In this lesson, we're going to look at deviations from ideal behavior. And the first deviation that we're going to look at from our ideal isomorph system is something that we refer to as a congruently melting minimum. When you look at the diagram, what you see above is a liquid phase and down below you see a solid phase. So these materials are essentially isomorphic with respect to the phases that are present. But over limited temperature ranges, we'll have regions of two-phase equilibrium. But, for example, once we're below the congruently melting temperature, we have a continuous solid solution form left to right. Once we are above the congruent melting temperature and above the melting temperature of pure component B, we will then again have a single phase field of liquid that goes from 100% a to 100% b. Now, one of the things that I want to point out is this minimum point here, and that particular point is referred to as a congruently melting minimum. When we expand and look at the behavior of the liquidus and the solidus space boundaries, what we're seeing here is, at that congruent point those two boundaries are touching one another. In other words, what this is telling us is, that we have the same composition for the liquid phase as we have for the solid phase. So in as sense it's acting as though it were a pure substance. In that, at this particular composition of the congruent melting minimum, at that particular composition, at that temperature, we have melting at only that temperature for a fixed pressure. So the composition of b in the liquid is exactly equal to the composition of b in the solid. Now let's take a look at a diagram where I'm going to include a discussion of the phase boundaries that we're seeing here, the degrees of freedom as we go through this system. So, the first thing we want to talk about is the liquidus boundary. So what you can see is the liquidus boundary is given in red, and we have a liquidus boundary that's associated with the left hand side of the diagram, and a liquidus boundary that's associated with the right hand side of the boundary. But, because we're still separating a liquid phase field from a liquid plus solid phase field, the boundary is still called the liquidus boundary. When we come down here and we look at the blue boundary, exactly the same thing that's going on. Regardless of which side of the diagram we're looking at, with respect to the congruently melting minimum phase, we still see something that we're calling a solidus boundary that goes all the way across. Now when we go through and we consider the phase rule again, this time again we're fixing the pressure, so our phase rule becomes C minus P plus one. So when we go into our two faced field, or our single faced field rather, what we see here is F is now equal to two. And I've indicated those two points on there to tell you that in order for me to be able to identify where we are thermodynamically, I have to provide two pieces of information, the composition of the alloy, as well as the temperature of the alloy. Now when we move into a region where we have one degree of freedom, that is, we're in a situation where we specify the temperature just as we described previously,and having done that, we are able to fix the composition of the solid phase and the composition of the liquid phase and again those are given on the bottom of the diagram. So that's the composition of being a solid to the left, the composition of the liquid phase to the right. Now, when we come to that point on the diagram where we have the two phases that are equal to one another, the material is, in effect, behaving as a pure substance. That is, the composition of the solid and the liquid are the same, and at that particular pressure, we have only a single melting point. Namely, the melting point at the congruently melting minimum. So here we are ascribing a value of F is equal to zero at that particular point. All right, now, let's look at another possible type of deviation that we can have, and that is a deviation where we have a congruently melting maximum. So here is the picture over to the right, and now, again, we still have an isomorphous system, Above the congruently melting maximum we have the same liquid that goes all the way from left to right and when we look down below the melting point of the lowest material we will see that we have a homogenous solution of single phase material. But regardless of where we are, once we're in a single phase field we have a homogenous liquid or a homogenous solid depending upon the temperature and the composition in that single phase field. So, we have our congruently melting maximum. And like the congruently melting minimum phase, we have the same sort of requirements with respect to the liquidus and solidus phase boundaries. And now what I've done is to insert that Into our figure to the right. And what we see is the composition of the liquidus and the composition of the solidus where they just touch that maximum point. And remember, this must be a maximum point on the diagram. We have the compositions of those two phases are in equilibrium with respect to one another. Hence the composition of being a solid is equal to the composition of being in the liquid phase. We're looking now, again, at this idea of having a congruently melting maximum diagram and what I want to focus on with this particular diagram to make some discussion around it Is that if we choose an alloy composition that's on the left-hand side with respect to the congruently melting maximum phase, we are only interested in cooling through that portion of the two phase field. We're only interested in that area, for example, that has been circled. If our composition were over to the right as indicated by the region in the circle, what we would then do is to look at the associated compositions and fractions as we go down through that region of the diagram. Now what we can do is we can add some data to a diagram where, for example, we have our deviations from ideal behavior that leads to a congruently melting minimum phase. And what I want to do then is to choose a particular composition for my alloy. That's XB0. And then what I'm going to do is to determine what the compositions are as I go down for various temperatures through the two phase field. And so again what's up here on the slide, are pieces of data that you can use to calculate and make sure that you understand the Lever Rule and how to operate the Lever Rule in this two faced field. Again, we've chosen a composition to the left so that's the only portion of the diagram that we're going to focus on. So here is the composition at T1. At T2, these are our two compositions of our solid and our liquid phase. As we go down in temperature we see our compositions are changing, both the composition of the solid and the composition of the liquid are increasing in their content with respect to the element B. And we also see by looking at the distances between the composition of the alloy and the phase boundaries, we can see that we are increasing the amount of solid phase and we are decreasing the amount of liquid phase. Ultimately we go further down, we see a change in the fraction of solid and liquid. That solid boundary is getting closer as we come down in temperature to the composition of our alloy, which means that we are increasing the content of solid. And now, we come all the way down to the solidus temperature, at T6, and now, as we pass through, we find that the material is a single phase solid. So we're then able to make calculations as a function of temperature for these different compositions and what we can do is plot that, or put that table up again. Here are the compositions of the alloys or the compositions of the phases in that two phase, in the two phase field is the function of temperature. Now what we're going to do is calculate our fractions at these temperatures and here we are at temperature T2, the fraction of the liquid and the fraction of the solid as we come through that two faced field and stop at equilibrium at temperature T2. Now at temperature T3, we're increasing the fraction of solid, decreasing the fraction of liquid. And eventually when we now get to the temperature at T4, we're then able to calculate from the data off the phase diagram what the fraction of solid phase is and the fraction of the liquid. So I charge you that you should be going through and doing these calculations and make sure that you understand how to get the information that comes out of cooling through a two phase field. Thank you.