# Ternary System with Intermediate Compounds

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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Mixtures of three distinct materials often melt and solidify in a ternary eutectic relationship. A good and very important geological example is the system quartz-anorthite-K-feldspar. If you understand binary eutectics well, ternary eutectics are very straightforward. Since ternary systems are plotted on triangle diagrams, a little review of triangle diagrams is in order first.

## Ternary Eutectics

 Any possible binary system can be part of a ternary system as well. Here the pair A-B form an intermediate compound AB. In a simple ternary system we didn't have to worry about anything but the liquidus surfaces, since the end state for every system was solid A, B and C. In more complex ternary systems we must be concerned with the solid state as well. We have to imagine that we are looking down into a three-dimensional solid.Here we see the liquidus surfaces above two solid fields, one ending in solid A, AB and C, the other in solid AB, B, and C.Often the people who plot these diagrams don't bother to plot the position of the intermediate compound. In that case you have to figure it out. The ternary phase diagram for this system looks like this. The red tie line AB-C divides the triangle into two regions. Each can be considered a distorted triangle plot. The geometrical rules are exactly the same as for a simple ternary eutectic. In effect, we have two triangle diagrams joined side-by-side.The place where the tie line crosses the AB-C boundary represents a saddle in the temperature surface. Two slightly different melts on opposite sides of the tie line will slide in opposite directions. Just as with a single ternary system, we can divide this plot up into regions with a predictable order of crystallization. This sort of diagram really doesn't present any serious complications. Simply treat each half as a ternary eutectic.

## A Complication

 This is a slightly more complex case. Systems involving A, AB and C crystallize as in an ordinary ternary eutectic. But the ternary eutectic AB-B-C lies outside triangle AB-B-C. What happens here?For any system initially within triangle AB-B-C, the melt will end up at eutectic AB-B-C. So we expect to form AB, B and C in some order and end up with solid AB, B, and C. So far, no problem. However, once the melt is outside triangle AB-B-C, it is too rich in A to be fully compatible with B. The amount of B will decrease (it will react with the melt to make AB). Systems in Field B but outside triangle AB-B-C will end up consisting of solid A, AB and C. Thus we expect to begin by forming B, but have none present when the system solidifies. Therefore it should disappear. A melt in the B field and in the AB-B-C triangle mostly follows a simple ternary eutectic path. The melt crystallizes out B first and the melt composition moves away from B until it hits the AB-B cotectic. The melt now crystallizes AB as well. The solid composition shifts toward AB and the melt composition shifts down the cotectic toward the AB-B-C triple junction. At the triple junction, C begins to form as well. The melt crystallizes AB, B and C in the proportions dictated by the triple junction. However, the solid being crystallized is richer in A than even solid AB is.

Created November 22, 1999, Last Update 04 March 2011

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