Lecture 34: Two-component Phase Diagrams

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What I want to do today is finish the second installment of phase diagrams. Last day, we looked at unary phase diagrams. That is to say, single component. That meant all we had to do was worry about pressure versus temperature because everything is of simple composition.

And I have up here on the display a phase diagram of water which we looked at last day. And I have redrawn it here for convenience. And I just wanted to draw your attention to several things. We are looking at how the stability of the different phases of water varies with pressure and temperature.

I have drawn the solid region over here, single phase, liquid region up here single phase, and vapor region over here single phase. And, at some point, we transit from solid to liquid. And it does not happen at a single point, it happens over a range of temperatures and pressures along this line which is called the coexistence curve.

Whenever you have two phases in equilibrium, they define a coexistence curve. And so here is the solid-liquid coexistence curve, liquid-vapor and solid-vapor. We saw that happens at R life, which is the one atmosphere isobar.

This equilibrium solid-liquid, that is ice-water at zero degrees C. And the normal boiling point, that is to say, one atmosphere applied pressure which is nominally sea level is 100 degrees C. And we saw how boiling point varies with applied pressure.

And that is defined along this coexistence curve. The other thing to note is that when the three coexistence curves intersect, we have this unique set of circumstances called the triple point where all three phases coexist.

And they coexist at only one point. That is to say, one temperature-pressure combination, which is very nearly identical to the solidification temperature. This is not to scale. This is slightly higher than zero degrees C.

It is about 1/100th of a degree above zero at a reduced pressure of 4.58 millimeters of mercury. And at this point here, the triple point, you, in fact, have ice cubes floating in boiling water. And there is the triple point.

And then the last thing was I talked about supercritical fluids at the end of last lecture. Just for completeness, in the case of water, water turns into a supercritical fluid at the elevated temperature of 374 degrees Celsius, 218 atmospheres.

Above this pressure-temperature pair, we have something that is simply fluid. It is neither a liquid nor a vapor. You could argue that it is a highly condensed vapor or highly rarefied liquid, but it has the properties of a supercritical fluid.

What I want to do today is to now look at multi-component systems. And we want to start with two component systems. We are not going to be talking about pure materials. C will equal two, so that means now we have to think about temperature, pressure and composition, because composition is a variable between the two components.

And that gets to be messy because we already had a pressure-temperature diagram for let's say component A. This is component A. And, over here, I have the pressure temperature variation of component B.

And here I have drawn the solid liquid coexistence curve as it normally is found in most materials, which is to say positive because solids are generally denser than the liquids. Water is one of the exceptions.

Now the question is how do various properties change with composition? If I ask what is going on in between here so I can join these two -- I am going to need a three-dimensional plot; pressure, temperature, composition.

I have an infinity of unary phase diagrams all across here from pure A all the way over to pure B with all of the different composition ratios in between. For example, here is the melting point of A and here is the melting point of B.

I might ask how does the melting point vary with composition. Is that a case of just connect the dots? If I know the melting points of the two end members, say copper and nickel. And I want to know what the melting point of a 50/50 copper-nickel alloy.

Is it just the halfway temperature between the two, or does the temperature go through a local maximum, or does it go through a local minimum or does the temperature go nuts? I mean, the question is how does temperature of some critical feature vary with composition? We need to look at three-dimensional stability maps.

And this is a pain in the neck because it is 3D and it is messy. But, fortunately, this is 3.091. And 3.091 is concerned about solid-state chemistry. In 3.091, we care more about liquid-solid equilibrium instead of liquid-vapor equilibrium because we do not process too many materials in the vapor state, we don't use too many materials as vapors.

This is the equilibrium that is most important. We know that equilibria depend upon temperature, pressure and composition. And it turns out that when it comes to the liquid-solid equilibrium, liquid-solid equilibrium is strongly dependent, there is a strong dependence between the temperature of transformation and composition.

Whereas, the relationship between the temperature of the transformation and pressure is weakly dependent. There is a weak dependence between pressure and the temperature of the transformation. And we saw that last day.

These are not to scale. In other words, these lines are nearly vertical for solid liquid. You would have to apply geological pressures to alter the melting point of water substantially. Whereas, we saw it doesn't take anything more than just a rise in elevation of several thousand feet to move the boiling point along.

That means I can throw away the pressure dependence and just focus on the two-dimensional relationship between the temperature of a transformation and the composition. So that is what we are going to do.

We are going to look at three different types of binary systems. And, in each case, we are going to assume that the pressure is one atmosphere. And we know that the dependence of the transformation temperatures that we write is going to be negligible in terms of the impact that pressure might have on them.

We are going to look at three different types of systems, and they are all dependent upon the extent of solubility. Oh, what is the word? I have given them the very "catchy" distinctions of type one, type two and type three.

Let's look at the type one type of binary system. And type one binary system has complete solubility. By this I mean complete solubility of the two components. Complete solubility in solid and liquid states.

That is to say, if I mix A and B, they will mix in all proportions as solids and will mix in all proportions as liquids. And the second thing is we are looking at change of state. This diagram applies to a change of state.

And since we are talking about solid-liquid that is the only one we need to document. Let's think about what the relevant chemistry here is. I mean, I have been telling you that phase diagrams are stability maps and you can just look at them and consult them.

But there are always some basic chemistry embedded in these diagrams. For example, if it were a metal system and I were to tell you that these two metals, A and B, mix in all proportions as solids and liquids, what would have to be the characteristics of those two metals? They would have to be either very nearly similar or maximally different.

They would have to be very nearly similar. And, in fact, it is sort of a takeoff on like dissolves like. Complete solubility in a liquid state with respect to metals, when it comes to metals there is a set of rules called the Hume-Rothery Rules.

Hume-Rothery was a British metallurgist, and he annunciated a set of rules for identifying candidate systems that will have this type of phase diagram. And they are very simple. Anybody in 3.091 would have come up with these rules if you had thought about it before Hume-Rothery.

But he beat you to it so you cannot get the glory anymore. But let's think about it. What would have to be the situation? If the two metals, A and B, are going to mix in all proportions then they must be very similar.

They must have similar crystal structures. That way you get simple substitutional solid solutions. And, furthermore, if they are going to substitute solid for solid, they should have similar atomic dimensions.

It does no good to have two FCC metals mixing where one has an atomic radius that is so large it has to force fit into the lattice of the other. Similar atomic volumes. And, lastly, bring in some chemistry.

We want them to mix and not chemically react, so they should have a small value in electronegativity difference. If they are both the same size, they are both crystal structure but have a high electronegativity difference, they are going to engage in electron transfer.

That is no good. But I think this set of Hume-Rothery Rules is nice to reflect upon, in light of everything else we have learned in 3.091, because the phase diagrams, as I said earlier, have embedded in them a lot of basic chemistry which goes back to electronic structure of the constituents.

Let's draw a schematic of an AB diagram for one such system that I call type one. I am plotting A versus B. This is temperature on the vertical axis. Horizontal axis is composition. On the left side, I have pure A.

The right side, I have pure B. And I am looking at solid-liquid equilibrium. At this extreme, pure A, this end member must be the melting point of pure A. And the other extreme is pure B. This is the melting point of pure B.

And I have drawn it just arbitrarily where the melting point of B happens to be higher than the melting point of A, but it does not matter. One has to be larger than the other. This is going to answer the question how does melting point vary as a function of composition? It varies like this.

It is not a straight line for two reasons. The first one being that when you take thermodynamics, subsequently, if you choose to do so, you will understand the physical chemistry behind what I am going to tell you.

Let me just state it without proof that if C is greater than one, in other words, if you are not in a pure material, if you are in a multi-component system, if C is greater than one, it is impossible to go from phase 1 to phase 2.

You cannot go from phase 1 to phase 2 without a two phase region in between. We cannot go from all liquid to all solid. Remember, we said these mix in all proportions down here. Solids, you can mix any mix, any ratio of A and B as solids, any mix of A and B as liquids.

But, because we must go through a two phase regime, this opens up to give a two phase regime. Up here this is all liquid. Down here this is all solid. And in between is a two phase regime of liquid and solid.

We can call it slush. We have seen slush before. We have seen ice slush in water. The two phase equilibrium for a pure material. This is now liquid plus solid in a multi-component system. Up here we have single phase liquid because they are mixing in all proportions, so this is a solution.

Down here, these are solid solutions. And in here we have a two phase regime, a liquid phase homogenous, a solid phase homogenous. And these lines are now no longer called the melting line or the freezing line.

We have two different lines. The upper line defines the lowest temperature for any composition. Pick any composition you want. This temperature is the lowest composition at which you have only liquid present.

Change the composition and that temperature changes. But, below this temperature, you start to see the emergence of solids. This line here is called the liquidus. Liquidus is the line associated with this reaction.

Single phase liquid goes to liquid plus solid. And the lower line is called solidus, and it represents the complimentary set. The solidus is the highest temperature at any composition for which you have only solid present.

If you see the line that I have drawn, the solidus temperature is the highest temperature for which we have solid solution present. If we raise the temperature anymore, we go in a two phase regime, some liquid starts to emerge.

The solidus represents the highest temperature for all solid, and it represents solid goes to liquid plus solid, homogeneous solid. Let's write it again. This is the lowest temperature for only liquid.

And this is at any C, at any value of composition. And a solidus is the highest temperature for only solid to be present at any composition. And this only applies once you move off of purity. In here this is showing you how things vary as a function of composition.

And such a diagram that has such similarities because the end members must have common bonding, common size and so on, this type of a diagram is called isomorphous. This is an isomorphous diagram. And the shape looks like a lens.

It is a lens-shaped diagram. But if you want to get fancy, we don't say lens-shaped. We say lenticular from the Latin. Lens is lent, degenerative is lentis, so lenticular. It is a lenticular diagram.

Now we have it. Let's look at some example systems that exhibit this kind of behavior. Before we do that, I meant to show you this. We talked about what happens at ultra high pressures. This is water.

We are down in here. This is now kilobars, thousands of atmospheres. This is the normal line that you see. That is this line that I have shown you. That is here. There is ice at a density of about 0.92.

And normal water is about one, so ice floats on water. But, if you keep pressing, eventually you will force that crystal structure to change and it will become more closely packed. And now you see normal behavior.

Liquid goes to solid. And all of these different Roman numerals represent different crystal structures. Ice has at least nine different crystal structures, and some of these are really interesting.

Look at this one. These are all triple points. This is ice III, ice I and liquid. In a single component system, that is a triple point. That is uniquely defined. Now, looks what happens over here.

This is a triple point between ice VI, ice VII and liquid. And it is at about 80 degrees C, way up there. Now look at this one. This is ice VII. I am in a single phase regime. It is 100 degrees C.

I have to go to 25 kilobar, but we have laboratories. It is 100 degrees C. And it is not vapor. Remember, water boils. Normal boiling point is 100 degrees C. But, if I apply 25 kilobars, I go not only through liquid, I go right across the solid.

You saw I brought the dry ice into the classroom. By the way, I was here yesterday and half of the block was still sitting there because I left it in the box and it had this little comfort zone of CO2 vapor around it.

It was just naturally thinning in. It took a long time. What is my point? My point is when you make such a metastable state and bring it into some unnatural conditions, it will last for a long, long time.

The kinetics are quite slow. Let's say we go into the lab. We make ice VII. It is 100 degrees C, it is 25 kilobar, and there is a party going on down the hall. We come out and we have some ice seven.

It is going to start to want to melt because the temperature is going to fall. You are going to move this way and down. But some of it is going to be left. Now you go up to somebody, you take some ice seven, you drop it in the drink and the drink heats up and starts to boil.

And the ice sinks to the bottom of the glass. That might get someone to rethink their drinking habits. This is the power of changing pressure and temperature. By the way, those of you who know "Cat's Cradle" by Kurt Vonnegut, there is ice IX.

It exists. It has been characterized. Somebody actually measured this stuff, and we are still here. We didn't freeze the whole world, so you can relax. He needs to rename that maybe ice 11 or something.

I don't know if there are any more phases here. Here is a phase diagram copper-nickel. That is a lenticular diagram. Copper and nickel both FCC metals, very similar in atomic dimension, very small electronegativity difference.

You have a lens-shaped diagram. Copper melts at 1085 centigrade, nickel melts at 1455, and there is the liquidus and the solidus. And in between, if you cool it at any one of these concentrations, you are going to go through this two phase regime.

And we are going to talk a little bit more about that in a second. Here is a ceramic system. Here is nickel oxide, magnesium oxide. This is an ionic solid. It is nickel cations, magnesium cations and oxide anions.

And the nickel and magnesium are roughly similar in size, modest electronegativity difference. And so this one starts at 2000 centigrade, goes up to 2800 centigrade and has a lens-shaped diagram. Here is one.

This is gold nickel. It is almost lenticular. Look at the top part here. The nickel melting point is up around 1450. Gold melts at 1063. It is almost perfectly lenticular with this little bit of a dip here, sort of the liquid-solid analogy to an azeotrope.

Again, you see they are both FCC metals. But, in this case, the electronegativity difference is a little bit larger than you would like. And so you see a little bit of a freezing point depression here.

Now I want to go back and talk about what is going on inside that two phase regime, because that two phase regime is peculiar. Let's see what happens if we take something of a particular composition and cool it.

Here is what I am doing. I am going to blow this up. And, what I want to do is take something that is about 40%. Here is where we are. We are looking at the liquidus here. Liquidus line. And here is the solidus line.

This is all solid. This is single phase, P equals one, this is all liquid single phase, and this is liquid plus solid. And let's say we drop the temperature down into the middle of this two phase regime.

What is happening here, this is a two phase system, and we have a liquid and a solid. And the phase diagram tells us the composition. Here is the sequence. Let's look at, say, composition C2 there.

Composition C2 is about 40% nickel in copper. At 1300 degrees C, we have homogeneous liquid. And, if we go down to 1200 degrees C, we have a homogeneous solid. These are the different grains. This is liquid, this is solid, and it is polycrystalline.

And the composition of each of these grains is the same. What is happening at 1250? This diagram says I should have solid and liquid, but, look, the composition of that liquid is not 40% nickel in copper.

The composition is way over here. It is about 32%. And the composition of the solid is up here at about 45%. This is 32% nickel and this is 45% nickel. I have a nickel rich solid and I have a copper rich liquid.

There is a shift. Suppose I take something of a different composition. This is the C2 that is on the diagram. Here is C1. I think it starts at around 35% nickel. This started at 40% nickel. C1 is 35% nickel.

I cool it down to the same temperature. It is the same end members. The liquid at this temperature has a unique value of nickel content. It does not matter what the composition is, I will always end up with a liquid of one composition and a solid of the other composition.

Well, how can I start with two different? This is 40% and this is 35% nickel. These end members are the same. There is only one variable left. It is the relative amounts of these because I need conservation of mass.

Because, at the end of the day, if I add up all of the nickel in the liquid and all the nickel in the solid, it still has to be net 40% nickel. Only in here it is 45% nickel. Up here it is 32% nickel.

I have a Vernier scale. I have a sliding scale that I can move so that if I have something that is 35%, in other words, it needs less of this phase, so the 35% is going to end up doing this. Whereas, the 40% is going to end up doing this.

It is the relative amounts. This line that tells me what the concentration of the solid and the liquid at any temperature is called the "tie line." The tie line defines the composition end members, the liquid and the solid in that two phase regime.

And we can take all of this that I have been talking about and we can codify it in terms of a simple rule that captures the notion of phase separation and conservation of mass. And that is called the "lever rule."

The lever rule answers the question, how much of each phase is present? The relative amount present of each phase in the two phase region. For example, here we are with the 40% nickel. It is 40% nickel in copper.

We have dropped down into the two phase regime, draw the tie line. And the tie line tells us that the liquid will proportionate as follows. This is 40% nickel at all liquid. Now we drop the temperature.

This is 1300. Now we drop down to 1250. And we know, according to the phase diagram, we are going to end up with a liquid and a solid. And, furthermore, the tie line tells us that the solid is going to be 45% nickel and the liquid is going to be 32% nickel.

The question is what are the relative values? It is shown right up there on the transparency that the percent of the liquid is equal to, in this case, the end member 45 minus the individual amount at the concentration of the bulk divided by the end members of the tie line.

And we will multiply that by 100%. And that gives us a value of 38% present as liquid. And why is it called the lever rule? Because, if you look at the tie line, here is where we are. We are at this value which is shown in the phase diagram as z.

This is our 40%. And the amount of the liquid is x and the amount of the solid is y. And so, when I am asking how much liquid is present, I choose the amount opposite, as you do on a seesaw or teeter-totter.

In other words, to calculate what the force is here, you take the amount between the fulcrum and the opposite side divided by the total length. This is yz over xy. It gives us liquid. And then the compliment gives us the amount for solid.

You see that worked out for you on the transparency. And this works for any two phase regime. Whenever something drops into a two phase regime, disproportionation has to occur, and the lever rule will give you the relative amounts.

The tie line tells you the composition and the lever rule tells you the relative amounts. Two things. I want this to be like you are that Manchurian candidate. This is your cue. From now on, if you hear two phase, you just go lever rule.

What are the end members? Tie line, lever rule whenever you see two phase regime. And it will keep you out of trouble. I mean, many times I get into trouble. I just think of the lever rule and I am out of trouble.

Now let's look at a second case. Second case is type two phase diagram in contrast to complete solubility. Type two phase diagram is characterized by a system that has partial or limited solubility.

When you try to mix A and B, they do not mix in all proportions. They only mix up to a certain point. That is like a solubility limit or a miscibility. Miscibility and solubility are synonymous. This leads to a miscibility gap.

A range of composition over which you cannot mix the two of them and form a homogeneous solution. And, in this case, there is no change of state. That is either always liquid or always solid. Let's look at the phase diagram for one of these type of systems.

A. B. I am plotting composition across the abscissa. The ordinate is temperature. And this gives us a synclinal phase diagram. Above we have single phase. This is single phase and this is dual phase.

For example, this could be all liquid. And then in here we have two liquids. Or, it could be all solid. And inside here we have two solids. When it comes to solid solutions people use Greek letters and call this alpha and beta.

This is the coexistence curve or the solubility limit. What is the coexistence curve? The coexistence curve is liquid is in equilibrium with liquid one and liquid two. In other words, if you drop into this two phase regime, what happens as soon as you hear two phase? Tie line, lever rule.

The tie line will give you the concentrations at the end, or solid goes to alpha plus beta. Both of these are solid solutions. Let's take a look at some of these. This is gold nickel. At low temperatures look what happens.

Gold nickel will actually phase separate. If you take something like this one here, which is 50 weight percent nickel, at high temperatures they mix in all proportions. Drop into here, we have a slush consisting of liquid and solid.

And they have different compositions given by the tie line. Drop even lower in temperature and all of a sudden it is a single phase solid solution, FCC lattice with gold and nickel atoms 50/50. Well, in this case it is weight percent so it is not exactly on an atomic basis.

There it is about 75. And then we drop into lower temperatures, and now they phase separate. We end up, for example, at 600 degrees. Let's get down to, say, room temperature. This is 300 degrees C, but the lines are starting to get fairly steep.

What you find is that it will phase separate so that you will end up with zones that are nickel rich and zones that are gold rich. And the tie line tells you the compositions of both of those end members.

Here is one, hexane-nitrobenzene. At high temperatures they mix in all proportions. You drop the temperature and then they phase separate, just as oil and water. Down at this temperature, you will have a hexane rich phase and a nitrobenzene rich phase.

And, the lower and lower you get in temperature, the greater that separation. Think about it at this constant temperature. What this is saying is that you can put a certain amount of nitrobenzene into hexane, and that is the solubility limit.

If you try to put any more nitrobenzene into hexane, it won't go in. On the other side, it says you can put a small amount of hexane in nitrobenzene. If you try to put any more, it won't go in. It will just precipitate out.

This makes sense to you, doesn't it? Furthermore, at this temperature, I can put, say, 0.1 units of nitrobenzene. If I raise the temperature, the solubility goes up with temperature. All of this is making sense.

Finally, you get to a temperature here above which they mix in all proportions. This temperature is called the "consolute" temperature. Above the consolute temperature, even a system that has a propensity for limited solubility will mix in all proportions.

You see this in different systems. This one is a surprise. This is two alkali halides, sodium chloride and potassium chloride. You would expect those to just trade off with one another, but there is a problem here.

The sodium ion and the potassium ion are different enough in atomic dimension, different enough in charge density that, as you get to low temperatures, they phase separate. Instead of making a perfect solid solution at lower temperatures, the single phase solid solution breaks into a potassium rich solid solution and a sodium rich solid solution.

Here is from the polymer world. This one is polystyrene, polybutadiene. At high temperatures, you can mix them and make a copolymer, a copolymer mix in all proportions. As you drop the temperature, they will phase separate.

And you will end up with something that has islands of a polystyrene rich phase. Not pure polystyrene. There is a certain amount of polybutadiene in it. And then the other phase will be polybutadiene with a certain amount of polystyrene.

They phase separate. Here is one. Certain systems, instead of exhibiting a consolute temperature in this fashion, for entropic reasons the system is flipped upside down. This is a lower critical temperature.

This is weird because normally you think as you raise temperature you increase solubility. This is one case where it goes the inverse. Water triethylamine mixes in all proportions at low temperature.

At higher temperatures there is the -- Instead of being synclinal, this is anticlinal. It is a U shaped curve. Single phase out here. Down here they mix in all proportions. Up here you can put a certain amount of triethylamine in and then it stops.

Then you get the second phase. Here is the weirdest one of all. This is nicotine and water. It has an upper critical point and a lower critical point. At low temperatures, you can mix nicotine and water in all proportions.

And, at very high temperatures, you can mix nicotine and water in all proportions. And at intermediate temperatures they phase separate. There is the map that tells you how the system behaves as a function of temperature and composition.

In here you cannot get a homogeneous solution. If you try to make a 50/50 mix of water and nicotine and you heat that to 100 degrees C, it will phase separate. Even though you will mix it at room temperature, and it will be homogeneous, as you raise the temperature all of a sudden you will see milkiness, globs of one forming in the other.

What would happen if we were to take 60% sodium chloride and cool it down to, say, 400 degrees C? What happens? Bingo. Tie line. P equals two, so the homogenous solid solution breaks into an alpha, which is the designation for the potassium chloride rich solid solution, and beta, which is the designation for the sodium chloride rich solid solution.

And how do we figure out the relative amounts of alpha and beta? Lever rule. It is a two phase regime. Lever rule. That is it. Now I will do a little experiment here to show you how this works. I want to work with a simple system.

This is ouzo and water. Ouzo is a drink, a liqueur from the absinthe family. And wormwood is the chief flavoring agent. It contains licorice, hyssop, fennel, angelica root, aniseed. The thing is it has a lot of oil in it.

It is very oily. It is clear and colorless but very oily. And then water, of course. You know what water is. Let's have a look. Can we cut to the document camera here? What I am going to do is -- Here is water and here is ouzo.

These are at room temperature. I am assuming the phase diagram looks like this. I can put a little bit of ouzo into water, and I can put a little bit of water into ouzo, but if I exceed these solubility limits, in here this is milky because it is two phase.

This is milky and this is clear. Why? Because this is single phase and this is P equals two. We are going to do an experiment here. What I am going to do is put, this is just pure water, and you know what pure water looks like, distilled water.

And here is some ouzo. And this is clear and colorless as well. Now what I am going to do is pour water into the ouzo. If I pour a little bit in, I can stir this, and it will dissolve. What I am doing here is pouring water into ouzo and I am coming across.

If I pour too much water in, I am going to hit this miscibility gap, and this will precipitate out. And when it precipitates out, it has a different index, it is going to look milky. In fact, I think I have already hit there.

Look at this. I have crossed the miscibility gap. Now, if my hunch is correct, I should be able to keep adding water and eventually emerge on this side. Let's see what happens. We will dilute it.

I am going to pour this down to almost a tiny fraction. And I will pour in more. I have crossed the miscibility gap. I can do it the other way. Let's start with water. We can go across or we can do the other.

It doesn't matter. Now, what is the difference between this and absinthe? Absinthe is similar, but it has a little more color to it. Absinthe is green. And so, when you add water to absinthe, you are supposed to add it five parts water and one part absinthe.

We are going to make the louche which is the milky. This is the way absinthe would be drunk. You can see how milky this is. Now, when Toulouse-Lautrec drank, he made a drink called the "Earthquake."

What he did with the earthquake is he added cognac to the absinthe louche. What are we going to do here? What is the chemistry? The chemistry is the following. I have oil droplets here in water.

Oil. And then over here is water. What I am going to do is put ethyl alcohol, CH3CH2OH. And what does the OH do? The OH makes a hydrogen bond. I have a hydrophilic head. Ethyl alcohol is amphipathic.

And this is a hydrophobic tail. The hydrophobic tail can stab the oily phase of the louche. This is what you do in cooking. How many recipes will ask you to add a little bit of alcohol? And they will subsequently ask you to heat it.

And you say, well, wait a minute, alcohol is going to evaporate. What is going on? Whenever they are asking for alcohol, chances are you are adding something fatty to an aqueous solution and it does not want to mix.

As soon as you add the alcohol it cosolvates. Alcohol is magical for this amphipathic character. Let's make the Earthquake. The Earthquake is like this. We are going to add a little bit of this. It is a beautiful green-gold color, but it is clear because what has happened now, I have put in a third component.

Now I have got water, ouzo, alcohol. And as I add alcohol, I narrow the miscibility gap. The miscibility gap narrows as a result of that. It is fantastic. May we go back to the computer graphic, please? This is where we were.

We were along this tie line. And I figured the louche is here. It is five parts water, one part absinthe. And then away we go. This is the late 1800s. Why did absinthe take over in France? Because there was a blight that wiped out the vineyards.

And so the price of wine shot up and people started turning to absinthe. You hear he is making the louche. He is pouring water through a slotted spoon on which there is a sugar cube. And here is a woman looking at him saying, wow, is he ever cool, what a guy.

Hey, it's the 1800s. This is an object of art. This is Van Gogh. This is Picasso. This is the absinthe drinker. This is Picasso after he, I guess, had a lot of absinthe. The only thing I can recognize here is the slotted spoon with what appears to be a rather large sugar cube.

And this is somebody's mind after huge quantities of it. The thing about it is it had thujone in it, which comes from the white cedar. And what this does is it antagonized the receptors that regulate neuron firing.

We can think much faster, but we kind of slow ourselves down. It is the gamma-aminobutyric acid that helps us stay in place. Actually, epileptics suffer from a lack of regulation. And that is a motor regulation, but in the case of mental acuity.

This is one of these cases where the alcohol tracks with the thujone. And so instead of making you drunk and stupid, it makes you drunk and very, very highly active. But unfortunately large quantities of it also had other neurological disorders.

If you have seen Moulin Rouge, you will see here, it is all about absinthe in that period. What happened was this absinthe took over. I mean, people drank huge quantities of this in place of wine. Eventually, the wine was restored.

The vineyards in France were restored by grafting onto American stocks. There are very few wines in France that are not produced as hybrids on American stock. Occasionally, you will see a bottle of wine that says vieux vin, old vine, meaning that it was spared from the Phylloxera blight.

By and large, it is not American vine. French wines are grown on American roots, just remember that. Now the wine cooperatives wanted to get people to switch back to wine, so there was this strange alliance between the wine cooperatives and the temperance movement to get people to stop drinking absinthe.

And so what happened was there were a number of murder trials in which somehow it was portrayed that absinthe figured prominently. And so, little by little governments banned it. This is October 7, 1910 where absinthe is being banned in Switzerland.

Here it says, Gentlemen, this is the hour. And this is the symbol of absinthe. Absinthe was known affectionately as the "green fairy." That is why in Moulin Rouge you will see this sort of Tinkerbell type figure, Nicole Kidman playing this Tinkerbell figure in an animation.

Well, she is the green fairy. And she has a wand made of opal because the beverage is opalescent. When it shimmers, you have gradients in index of refraction to give you that internal incipient surface.

Here is the green fairy slain by the temperance movement and so on. The last thing I wanted to comment on is how we use the two phase regime in purification. Much of what we know about purification requires that we go into a two-phase regime.

Because the thing that happens in a two phase regime is two phase region implies compositional differentiation. For example, here is the phase diagram. For one time, I am going to go to liquid vapor.

This is the liquid vapor phase diagram of ethyl alcohol and water. We know that water boils at 100 degrees C. This is normal boiling point. And ethyl alcohol boils at 78.5 degrees C. And they are both polar liquids.

Ethyl alcohol is a little bit more elongated than water. It is very nearly an isomorphous phase diagram. There is a tiny little dip but, by and large, it is an isomorphous phase diagram. Alcohol and water, miscible in all proportions in the vapor, obviously.

And this is the liquid. This is the two phase liquid plus vapor regime. Let's say you have some wine and it is 10% alcohol. What do you do? You heat the wine up to this two phase regime. And now, in the two phase regime, tie line.

What do you note? You note that the alcohol content of the vapor is much higher than the alcohol content of the liquid. What we can do is condense the vapor, which puts us down here, and now reheat.

Condense. Reheat. Condense. And, by doing so, we can raise the alcohol content. Or, in some cases, this could be the way you purify for the liquid. It doesn't matter. You either want the condensate or you want what was the base from which you took the condensate.

And this is used over and over again. It is used in the solid-state to purify metals. Look up here on the slide. Suppose I have a solution that consists of, over here of, say, 60% nickel. It is all liquid.

Drop it down into this two phase regime. The solid that comes out has very much less gold in it. That means that the liquid behind, the last liquid to solidify is going to have more gold in it than the bulk that I started with.

I can keep taking that fraction by moving into a regime where the composition splits. And I either want the high fraction or the low fraction. This is the principle by which, in fact, the computer-grade silicon is made.

We start with beach sand. We upgrade to something that has to be about four or five nines silicon for single crystal growth. How do we go from something that is about 98% silicon, 2% impurities to such a high degree of purification? By dropping repeatedly into the two phase regime and pulling out the pure fraction.

The key here is compositional differentiation, which then allows you to distill. You start with 10%, you end up 40%, you go from wine and end up with brandy or cognac. There it is. It is all back to chemistry, chemistry, chemistry.

OK. We will see you on Wednesday.

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