I want to move away from talking about essentially pure substances, and I want to begin to talk about effects where we start introducing intentional second phase or second component additions. And what we're going to be describing in this lesson, is what we mean by the terminology of a substitutional solid solution. And that's given in the visual that's on the screen now. We have two ingredients here. One of them is the solvent and the other is the solute. And they're distributed throughout the material. And as a result of that distribution, will have a random distribution, in this case, of the solute and the solvent. As we increase the concentration of solute, at some point, that terminology flips and the solute ultimately becomes the solvent. And what was the solvent becomes the solute. Now we want to think a little bit about, can we come up with a set of rules or guidelines that will talk about the solubility limits that we can have in a material? And Hume-Rothery a number of years ago came along and put together some empirical rules by looking at what is meant by a solid solution. So, let's go back and look at a picture of our solid solution. So that red circle in there is representing an atom that we have intentionally added to the system. And we immediately can figure out how we might begin to think about rules that would govern how much of those red atoms that we can put in there. First of all, we would expect that in order to make a reasonable substitution, the radius of the red atom and the radius of the blue atoms need to be the same. Well, what Hume-Rothery said was, after having looked at a number of materials that had reasonably extensive solid solubilities, that is, lots of reds included in with the blues. That in order for that to be the case, that the volume of this must be, or the size difference must lie within plus or minus 15%. So, there's a restriction on the size of the radius of the solute with respect to that of the solvent. There are other issues that control how much we can add. And that basically has to do with where these elements are located on the periodic chart. And in the first case, when these materials are close to one another along the same row, what we find is that these materials will have the same electronegativities. Another characteristic is, that the valence will be very similar. So, now we have three rules, or observations, that Hume-Rothery has put together. And they are size, which becomes pretty obvious. The next two, which have to do with where they are located on the periodic chart and hence their chemical similarity. The last one, on the other hand, has to do with the crystal structure. Now there's certain metallic materials like copper and nickel, which are completely soluble in one another. So you can make a whole series of alloys starting out with pure copper, going all the way over to pure nickel. So it's a continuous solid solution. Another example of a material that would behave that way are the semiconductor materials, silicon and germanium. Silicon and germanium are both diamond cubic. If you go back and you look at copper and nickel, both of those elements have the same crystal structure. So, in order to have complete extensive solid solubility from one component over to the other component, you are necessarily then required to have a material in which the two components have the same crystal structure. What we're going to do, is using this basic idea of the iron having two different alatrobes, we're going to be able to determine what the effect of the coordination number is. And remember back from an earlier module, when you look at the coordination number of the body center cubic, it has a coordination number of eight. Where when we look at the face center cubic structure, it has a coordination number of 12. Now focusing once again on the two different coordination numbers. The radius that we would have iron, when it is in the FCC structure, we're going to use that as unity. And when we look at what happens to the effective radius when we go from a coordination number of 12, face center cubic, to that of body center cubic. What we find is, that there is a modification to the radius of about 97%. So that radius is actually smaller in the BCC than it is in the FCC structure. By looking at a number of other systems in which there are different coordination numbers, the entire chart then is available. So we can look at coordination numbers of 12, 8, 6, and 4. So how do we use this? Well we use it, for example, when we look at alloys which contain iron where we have added the intentional addition of chromium. Now, if we're talking about iron when it's body center cubic, then it's not a problem, because both iron and chromium are body center cubic. On the other hand, if we're looking at iron and we're in a temperature range in which the face center cubic phase is the stable phase, then what we find is we have to take the chromium. Which is normally body centered cubic, and we have to modify it, so its radius is now slightly larger when we put it in the FCC structure. Now, up until this point, we have been looking at solid solutions where we have added elements to a material like a metallic material. Now, we can do the same thing when we look at ionic crystals. Here what we're looking at is a solution of sodium chloride. But there are some additions of another element, namely magnesium. So magnesium is now an addition. And remember that in this structure, we're talking about cations and and anions. And the magnesium cation addition, in order for us to actually balance the charge in the vicinity, we have to actually create a sodium plus vacancy. So that extra electron that we have with magnesium, when it's added to the structure of sodium chloride, means that we have to remove the associated sodium. So, our Mg2+ is sitting here. And then, when we add that to it, we have to have a vacancy associated with the sodium. And this then maintains electrical neutrality throughout the crystal. So that's an additional requirement that we would have when we start looking at alternative materials. Now when we look at a polymer, what's interesting about a polymer is we're going to look at one particular type of polymer. And we're going to look at a polymer of polypropylene. Now, in this case, we're looking at the propylene mer, and that propylene mer is indicated by the arrow. Now, if we take that long chain of polypropylene, and we add to it a mer of ethylene. Now what we can do, is we can create a solution of these two different polymers, and we can create a chain or a solution of polypropylene with the ethylene mer dissolved in it. So when we look at that, we have the length of that polymer, we'll have some distribution of the second mer. And we are of course doing this to enhance the characteristics of the original polymer chain by adding a second mer. So this then gives you an idea that we're going to see these types of solutions. Not just in metals, we're going to see them in ceramic or ionic materials, and we're also going to see them in polymeric materials. Thank you.
