In this lesson we're going to continue our discussion of these off-eutectic alloys, but this time we're actually going to do some calculations. Here is the picture of the phase diagram, the eutectic portion of the diagram that we're interested in. What we have done is to choose an alloy composition that lies to the left of the eutectic. So first we're looking at a hypo-eutectic alloy, as determined by the way the diagram was drawn, and our primary phase is alpha phase. That is, when the liquid transforms first at the liquidus temperature, the first solid that's forming is the alpha phase. So knowing that, when we are just above the eutectic temperature, we can calculate what the fraction of liquid and the fraction of solid are. So if we look at the compositions that are along the eutectic line, and remember this is just our approximations of these compositions. We are then able to calculate what the fraction of alpha is in the fraction of liquid. So we have both of those now calculated. So there is 41% of one of the phases in terms of the liquid phase. And 59% with respect to the alpha phase. Now let's continue the development of the microstructure. Now we have just calculated how much primary alpha we have. And now when we come to the eutectic temperature and drop below the eutectic temperature, we're now going to calculate how much alpha we have that is related to the eutectic liquid that has transformed from liquid to alpha plus beta. So, we calculate the fraction of alpha that comes out of the eutectic liquid. We calculate the fraction of beta using the data along the eutectic temperature. And then what we're able to do is to calculate, based upon the fact that we know how much alpha there was in the eutectic, we know how much liquid there was before that alpha phase formed. We can then calculate the total amount of alpha as being given by the fraction of alpha that formed as primary phase, as we cool through the liquid plus alpha phase field, plus the fraction of alpha that we had as a result of the decomposition of the eutectic liquid. And when we do that, we wind up with a value for the composite or the fraction of eutectic of alpha. Now what's nice about this calculation is, this is in effect the way this structure develops. That is, if we cool it down from the liquid phase, through that liquid plus solid field then down into the solid, we now have the picture of actually the way the structure develops as a consequence of that solidification or that cooling reaction. Now, there is an alternative way to calculate the fraction of alpha. We could actually do that directly for the composition of the alloy. And so what we're going to do is to set up a lever rule problem again. And this time what we're going to do is to determine the actual fraction of alpha at this particular temperature that is just below the eutectic temperature. And when we do that and we put in the appropriate values for the range of compositions and the appropriate values for the composition of the alpha phase and the compositions of the beta phase. What we're going to wind up with is the same value, which is what we should have done, but this time what we now have is just what happens if we were to cool it directly to that point and just have alpha and beta. So even though this is a correct answer and it is exactly the same as the answer we have above, the answer that we have above actually provides more information. It has the information that tells us how the microstructure develops. So, here is our structure just above the eutectic temperature. What we have are primary alpha. And now, as soon as we drop below the eutectic temperature, we now have the liquid transformed into alpha plus beta. So, looking at our alloy what we want to do then is to consider what that microstructure ought to look like. So, we have done these calculations and this is the picture of our alloy. Now what we want to do is, let's consider the possibility of changing the composition, first increasing the amount of B in the system. So when we do that, what we're doing is we're moving closer to the eutectic. So the amount of primary alpha that we see is reducing. On the other hand, if we were to add less b, that is, increase the content of a. Now what we would see is we're moving closer to the alpha boundary. And as a consequence, the primary alpha phase has increased. So we are then able to make a comparison between the structure that we began with, of that particular composition, and compare what the picture would be either to the right or to the left of that composition. Thank you.
