We can check this by drawing tie lines between the liquidus and the solidus for any temperature in which melt coexists with solids. Tie line C–D provides an example. In horizontal (An) units, this tie line is ~45 units long (An86 – An41 = 45). The proportion of the tie line on the liquidus side of the system composition (x) that represents the percentage of crystals is 20% (9/45). The proportion of the tie line on the solidus side (y) that represents the percentage of liquid is 80% (36/45). The system is 20% crystals of composition An86 and 80% liquid of composition An41. As the system cooled from temperature A–B to temperature C–D, existing crystals reacted continuously with the melt and new crystals continued to separate from the melt. Therefore, the percentage of crystals progressively increased as crystal composition evolved incrementally down the solidus line and melt composition evolved incrementally down the liquidus line. When the system has cooled to the solidus temperature (1225 °C), the proportion of the tie line (E–F) on the liquidus side approaches 100% indicating that the system is approaching 100% solid and the proportion on the solidus side approaches 0%, implying that the last drop of liquid of composition An10 is reacting with the remaining solids to convert them into An50. We can use the albite–anorthite phase diagram to trace the progressive crystallization of any composition in this system. The lever rule can be used for compositions and temperatures other than those specifically discussed in this example.
The crystallization behavior of plagioclase in which An‐rich varieties crystallize at high temperatures and react continuously with the remaining melt to form progressively lower temperature Ab‐rich varieties forms the basis for understanding the meaning of the continuous reaction series of Bowen's reaction series, as discussed in Chapter 8. Phase stability diagrams summarize what happens when equilibrium conditions are obtained. In the real world, disequilibrium conditions are common so that incomplete reactions between crystals and magmas occur. These are discussed in the section of Chapter 8 that deals with fractional crystallization.
In addition, phase diagrams permit the melting behavior of minerals to be examined by raising the temperature from below the solidus. Let us do this with the same system we examined earlier (An50). As the system is heated to the solidus temperature (1225 °C), it will begin to melt. The lever rule (line E–F) indicates that the first melts (An10) will be highly enriched in the albite component. As the temperature increases, the percentage of melt increases and the percentage of remaining crystals decreases as the melt and crystals undergo the continuous reactions characteristic of systems with complete solid solution. The melt continues to be relatively enriched in the albite (lower temperature) component, but progressively less so, as its composition evolves incrementally up the liquidus. Simultaneously, the remaining solids become progressively enriched in the anorthite (higher temperature) component as the composition of the solids evolves up the solidus. The lever rule allows us to check this at 1400 °C where tie line C–D provides an example. The proportion of the tie line on the liquidus side of the system composition that represents the percentage of crystals is 20% (9/45), whereas the proportion of the tie line on the solidus side that represents the percentage of liquid is 80% (36/45). The system is 20% crystals of composition An86 and 80% liquid of composition An41. Complete equilibrium melting of the system occurs at 1420 °C (point A), where the last crystals of An90 melt to produce 100% liquid with the composition of the original system (An50).
Why are phase diagrams important in understanding igneous processes? Several important concepts concerning melting in igneous systems are illustrated in the plagioclase phase diagram.
1 All partial melts are enriched in low temperature components, in this case albite, relative to the composition of the original rock.
2 The smaller the amount of partial melting that occurs in a system, the more enriched are the melts in low temperature constituents such as albite.
3 Progressively larger percentages of partial melting progressively dilute the proportion of low temperature constituents.
4 If melts separate from the remaining solids, the solids are enriched in high temperature, refractory constituents.
During crystallization, the liquidus indicates the temperature at which a system of a given composition (An content) begins to crystallize; and the stable composition of any liquid in contact with crystals in the melt plus solid field. During crystallization, the solidus represents the stable composition of any solid crystals that are in contact with liquid in the melt plus solid field as crystallization continues and the temperature of final crystallization for a system of given composition.
It might be useful to briefly note that olivine group minerals exhibit behavior that is similar to that of plagioclase in that there is complete substitution solid solution between the two end‐members, high‐temperature forsterite (Mg2SiO4) and fayalite (Fe2SiO4). In this case only one substitution, Mg+2 for Fe+2 and vice versa, occurs (Chapter 2). Olivine exhibits continuous chemical reactions between solids and melts, similar to those discussed above with plagioclase group minerals. During cooling below the liquidus, crystals are enriched in high temperature, Mg‐rich forsterite, relative to system composition, and liquids are progressively enriched in low temperature, Fe‐rich fayalite. Eventually, the melt has completely crystallized and the system crosses the solidus. Similarly, with increasing temperature, as the system crosses the solidus, early melts are enriched in low temperature, Fe‐rich fayalite and residual solids are progressively enriched in high temperature, Mg‐rich forsterite. More detailed descriptions of this system are available in the references cited above.
Phase stability diagrams deliver quantitative information regarding the behavior of melts and crystals during both melting and crystallization. This provides simple models for understanding such significant processes as anatexis (partial melting) and fractional crystallization, which strongly influence magma composition and the composition of igneous rocks. All these topics are explored in the context of igneous rock composition, magma generation, and magma evolution in Chapters 7 and 8. Phase stability diagrams are also important in understanding the conditions that produce sedimentary minerals and rocks (Chapters 11–14) and the reactions that generate metamorphic minerals and rocks (Chapters 15–18). Let us now consider two‐component systems with distinctly different end members, between which no solid solution exists, using the diopside–anorthite binary phase diagram.
3.2.4 Two component phase diagram: diopside–anorthite
Figure 3.8 illustrates a simple type of two‐component or binary phase stability diagram in which the two end members possess entirely different mineral structures so that there is no solid solution between them. The two components are the calcic plagioclase anorthite (CaAl2Si2O8), a tectosilicate mineral, and the calcium‐magnesium clinopyroxene diopside (CaMgSi2O6), a single‐chain inosilicate mineral. The right margin of the diagram represents 100% anorthite component and the left margin represents 100% diopside component. Compositions in the system are expressed as weight % anorthite component; the weight % diopside component is 100% minus the weight % anorthite component. Temperature (°C) increases upward on the vertical axis. Because anorthite‐rich
