# 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.

## A Eutectic Animated

Below is an animation of a eutectic evolving from an A-rich melt and a B-rich melt. In both diagrams, the melt composition is red, solid A is blue, solid B is green and the overall melt composition is black. Observe the behavior of all three phases as the system cools.

## Why Does the System "Hang" at the Eutectic?

It actually doesn't. Since temperature is plotted on the vertical axis, it's easy to be misled into thinking temperature is an independent variable. We watch the melt drop down the plot, then it hangs up at the eutectic. Time is the independent variable and temperature is dependent on time plus the physical processes in the melt.

The diagram above shows the evolution of a binary eutectic over time. If we start off with 100 grams of the melt shown, it contains 75 grams of A and 25 grams of B. As the melt crystallizes out A, it moves toward the eutectic. At that point, there are still 25 grams of B left (none has crystallized) and it makes up 60% of the melt (because the eutectic melt is 40% A and 60% B). So we can find out how much melt is left. 25 grams = 0.6 * melt, so melt = 42 grams. Therefore 58 grams of A have crystallized. Since there are 75 grams of A in the melt, the melt consists of 25 grams of B and 17 grams of A.

Up until now, heat has been lost to the environment and gained by converting melt to solid, and overall there has been a decrease in temperature. At the eutectic, heat is released by crystallizing A and B and the temperature remains constant as long as A and B are crystallizing. A and B crystallize in a 4:6 ratio until the melt is all gone. The 25 grams of A still in the melt crystallize as well as the 17 grams of A. Once crystallization is complete, the melt resumes cooling.

## Familiar Eutectics

### Water and Ethylene Glycol

 A familiar eutectic mixture is water and ethylene glycol (antifreeze). Ice melts at 0 C and ethylene glycol at about -14, but a suitable mixture stays liquid below -50C.So if it's -20C outside and you decide to put in antifreeze, it's not frozen solid in the jug. Why not? Because it's diluted with water enough to have a very low freezing point. But the mixture is still to the right of the eutectic. If it were to the left, putting it in your radiator would dilute it too much to yield a suitably low freezing point. One slight complication is we can't count on reaching the absolute bottom of the curve above because ethylene glycol forms an intermediate hydrate. So actually we have two eutectics side by side. This is actually a common situation.The hydrate doesn't crystallize very readily so the mixture often supercools. Ths supercooling, or metastable melting curve is shown in green. But we don't want to rely on this process to protect engines. Any time it gets that cold, people usually use engine heaters anyway.

### Salt and Water

The only thing complicated about this diagram is our intuition. Salt and water have such enormously different melting points it's hard to picture the extremes. The situation with less than 23% NaCl is a straightforward eutectic. However, again there's an intermediate hydrate. So what actually happens at -21C when we freeze salt water is that NaCl hydrate (more properly, salty ice) forms.

On the NaCl side, above 100 C water vaporizes so we have water vapor plus solid salt. At 801 C salt melts so we would have water vapor plus liquid salt. If we cool a system of water vapor and salt below 109 C, one of two things happens. If there is excess salt, we get liquid plus solid salt. That concentrated a solution condenses at 109 C rather than 100 C. If there is less than 23% salt, the water will condense and dissolve all the salt. The condensation will start at 109 C and there will be a tiny amount of saturated salt solution. Depending on the salt content, more condensation and solution may occur at lower temperatures. That's why the tiny wedge shaped field of water vapor and liquid at upper left.

## 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.

• 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.

Created December 1, 1997, Last Update 14 Dec 2009

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