Consdier the stoichiometry of single unit cell. Each of the corner calcium ions is 1/8 inside the cell; since there are eight corners these add up to one ion inside the cell. There are six faces to a sigle cell, each with a calcium ion one-half inside the cell. Therefore a single cell contains four four calcium ions. A single cell also contans eight fluoride ions, each one located entirely within the unit cell. Since there four calcium ions and eight fluoride ions inside the cell, the 1:2 stoichiometry is maintained.

View a VRML model of the fluorite structure

In the fluorite structure, the fluorude ions reside within the tetrahedral holes formed by the face-centered cubic array of calcium ions, and the octahedral holes are vacant. In this illustration the green cylinders outline eight of the vacant octahedral holes.

This illustration shows the location of the tetrahedral holes in the fluorite structure. Consdier why the fluroide ions would reside in the tetrahedral holes rather than the octahedral holes. The most obvious answer to this question is, of course, stoichiometry. There are two fluoride ions for every one calcium ion, and since an array of N atoms results in the formation of N octahedral holes, there would simply not be enough spaces for all fluoride ions. If the ions were reversed, with the fluoride ions forming the face-centered cubic array, there would be enough calcium ions to fill only 1/4 of the tetrahedral holes or 1/2 of the octahedral holes; this would be terribly inefficient.

Technically, the descriptions of the fluoriute structure given above are inaccurate in the sense that becasue the fluoride ions are in fact larger than the calcium ions, they therefore do not "fit inside" the tetrahedral holes. As can bee seen here, the calcium ions form a sort of "expanded" face-centered cubic structure and do not physically touch each other. Nevertheless this does represent the most efficient packing arrangement.