Primary Mineralogy Tutorial

Introduction to Primary Mineralogy – 3D Models


The basic building blocks of primary silicate minerals are the silica tetrahedra. In this case the silicon cation is in four-fold coordination with oxygen. The coordination of a cation with oxygen depends on the size of the cation. A cation is stable in a particular coordination environment, as long as it is able to keep the oxygen anions from touching, thereby preventing repulsive forces from destabilizing the structure. For example, Si is small enough that only 4 oxygens are able to fit around it and the most stable arrangement of these oxygens is in tetrahedral coordination. Cations such as Mg, Fe(II) and Fe(III) are larger and thus able to accommodate 6 oxygens in their coordination environment. Aluminum’s size is in between Si and Fe/Mg, therefore, it has the ability to fit in either octahedral or tetrahedral coordination. View the first four models which show the Si-tetrahedra and Al-octahedra. These models are displayed as polyhedra, ball ans stick, or as space-filling representations. The space filling models are scale represenations of the size of the cation (Si or Al) and anion (Oxygen). Notice how much larger the oxygen anion is compared to the central cation. You can see that as the cation becomes larger more oxygens are able to fit in the coordination sphere without touching. Also notice that Al is coordinated by both Oxygen and hydroxyl anions. Since the proton is so small the hydroxyl anion is essentially the same size as the oxygen anion. Also, if you have access to a cheap pair of red/blue stereo glasses you can view the primary mineral models as “out of screen” red blue stereo by clicking on the primary mineral stereo button . The models range in size from about 200K to 1MB for some of the stereo models. Therefore, if you are accessing the internet via a modem the red/blue stereo models may take a long time to download.


Ball and Stick

Space Filling


Si Tetrahedra – Polyhedral             Al Octahedra – Polyhedral
 Si tetrahedra – Ball and Stick       Al Octahedra – Ball/Stick
 Si Tetrahedra – Space Filling        Al Octahedra – SpaceFill


Computer Requirements

The 3D models listed on this page require the use of Quick Time Plug-ins. If your computer does not have these plug-ins, they can be downloaded by clicking here. This is the quicktime web site — follow the directions on the left-side of the screen and click either the Mac or PC button depending on your platform. Once the download is complete you may have re-boot your computer. If you are having difficulties e-mail me or talk to someone at the computer help desk by dialing 231-4357.

Pauling’s Rules
Linus Pauling established a set of rules to explain how polyhedra are arranged in silicate minerals. The first rule is summarized above. This is called the limiting radius ratio. The coordination number is determined by the ratio of the radius of the cation to the radius of the anion (oxygen for silicate minerals). Since oxygen is the dominate anion in silicate minerals, the coordination number is essentially determined by the size of the cation. It is called the limiting radius ratio because below this number, the particular coordination is not stable.

Table 1. Limiting Radius Ratio for Coordination Numbers Commonly Found in Silicate Minerals
Coordination Number Geometry Limiting Radius Ratio
4 Tetrahedral 0.225
6 Octahedral 0.414
8 Cubic 0.732
12 Dodecahedral 1.00

For example, the most common elements in the earth’s crust (after Oxygen) are Si and Al. Si and Al have radius ratios of 0.29 and 0.36, respectively. Both of these numbers fall between 0.225 and 0.414 so these elements are predicted to be in tetrahedral coordination with oxygen. Aluminum’s radius ratio is close enough to the limiting radius ratio for octahedral coordination that it can be found in both tetrahedral and octahedral coordination.

Pauling’s second rule is known as the Electrostatic Valency Principle. This rule states that the electrostatic bond strength (s) between the central cation and each coordinated anion is s=Z/CN, where Z is the valence or charge of the central cation and CN is the number of oxygens in the coordination sphere. For example, Si is in tetrahedral coordination with oxygen. Since Si has a +4 charge the electrostatic bond strength of each Si–O bond is +4/4=1. Aluminum has a charge of +3. When it is in tetrahedral coordination the electrostatic bond strength of each Al–O bond is +3/4=0.75. When it is in octahedral coordination the electrostatic bond strength of each Al–O bond is +3/6=0.50

Pauling’s third rule deals with the arrangement of polyhedra in a crystal structure. The most stable arrangement of these polyhedra is point to point followed by edge to edge followed by face to face. This will become important as we discuss the various silicate minerals and talk about there stability at the earth’s surface.

Pauling’s fourth rule states that in a crystal structure containing different cations, highly charged cations stay as far from each other as possible in order to lessen the crystal’s coulombic energy (making the crystal more stable)

Pauling’s final rule states that the number of essentially different kinds of constituents in a crystal tends to be small. In other words less is best. A crystal composed of many different constituents would be very complex and difficult to fit together. Consequently, it would be characterized by various strains causing high potential energy and instability.

If these rules seem a little confusing right now don’t worry, they will become clearer when we discuss and view the various silicate minerals, in particular Rules 1 and 2.

The Primary Silicate Minerals
Ok, you understand how and why cations have different coordination environments with oxygen. Now let’s take the basic Si tetrahedra and build the different classes of silicate minerals. Silicate minerals are classified based on the arrangement of connected Si tetrahedra. There are a total of six classes of silicate minerals. We will start with the least and move to the most complex arrangement of the Si tetrahedra. Each class of silicate minerals will have two 3D models (except the first which will have 6). The first model will only show the arrangement of the Si tetrahedra. The other model will show the entire basic polyhedral structure. Pay particular attention to the arrangement of the Si-tetrahedra as we move from the least to most complex silicate minerals!! For all of the models Si is dark blue while Al is light blue. Depending on the silicate structure, alkali and alkaline earth metals (i.e. Ca, Na, Cs) may balance excess charge and hold the linked Si-tetrahedra or Al-tetrahedra/octahedra together. Since these cations are often in eight-fold coordination or higher they are not pictured as polyhedra but as ball and stick models (the ball being the cation and the stick or lines being the bonds or coordination number). These cations are represented by various colors.

To view the red/blue stereo images you must have access to red/blue stereo glasses!!!

This class of silicates is the most simple and consists of isolated Si tetrahedra (click on Si tetrahedra in olivine). If you remember Pauling’s second rule (electrostatic valency principle), the electrostatic bond strength of each of the Si–O bonds is +1. The valence or charge of oxygen is -2. Consequently, the oxygen has an excess -1 charge an additional polyhedra are necessary to satisfy that charge. In the case of olivine either Fe(+2) or Mg(+2) octahedra fit between the Si tetrahedra and share oxygens in order to balance the excess negative charge. Click on the olivine model (polyhedral) and notice that Mg octahedra share edges with each other and faces with the Si tetrahedra. According to Pauling’s rule 3, these are less stable arrangements than point to point sharing of oxygens. Because of these arrangements and the isolated Si tetrahedra, nesosilicates are the least stable of the silicate classes and rapidly weather when exposed at the earth’s surface. Silicate minerals become more stable as the Si tetrahedra share more oxygens because of the strength of the Si–O bond (electrostatic bond strength). This is reflected in the Si:O ratio. The smaller the Si:O ratio the greater the sharing of oxygens between Si tetrahedra. In the case of nesosilicates the Si:O ratio is 1:4.


 Olivine Si polyhedral                Olivine Si Ball and Stick             Olivine Si Space Filling
 Olivine Polyhedral                   Olivine Ball and Stick                 Olivine Space Filling
 Olivine Polyhedral 3d              Olivine Ball and Stick 3d            Olivine Space Filling 3d

Now let’s take two Si tetrahedra and link them point to point. We now have the basic structure of the sorosilicates. In this class of silicate minerals more of the oxygens are shared between Si-tetrahedra, hence, they require less additions of other polyhedra to balance the charge. Epidote Si Only,  Epidote,epidote3d. In this case of epidote the Si:O ratio is less than olivine (2:7) and the mineral is more stable. Iron is orange while calcium is green..

Ok, now let’s take the Si tetrahedra and link them in a ring like structure (hence the name cyclosilicate). We now reduced the Si:O ratio to 1:3. Again since more of the oxygens in the Si tetrahedra are shared, this class of minerals is more stable than the previous two. Click on both of the beryl models to view the arrangement of the Si-tetrahedra and the entire structure. BerylSiBeryl, Beryl3d. This class of silicate minerals contains the precious gemstones emerald and tourmaline. This mineral has many different cations in its structure. Sodium is yellow, cesium is pink, and beryllium is light green.

This is an important class of soil forming minerals. Inosilicates are often called chain silicates because the Si tetrahedra are linked in either single chains (pyroxenes) or double chains (amphiboles). The Si:O ratio for pyroxenes is 1:3 and for amphiboles it is 4:11. Click on the Si tetrahedral models to view the single and double chains. DiopsideSi, TremoliteSi.  These chains are held together by cations that are in 6 or 8 fold coordination with oxygen. In general these minerals are more stable than the previous 3 classes of silicates. Diopside is the pyroxene (single chain) while tremolite is the amphibole (double chain). In the diopside structure magnesium is yellow and calcium is aqua. In the tremolite structure sodium Si green, magnesium is yellow and calcium is light blue . Diopside, diopside3d, Tremolite, Tremolite3d.

Now if we take the chains and link them in sheets we have the phyllosilicate class of silicate minerals. This class of minerals contains both primary and secondary minerals. Many of the minerals in this silicate class make up the clay mineral fraction of soils. A similar tutorial for clay minerals can be viewed by clicking the clay mineralogy tutorial link at the bottom of the page. In the case of the phyllosilcates the Si:O ratio is reduced further to 2:5. The stability of these minerals is greater than the previous 4 classes, hence they are commonly found in highly weathered soils such as those in the southeast portion of the US. The phyllosilicate displayed is pyrophyllite. Pyrophyllite is a 2:1 clay mineral because it consists of a Al-octahedral sheet sandwiched between 2 Si-tetrahedral sheets. PyrophylliteSi, pyrophyllite, pyrophyllite3d

Tectosilicates are the last class of primary silicate minerals. Two common minerals that make up the tectosilicate class are feldspars and quartz. In tectosilicates all of the oxygens of the Si tetrahedra are shared, giving a Si:O ratio of 1:2. Because all oxygens are shared the oxygen’s charge is balanced and many of the tectosilicates are only composed of Si (i.e. Quartz). In the case of feldspars Al in tetrahedral coordination substitutes for Si in the structure. Since Al has a valence of +3 the charge on the oxygen atom in tetrahedral coordination with Al is not totally satisfied. Consequently, cations with different coordination environments fit in the structure to balance the charge. Compare the structure of the feldspar (albite) AlbiteSiAlbite, Albite3d to that of quartz Quartzquartz3d . The light blue tetrahedra is Al and the yellow cation is sodium. Since tectosilicates have the lowest Si:O ratio, they are the most stable of the primary silicate minerals. However, feldspars are less stable than quartz because of Al substituting for Si which creates a charge imbalance that must be satisfied by the presence of other cations.

In summary, as we move from the nesosilcates to the tectosilicates we decrease the Si:O ratio or increase the sharing of oxygens between Si tetrahedra. The stability of these minerals at the earth’s surface is related to the mineral’s structure; the lower the Si:O ratio (more sharing of oxygens) the more stable the mineral structure.

This web page was constructed by M.J. Eick and R.W. Burgholzer from Department of Crop and Soil Environmental Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0404. If you have comments or suggestions, email us at or

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Welcome to my Environmental Soil Chemistry blog.  This blog will be used primarily to house tutorials and links to bu used for students enrolled in my Environmental Soil Chemistry Course.  While I may make posts periodically most course information will be located on the Scholar course site.