3.6, two phases coexist under the conditions marked by phase stability boundary lines rather than points. As a result, the phase rule (P = C + 2 − F) yields 2 = 3 − F, so that F must be 1. For example, under the conditions at point Y (900 °C, 9.2 GPa), both coesite and stishovite can coexist. If the temperature increases the pressure must also increase, and vice versa, in order for the system to remain on the phase stability boundary line where these two phases coexist. There is only one independent variable or 1 degree of freedom. The temperature and pressure cannot be changed independently. In a similar vein, two phases, one solid and one liquid, can coexist anywhere on the melting curve that separates the liquid and a single solid stability fields.
However, for any point within a phase stability field (e.g., point Z) only one phase is stable (e.g., low quartz). The phase rule (P = C + 2 − F) yields 1 = 1 + 2 − F, so that F must be 2. This means that the temperature and the pressure can change independently without changing the phase composition of the system. For point Z, the temperature and pressure can increase or decrease in many different ways without changing the phase that is stable, as long as they remain within the stability field. There are two independent variables and 2 degrees of freedom. All points to the right of the melting curve in the liquid field represent the stability conditions for a single phase, liquid silica.
One can also use this diagram to understand the sequence of mineral transformations that might occur as Earth materials rich in silica experience different environmental conditions. From a liquid silica system cooling at a pressure of 0.3 GPa cristobalite will begin to crystallize at ~1650°. As the system continues to cool, it will reach the cristobalite/tridymite phase boundary (~1460 °C), where cristobalite will be transformed into tridymite. Ideally, the system will continue to cool until it reaches the tridymite/high quartz phase boundary. Here it will be transformed into high quartz, then cool through the high quartz field until it reaches the low quartz/high quartz phase boundary, where it will be converted to low quartz and continue to cool. Two phases will coexist only at phase boundaries during phase transformations that take finite amounts of time to complete (Chapter 4).
Similarly, a system undergoing decompression and cooling as it slowly rises toward the surface might follow line W–W′ on the phase diagram. It will start as coesite and be converted into alpha quartz (low quartz) as it crosses the phase boundary that separates them. Note that low quartz is the common form of quartz in low temperature, low pressure Earth materials.
3.2.3 Two component phase diagram: plagioclase
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
