In this lesson, we're going to extend the concept of describing the microstructure of a eutectic, and we're going to be talking about an off-eutectic alloy. When we talk about an off-eutectic alloy, it means we're talking about alloy compositions that lie to the left, or to the right, of the eutectic composition. When we consider elements that are alloys that are to the left, we refer to these types of alloys as hypoeutectic. When we look at alloy compositions to the right, we refer to these as hypereutectic. Now we do this in a very arbitrary way. If we were to take this image, make a transparency and flip it, we would have beta as the hypo and alpha as the hyper. It's only a reference point with respect to the location of the particular eutectic that you have and the way the eutectic diagram is drawn. Now, when we look at compositions that are not at the exact eutectic composition, we need to know that between the end points in and along that three-phase equilibrium line, at the eutectic temperature, any one of those compositions will have all three phases present. The alpha phase, the liquid phase, and the beta phase. Now, when we look at a composition that lies to the left, meaning a hypoeutectic alloy, we now need to describe what we mean by the primary solid. The primary solid is the first solid that forms out of the liquid. So as we cool below the liquidus temperature, for a hypoeutectic alloy, the first solid phase, the primary solid, is alpha. When we look at a composition that is in the hypereutectic range, now what happens, the first solid to form out of our liquid is referred to as the beta phase, and beta then is the primary solid phase. Now let's return to our diagram, and when we look at the diagram we have three compositions of interests, the alpha phase, the beta phase, and the corresponding composition of the eutectics. So we can read those directly off of the diagram. We do that by drawing a horizontal line, and then what we would do is choose a particular alloy composition. Here I'm choosing alloy 1. The composition is given as XB zero, meaning that is the composition of B in the alloy that I've chosen. Now what I'll do is look at the three compositions of interest, the composition of the beta phase, the composition of the eutectic, and the composition of the alpha phase. Now what I'm going to do is cool under equilibrium conditions. And as I drop below the liquidus temperature into that two-phase field, I'm going to wind up decreasing the amount of liquid and increasing the amount of alpha. Now what I know is, at the eutectic temperature, I can't really tell you how much of any of the phases that I have because it is an invariant reaction at one atmosphere pressure. However, what I can do is I can go to a temperature that is very, very small, just above the eutectic temperature. And then, because I am so close, I can actually use the compositions of the amount of B that's in alpha, the composition of the eutectic, and the amount of B that's in the beta phase. And I can us these out of convenience because, most often times on the phase diagrams, these compositions are actually provided. Now if I take a look at alloy 1, it's cooled down to that dotted line. And now what I'm going to do is make a calculation and I'm going to get an idea of how much alpha I have and how much of the liquid I have. So I use the compositions at the bottom of the screen. And what I can do is calculate each of those two compositions, the fraction of the alpha phase, and the fraction of the liquid phase. Now what I'm going to do is I'm going to take that material, I'm going to cool it down below the eutectic by a very, very small amount. And when I do that, what happens is, not much is going to change with respect to the primary alpha that I form. But what is going to happen is, the eutectic actually then transforms into two solids, the alpha solid and the beta solid. So, now just below the eutectic, I can calculate what the fraction of alpha is and what the fraction of beta is, of the composition given by the eutectic liquid. So what does that mean? Well what that means is, I can write a fraction of all of the phases that are present at a temperature below the equilibrium eutectic temperature. I can say that the total fraction of alpha phase is going to be composed of the amount of alpha that we calculated as primary alpha, plus the amount of alpha that we calculated that is in the eutectic phase that transforms below the eutectic temperature. So, for example, above the eutectic, I have primary alpha and it's in a field of liquid. And then what's going to happen is below the eutectic temperature, what I then do is all that liquid in the back winds up transforming to this lamellar structure of alpha and beta. So that if I calculate how much alpha as primary alpha plus the alpha that came out of the eutectic, I then have the amount of alpha that is in the microstructure below the eutectic. And what's interesting here is by doing the calculation in this manner, we can, in effect, describe what the microstructure ought to look like as we do a cooling curve and follow the cooling process down below the liquidus temperature. So, that's our fraction of total alpha being made up of the fraction of primary plus the fraction of alpha in the eutectic. So we describe then how we can evaluate the off-eutectic alloy as we go through equilibrium cooling. In the next lesson, we're going to actually look at calculations using data that's on the phase diagram. Thank you.
