Octahedral Sheets
Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay
If we stack two close-packed sheets of atoms on top of each other, between the sheets we find two types of holes or interstices. Where one atom sits over a triangular hole between three other atoms, the four atoms form a tetrahedron. The enclosed space is tiny. But other spaces are formed when a cluster of three atoms in the upper layer sits over a cluster pointing in the opposite direction in the lower layer. These openings are quite a bit larger and enclose octahedra.
In the figure above, tetrahedral openings are illustrated in light green and purple. There are two sets, one pointing up (light green) and one down (purple). Octahedral openings are shown in red. We can picture the two layers of atoms as defining a layer of octahedra with tetrahedral holes in between, as shown at right.
The diagram above shows how the atoms and the octahedral sheet are related.
In the most common cases, the close-packed sheets are made of oxygen atoms or hydroxyl ions and have cations in the octahedral interstices. What's the ratio between them? Each octahedron is surrounded by six anions, but each anion is shared among three octahedra, making a total of two anions per octahedron. If there's a cation in every octahedral opening, the ratio of anions to cations is 2:1.
In the mineral brucite, (Mg(OH)2), we find exactly this structure. The anion sheets are hydroxyls and the cations are magnesium. Ideally the sheets are electrically neutral and held together by weak residual forces.
If the cations are trivalent, like aluminum, we have to leave one third of the octahedra unoccupied to maintain charge balance. There's a nice, symmetrical way to do this: leave every third octahedron vacant in all directions, as shown below:
This gives us a sheet with hexagonal rings of octahedra. The anion sheets are still close-packed and the missing octahedra lack only the central cation. The mineral gibbsite (Al(OH)3), one of the bauxite minerals, has this structure. Gibbsite and brucite sheets are fundamental units of thephyllosilicates as well
Now comes the tricky part. The divalent cation forms a structure called trioctahedral, and the trivalent cation forms a structure called dioctahedral. Why? Dioctahedral and trioctahedral have nothing at all to do with the valence of the cations. They refer to the fraction of octahedra occupied. In dioctahedral sheets, two thirds of the octahedra are occupied, and in trioctahedral sheets, three thirds are occupied. Another way to see it is that in dioctahedral sheets only two octahedra meet at a vertex, and in trioctahedral sheets, three octahedra meet.
Seen from edge-on, as they are in visualizing the phyllosilicates, trioctahedral sheets look like the figure below. In diagrams they are often represented as rectangular boxes.
Dioctahedral sheets, shown below, look pretty much the same except for missing every third octahedron.
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Created 22 Sept 1997, Last Update