Earth Materials. John O'Brien

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