Simple Eutectic

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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If you ever made frozen juice bars in the home freezer you have probably observed some simple facts about melting and crystallization. A half-frozen juice bar consists of a mix of ice crystals and concentrated juice. Many mixtures of materials, when they solidify, crystallize into two distinct materials. As they solidify, first one component forms, then the other. A system of this sort is called a simple eutectic.

Consider a system of two distinct minerals A and B. Potassium feldspar and anorthite are a good example. Rather than present a phase diagram with rules for interpreting it, it's better to reason out how the system will behave and why the diagram looks like it does.

	The mixture starts out as molten at point X. As the temperature falls, one of the two components begins to crystallize. Since the composition of the melt is rich in A, more than likely A will crystallize first. As A crystallizes, two things happen: The composition of the remaining melt shifts right, toward B The temperature continues to fall The combined result of these two effects is that the point representing the liquid shifts down and to the right. (Where does the point representing the solid component of the system plot?) Answer: The only solid so far is A. The solid composition plots on the vertical A line at the appropriate temperature.
	As the system evolves, there are three points to track. All three always plot at the same temperature. The proportion of melt to solid is found as shown. Note that as temperature falls, the proportion of solid increases. When solid A first starts to form, the composition of the melt and the overall system are the same, and the amount of solid is zero. The point representing the melt moves down and away from the solid composition. As solid A forms, the melt gets richer in B The point representing the solid. As long as only one component is forming, this travels down the outside of the diagram as shown. The point representing the overall system travels straight down, since only temperature changes.
	The melt composition continues to move down and away from A (top, red line). Eventually, the liquid becomes so enriched in B that B begins to form along with A. The composition of the solid moves horizontally toward the right because solid B is now present as well. Note that the proportion of melt continues to decrease Once the solid composition reaches the same composition as the original melt, the melt percentage reaches zero and the system is entirely solidified. From there on, as temperature falls, the point representing the overall system moves straight down.
	A complete binary eutectic diagram looks like this. To understand what is happening, always read the fields. For example, what's happening on the boundary between Liquid (purple) and Liquid plus B (yellow)? Answer: as temperature falls, you change from a system with only liquid to one with liquid plus B. Hence B must form. What happens at the minimum? The surrounding fields contain liquid, Solid A, and Solid B. Hence all three phases must be present at the minimum (called the eutectic).

Note that when the melt is at e (called the eutectic), the temperature does not change as long as there is melt remaining. Heat being taken out shows up as phase transformations rather than a drop in temperature. This heat is called latent heat of crystallization. It also occurs as solid A is forming; some lost heat is manifested in phase transformations and some as lowering of temperature.

For a melt of composition X:

The system moves down until it intersects the melting curve (called the liquidus) at a.
Solid A begins to form. The melt shifts down and to the right (away from A) from a to e.
The solid phase moves from b to c as the system cools.
When the melt reaches e, solid B begins to form as well. The solid composition moves inward from c to d.
When the solid composition reaches d, the entire system is solid. From here on the system can only cool down.

For a melt of composition Y:

The system moves down until it intersects the liquidus at f.
This system is so rich in B that solid B begins to form first. The melt shifts down and to the left (away from B) from f to e.
The solid phase moves from g to h as the system cools.
When the melt reaches e, solid A begins to form as well. The solid composition moves inward from h to i.
When the solid composition reaches i, the entire system is solid.

Important Points

How Points Move

In a phase diagram where temperature and composition are the variables, a cooling system always moves down.
If material is not added to or removed from the system, the point representing the overall system composition only moves vertically downward.
The evolution of a solid as it melts can be traced by simply reversing the sequence of events in the cooling of an equivalent melt. In this case the system moves vertically upward.
Always track the movement of all three points: the overall system, the solid composition, and the melt.
Crystallizing a mineral from the melt drives the melt composition away from that mineral composition, and drives the bulk solid composition toward it.

Read the Fields

When a system plots within a field, only those phases within that field exist.
When on the boundary between two fields or the intersection of more than two fields, all the phases in all adjacent fields must be present. For example, at the eutectic, the fields Liquid, A+Liquid, B+Liquid and Solid A+B are all present. Thus, at that point, we must have Liquid, Solid A, and Solid B.)
When the system moves downward across a boundary, the events that happen on the boundary must reflect the changes that take place across the boundary. (For example, system Y above moves from the field B+Liquid to Solid A+B. Thus, while crossing the boundary, the liquid must disappear and A must appear.)
You can predict the changes that will take place in a system by drawing a vertical line down from the initial composition and reading the successive fields. (System Y above passes from Liquid to B+Liquid to Solid A+B. Thus we expect B to form from the melt first, then the simultaneous formation of A and disappearance of the melt, then a solid mix of A and B.)

Phase Diagrams and Real Rocks

When we look at a simple phase diagram, we temporarily ignore other phases in real rocks. For example, when studying the system K-feldspar and quartz, we ignore plagioclase, pyroxene, etc.
In real systems, every phase affects every other. Even non-participating components can change the temperature or pressure at which things happen. Minerals compete for cations in ways that can have far reaching effects. For example, pyroxene might take calcium out of a melt, leaving more aluminum available to form feldspar and thus changing the dynamics of the system quartz-K-feldspar, even though neither contains calcium.

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Created December 1, 1997, Last Update 17 Nov 2011

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