The following provides more detail that in required for students of EPS 2

In oxides and silicate minerals the anion is oxygen and an oxygen ion (2-) has a diameter of about 1.4 Angstroms (an Angstrom is 10^-10 m).

A simplistic, but very adequate basic way to think about the arrangement of oxygens in many minerals is to imagine them as spheres in a closest packed arrangement.

The first layer has a hexagonal pattern - each sphere is surrounded by 6 other spheres. The second layer is identical but the rounded bottoms of the spheres nestle into the depressions of the first layer (the second layer can nestle into one of two sets of positions). The third, fourth, etc. layers are similarly stacked. This is called "closest packing" of anions.

About 64% if the space is filled by spheres (oxygen) in a close packed array. Most of the remaining volume is in two types of sites. One of the two exists directly under a sphere that sits at the center of a triangle of spheres in the layer below. The space is surrounded by 4 oxygens, and so is 4 coordinated (or tetrahedral).

Given the oxygens have a fixed size, the size of the site is also fixed. The simple, semi empirical observation of Pauling was that sites tend to be occupied by cations that are not so small (that they would rattle) or so big that they would distort the site.

If we generalize this to all anions, the size of the site is determined by the size of the ions that enclose the site. The type of ions that will go in this site is determined by their size. Thus, we can define a range of radius ratios that will be appropriate for that site. The exact numbers are available on the web site (I will give you the http if you cant find them).

Charge balance considerations must be satisfied. This is achieved by filling only a fraction of the available sites.

Example: Al2O3 (corundum). The oxygens are closest packed. In this case, the Al sit in the other type of site (6 coordinated, or octahedral). However, because the charge on Al is 3+ and O is 2-, only 2/3 of the possible sites are occupied. (thus the ratio of Al:0 = 2:3).

Not all minerals are based on close packing of oxygen or other anions.

However, it remains true that the relative sizes of the anions (-ve charged) and cations (+ ve charged) determine their arrangement. In general, the larger the cation, the more anions that must surround it to make a sufficiently large site.

Boron, which occurs as the 5th element of the periodic table and is found in tourmaline, is usually 3-coordinated (e.g., BO3).

Uranium, which occurs in zircons as a minor element, is often 8-coordinated.

Here is what a range of sites found in gems look like!