Ternary Systems
Multi-component phase relationships can be visualized on a triangular ternary plot. On such plots, three components can be shown as the corners of a triangle as shown below. At the composition at the "A" apex is 100% A, along the join between B and C there is 0% A, and in the middle the are both Ab, B, and C.
Ternary eutectic
Cotectic lines are drawn onto this composition diagram, lines where two or more phases are precipitating at the same time. The temperature of the liquidus surface can be contoured, or as is more often done, only the temperatures of certain important points (for example the melting points of pure phases and the temperature of the eutectic point) can be given and the rest of the surface more or less imagined. THe figure below shows such a ternary eutectic.
Ternary cotectic with solid solution
Consider an example involving the three components diopside, anorthite and albite (i.e., there are two phases: diopside and a solid solution of plagioclase), otherwise known as the Haplobasalt system, since most of the components of basalt are present in this system.
Figure 5-6
There are several features of this diagram to note:
- Concentration scale: any point adds to 100% of the three components, measured from base (0%) to vertex (100%)
- Contours: are temperature of the liquidus for that composition
- solid boundary in the interior: separates fields for diopside + liquid, plagioclase + liquid. Along this boundary (called the cotectic or divariant) the phases diopside + plagioclase + liquid crystallize.
- Along edges: The edges of this diagram are identical to the binary diagrams we considered earlier: diopside-anorthite and plagioclase.
As an example of the application of this diagram, consider the cooling of material of a composition from within the diopside field, say of composition Di60An20Ab20. As the initial liquid begins to cool, the liquidus is reached at 1300°C and diopside begins to crystallize. The composition of the residual liquid moves straight down (away from the diopside vertex, because only diopside is crystallizing). When the cotectic is reached, plagioclase also begins to crystallize with the liquid composition locked on the cotectic. Of what composition is the first plagioclase formed? This information can't be read from the diagram; we need additional information. The answer is about An80 for this composition, about 30% higher than liquid, consistent with what we might have guessed from the phase diagram for plagioclase alone. Upon further cooling, the liquid composition follows the cotectic. Travel down the cotectic stops when the solid has composition Ab=An, i.e., liquid about An20.
Contrast the behavior of plagioclase alone and the situation just considered, that of a diopside saturated plagioclase-rich liquid.
Figure 5-7
At 1200°C, for plagioclase alone the liquid is in equilibrium with An32 crystals contrasted with An50 crystals for the diopside saturated system. There is a much lower temperature of melting across the entire compositional range and as illustrated in the upper part of the figures, a smaller gap between liquid and solid compositions except at very high An content.
Returning to the question of crystallization paths in the system diopside-plagioclase, suppose that instead of starting in the diopside field we start in the plagioclase field. The liquid composition will move directly away from the solid plagioclase composition at that point in the crystallization path; see the diopside-plagioclase phase diagram. Thus, the liquid composition follows a curved path to the cotectic, with the tangent of the curve pointing down to the solid composition at that point in the crystallization sequence.