Earth Materials. John O'Brien

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 plagioclases and diopside‐bearing clinopyroxenes are the major minerals in mafic/basic igneous rocks, this phase diagram yields insights into their formation.

Figure 3.8 Diopside–anorthite phase diagram at atmospheric pressure.

      The diopside–anorthite phase stability diagram illustrates the temperature–composition conditions under which systems composed of various proportions of diopside and anorthite end member components exist as 100% melt, as melt plus solid crystals and as 100% solid crystals. At high temperatures all compositions of the system are completely melted. The stability field for 100% liquid (red) is separated from the remainder of the phase diagram by the liquidus. The liquidus temperature increases in both directions away from a minimum value for An₄₂ (Di₅₈), showing that either a higher anorthite (An) or a higher diopside (Di) content requires higher temperatures to maintain 100% melt. The phase diagram also shows that at low temperatures the system is completely crystallized. The stability field for 100% solid (blue) is separated from the remainder of the phase diagram by the solidus. For compositions of An₁₀₀ (Di₀) and Di₁₀₀ (An₀), which behave as one‐component systems, the solidus temperature is the same as the liquidus temperature so that the solidus and liquidus intersect at 1553 and 1392 °C, respectively. For all intermediate two‐component compositions, the solidus temperature is a constant 1274 °C.

      The liquidus and solidus lines define a third type of stability field that is bounded by the two lines. This stability field represents the temperature–composition conditions under which both melt and crystals coexist; a liquid of some composition coexists with a solid of either pure anorthite or pure diopside. Two melt plus solid fields are defined: (1) a melt plus diopside field for compositions of <42% anorthite by weight (yellow), and (2) a melt plus anorthite field (green) for compositions of >42% anorthite by weight. The liquidus and the solidus intersect where these two fields meet at a temperature of 1274 °C and a composition of 42% anorthite by weight (An₄₂). This point defines a temperature trough in the liquidus where it intersects the solidus and is called a eutectic point (E in Figure 3.8). Let us use a couple of examples, one representative of compositions of <42% anorthite by weight and the other of compositions of >42% anorthite by weight, to illustrate how this system works.

To investigate crystallization behavior, we'll start with a system rich in diopside component with a composition of An₂₀ (Di₈₀). We will start at a temperature above the liquidus temperature for this composition (Figure 3.8). As the system cools it will eventually intersect the liquidus at a temperature of ~1350 °C for this system composition (point B in Figure 3.8). To determine the composition of the first crystals, a horizontal tie line (A–B) may be drawn between the liquidus and the solidus. The intersection of the tie line with the liquidus (point B) represents the composition of the liquid (~An₂₀) because the melt has just begun to crystallize and its intersection with the solidus (point A) indicates the composition of the first crystals (diopside). As the system continues to cool, diopside crystals continue to form and grow. This increases the percentage of solid diopside crystals in the system while incrementally decreasing its proportion while increasing the proportion of anorthite in the remaining melt as the percentage of melt decreases. As the system continues to cool to 1315 °C (tie line C–D), the composition of the melt continues to change incrementally down the liquidus line (to point D) while the composition of the crystalline solid remains pure diopside (point C). As cooling continues, liquid compositions evolve down the liquidus and solid compositions evolve down the solidus until the vertical system composition line intersects the solidus at point E, after which any further cooling brings the system into the 100% solid (diopside plus anorthite) field. As the system approaches 1274 °C (tie line E–F), it contains a large proportion of diopside crystals and a smaller proportion of melt with the composition ~An₄₂. When the system reaches the eutectic point at 1274 °C, where the liquidus and solidus intersect, the remaining melt crystallizes completely by isothermal, eutectic crystallization of diopside and anorthite until all the melt has been crystallized. Cooling of the system below 1274 °C causes it to enter the all‐solid diopside plus anorthite field.

      The percentage of crystals must increase (from 0 to 100) and the percentage of melt must decrease (from 100 to 0) as cooling proceeds. During this process, the composition of the melt continuously changes down the liquidus and the solids are crystallized in the sequence all diopside prior to the eutectic and diopside plus anorthite at the eutectic. Can we quantify these processes? In Figure