4.7 Counting Chemical Components

To use the Mineralogical Phase Rule it is important to get a correct count of the number of chemical components. Why not just count all the different elements in the mineral formulas? This is a good question. One way to answer it is to look at an example. Figure 4.02, which showed the relative stabilities of the aluminosilicate minerals andalusite (Al2SiO5), kyanite (Al2SiO5), and sillimanite (Al2SiO5), was presented as a 1-component system, even though each of the minerals contain the 3 elements Al, Si, and O.

Here (Figure 4.06) the aluminosilicate minerals are shown on a Al-O-Si composition diagram. Click on the diagram for a larger version. Use the selction buttons to display each of the minerals, showing that they all plot at one point with no variation in the proportions of Al,O, and Si. Quartz and corundum also plot on the Al-O-Si composition diagram. But neither of these minerals is involved in the chemical reactions shown in Figure 4.02, so treating the aluminosilicate minerals as a 1-compent system follows the behavior expected for a 1-component system.

What if quartz or corundum is present in a rock with kyanite, andalusite, or sillimanite? Then another component is needed to describe the system. Figure 4.07 shows the equilibrium mineral assemblages of the Al2O3-SiO2 system as a function of temperature and pressure for bulk compositions selected using a slider. Click on the image for the larger, interactive version. You will see in Figure 4.07 that adding Al2O3 or SiO2 to the bulk composition does not affect the reactions among Ky, And, and Sil. And although the system has two components, permitting two minerals at a random temperature and pressure, those two minerals cannot be two aluminosilicate minerals.

A similar analysis can be applied to other examples. The 2-component NaAlSi₂O₆-SiO₂ system of Figure 4.04 includes the 4 elements Na, Al, Si, and O. The relevent minerals jadeite (Jd), albite (Ab), and quartz (Qz) are shown in Figure 4.08 on a quaternary, tetrahedral, Na-Al-Si-O composition diagram. Click on the image to see a larger version that can be rotated with a slider and magnified further with your mouse wheel. All 3 minerals (and also the mineral nepheline) lie on a line stretching between SiO₂ and NaAlO₂. Because the minerals all plot along a line, they are in a 2-component system.

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