Lecture 33: Phase Diagrams - Basic Definitions

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We are going to do the first of three lectures on the last topic. We're going to talk about phase diagrams starting today, Monday, and wrap it up on Wednesday. Phase diagrams is related to the question of stability and sustaining the solid state.

And, we talked about the behavior of solids, and we've used solids in order to teach the rudiments of chemistry. But today, I want to talk about the conditions under which solids are stable. And, under what conditions do solids remain stable when do they become unstable? This is important in industry, for example.

If you're running a cast shop, you're making auto parts; you want to know what the solidification temperature is of a particular alloy. It's important in failure analysis, something like the fall of the World Trade Center, looking at the metal specimens to determine, what was the mode of failure? The temperature excursions leave a signature, a thermal signature indicative of the history of what happened to that object.

And, by determining whether something went above a certain phase transformation temperature, we can retrace, reconstruct the incident. And you might say, well, gee, what's the big deal? I mean, you look up in the tables, everybody knows that water boils at 100°C.

But, maybe it's not so simple. Let's say you decide to realize your life's ambitions. And you're going to go climb Mount Everest. So, you plop down $10,000, you get a permit from the Nepalese government.

The next thing you know, you're at base camp, 20,000 feet. You have a hankering for soft boiled egg. So, you pitch a campfire, put on the eggs: five minutes, 10 minutes, 15 minutes. Pardon me, you want hard-boiled eggs.

After 15 minutes, you open the eggs and they're still running. You get really steamed. You go 20 minutes, 25 minutes, every time. The yoke is still runny. The white is converted, but the yoke is still runny.

What's going on? Well, we talked about denaturing. The white denatures at 65°C. But at 20,000 feet, the atmospheric pressure is reduced to the point that water boils at below the denaturing temperature of the egg yolk.

So, you can boil until the end of time. You'll always have soft boiled eggs. If you like soft boiled eggs, you cannot screw up. You cannot screw up, OK? So, what do we know from this little anecdote? This little anecdote is that the boiling point is a function of pressure.

So, it's not that simple. Let's go to another place. Let's go under the hood of a car, one of my favorite places. OK, so here's what's going on under the hood of a car. Here, you got the engine, and inside the engine we've got combustion.

And the combustion gives off a huge amount of heat. We have to dissipate the heat. So, we have water channels running through the engine and out to the radiator. And the radiator cools this water before recirculating it, thanks to the action of either fan, or wind, or some kind of movement of air.

And so, what's the principle here? The principle here is that inside the radiator, we've got solid. This is the rad, and it's probably made of, in the old days, they made them out of copper. But nowadays, they're making more and more of them out of aluminum.

And, we have liquid, which is the coolant. This is the coolant. This is water. And, we have a big delta T here, right? This is hot and this is cool. And so, we have a heat flux going in this direction.

And, this is working great because the density of water is high, and so therefore it's able to transfer heat very efficiently. So, this is good. This is really good. What can happen if things go out of control? Things go out of control, and we start to boil.

And, you know that the boiling point of water is more or less 100°C. We are down here. We are not at the base camp of Mount Everest. Here's what happens when things start to go out of control. We start to get gas bubbles.

These are the gas bubbles associated with the boiling of water. And, now, the heat transfer between gas and solid, between gas and solid is very poor. Think about it. What's transferring the heat? It's the atoms.

And the atom density in a gas is sparse. So, gas is a very poor heat transfer medium. So, we must avoid boiling. If we get boiling, then we get into a thermal runaway situation because now we've got boiling in the first place because the water was too hot.

But now we're doing a less efficient job of cooling, and it's going to get worse, and worse, and worse until finally: boom. So, what I want to do is I want to get my liquid range. I want to tailor the properties of the coolant.

I want a coolant that will be boiled over proof. So, if I could raise the boiling point, that would make the cars safer to drive under extreme conditions. Typically what happens is you are zooming down the highway on a hot summer's day, and then there is some reason to come to an abrupt stop.

And then, there's all that heat to be dissipated. And, no more do you get the benefit of the motion of the car. Now you're just relying on the fan. So, what can we do? If we go to the top of Everest, and the pressure goes down, and the boiling point falls, could I raise the boiling point by applying more pressure? Yeah, let's put a pressure cap on the radiator.

Let's keep the contents of the radiator high. And if you read the top, it will say 15 psi, which is 1 atmosphere. So, I've got 1 atmosphere here plus an extra atmosphere. So, I'm running a 2 atmospheres pressure.

So, that will raise the boiling point and stave off the dangerous gas evolution. And now, I can do one more thing. Instead of running pure water, I'll add ethylene glycol. I'll add ethylene glycol about 50/50 per volume.

You know this is antifreeze. It gives a freezing point depression. We'll talk about that next day. But it also gives boiling point elevation. So, in the summertime, you should always run with antifreeze because the combination of the pressure cap plus the addition of the glycol raises the boiling point from 212.

I'm talking about cars, so I am going to use Fahrenheit here, 212°F to 265°F. This buys you a much higher cushion. So, what are we doing? We are tailoring this by making the boiling point a function of pressure.

And now I'm showing you that it's also a function of composition. So, this whole business of solid-state stability I hope I'm showing you has a little bit more to it than just looking up the transformation temperature on the periodic table or the handbook.

So, I want to talk to you for the next three lectures about phase diagrams. Phase diagrams are atlases. They are maps. They are maps of stability that answer the question, if you specify pressure, composition, temperature, what are the stable phases? So, that's what you need to know.

So, let's talk about phase diagrams as stability maps. The stability of what? The stability of the state of aggregation. It's going to tell us if it's solid, liquid, gas, and under what circumstances? So, let's look at some simple phase diagrams.

But before we can do it, I need to define some terms for you. So, first of all, let's define the term phase. The phrase is a region of a substance that has the following characteristics: uniform in chemical composition.

It's uniform in chemical composition. The second thing about it is that it's physically distinct. And I'll give you some rich examples. I want to put this down just to document it and then after you see a few examples, these words will mean something to you.

So, it's physically distinct. And in the extreme, it's mechanically separable. It's physically distinct and mechanically separable. So, let's look at some examples of one-phase and two-phase systems.

And, this is one of these days where we are using symbols to mean multiple meanings, I've already used P to represent pressure. If I use P now to represent number of phases, you won't be able to tell one from the other.

So, I feel a little bit western today. So, I'll make it circle P. So, circle P equals number of phases, not to be confused with P, which is the pressure. So, number of phases I designate by circle P.

So, let's look at some simple single phase systems. So, let's look at P equals one. So, how about pure water? Pure water liquid, have a beaker of water, it's uniform chemical composition, physically distinct, mechanically separable.

How about white gold? White gold consists of an alloy of certainly gold to which we add silver and we add nickel. And these are all FCC metals. And at the atomistic level, you have them substituting for one another on the gold lattice.

And so, I have uniform chemical composition. I have no boundaries. There could be grain boundaries, but that's different. But the grain boundaries do not represent something that is a difference in chemical composition.

So, this is pure and this is a solution. So, if it's a pure material or a solution it will qualify as single phase. Let's look. So, here's a liquid. Here's a solid. Let's look at a gas. How about air? Air is a solution of nitrogen, oxygen, argon, increasingly CO2 in the city when you've got coal burning for electric power.

There's SO2. Oh, let's not forget our pal nitrous oxide. And if you live near an Alcoa smelter, you will have CF4. If you live near a magnesium smelter you'll smell chlorine. But in Cambridge, mercifully, we just have to enjoy these.

So, and this is all single phase. You don't see the gases settling according to density. They mix intimately in all proportions. And, one more solid: calcia zirconia. We talked about this one before.

This is the lime stabilizer zirconia for oxygen sensors and, I'll show you later that this is the material that's used for the faux diamond. This is a solid solution: calcium ion sitting on zirconium site.

So, this is single phase. There's no calcium islands, calcium oxide islands and zirconium oxide islands. This is a solid solution. So, therefore, it's all one phase. Now, let's contrast that to something that's two-phase to get a sense of what the difference is.

So instead of pure water, just liquid, suppose I have ice cubes in water. It's still pure. I didn't change the composition, but I've got two different states. I've got a solid state and a liquid state, and this fits the definition.

In other words, the ice floating in the water is uniform in chemical composition, and it's physically distinct. Or, I can say, I can put a boundary around it. And, I can isolate all of the ice cubes.

And, in fact, these are mechanically separable. I could pull out all of the ice cubes and be left with only the liquid, OK, solid in liquid. Two different phases because they are two different states of the same material.

I think we also looked at milk. We looked at milk, and milk has fat globules in the aqueous phase in the aqueous solution. All right, so, I've got fat globules. They're very tiny, and they scatter light.

But, if we got down to the micro level, we could find these fat globules as something that's mechanically separable, physically distinct, and of uniform composition, and different from this. So, this is two different phases because we have two different compositions.

We have two different compositions, and lastly, there was the visions cookware, the Pyroceram. That was the glass ceramic that's 95% crystalline and 5% glassy. So, what you have here is you have a glassy phase, glassy matrix, and crystalline precipitates.

OK, so again, we don't have a change in composition, but we have a change in atomic order. So, the glassy phase and the devitrified phase, so we can actually draw boundaries around all the crystalline precipitate.

So, I hope this gives you a sense of what's going on here. The second thing is these phase diagrams are drawn under conditions called equilibrium. That's why we talk about stability. So, let's define equilibrium.

Equilibrium is a condition which represents the lowest energy state of the system. In other words, if you take all of the constituents and give them infinite time and the energy they need to achieve the lowest energy state, this is where they will get to.

And, we will know that it's the equilibrium state because the properties are invariant. The properties are invariant with time. This is sort of like a steady state. But, steady state is something that could be sort of locked in on the road to stability.

So, this is the ultimate stability, as contrasted with metastability. Metastability is something that steady state but could get stabler yet. And the example of meta stability is diamond, which is not the stable form of carbon at room temperature, but diamond was formed under different conditions and then brought under ambient pressure and temperature.

But the activation energy to convert is so high that it stays apparently stable, but in point of fact, it's metastable. Another one is metallic glass. We know that metallic glass was formed under high quench rates.

If you take metallic glass and heat it moderately, you'll give it sufficient activation energy to then jump from this glassy state to the crystalline state, and ultimately achieve its equilibrium value.

So, those are examples of the equilibrium metastability. And then, the last thing, as you noticed, I talked about pure materials and then multicomponent materials. They have different elements that are mixed, and so we need a counter, a metric, that details what the level of chemical complexity is.

And for that, we call into play a term called component. And, it's the measure of chemical complexity. What do I mean by that? In the simplest terms, how many bottles do I have to pull off the shelf to make this thing, OK? Bottles off the shelf.

And, again, this is best given by illustration. So, I'll show you a mix of components and phases. So, we will do a little matrix here. I'll start on a new board. So -- OK, so across the top, I'll look at single phase and dual phase.

And down the column, I'll look at one component, two component, three component systems. So, the simplest is up here, one, one. One phase, one component, so, that's pure water. Pure water, all liquid, single phase, single component.

You could say, but don't you need hydrogen and oxygen? Well, if you take one of the thermo classes later, you will learn that the hydrogen and oxygen are linked by stoichiometry. So, it's still one bottle off the shelf.

There is no variation in the hydrogen to oxygen ratio. Diamond, even though it's metastable, all I need is carbon. And it's single phase. There's no change of phase across the diamond. In many cases, the diamonds that you will see, they are all single crystal.

Don't ever go to the jeweler and ask for polycrystalline diamond. It is not going to be very pretty. OK, please remember that. So, let's look at something that's now two components. Well, that would be calcia zirconia, right? It's one phase.

It's a single solid solution, but I needed two bottles. I needed a bottle of calcium oxide, and a bottle of zirconium oxide. But, they mix intimately, and I have a single phase. And then, the white gold is the gold, the silver, and the nickel, three different elements.

The mix intimately, and they give me a single phase. Over here, I've got one component. So, I'm working only with, say, water. So, this will be the ice water, or I call it slush. Two phases: and they are in equilibrium.

So, this is at 0° C. and they are stable over time. All right, the lowest energy state invariant. So, the slush remains stable. So, you can have dynamics. Some of the solid dissolves into liquid, and some of the liquid freezes out as solid.

But the net change is zero, stable, ice water, slush. The second one we saw when we talked about a solubility, we looked at the next of carbon tetrachloride and water, two liquids. We shake them up, and they phase separate.

I've been using that term, phase separate, two phases. There is an organic phase, or you say a carbon rich phase, a nonpolar phase, and a hydrogen bonded phase. So, these are immiscible, and I'll have two components, two phases.

And then the last one, this would be the Visions because that consisted of lithium oxide, alumina, and silica. I need to get three bottles off the shelf. Remember, I had a network former, a network modifier, and an intermediate.

And that gave me this remarkable two-phase mixture that triggered the exsolution of a crystalline phase. So now, let's look at some real example stability maps. So, I want to learn to crawl before we learn to run.

So, let's look at simple ones. So, we're going to put C equals one. So, this is pure materials. C equals one, one component. And, we're going to look at, C equals one, it's fixed. All I have left then; we have pressure composition.

Temperature composition is fixed because it doesn't vary here. So, I just have to look at P versus T. Those are the only variables that I had to deal with. So, let's look at some of these. Now, the first one I want to look at is one that you are pretty familiar with: water.

Let's look at the phase diagram of pure water. So, we're going to plot how the phases of water vary over pressure and temperature. And, I'm going to plot temperature in degrees Celsius. And I'm going to plot pressure in atmospheres, although I will give you the conversion to SI.

So, let me just put the general diagram on. It's sort of a Y shaped looking diagram. So, lowest temperature, this is where we have the solid regime, solid water ice. The highest temperature must be where we have the gas or water vapor.

And, in between, we have the liquid. And, these lines represent the equilibria. These lines, this one is the equilibrium between liquid and vapor. So, this is a liquid equals vapor coexistence curve.

And, it's not a single point. This one here is solid and liquid coexistence curve. Now, you know some of the data points on this graph. We live at 1 atmosphere. That's our world: the one atmosphere isobar.

So, let's put P equals one. And, you know that at one atmosphere, pure water freezes at 0°C. So, that's the point along the solid liquid coexistence curve at 1 atmosphere applied pressure. And, furthermore, you know that at sea level where we have 1 atmosphere pressure, the liquid turns to vapor at 100° C.

So, when we go to Mount Everest, we are over here. See, we are at lower pressure. And if we are at lower pressure, we are at lower temperature. And then, if we are in the radiator, the cooling system of the car, we applied a higher pressure.

We trapped in a higher pressure, and thereby extended the temperature range over which the liquid is stable. See, at two atmospheres, the liquid is stable over a wider range of temperature. At one atmosphere, it's what we know zero to 100 Celsius.

And at lower pressures, it's stable over an even narrower temperature range. So, the boiling point, I'm showing you how it varies as a function of pressure. And, down here, we have, this is solid equals vapor coexistence curve.

Below a certain pressure, you can go directly from solid to vapor. If you hang your clothes out on a clothesline and it is -20°C, the first thing that happens is the water freezes. But, if you come back hours later, the clothes are dry.

What happened? Did somebody come in a truck, grab all the clothes, and take them down to the laundromat, put them in the dryer, and then come back and hang them on the clothesline? How did it happen? It went directly from solid to vapor.

This is sublimation. This is sublimation. Here, liquid goes to vapor is called evaporation. Vapor goes to liquid is condensation. These are the phase transformations. Solid goes to liquid: you know that's melting.

And liquid goes to solid, that is solidification. And I say that without prejudice. It could be to form the glassy solid or it could be to form the amorphous solid. And sublimation talks about both directions: vapor to solid or solid to vapor is sublimation.

So, this is a coexistence curve. So, along here, we can even put some labels. We can put over here single phase, over here, single phase, and over here single phase. And, along these coexistence curves, liquid equals vapor.

So, I have two phases along all the coexistence curves. Look at this point here. That's a curiosity, isn't it? What do I have here? According to this diagram, I have solid, liquid, and vapor in equilibrium.

This is ice cubes in boiling water: all three phases at this point here. And this point, first of all, as you can imagine, not to scale because some of the features are rather subtle. It wouldn't be seen if I drew this to scale.

This is at a very slight elevation in temperature. It's about one 100th of a degree above zero Celsius. And, the pressure here is about, oh, it's not about, I know what it is. It's about 4.58 millimeters.

How want to squeeze that in here. It's 4.58 mm of mercury. And, you need to know that 1 atmosphere, if you remember Torricelli and his vacuum tube, it's 76 cm, or 760 mm of mercury. So, that's the pressure.

It's 4.58 mm. And so, if you were to take water, pour it into a beaker, cover the beaker with some enclosure that allowed you to pump the temperature down, eventually you would reach, excuse me, pump the pressure down, eventually you'd reach the pressure at which water boils at room temperature.

Remember this number: 20-20, roughly 20°C, 20 mm of mercury, round numbers. It is not exactly that, but it's very close. So, if you get 20 mm of mercury, you will have boiling water at room temperature.

But if you get down to 0°C at just 100th of a degree higher, you have all three phases: ice cubes with water boiling in liquid. So, here we are with all of the different phases. And, this last thing I wanted to tell you, last thing is, you see this slope here? It's a negative slope.

And, it kind of puzzles me because when you look at it, normally you would think, you see, if you go at a constant temperature, let's say that we start at 0° and very, very low pressure. So, we have something that's a gas.

And then, we press atoms closer and closer together. And then it says you make a solid. And then, at the constant temperature, you press the solid atoms closer together. And it says you make a liquid again.

Doesn't that sound kind of backwards? Wouldn't you think that you start with gas atoms far apart? Then you move closer, you get liquid atoms, and you press the liquid atoms and you get a solid. But water is special.

Water is special because the bonding in the solid is more open than bonding in the liquid. And, I can look at this and say, because when I press from solid to liquid, this tells me that the density of the solid is lower than the density of the liquid.

I look at that and I say ice cubes float. And, there are other systems for which the same happens. Here's silicon. Look at silicon. Here's the phase diagram for silicon: pressure versus temperature.

You see down here it's FCC, the diamond cubic structure, and if we go, there is the melting point of silicon. We go to the liquid: it's got more nearest neighbors. How many nearest neighbors does the solid have? It's sp3 hybridized.

It has four nearest neighbors. Most liquids have about six nearest neighbors. So, when you have these open structures like silicon, germanium, the silicate glasses, and ice, you actually go to a more condensed system when you first liquefy And this is how you skate, by the way.

You know, you're down here at 1 atmosphere about -5°C and you put your weight on the blades. So that's a mass which then becomes a force on a small area which becomes a pressure. And then that allows you to cross this line.

So, you glide on a thin film of water. And if the temperature gets really cold, if it's down here at around -20, and I've had the pleasure of skating when it's -20, my mass converted to appropriate pressure on the blades is not high enough to cross this line.

And, the skating experience is very different because now it's just steel blades on ice. And, you don't get traction. To put it simply, you fall: not good, not good. OK, so let's look at a few others.

If you contrast here, this is aluminum, a simple FCC metal. And what do we see with aluminum? In this case, it's normal. Liquid has about six to eight nearest neighbors, and the solid has 12 nearest neighbors.

So, the solid is denser than the liquid, and you see that in the phase diagram. Here's nitrogen. Nitrogen is, let's see, what do we have? At 1 atmosphere pressure, its melting point is 63 Kelvin. Its boiling point is 77 Kelvin.

You can remember that because MIT is 77 Mass. Ave. So, nitrogen boils at 77 Kelvin. And, the triple point is down here. It's about a hundredth of a degree below, and it turns out it's about an eighth of an atmosphere pressure.

This is the triple point of nitrogen ice in boiling liquid nitrogen. But, this has a positive slope. So, this means that the solid nitrogen ice sinks to the bottom of the liquid nitrogen. And I thought, since it's Friday, maybe we could have just a little bit of fun here with the liquid nitrogen.

So, I'm going to get dressed. I have to practice safe science. I have to set an example for you. This year, one of my staff said why don't you wear a lab coat? So, I said, OK. I try to do this properly.

Which design house to go to for this? Valentino, Versace? So, what are we going to do? We're going to get some nitrogen. Let's get some nitrogen and have some fun. So, we're going to be working at 77 Kelvin.

And for those of you in the back, I'm going to put this up on the monitors. Oh, no food in the laboratory. Let's put that over there. OK, let's pour a little bit of this out. Fantastic. OK, so, first thing we'll do is let's look at the glass transition temperature.

So, I have some rubber gloves. So I have to face Craig over this way. OK Craig, I'm going to do it this way. So here's some rubber gloves. And so, you can hear that they are acting elastic. They are above their TG.

So, this is just the covalent bonds. And, what I'm going to do is pour a little bit of nitrogen in here. I don't know if you noticed, but these gloves are chiral, just in case you noticed. I chose chiral gloves.

OK, so now, so they are below the glass transition temperature. I'm sorry, Craig. Here, let me get that. We'll do it one more time. Glass transition temperature, also, if you wanted to drill the rubber stopper, of course, now, you can hear, so you can hear that it's rubbery.

I'm going to drop it in there, let it mind its own business. Oh, Saran wrap, it's also got glass transition temperature. So, we can show that, getting it into liquid nitrogen. OK, so you hear how it's flexible? So what we'll do is we'll put that in there.

OK, now you can hear how it changes. It's below the glass transition temperature. I should have been wearing gloves and all that, but forget it. How about protein? Oh, you know, the other thing we can do is I want to make some liquid oxygen.

So, I don't know, can we just cut to the computer slide for a second? I want to show people what we're going to do here with this next one. All right, so what I'm going to do is I'm going to put a graduated cylinder inside, fill this with liquid nitrogen.

And these are the boiling points of oxygen, argon, and nitrogen. And, nitrogen is at 77. So, this is all 77 Kelvin. But oxygen condenses at 90. So, we're going to make liquid oxygen with a little bit of argon ice.

I'm just going to let it sit there for the balance of the lecture. And maybe at the end, we will see some of the liquid oxygen. So, let's just pour that. OK, so we'll let that work. And, oh yeah, how about proteins? We said they were polymers.

So, let's see if we can do something with the proteins here. Oh yeah, we're going to put the roses in. They have glass flowers at Harvard at the Fogg Museum. We have glass flowers here at MIT. OK, so this is a rose.

It's very soft. OK, let's go. It's not a kitten. Come on. Maybe it only works on roses. Maybe we should do one more. Be a scientist. You don't know. Maybe it's just roses that do this. So, let's look at this one.

Glass transition temperature: there it is. OK, so we've got that going. We'll let the oxygen condense. And, let's see, let's go back to the computer. I think we're going to take a break and go back to some more learning here.

Yeah. OK, hang on, there's one other one here I think. All right, so we've seen this one. Here's nitrogen with all of its different solid phases. Nitrogen actually has different crystal structures.

And so, this diagram shows what's going on. As you change pressure at constant temperature, here we are still down around -70 Kelvin. So, there we go from liquid to solid. It's HCP, and then it becomes simple cubic, and then rhombic, and so on.

So, this property, that certain elements have multiple different crystal structures, is called polymorphism. So, these are called different polymorphs. You've already heard that iron has, in some instances, BCC crystal structure, and FCC crystal structure.

And, the phase diagrams will reveal when these transitions occur. Here's carbon dioxide: solid, liquid, gas. It's got a positive slope. What's interesting about carbon dioxide is, look here. The 1 atmosphere isobar takes you directly from solid to gas.

So, it doesn't go liquid. And, that gives it value as a refrigerant because when it gives up its enthalpy of transformation, you don't end up with a liquid which can mess up your contents. And so, this is often used in shipping certain materials.

So, we've got some here. Let's play it with some dry ice. There's a great big ice cube here, but there's some that's already broken off, see? So, actually, OK, so here we are. This is the big ice cube.

I guess Craig is going to want to see this. So, let's let Craig and the people watch the video. This is what I call an ice cube. OK, now, this is at -78°C. And so, it can go directly, you are seeing it sublime.

Let's see, we can do something. Just to prove, let's prove that it's going directly from solid to gas. So, I have just some plain spring water here, non-carbonated. This is flat. OK, so this is flat, put that on the edge there for Craig.

And then, just to show that we're going directly, I'll take this -- OK, see, I'll hold still, Craig. So, there we go. You see the bubbles coming off? Giant bubbles. So, we are making CO2 in water.

And, [LAUGHTER] [APPLAUSE]. This is good. I want you to notice something. You can buy this bottled water, and Craig I don't know if you can catch this, but you see, they have these tiny wimpy bubbles.

We have big bubbles. So, that's CO2. Let's see, what else have we got going? Let's see if we still have some liquid, we've made any liquid oxygen yet. Oh yeah, there's just a little bit. He won't be able to pick up on the camera.

OK, so now, the last thing I want to do is to go back to the computer image, if we could, please. OK, so we've got carbon dioxide. All right, here's a couple other phase diagrams. Zirconia, I mentioned to you the zirconia.

This is just pure zirconia, ZrO2. And, what do we find? Cubic is the form that gives you that faux diamond. But, look, it's stable only above about 2000°C. So, if you're going to give your sweetheart that faux diamond, that's going to be too hot.

It's too hot. So, what we're going to learn next day is how to open up this range of stability the way we opened up the range of liquid stability by adding ethylene glycol to water, and see if we can get cubic zirconia stable down to room temperature.

Right, but normally it's monoclinic. Then it goes to tetragonal. It goes cubic. It goes liquid, and so on. Then it even goes vapor. Here's carbon. At room temperature over a wide range of pressure is graphite: hexagonal close packed.

Then, at elevated pressure, it becomes diamond. And, here's liquid carbon. It turns out that by judicious choice of chemistry, people at General Electric about 30 years ago reasoned that steel consists of carbon in iron.

And, if we quench steel, we end up with carbon in the iron lattice. If we put too much carbon, the carbon will exolve as precipitates. Well, if we could exolve at elevated pressure, could we get the carbon to exolve not as graphite but diamond cubic? And they did it.

They generated artificial diamonds. And, one of the leaders of the team was a course three alum from MIT whom I met years later on a committee in Washington in connection with the aluminum industry.

And he told me, he was in the team that went to London to negotiate with De Beers, the big South African diamond concern. They were scared because General Electric reported that they could make artificial diamonds.

And, General Electric had reported that they could make large, artificial diamonds. Well, large, they were trying to make diamond dust. They actually had one that was about 1 millimeter. It was tiny, but De Beers was nervous.

And, the fellow's name was Rod [Hanneman?]. He told me the thing that scared him most was not sitting down with De Beers, because he had them bluffed. The hardest thing was getting through British customs because he had this on his person.

Now, if he opens up and they see all of this diamond material, remember, artificial diamonds don't exist yet. So, he's going to tell the customs agent, well, these are artificial diamonds. I don't think that's going to work.

So, there's always, what is it, the early bird gets the worm, but it's the second mouse gets the cheese. So, you can be too early sometimes with that stuff. OK, here's bismuth. Here's bismuth. Bismuth has a lot of phases.

Look at all the different phases of bismuth. And, look at here. What does this tell you about the solid bismuth? It will float in liquid bismuth. And then, if you go to high enough in pressure, it compresses.

Here's sulfur. The sulfur is really one confused element. Look at all the solid phases. Look at all the liquid phases. Sulfur is one mess. Look at: so, it has allotropes. Allotropes are different bonding forms.

For example, oxygen can exist as atomic oxygen, the molecular oxygen, O2, and O3, which is ozone. So, we say that O2 and O3 are both allotropes of oxygen. Well, sulfur has 16 allotropes. It exists as discrete, atoms, as the dimer, this hexamer; the common solid form is this eight member circular linkage.

And then, it polymerizes in the melt. So, here's the low temperature. Room temperature sulfur is rhombic. And, at elevated temperature, it goes monoclinic. It's a solid-solid phase transformation.

That's what you're seeing in that phase diagram when you look back here. That's what all this is. There's a monoclinic, and then the rhombic. All right, and then if you melt it, at first it gives the straw colored liquid, which they call lambda, at 119°.

And, around 160, this turns into, the rings start to open up and it turns an orange color at 160. And then, this is at some elevated temperature of about 200°C. They poured this long polymer sulfur goo into water, quenching it, and guess what you form? You form a glass.

It's plastic sulfur. So, all this is happening as a result of the different phases that are present. So, this is forming plastic sulfur. The last thing I want to tell you about is this last phase, supercritical fluid, which is a very high temperature, high-pressure phase where you can't tell a gas from a liquid.

You can think of it as a highly compressed gas, or a highly rarefied liquid. The bonds get far enough apart that the liquid is behaving a little bit differently. The solvation properties are those of a liquid.

But here's what happens in the supercritical fluid. You have transport properties of a gas. So, you have something that's liquid-like in terms of its ability to solvate things, but it has gas-like diffusivity, gas-like viscosity.

And, this is very, very much in the research agenda these days, using supercritical fluids to attack things like toxic waste and so on without having to resort to very aggressive solvents. There's no sense going after aggressive toxins when you have to use aggressive organic solvents.

But this will give you something of low polarity dissolving nonpolar things. And, here's one that you use more often that you know: decaffeinating coffee. Use a solvent extraction. When I was your age, they actually used this stuff called methylene chloride.

I subsequently used it in stripping paint. It's very vicious. You see, the trick in decaffeinating coffee is to get the caffeine out but not to brew the coffee. You want to selectively get the caffeine.

So, the use supercritical carbon dioxide. So, carbon dioxide leaches out the caffeine but doesn't touch the coffee. So, you get up into that temperature pressure regime, leach out the caffeine, and then you change temperature and pressure.

And now you have this pregnant liquor that is exceeding the solubility product. And, now you exolve the caffeine. And then, you reflux the CO2. And, that's how we go about with the coffee. The last thing I want to do before introduce, someone's going to tell you about some other activities that will happen during IAP is to tell you about, I guess this lesson is that there are no limits to the depths of human stupidity.

This will tie in denaturing of protein from last day. This is a news thing. Dick Kromminga, a principal at Silverton High School, said, this is in Silverton, OR. And I'm not making this up, said a pep rally stunt that burned four students won't ever be repeated.

The four suffered severe burns on their buttocks from sitting on blocks of dry ice. The girls were chosen by their classmates for a stunt to see who could sit on the ice the longest. The dry ice, or solid carbon dioxide, can be as cold as 112°F below zero.

The four were treated at Silverton Hospital. Dr. Frank Lord said some of the girls may need skin grafts. They have denatured the proteins. This is a quote: the truth is I've never seen any frostbite on this part of the anatomy.

Anyways, it goes on about how this was tied in with some football homecoming and somebody just didn't pay attention.

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