Steven Dutch, Professor Emeritus, Natural and Applied Sciences,
Universityof Wisconsin - Green Bay
Above we see several common ways of visualizing atomic structures. The top row shows a water molecule. At left is a "skeletal" model showing atomic symbols and bonds. In the middle is a quasi-pictorial view with atoms indicated as small spheres and bonds shown. At right is a somewhat more literal view with true relative sizes of atoms shown. Oxygen is blue and hydrogen is red.
On the bottom row is a silica tetrahedron. A skeletal view is at left and we can immediately see a problem: since the structure is three dimensional we have to represent atoms out of the plane of the diagram. The middle oxygen atom is not on the same plane as the other three. The quasi-pictorial view next to it has the same problem. Here silicon is shown in magenta. The literal representation reveals an even worse problem: we can't see the central silicon atom at all. At far right, we dispense with atoms entirely and connect the centers of the oxygen atoms with straight lines. The result is a four-sided figure with equilateral triangle faces called a tetrahedron. We still can't see the central silicon atom, but we can often use the convention that anions occupy the vertices of a three-dimensional shape, a polyhedron, and there is a cation in the center. Color coding the polyhedron can serve to identify the cation.
Our conventional system of representing molecules runs into real problems when we try to represent crystalline solids. Let's use a relatively simple mineral, Forsterite (Mg2SiO4). Above is a skeletal model showing bonds. Blue dots represent oxygen atoms, yellow is magnesium and purple is silicon. First of all, we need to understand that this is just a small part of a large repeating structure and so we'd have to repeat this structure in all directions. Second, it's impossible to get much idea of the third dimension here. Worst of all, bonds are largely meaningless in ionic structures like this.
Above is a quasi-pictorial view. It suffers from the same drawbacks as the skeletal view, but it does make the atoms a bit easier to see. We can hint at a third dimension by coloring more distant atoms lighter and showing where silicon atoms overlie background atoms.
A literal depiction of atom sizes gives some three-dimensional information, but the magnesium atoms are badly obscured and some silicon atoms are completely hidden.
A polyhedral representation is a lot more open. We understand that cations are in the centers of each polyhedron and each vertex is an anion. Usually the anion is oxygen but it can be sulfur or a halogen. It is possible to represent several layers at a time.
Here's a hybrid representation that shows the polyhedra as well as some of the atoms. The oxygen atoms are shown at upper left. This can be useful for visualizing unusual coordinations. Atoms that don't fit into polyhedra can also be shown, for example, hydrogen atoms attached to hydroxyl or water, or inter-layer cations in mica. Anything that makes it easier to visualize the structure is fair game. Also, anything you find hard to understand, others are likely to find challenging as well. If you have to generate intermediate figures to really get a grasp of something, others will likely find those figures useful, too.
Return to Mineralogy-Petrology Index
Return to Thin-Section Index
Return to Crystals and Light Index
Return to Crystal Structures Index
Return to Mineral Identification Tables
Return to Professor Dutch's Home Page
Created 22 Sept 1997, Last Update 22 Sept 1997