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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 1114) and the reactions that generate metamorphic minerals and rocks (Chapters 1518). 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

Schematic illustration of 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.

      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

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