 In our discussion of phase diagrams so far, we've considered three different phases. Solid phase, liquid phase, gas phase. We've talked a little bit about how liquid and the gas phase, since they're both just disordered substances, either a dense disordered liquid or a less dense disordered gas. There's really only one way to be disordered at a given density. So as the temperature increases or the pressure increases, the difference between liquid and gas becomes smaller than in the supercritical fluid phase, which is also just a disordered fluid. There's really no difference between liquid supercritical fluid and gas other than the density of the fluid. Solid phase, for example, is an ordered phase, a crystal lattice, molecules arranged in a particular arrangement. And there are more than one way you can be ordered. You're probably familiar with the fact that a monatomic solid could be face-centered cubic or body-centered cubic or simple cubic. There's various arrangements of the atoms. Things get even more complicated, of course, for molecules. There's a lot of different arrangements. The molecules can have relative to one another, and that gives rise not just to a single solid phase, like we have a single liquid and a single gas phase, but multiple solid phases. And you're familiar with the fact that solids have multiple phases, at least for a few substances like carbon, for example, has multiple solid phases. And I can show you that on a phase diagram that I can pull up here. Carbon has a solid phase that you're familiar with in the form of diamond. Also has a solid phase in the form of graphite, both of which you've at least seen in everyday life and have not had personal experience with. So notice this phase diagram. Again, it's a temperature pressure phase diagram. It has a gas and a liquid and a solid. So this solid region, the range of pressures in this case is large, going from 10 bars, roughly 10 atmospheres, up to 10 million atmospheres. So room pressure is, in fact, another decade below it down here. So this is a high temperature portion of the phase diagram. We still have a triple point where we can have solid, liquid, and gas coexisting, the solid being graphite. But we have two different solid phases. And everything we've learned about phase diagrams can, again, be applied to understand this phase diagram. What this phase diagram tells us is which phase is most stable at a particular set of conditions. So if I want to know which phase of carbon is most stable at room temperature and room pressure, so temperatures in Kelvin, 300 Kelvin, is going to be way down here somewhere. One atmosphere pressure is going to be off the bottom of this chart. So this is clearly somewhere in the solid graphite phase of the phase diagram. So as you likely already knew, the most stable phase of carbon at room temperature and room pressure is graphite. That's the phase with the lowest free energy. Likewise, I can look at features of this phase diagram like the fact that the slopes are positive sometimes and negative in other locations. So this positive slope mean the fact that diamond, this phase diagram, shows a positive slope on the phase coexistence curve between diamond and graphite means that, as we've seen before, the molar volume of graphite must be bigger than the molar volume of diamond. If this line were sloping in the opposite direction, the slope like that, the opposite would be true. That tells us that diamond is more dense than graphite. Molar volume of graphite is bigger than that of diamond. What that means is eventually, no matter what the temperature is, eventually, as we increase the pressure, we'll eventually be able to convert graphite into diamond. So again, you likely knew that diamonds get formed in the earth, typically at high pressures and relatively high temperatures, where graphite can be compressed to high pressures to form diamond. We can talk about phase transitions as we increase the temperature. If we take our room temperature and room pressure sample of graphite, if I were to heat the temperature, trying to perhaps eventually melt a sample of graphite, turns out we see that's not going to happen. It's going to cross the solid gas coexistence curve rather than a solid liquid coexistence curve. So we can't melt graphite at room pressure. It will sublimate. Atoms of carbon will evaporate off the graphite sample and enter the gas phase directly without forming liquid carbon. If we want to make liquid carbon, we've got to get up to pressures of at least 100 atmospheres or so. However, if we're at pressures above 100 atmospheres, we could take graphite under compression and melt it. If we're at even higher pressures, we could take diamond under high pressures and melt it as well. So we can melt either the solid graphite phase or the diamond phase because there's coexistence curves separating graphite and liquid and separating diamond and liquid. I guess it's worth pointing out also that we have not only this traditional triple point between the solid, liquid, and gas phases, but there's a triple point up here as well between the diamond, graphite, and liquid phases. So there is a set of a single thermodynamic state, a single temperature and pressure, where in equilibrium we could have graphite and diamond coexisting in coexistence with their liquid as well. So all these features of the carbon-carbon phase diagram are similar to ones we've discussed for other substances with the extra complication now of just having more than one solid phase. And in fact, most substances will have more than one different solid phase that is stable at different conditions. Another familiar substance that has more than one solid phase is water. So if I replace this phase diagram with one for water, now notice the conditions we're studying. So let's locate the, let's say, actually, no, down here. So I guess this would be close to the normal melting point of water, not at a pressure of 100, but 1,100 times as small. So way down here toward the bottom of this liquid ice coexistence curve at a temperature pretty close to 273 Kelvin, that would be the normal boiling point of water. So one atmosphere in 273 Kelvin. So this is the melting transition that we're familiar with. But if we go to higher and higher pressures, we can convert ice, ice 1, which is the thing we normally call ordinary ice. This ice 1 or ice 1H phase of ice is only one solid phase of ice. There's more than one solid phase of ice, which are just distinguished by different ways of arranging the molecules in that solid, just like diamond is a different arrangement of carbon atoms than graphite is. Ice 1 has an arrangement with the hydrogen bonds pointing in a direction that's different than the arrangement of those hydrogen bonds in ice 2 or ice 3 or ice 5. And you might guess by the fact that there's a 2 and a 3 and a 5. Elsewhere on this diagram at higher pressures, there's also an ice 4. In fact, the numbering of these phases goes as high as I think ice 18 is the highest phase that's been identified so far. There's at least 18 different phases of solid water distinguished by this different arrangements of their molecules. So these are unfamiliar phases of ice because we don't typically operate at pressures of, actually I've misread this. It's not bars, it's megapascals. So this 100 megapascals, that would actually be about 1,000 atmospheres or 1,000 bar. So again, room pressure is still very low on this diagram, practically down to the lower axis. So we don't typically work at pressures as high as 2,000, 3,000, 4,000 atmospheres, except in very specialized circumstances. So you're probably not familiar, don't have any first-hand experience, certainly with ice 2 or ice 3. But those are phases that do exist and become more stable than the traditional phase of ice as we go to high pressures. So now that we understand the solid portion of a phase diagram can have multiple phases of the solid on it, that sort of completes our tour of phase diagrams, but only for single component phase diagrams. Everything we've talked about so far has been a single component, whether it's carbon or water or whatever the substance is. That's the only substance we're talking about on each one of these phase diagrams. Most interesting chemistry, of course, happens when there's more than one component in the system at the same time. And in that case, phase diagrams get a little bit more complicated in multiple component systems. In solutions, for example, where we have a solute dissolved in a solvent. So that's our next step is to begin talking about multiple component thermodynamics.