and exceptionally rare phases such as the SiO2 polymorph, stishovite, where Si is found in octahedral coordination).

Radius ratio
Arrangement of anions
Coordination Number
around cation
of cation
0.15-0.22 corners of an equilateral triangle
0.22-0.41 corners of tetrahedron
0.41-0.73 corners of an octahedron
0.73-1 corners of cube 
1 corners of an icosahedron (close packing)