4.8 Still Counting Chemical Components

All the phases in the examples considered so far in this chapter have a fixed chemical composition. What about systems with solid solution minerals and liquids that have variable compositions? If a phase can have more than one composition, it must have more than one chemical component. However, the same criteria apply for counting system components. If all the phases in a system, including the variable composition phases, have compositions that can be plotted on a line, it is a 2-component system. If all the phases in a system, including the variable composition phases, have compositions that can be plotted on a plane, it is a 3-component system. Et cetera. And at equlibrium the maximum number of phases at a random T and P is equal to the number of chemical components. However, it is more likely that a random composition in systems with solid solution phases will have fewer phases than the maximum possible number.
CaArtesian Plot

Figure 4.05. 3-component assemblage diagram. Notice that most of the compositions on this diagram lie within 3-phase assemblage triangles. Click on the diagram to see a larger, interactive version with more information.


Look at the mineral assemblage diagram from Figure 4.05 shown again on the left. If you pick a random bulk composition (throw a dart at the diagram), the odds are that it will be a 3-mineral assemblage (the dart lands in one of the small triangles) for this 3-component system. You can see those assemblages by clicking on the diagram and choosing various compositions with the tools of Figure 4.05.
Salt Water equilibria

Figure 09. H2O-NaCl-KCl Equilibrium Assemblage Diagram. A ternary phase assemblage diagram for the 3-component system for salty (NaCl-KCl) water at 20°C and 0.1 MPa pressure. Click on the diagram to see a larger version with interactive features.


Now look at Figure 4.09, the equilibrium phase assemblage diagram for H2O-NaCl-KCl at 20°C and 0.1 MPa. This is a 3-component system with 3 possible phases: halite (Hl), Sylvite (KCl), and salty water (Brine), which has a variable composition. Click on the diagram to see a larger version with phase assemblage information and then click on the "Show Phase %" button. Mouse over the diagram to see the equilibrium assemblages highlighted. Many of the possible chemical compositions fall in a 3-phase (pink)
Salt Water equilibria

Figure 4.10. NaAlSi3O8-CaMgSi2O6-CaAl2Si2O8 Equilibrium Assemblage Diagram. A phase assemblage diagram for a 3-component model basalt system. Click on the diagram to see a larger version with interactive features.

triangle (Brine-Hl-Syl), but some compositions are in 2-phase (green) regions, and some compositions are in the 1-phase (blue) Brine region. So if you pick a random composition, the equilibrium assemblage might be a 2-phase or a 1-phase assemblage. Another 3-component example is the system NaAlSi3O8-CaMgSi2O6-CaAl2Si2O8 at 0.1 MPa pressure shown in Figure 4.10. Most compositions can have 1-phase, 2-phase, or 3-phase equilibrium assemblages, depending on the temperature (use the slider and the "Show Phase %" button).