Earth Materials. John O'Brien

(alpha and beta), coesite, and stishovite. Each polymorph of silica is stable under a different set or range of temperature and pressure conditions. A phase stability diagram (Figure 3.6), where pressure increases upward and temperature increases to the right, shows the stability fields for the silica minerals. The stability fields represent the temperature and pressure conditions under which each mineral phase is stable. Each stability field is bounded by phase boundaries, lines that define the limits of the stability field as well as the conditions under which phases in adjoining fields can coexist in equilibrium. Where three phase boundaries intersect, a unique set of conditions is defined under which three stable phases can coexist simultaneously.

Figure 3.6 Phase diagram for silica depicting the temperature–pressure stability fields for the major polymorphs and the liquid phase.

      Source: Adapted from Wenk and Bulakh (2004). © John Wiley & Sons.

The positions of the stability fields show that stishovite and coesite are high pressure varieties (polymorphs) of silica and that tridymite and cristobalite are high temperature/low pressure minerals. In this diagram both high temperature/low pressure polymorphs are the beta varieties. The high pressure polymorphs, coesite and stishovite, occur in association with meteorite impact and thermonuclear bomb sites, and stishovite is very likely a constituent of the deep mantle. The diagram shows that quartz is the stable polymorph of silica over a broad range of temperature–pressure conditions common in Earth's crust. This wide stability range and an abundance of silicon and oxygen help to explain why quartz is such an abundant rock‐forming mineral in the igneous, sedimentary and metamorphic rocks of Earth's crust. Figure 3.6 also shows that alpha quartz (low quartz) is generally more stable at lower temperatures than beta quartz (high quartz). Lastly, the diagram shows a phase stability boundary (liquidus or melting curve) on the far right that separates the lower temperature/pressure conditions under which silica is solid from the higher temperature/pressure conditions under which it is a liquid. The phase rule permits a deeper understanding of the relationships portrayed in the diagram. Places where three phase boundaries intersect represent unique temperature and pressure conditions where three stable mineral phases can coexist. For example, at point X at ~1650 °C and ~0.04 GPa high quartz, cristobalite and liquid coexist because the high quartz/liquid, high quartz/cristobalite, and cristobalite/liquid phase boundaries intersect. Because there are three phases and one component, the phase rule (P = C + 2 − F) yields 3 = 1 + 2 − F, so that F must be 0. This simply means that the temperature and pressure cannot be varied if three phases are to coexist. There are no degrees of freedom. Figure 3.6 shows additional triple points where three phases, all of them solid, coexist under a unique set of temperature and pressure conditions. If either temperature or pressure is varied, the system moves to a place on the diagram where one or more phases are no longer stable. At triple points, there are no degrees of freedom; the system is invariant.

      In other situations depicted in Figure 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