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Figure 3.7 is a phase stability diagram for plagioclase, the most abundant mineral group in Earth's crust. One critical line on the phase stability diagram is the high temperature, convex upward liquidus line, above which is the all liquid (melt) stability field that comprises the conditions under which the system is 100% liquid (melt). A second critical line is the lower temperature, convex downward solidus line, below which is the all solid stability field that comprises the conditions under which the system is 100% solid (plagioclase crystals). A third stability field occurs between the liquidus and the solidus. This is the melt plus solid field where conditions permit both crystals and liquid to coexist simultaneously.

Figure 3.7 Plagioclase phase stability diagram at atmospheric pressure, with a complete solid solution between the two end member minerals albite (Ab) and anorthite (An).

To examine the information that can be garnered from the plagioclase phase stability diagram, let us examine the behavior of a system, with equal amounts of the two end member components albite and anorthite. whose composition can be expressed as An₅₀ (Figure 3.7). On the phase diagram, the system is located on the vertical An₅₀ composition line. This line is above the liquidus (100% liquid) at high temperatures, between the liquidus and solidus (liquid + solid) at intermediate temperatures and below the solidus (100% solid) at low temperatures. If this system is heated sufficiently, it will be well above the liquidus temperature for An₅₀ and will be 100% melt, much like an ideal magma. Now let us begin to cool the An₅₀ system until it reaches the liquidus temperature (1420 °C) at point A. Once the system moves incrementally below A, it moves into the melt plus solid field. This means that crystallization of the melt begins at point A. To determine the composition of the first crystals, a horizontal line (A–B), called a tie line, is constructed between the liquidus and the solidus. The tie line represents the composition of the two phases (liquid and solid solution) in equilibrium with each other at that temperature. The intersection of the tie line with the liquidus (point A) represents the composition of the liquid (~An₅₀), because the melt has just begun to crystallize. The tie line intersection with the solidus (point B) represents the composition of the first solid solution mineral (~An₉₀) to crystallize from the melt.

As the system continues to cool, the composition of the melt continues to change incrementally down the liquidus line (e.g., to point C) while the composition of the crystalline solid solution simultaneously changes composition as it moves incrementally down the solidus line (e.g., to point D). This process continues as liquid compositions evolve down the liquidus and solid compositions evolve down the solidus until the latter reaches the vertical system composition line where it intersects the solidus at point F. Any further cooling brings the system into the 100% solid field. The tie line E–F at this temperature indicates that the last drops of liquid in the system have the composition ~An₁₀, whereas the final solid crystals will be the same as the system composition (→An₅₀).

Clearly the percentage of crystals must increase (from 0 to 100) and the percentage of melt must decrease (from 100 to 0) as cooling proceeds. Meanwhile the composition of the melt and the crystals continuously changes down the liquidus and solidus lines, respectively. How does this happen? As the system cools through the melt plus solid field, two phenomena occur simultaneously. First, ideally the melt and the existing crystals continuously react with one another so that crystal compositions are progressively converted into more albite‐rich crystals (lower An) stable at progressively lower temperatures. Second, newly formed (lower An) crystals of the stable composition form and earlier formed crystals continue to grow as they react with the melt, so that the percentage of crystalline material increases progressively at the expense of melt. Crystal compositions evolve down the solidus line toward more albite‐rich compositions (decreasing An) as temperature decreases. Liquid compositions evolve down the liquidus, also toward more albite‐rich composition (decreasing An), as temperature decreases because the additional crystals that separate from the melt are always enriched in anorthite relative to the instantaneous melt composition.

The precise proportion of melt and solid at any temperature can be determined by the lever rule. The lever rule states that the proportion of the tie line on the solidus side of the system composition represents the proportion of liquid in the system, whereas the proportion of the tie line on the liquidus side of the system composition represents the proportion of crystals in the system. In Figure 3.7, the proportion of tie line A–B on the solidus side of the system composition line is ~100% and the proportion on the liquidus side of the system composition line is ~0%. This makes sense because crystallization has just begun. So tie line A–B indicates that, just as crystallization begins, ~0% solids of composition An₉₀ coexist with ~100% liquid of composition An₅₀,. As the system cools (1) the percentage of crystals increases at the expense of the melt; (2) crystal composition evolves down the solidus; and (3) liquid composition evolves down the liquidus during continuous melt–crystal reaction and additional crystallization.

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.