 Okay, so solid, liquid phase diagrams often have the shape we've talked about here for this was for the lead and tin phase diagram, there's a cartoon to remind us of what that looked like. That points out a feature we need to talk about about other solid, liquid phase diagrams which is the degree to which we can mix the two components of the phase diagram. So in lead and tin, for example, in the solid phase, they're only partially miscible. I can form a lead-rich phase over a range of compositions, but not any composition I want. Likewise I can form a tin-rich phase under a very narrow range of compositions that needs to be nearly pure tin. I can't put very much lead and tin and have it remain a single solid phase, otherwise I end up in this mixture of two solid phases. These metals don't always behave like that, sometimes I can combine two metals in any arbitrary composition I want, even in the solid phase. So what that would look like for an alloy forming pair of metals like, in this case, if I combine copper and nickel, those two metals I can combine in any combination I want. So if I draw mole fraction of nickel, temperature composition phase diagram, I'll have to look up the melting points, but pure copper melts at a little above a thousand Celsius, and pure nickel melts a little higher at 1455. And then what happens in between is much simpler than it is here, because in the solid phase I only have a single solid phase, not a mixture of two solid phases. It's a relatively ideal mixture of these two metals, and I can form an alloy of copper and nickel anywhere from 0% to 100% nickel at temperatures up to this lower line. In between here we have liquid and solid coexisting, and if I get above the upper line I've got a liquid, again at an arbitrary range of composition. So copper and nickel are much simpler, they're fully miscible in the liquid phase and I can form an alloy at any composition I want. They're fully miscible in the solid phase as well. So that's a simpler case than the lead and tin mixture, but sometimes things get a little more complicated when we have, let's say we were to consider combining not two metals, but sodium and chloride, right? They form a covalent compound, sodium chloride, an ionic compound, so they're not metallically bonded and they form a stoichiometric complex. In fact, sodium chloride form NACL with a one-to-one stoichiometric ratio. So when I combine sodium and chloride, I certainly can't combine them in any arbitrary ratio and get a solid. The only solid that they form is either a sodium-pure chloride or a one-to-one ratio of sodium chloride. Likewise with many other solids, I can talk about iron with oxygen. I'll mention that one because there's a few different possibilities for the stoichiometric ratio. Iron-2 oxide combines in a one-to-one ratio, iron-3 oxide combines in a two-iron-to-three oxygen ratio, but again there's a stoichiometric ratio in the amounts of these two elements that I can combine. So I'll show you, I won't try to sketch this one, I'll put up some experimental data for what the phase diagram looks like for a compound that forms a stoichiometric complex. So this is what the phase diagram looks like for magnesium and calcium. And again, these form a stoichiometric compound and if we look at the details of this phase diagram, so up at high enough temperatures above 1100 Celsius, I can form a liquid and in the liquid phase the two elements are miscible. But when I cool that liquid down, of course I'm going to form a solid. So these are solid phases and if we look a little more closely we can tell what's going on in those solid phases. In particular, so this line right here at 0% mole fraction magnesium, that's going to be pure calcium, that's what melts at 1115 Kelvin, pure magnesium, melts at a little bit lower, 923 Kelvin. So if I prepare, let's say, pure calcium in the liquid phase I cool it down and it'll solidify. If I mix in a little bit of magnesium, so it's mostly pure calcium with a little bit of magnesium mixed in, I cool that down and it melts at a lower temperature, I'm sorry it solidifies at a lower temperature. So what I get here is when it solidifies, it solidifies into a mixture. These tie lines are connecting a liquid phase composition on this side and a pure solid composition on this side. Pure calcium combined with a certain amount of liquid at a different composition. If I cool it down far enough, I no longer have liquid, I've entered this pure solid phase but this solid phase is more complex than just a single solid phase because the tie lines here are connecting pure calcium to whatever this is. So let's think about that a little more carefully. This vertical line here, this vertical line occurs at a stoichiometric ratio of 67%, actually 66 and 2 thirds percent magnesium and 33 and 1 third percent calcium. So what this represents, this vertical line represents the stoichiometric compound MG2CA, I'll write that down here so we can see it a little better, the solid, the crystal and solid MG2CA. So that 2 to 1 stoichiometric ratio of magnesium and calcium, if I try to prepare a solution at a different concentration, this tie line tells me I can't make magnesium calcium mixtures in any ratio I want. If I try, just like if I tried to make Na2Cl, I can't, I'll get a mixture of pure sodium and NaCl in whatever proportions add up to the total amounts of sodium and chloride I mix together. Likewise, if I try to make some arbitrary proportion of magnesium and calcium at some particular temperature, I'll end up with, according to this tie line, a mixture of pure calcium and MG2CA. So this is a solid plus solid phase coexistence region with all these tie lines in it and in particular it's a calcium and MG2CA phase coexistence region. Likewise over here, if I make 90% magnesium, only 10% calcium as a mole fraction, I can't prepare that by itself. As a single phase, I'm going to get phase coexistence between pure magnesium on this side and MG2CA on this side. So this is, again, two solid coexistence regions. It's MG2CA coexisting with solid magnesium. So if we continue labeling the portions of this phase diagram, these wedge shaped regions are liquid solid coexistence regions, but the solids that the liquid coexist with is different in each one of these cases. Just like for lead tin, this liquid solid coexistence region is liquid coexisting with the alpha phase, the lead rich phase. This one is liquid coexisting with the beta phase or the tin rich phase. Here we have liquid coexisting with pure calcium. In this wedge, these tie lines are connecting the liquid on one boundary with MG2CA. So if I take this liquid and I cool it down, what precipitates out of that solution, solidifies out of that solution, is MG2CA. If I were to take a liquid at a different composition over here and cool it down, what's going to solidify out of that solution is pure calcium. Over here, now you can predict how this is going to work. This region, liquid and solid, is liquid and MG2CA. That's what's on the left side of this particular tie line in these coexistence regions. And then this smaller region over here is liquid coexisting with pure solid magnesium. So the phase diagrams are significantly more complicated for a compound forming substance like MG2CA, more complicated than they were for this non-compound forming lead tin case. One way to make them look a little bit simpler would be visually to take this phase diagram and say, divide it in half, not equal halves, but cut it with this vertical line that I've just drawn here. This now looks about as simple as this one does. This one looks like the phase diagram for mixtures of calcium and MG2CA. And on the right, I have a different phase diagram that represents mixtures of MG2CA with pure magnesium. So this is a little bit like taking two different solid liquid phase diagrams for a pair of solids and combining them next to each other, because MG2CA is a stoichiometric mixture between calcium and magnesium. One other thing I should point out here is the eutectics. So again, these mixtures of solids do form a eutectic. The lowest melting point I can get by combining calcium with MG2CA is at this point over here. Likewise, if I combine MG2CA with magnesium instead, I get a different eutectic over here. So there's a separate eutectic on the calcium-rich side and on the magnesium-rich side of this diagram. Both of those eutectics are lower in melting point than the solids they are formed by mixing together. This one is lower than either the calcium melting point or the MG2CA melting point. This eutectic is lower than either the MG2CA or the magnesium melting point. So these solid liquid phase diagrams get significantly more complicated in cases where we have more than just one stoichiometric combination. The iron-oxygen phase diagram would be complicated. Many two-element phase diagrams get quite complicated. But by learning how to read the details of these eutectics in the phase coexistence regions, we can make a lot of sense out of how the complex behavior of these binary materials work.