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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 3.8, 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 ~0% solid diopside coexists with ~100% melt of composition An₂₀, at the moment crystallization begins. As the system cools, the percentage of crystals should increase at the expense of the melt as liquid composition evolves down the liquidus, with increasing An content caused by the continuous crystallization of diopside crystals. 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 ~35 units long (An₃₅ – An₀ = 35). The proportion of the tie line on the liquidus side of the system composition that represents the percentage of crystals is ~43% (15/35), whereas the proportion of the tie line on the solidus side is ~57% (20/35). The system is 43% diopside crystals (An₀) and 57% liquid of composition An₃₅. As the system cools from temperature A–B to temperature C–D, existing diopside crystals grow and new crystals continue to separate from the melt so that the percentage of crystals progressively increases. During this time, melt composition evolves incrementally down the liquidus line toward more anorthite‐rich compositions. When the system approaches the eutectic temperature, the tie line (E–F) is ~42 An units long. The proportion of the tie line (E–F) on the liquidus side approaches 52% (22/42), indicating that the system contains 52% diopside crystals, and the proportion on the solidus side is ~48% (20/42) liquid of composition An₄₂. At the eutectic temperature, diopside and anorthite simultaneously crystallize isothermally until the remaining melt is depleted. The proportion of crystals that form during eutectic crystallization of the remaining melt (48% of the system) is given by the lever rule as 42% (42/100) anorthite crystals and 58% (58/100) diopside crystals. The composition of the final rock is given by the proportions of the tie line between the solid diopside and solid anorthite that lie to the right and left of the system composition line. For this system, with a composition of An₂₀, the lever rule yields a final rock composition of 20% anorthite and 80% diopside.

The specific example related above is representative of the behavior of all compositions in this system between An₀ and An₄₂. When the system cools to the liquidus, diopside begins to crystallize, and as the system continues to cool, diopside continues to crystallize and grow. This causes the composition of the increasingly An‐rich remaining melt to evolve down the liquidus toward the eutectic. Separation of crystals from the melt causes melt composition to change. When the system reaches the eutectic composition, isothermal crystallization of diopside and anorthite occurs simultaneously until no melt remains.

For compositions between An₄₂ and An₁₀₀ (e.g., An₇₀), the system diopside–anorthite behaves differently. For these compositions, when the system cools to intersect the liquidus, the first crystals formed are anorthite crystals (tie line G–H). Continued separation of anorthite crystals from the cooling magma causes the melt to be depleted in anorthite component (and enriched in diopside component) so that the melt composition evolves down the liquidus line to the left. Tie lines can be drawn and the lever rule can be used for any temperature in the anorthite plus liquid field. When the system cools to approach the eutectic temperature (tie line E–I), it contains a proportion of anorthite crystals in equilibrium with a liquid of composition ~An₄₂. At the eutectic temperature, both diopside and anorthite simultaneously crystallize isothermally in eutectic proportions (58% diopside, 42% anorthite) until no melt remains.

Several important concepts emerge from studies of the equilibrium crystallization of two‐component eutectic systems such as diopside–anorthite:

1 Which minerals crystallize first from magma depends on the specifics of melt composition

2 Separation of crystals from the melt generally causes melt composition to change

3 Multiple minerals can crystallize simultaneously from a magma.

This means that no standard reaction series, such as Bowen's reaction series (Chapter 8), can be applicable to all magma compositions because the sequence in which minerals crystallize or whether they crystallize at all is strongly dependent on magma composition, as well as on other variables. It also means that the separation of crystals from liquid during magma crystallization generally causes magma compositions to change or evolve through time. These topics are discussed in more detail in Chapter 8, which deals with the origin, crystallization and evolution of magmas.

Phase diagrams can also provide simple models for rock melting and magma generation. To do this, we choose a composition to investigate starting at subsolidus temperatures low enough to ensure that the system is 100% solid, and then gradually raise the temperature until the system reaches the solidus line where partial melting begins. As temperature continues to rise, we can trace the changes in the composition and proportions of melts and solids, using the lever rule, until the system composition reaches the liquidus, which implies that it is 100% liquid. Let us examine such melting behavior, using the two compositions previously used in the discussion of crystallization. A solid system of composition 20% anorthite (An₂₀) and 80% diopside (Di₈₀) will remain 100% solid until it has been heated to a temperature of 1274 °C where it intersects the solidus. Further increase in temperature causes the system to enter the melt plus diopside field as indicated by tie line E–F. The composition of the initial melt is given by the intersection of the tie line with the liquidus (point E), so that first melts have the eutectic composition (An₄₂), and the composition of the remaining, unmelted solids is indicated by the intersection of the tie line with the solidus (point F = An₀ = Di₁₀₀). As the system is heated incrementally above the eutectic, the tie line (E–F) is 42 An units long and the proportion of the tie line on the liquidus side is ~52% (22/42) indicating that the system contains 52% diopside crystals, and the proportion on the solidus side is ~48% (20/42), indicating that all the anorthite and some of the diopside have melted at the eutectic to produce a liquid of composition An₄₂. At the eutectic temperature, both diopside and anorthite simultaneously melt isothermally until the remaining anorthite is completely melted. The proportion of crystals that melt during eutectic melting (48% of the system) is given by the lever rule and is 42% anorthite crystals and 58% diopside crystals as reflected in the melt composition. Further increases in temperature cause more diopside to melt. This increases the amount of melt and changes the melt composition toward less An‐rich compositions as melt composition. As temperature continues to increase, melt composition evolves up the liquidus toward progressively diopside‐enriched, anorthite‐depleted compositions. When the temperature approaches the liquidus temperature for the bulk composition (An₂₀) of the system, the lever line (A–B) clearly indicates that the system consists of nearly 100% melt (An₂₀) and nearly 0% diopside (An₀) as the last diopside is incorporated into the melt. For the composition An70, the initial also have the eutectic composition (An42).

Several important concepts emerge from an examination of melting behavior in two‐component systems such as diopside–anorthite:

1 The composition of first melts in such systems is the same – is invariant – for a wide range of system compositions

2 Melt compositions depend on the proportion of melting so that increasing degrees of partial melting cause liquid compositions to change

3 Changes in liquid composition depend on the composition of the crystals being incorporated into the melt.

Invariant melting helps to explain why some magma compositions (e.g., basaltic magmas) are more common than others, because some magma compositions can be generated by partial melting of a wide variety of available source rock compositions. The dependence of melt composition on the degree of partial melting suggests that it might be an important influence on ultimate melt composition. The ways in which magma composition depends on the incorporation of constituents from crystals in contact with the melt is also discussed in Chapter 8 in conjunction with a discussion of magma origin and evolution.