Eutectic Systems
When two minerals do not dissolve into each other - that is, when they do not form a solid solution - their melting and crystallization behaviour is governed by a distinctive pattern in which neither mineral alone controls the temperature at which solidification is complete. Instead, the system converges on a fixed point, called the eutectic, where both minerals crystallize together at the same temperature from a melt of fixed composition. This eutectic behaviour is one of the most important concepts in igneous petrology because it explains why magmas of varying starting compositions can all produce the same final crystallization assemblage. [1]
Reading a Binary Eutectic Diagram
In a binary diagram with no solid solution, the horizontal axis represents composition - the relative proportion of two end members - and the vertical axis represents temperature. Two curved lines called the liquidus separate the melt-only field (above both curves) from fields where crystals and melt coexist. Below the liquidus on the diopside-rich side is the diopside + melt field; below the liquidus on the anorthite-rich side is the anorthite + melt field. Vertical lines at each end of the diagram are the solidus lines; they are vertical here precisely because there is no solid solution, so the crystal composition of each mineral does not vary with temperature. [1]
A tie-line is a horizontal line drawn at a specific temperature across one of the crystal + melt fields from the solidus to the liquidus. The two endpoints of the tie-line give the compositions of the coexisting crystals (on the solidus) and melt (on the liquidus) at that temperature. The relative proportions of crystals and melt can then be read off using the lever rule: the percentage of phase A equals the length of the tie-line segment on the B side divided by the total length of the tie-line. [1]
Pure diopside melts at 1392°C and pure anorthite melts at 1553°C. Any mixture of the two melts at a temperature lower than either pure end member - the mixture of two components depresses the melting point. [1]
Crystallization of a 75% Anorthite Melt
Consider a melt with 75% anorthite (An) and 25% diopside (Di) beginning at 1600°C. Tracking a vertical line through this bulk composition as the system cools reveals the complete crystallization history under equilibrium conditions - meaning that crystals and melt remain in full chemical communication throughout. [1]
At 1600°C the system is entirely melt. Cooling proceeds without event until the melt reaches 1445°C, which is the liquidus temperature for this composition - the point at which anorthite crystals and melt have equal free energies. Below 1445°C, anorthite crystals begin to form. Anorthite has no solid solution with diopside, so its composition remains fixed regardless of temperature. [1]
Cooling to 1400°C causes progressive crystallization of anorthite. As anorthite grows, it removes Ca and Al from the melt, so the residual melt becomes progressively enriched in the diopside component. At this temperature the melt has a composition of 68% An, and the system is 77% melt and 23% anorthite crystals by mass (from the lever rule). [1] Continued cooling to 1350°C brings the system to 38% anorthite crystals and 62% melt now at 59% An composition. [1]
The Eutectic Point
At 1273°C - the eutectic temperature - diopside crystals begin to form alongside the anorthite crystals already present. Three phases now coexist: melt, anorthite crystals, and diopside crystals. This three-phase coexistence at 1 atmosphere pressure can only occur at a single fixed temperature, which is why it is called the eutectic temperature. The melt composition at this point - 48% An - is the eutectic composition, defined by where the two liquidus curves meet. [1]
As long as all three phases coexist, the temperature cannot drop below 1273°C - removing heat simply converts more melt into crystals of both anorthite and diopside, in the same proportions as the eutectic melt composition (48% anorthite crystals and 52% diopside crystals). Only once all the melt has been consumed can the temperature fall further. [1]
Once fully solidified at around 1200°C, the rock consists of 75% anorthite crystals and 25% diopside crystals - exactly the bulk composition of the starting melt. The crystallization process redistributed the same atoms into a different physical form, but the overall chemistry of the system did not change. [1]
Equilibrium Melting (The Reverse Process)
Equilibrium melting of a solid rock made of 75% anorthite and 25% diopside is the exact reverse of the crystallization sequence. Heating the solid rock, the first melt appears at the eutectic temperature of 1273°C, with the eutectic composition of 48% An. Both anorthite and diopside dissolve into this melt simultaneously. Since diopside makes up only 25% of the rock but 52% of the eutectic melt, the diopside is exhausted first. Once diopside crystals are used up, the temperature can continue to rise, with anorthite continuing to dissolve and progressively enriching the melt in the anorthite component. The last crystal of anorthite melts at 1445°C, and the melt at that point has recovered the original bulk composition of 75% An. [1]
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References & Citations
- 1.Introduction to Mineralogy Nesse, W. D.
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