Lecture 35: Wrap-up

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You think you're happy? I'm happy. I'm very happy. What we will do, today is wrap up phase diagrams, make some comments about the final exam, and then we're going to get some people that aren't associated with class are going to come in, they will pass out paperwork and do the course evaluations.

And, we'll get you out of here at 11:55. Before I go any further, draw your attention to another IAP subject. If you're looking for something to do during January, and this will be offered by myself and my postdoc, Patrick Trapa.

We are going to offer a lab subject without a lab. It's part of an experiment that we are conducting for the National Science Foundation to see if large classes such as these that don't have a lab experience can get much of the lab experience, that is to say, planning for discovery, preparation of the background information, and then mining the data from data sets that are in the public domain, and then analyzing the data and then presenting the data.

All of that you get without turning the knobs. And, that's about three quarters of a lab experience. So, I think three quarters is better than none. That's what we want to try to do. It's a limited enrollment of 20 people, and it's going to run for two weeks during IAP in the mornings, and you can go to the IAP website.

And, it's worth six credits as well. So, OK, enough said about that. My office hours, I'll have a little bit of extended office hours Friday 4:00-6:00, next Tuesday 4:00-6:00. And, there will be a question and answer session on the evening of Tuesday, the 14th of December.

Professor Ballinger is going to run that in 54-100. All of these, and I know the TAs, some of them are going to run review sessions. All of these are optional. They have strict instructions not to teach new material.

If you don't want to go to those, you don't have to. If you want to, bring your questions, and I just want to make it totally value neutral. OK, last day we talked about phase diagrams. I want to continue the discussion today.

We looked at type one, which involves very nearly similar materials. So, that gives a lenticular phase diagram shown here. And, then we looked at type two where we have a phase separation without change of phase, giving us a miscibility gap.

Remember, whenever you're in a two-phase regime, two-phase regime, queen of diamonds, bingo, that means tie line, lever rule. So, phase separation will give us a single phase, whether it's a homogeneous solid solution breaking into two phases, or a homogeneous liquid solution breaking into two phases.

Those two phases have different compositions, and the compositions of each of those two phases is given by the end members of the tie line. And the relative amounts of the two phases is given by the lever rule.

Today I want to look at type three. And type three is characterized by sort of a mix of the two. And on the left, we have change of state, and on the right, we have no change of state. On the left, we have perfect solubility.

On the right we have partial solubility. So, we're going to take the solubility characteristics of type two, and the change of state from type one, and put them together. And that's what we end up with as the overarching features here.

And, this is what the phase diagram looks like, where we have something that's similar to, you see the bottom here? The bottom here looks like that syncline. And the top here looks like the beginning of the lens.

So, we have liquid, and then beta here. Beta is a solid solution, alpha is a solid solution. So, let's designate those. Alpha is a solid solution of A and B, only it's A rich. It's very near pure A, but it's not exactly pure A.

So, this is homogeneous solid solution just as you'd have in a lenticular diagram. And, beta is a solid solution of A and B, only it's B rich. And L, that's a liquid solution. That's a liquid solution of A and B.

So, these are all single phase. These are all single phase. Let's put that up here. This is P equals one, single phase. This is P equals one, single phase. And, this is P equals one, single phase.

Now, if I want to go from one single phase to another single phase, I have to go through a two-phase regime. So, this is slush, liquid plus solid alpha. This is slush, liquid plus solid beta, and now I have a solid solution on the right.

I have a solid solution on the left, and I can't go from one single phase regime to another single phase regime. I had to go through a two-phase regime. So, this is alpha plus beta. And, now I've got two phases down here, one phase here.

Look at this point here that I've indicated in purple. What is this? This is a special. This is alpha, beta, and liquid in equilibrium. And, this is called the eutectic. It's the equilibrium between solid alpha, solid beta, and liquid.

And, this type of diagram is called a eutectic diagram. It's a eutectic diagram, and it has some remarkable properties that make it advantageous in processing. Look at here in the type one diagram.

There's no point on the type one diagram where we see all liquid below the melting point of the lower of the two components. We essentially have a lens extending from the lower melting point to the higher melting point.

If you look here, if I add A to B, the melting point drops. We go down this liquidus. That's not surprising. What's surprising in the case of the eutectic is when you add B to A, the melting point drops.

So, we get freezing point depression from both ends with the result that, you see this whole liquid zone in here? This whole liquid zone has liquid lying at temperatures below the lower melting point.

So, this gives us a much, much greater range in which to process. So, we have a depressed liquid region. So, let's call this the characteristic is freezing point depression of both components, of both A and B, which is something we didn't see in the case of the lenticular.

And this eutectic point is the equilibrium of alpha, beta, and liquid. And, it's unique. It exists at only one value of temperature and composition. So, that's unique to every particular system. So, let's look at some examples.

So, here's one apropos of the coming winter. This is water and ethylene glycol. And, we talked about water ethylene glycol in the coolant system with reference to controlling boil over. And, as the winter is coming, we want to avoid freezing of water in the channels of the engine block because the water is going to freeze from the outside in.

That means the last water to freeze will already be plugged by ice at the ends. And, as you know, when water freezes, it expands. How do you know? You know for the negative slope on the PT diagram.

And, that expansion is so energy-laden that it'll crack the iron of the engine block. So, you have to keep the water from freezing. So, what we can do is we can add a second component and give ourselves a eutectic type system.

So, here's pure water on the left. Here's pure ethylene glycol on the right. It's a double alcohol. There is the chemical formula for it. And so, pure water, which we see the melting point of pure water is 0°C.

And, what this is showing is that this alpha region of ethylene glycol, and water is so narrow that for all intents and purposes this appears as a straight line. That's why you go automatically from seemingly pure water to this eutectic regime.

So, if we add, typically, about 50 volume percent ethylene glycol, that's the recommended mixture, what do we see? We see we get freezing point depression down to about -35 or so Celsius which ought to take care of most driving needs.

Now, if you want, you can get maximum freezing point protection by adding about two thirds. In other words, 68 volume percent glycol gives you a eutectic at -69°C, or -92°F. That ought to take care of everybody in this room.

I don't know anybody here that's driving when it's more than -92°F. So that should be OK. But, if you want to be an enthusiast and decide I'm not a cheapskate; I'm going to use pure ethylene glycol.

Why dilute it with water? Well, pure ethylene glycol freezes at about, here it is. This is the Fahrenheit scale here. We are talking about cars after all. So, it freezes at, what is it, about 10°F, all right? And then, adding water to glycol gives you the freezing point depression here.

So, actually if you go beyond two thirds glycol, one third water, the freezing point is actually rising. So, that's not such a smart idea. The second thing is, here are the chemical properties of some of these.

And, you see here is glycol -13° Celsius is the freezing point. But, look at here. The viscosity of water is roughly one in units of centipoise. And, the viscosity of ethylene glycol at 20°C is 21.

It's 21 times the viscosity of water. And, you know the viscosity is a transport property much like diffusion. And so, it has an Arrhenius temperature dependence. So, if we get the temperature down to, say, -10°C this is so highly viscous that you run the risk of burning out your water pump.

So, bottom line is don't do something stupid and run high intensity glycol. Here, I've plotted both the solid-liquid equilibrium and liquid-vapor equilibrium. And, this is one of the few times when nature has been kind to us.

When we add 50% glycol to water, we get the freezing point depression down to about -35°C. And we get boiling point elevation. So, what we've done is we've taken this interval of liquid water which is at purity is 100°C.

I haven't put the pressure cap on. If I just use 1 atmosphere pressure, water freezes at zero Celsius and boils at 100 Celsius. If I add 50% glycol, it freezes at -35 Celsius and boils at about 106°C.

So now, I've widened the liquid regime. And then, if I put the pressure cap on, then this line is going to move. These lines don't move at all for 1 atmosphere pressure. That's why we can throw away the pressure variable.

So, by changing pressure and composition we are able to widen the liquid range and thereby protect against boil over and protect against freeze out. Remember, boiling, we want to make sure we have good heat transfer.

Here's one that's used in keeping things safe in the wintertime. This is ice, and this is the water-sodium chloride phase diagram: again, a eutectic diagram. And, if you add sodium chloride, you will extend the liquid range.

And so, we sprinkle salt on walkways and roadways in order to melt the ice and make the roads and sidewalks safe in giving us some traction. And what I've done is I've color-coded all of these so that you will know liquidus, solidus, and, oh, we've got a new one here.

This is called the solvus. This line here is called solvus. You already know this is liquidus. We met liquidus last day and we met solidus last day. There are old friends. But here's a new friend, solvus.

So, I've got all these diagrams. I've color-coded them the same way and I've written the equilibrium for you. So, if you add salt to water, you can get down to about -21°C. And, notice that it's an almost 0°F.

In fact, Daniel Fahrenheit determined the baseline of the Fahrenheit temperature scale by putting salt in water. He used ammonium chloride. And, ammonium chloride in water gave a minimum at what he calibrated as 0°F.

And then, he took body temperature by putting his thermometer, he was a maker thermometers in Amsterdam, very good glassmaker who could put mercury in glass thermometers, he put the thermometer under his wife's armpit, and she came out at 96°F.

She was running a little bit cool, all right? And so, he said, OK, that will be 96 units, and then water is 32. And the boiling point of water is 212, and so on. And then subsequently we went to the Celsius scale.

We don't use sodium chloride on the walks. We use calcium chloride. And you can see why. Calcium chloride gives us a greater freezing point depression. Sodium chloride in many instances would not be that effective.

So, most of the stuff you see thrown on the roads is calcium chloride, potassium chloride. If you are hypertense and you want to use potassium chloride and avoid sodium, is not going to help you much.

You won't get hypertension, but you'll fall down because the walks will be slippery. So, you'll have other problems to worry about, but that's the way you take your mind off the hypertension. You've got a broken hip.

Oh, he's mean. Why is he saying that? OK, the holidays are coming. Here's zirconia. Zirconia, remember zirconia at room temperature is monoclinic. And that's no good. Cubic zirconia is stable only at very high temperatures.

But look at this. If we add calcium oxide to zirconia, we have this huge range. It's a eutectic system. There's the eutectic. But en route, we stabilize the cubic form all the way down to room temperature.

So, when you are buying a stabilized zirconia, meaning that the cubic form has been stabilized, that's the one that's got the high refractive index. And again, liquidus, solidus, solvus. And, look, it's a single phase regime.

It must be bounded by two phase regime. So, if I look to the right, it's cubic zirconia, solid solution plus calcium zirconate. If I go to the left, it's a zirconia calcia solid solution with another tetragonal form.

So, again, the model is, if you're moving across a multicomponent, two component phase diagram, single phase bounds dual phase, bounds single phase, bounds dual phase, bounds single phase, bounds dual phase.

This is really fantastic stuff. Oh, this is good. Aluminum magnesium: this is the beverage can. This is the beverage can. So, we're looking at it. It's a eutectic system. So, we're going to add a few percent of magnesium into aluminum, which is going to put us here: alpha solid solution.

If we have too much, we end up in a two phase regime, and that's no good because when we go to deform the can, it will tear. The metal will tear. So, we have to have single phase, freezing point depression.

And then, this is important in metal recycling. We want to be able to process this stuff, and energy is costly. So, if we can process at lower temperatures, it's advantageous. This is a very important one for microelectronics.

This is lead 10. Lead melts at 327. Tin melts at 222 Celsius. And, there is a eutectic down at 183. I learned this in high school. We had this industrial arts class. It was 374°F is the eutectic point of soft solder.

I'll know that on my deathbed. So, what does this tell us? It tells us that if you are building a micro device, whether it's a cell phone or computer, you've got to solder in all the lead wires. And, when you solder, you have to energize the system.

You have to melt the solder, and then it has to bond to the metal and then freeze. And every time you go in with that energy source, you heat not only the solder but you heat everything else. And, you know, if you're making a P-N junction, you want it sharp.

But, what happens if you heat a sharp positional gradient? Diffusion will occur, and diffusion increases as temperature rises. So, you are looking for a solder that has the lowest melting point possible so that you can get in and out doing minimal thermal damage.

In fact, when you design one of these large devices, you have in your design scheme a thermal budget. And, you look at processing routes that consume less energy not only because you want to be energy efficient from a manufacturing standpoint, but because every time you put joules of energy in, you run the risk of having more and more diffusion.

And, those sharp P-N junctions will become diffuse P-N junctions. And, as our feature size is getting smaller and smaller, the diffusion distances are shorter and shorter and you've got less time before you've blurred those interfaces and then the device is useless.

So, right now, there is a huge effort to look at lead free solders. Lead, mercifully, has this low melting eutectic below 200°C. That's the good news. The bad news is its lead. And so, now we've got two alternatives.

And that's something you're going to be faced with. Either we have something that is lead free and very costly, more costly than the device itself, or we have something that is not terribly effective.

It cold freezes in the joint and the joints pop off, and so on. So, this is a eutectic diagram indicating the value of freezing point depression in processing. Last day I showed you how to use compositional variation.

Let's look at how we make silicon. This is the iron-silicon phase diagram. Iron-silicon phase diagram is a little bit messy but I draw your attention to the top right corner. Unfortunately, this one is drawn the other way around; it's got iron on the left and silicon on the right.

And, I want to draw your attention to dilute concentrations of iron in silicon. So, we've normally been looking at things from the left. But I think you're capable of flipping that around in your mind.

And what do you notice? You notice that the alpha region of iron in silicon isn't present there. That is to say that there is only a tiny, tiny solubility for iron in silicon. So, if we want to purify, remember, we are starting with something really cheap.

We are starting with beach sand, and we need to go to five nines, that is, 99.999% purity. And, iron is death to a silicon microdevice. We've got to get the iron out. One of the ways to get iron out is to start with something in the liquid.

So, this is pure iron over here, pardon me, this is pure silicon over on the left side. So I've turned that phase diagram around: pure silicon, and this is percent iron. And, I want to get the iron out.

And, I'm not going to boil the stuff off and use fractional distillation. These things are too high melting. They melt at such high temperatures. They boil at such high temperatures. I don't know what I contain them in.

So, what we can do, so this melting point of silicon. It's the melting point of pure silicon which is about 1,430°. What I could do as I could take some. Let's say this is C naught; the original impurity level of iron in silicon.

What I can do is I can cool this melt down into the two-phase regime and hold. And, what happens if I hold it in the two-phase regime? This is alpha. This is liquid. So, this must be slush. Alpha plus liquid: it's going to phase separate.

And, what do I see? The solid phase here has a value of iron at CS, which is less than C naught. So, the solid has less iron in it. It's a higher purity silicon. And the liquid has C;. And, what do we find? We see that CS is less than C naught is less than Cl.

And, this is the lowest value of iron. So now, I can take this stuff out, throw it into another furnace, melt it, and cool it. And, what happens? As I did with the distillation, I keep chasing it up.

Now, granted, I lose a lot of material. But, I'm gaining material that has very, very low levels. So, again, what's happening is that this phase separation leads to compositional differentiation. And, that's the paradigm: compositional differentiation.

So, we can do it with differentiation. We can do this with liquid vapor and do a distillation, or we can do it this way, which is a solidification. So, this is the impurity. The iron is a solute impurity, and we say what is happening in this process is the iron impurity is being rejected up into the liquid phase.

So, when we are holding here, what we have is, remember, the silicon is less dense than its liquid. So, this is high purity silicon, high purity, and this is low purity silicon liquid. Now, if I take this, throw it into another furnace, melt it, I can do it over and over again.

So, this is called zone melting. I'll show you how that works, where people speed the whole thing up. You take a giant salami of silicon, which now the standard is 12 inches in diameter. So, this thing is a single crystal of silicon, 12 inches in diameter, and several meters long.

So, we're not going to take that single crystal and remelt it. What we can do instead is put some induction coils around it. We put induction coils around it and send a current through it, what will happen as this will get so hot that it will melt.

And by surface tension forces, I can contain the molten zone here. And, what happens if I hold this long enough? I eventually drop the temperature and I get phase separation. So, on one side, I'm going to get accumulation of the impurity.

And then, I can drag this through and sweep all the impurities down to one end and chop that end off. And, then I could do it again. I say, well, why do it again? Why don't I just have another set of coils like this, and then another set of coils like this? And so, this stuff melts, freezes, melts, freezes, melts, freezes.

All the garbage gets sent down to the end, chop this off, and now we have five nines silicon exploiting the compositional differentiation in that two phase regime. So, that's really good, yeah. So, this is used in scrap metal processing.

It's used in making high purity silicon. If you ever find yourself in the North Atlantic, you could use this for desalination because you know that it's, if you looked at that phase diagram, what you have is the composition of ice and salt water is very nearly pure water.

There's very little salt content. So, this is called zone melting or zone refining. Zone melting is the technique. Zone refining is the result. We get the purity up. OK, so now let's look at another use of this.

Let's look at a use of this in the context of champagne, and at the same time honor an inventor. So, the person I want to talk about is Madame Nicole Barbe Ponsardin. And, she was a young lady who married Francois Clicquot of the Clicquot family that owns a large champagne winery.

And she was widowed at the age of 27 in an act that was atypical of French women in her day. Instead of just receding and being a silent partner, letting the winery go about its business, she took control of the winery and really became very aggressive about how this one should be made.

So, she did all these things, which was unheard of by anybody at the time marketing champagne to the courts of Europe and making the myth that champagne is this magical beverage. It was drunk only in pretty much France at the time, bought lands in the best vineyards to control the chemistry.

This is all about chemical control the product, fought fiercely against counterfeiting, used the court system to prosecute people who sold wine masquerading as champagne, strict quality control procedures, all of the sort of thing, making sure that the chemistry is under control, produced the first RosÈ champagne, again, good chemistry, leaving the skin on the juice and then oversaw this invention of a new technology, which brings together phase diagrams.

That's what I'm talking about it. You think I'm talking about it just because I want to talk about champagne. This is an application of phase diagrams. So, first of all: the problem. The problem is that back in the late 1700s, champagne was cloudy.

Champagne was cloudy. That's why the champagne glasses have all the cut facets on them, so you obscure the cloudiness of the beverage. It was actually ugly. It bubbled, but it was very cloudy. Why? Well, we need some chemistry.

To make champagne, or to make any wine, you start with sugar and you react with yeast. Yeast attacks the sugar, liberating CO2, and converting sugar to alcohol. And, it's a one-stop shopping. Everything is on the grape.

The sugar is in the grape juice and the yeast is in the grape skin. So you just press it and stand back. OK, but there are some other byproducts of this reaction. And these are various insolubles.

So, when this stuff is sitting in a big barrel and CO2 is bubbling out and alcohol is being created, there is all this solid stuff that's coming out of the grape pulp. And so, some of it sits to the bottom automatically.

And some of it is suspended. And so, if we want to treat this stuff, you've got to either use chemical coagulants to get these fine particles that are in suspension to grow too large enough size that they'll gravity settle.

Or you siphon. And this is the typical way with wines. Well, you can't siphon a champagne or you will lose all the bubbles because you keep the lid on the barrel and that's what traps the CO2. So, if you open the barrel to siphon, you lose all the gas and now you end up with flat champagne.

So, up until 1800 people would just put the stuff in a bottle, put the cork on, trapp the CO2, and then when you went to pour the champagne, all the sediment would come off the bottom, which explains why the bottle looks like this.

It's got these deep ruts so that you can keep as much of the sludge on the bottom. But, it's gassing, and this stuff gets churned up and so on. By the way, while I'm talking about this, I can't do this without teaching you how to chill champagne using heat transfer.

So: how not to chill champagne. How not to do it: this is how most people do it, but you're 3.091ers, so you know how not to do it. You do not simply put ice on it. This is lousy heat transfer because what do we have here? Here's the glass of the bottle and here's chunks of ice.

So this is probably, I don't know, -5°C, and there's all this air in here. And, the air is at room temperature. So, this is sloppy. So what should we do instead? Will we are going to do instead is we're going to use the ice-water phase diagram.

We are going to flood this with water. And now, I'm going to have intimate liquid solid contact. And this thing will be thermostatted (sic) at 0°C because that you know from the P-T diagram. That's where it is.

And that's how you chill anything. You chill your soda, your fruit juice, heat transfer. So, she had the idea: how are we going to get rid of all this sludge? She says, turn the bottles upside down.

And in fact she knew the optimum angle was 45°. And then, have people turn the bottle so that the sludge spirals its way down into the underside of the plug of the bottle. And, this is called remuer, to turn.

And, there are people that spend their lives doing this, quarter turn, quarter turn, quarter turn, quarter turn. And then you say, well, that's really dumb. How is she going to get the sludge out from underneath the cap of the bottle? Well, look at this phase diagram.

If you mix salt with water, you get a brine that freezes at -21°C. And, if you intersect that with the phase diagram of alcohol water, there is about 10% alcohol in champagne. That will freeze at a temperature a little bit higher.

So, what will happen is you will make an ice plug in the neck of the bottle by immersing the bottle upside-down in brine. So, it's the marriage of this and the knowledge of the phase separation in the liquidus regime.

You form solid ice starting at 0°C. So, you form an ice plug here in the neck of the bottle. And then, all you do after the ice plug has formed, what you can do is turn this right side up. You undo the cork.

It heats from the outside in. As soon as you get a skim coat of water on the outside, the pressure blows the cork out, takes all the sludge. You quickly recap it, and now you have clarified champagne.

And that's how every bottle of champagne is made to this day thanks to her invention. It's positively brilliant. So, here's the summary of it. You contain the lees in the plug of ice just before disgorgement and let this go.

Now, the French are very traditional. They still have people turning quarter turn, but there are a few wineries that have given in to mechanization. And they have this large device that actually shakes all the bottles that are set at 45° angles.

And they call this gyropalette. In the California champagne wineries, they also have such a thing. It's called VLM, which stands, I kid you not, this is California, very large machine. [LAUGHTER] Dude, very large machine, dude.

All right, so if you understand this phase diagram you know what's going on in here. All right, now let me say a few words about the final exam. I'm going to let this thing chill, and then what I'm going to do, I'll make a few personal observations.

Once I open that bottle, the class is over. So that's the way it's going to work. Right, so the final exam is on the 15th in the morning, Johnson Athletic Center. Be there at nine o'clock. Don't show up late.

Three hours: but not three times the work of a monthly test. Intensive coverage since test three, and extensive coverage of everything else. You get one aid sheet, not one and a half, not two, one.

One 8.5 x 11, bring your periodic table, your table of constants, calculator, and something to write with. So, there's the five items: aid sheet, periodic table, table of constants, calculator, and pen, always the same five items.

I'm not going to do anything different from the monthly tests, about comparable difficulty. It's redemptory. I want you to pass. You got to show me you've learned something. Read the entire exam, show your work, solve algebraically, try not to waste time on intermediate calculations.

Remain confident; don't give up because you feel your first couple of questions aren't going your way. Just stay there. You've paid your price of admission. Sit there for three hours. It's warm. Academic honesty: there's going to be 600 of us in the Johnson Athletic Center.

Keep your eyes on your own work. I do not want to have any episodes involving academic dishonesty. And, believe me, several years ago I had a couple fellows that decided that the strength of two is greater than one.

And, I ended up having to bring him before the committee on discipline, which took a huge amount of my time, which I was not happy about, and one of those people did not return for his sophomore year.

It's a dumb price to pay for a class that's a pass-no-record class. Do your best, but do your own. Overall grade scheme is based on many factors including trends. So, those of you who have a hard time at the beginning, if I see an emergence, and I'm not saying you have to write a 95 on the final to compensate for a 30 on the first test.

But if I see that you've made the effort, and learning is happening, your TA can vouch for you, I'm inclined to pass you. Look, if I take the batteries out of this watch, it's right twice a day. Give me something to point to.

Give me some thing to point to. But you can't tell me that you understood the material but you never passed one thing. And if you're going to pass one thing, I'd recommend it be the final. And, by the way, I'm looking at the other trend, too that if I see people who think that, hey, I only need a two on the final and I'll get a 50, and you somehow don't make the 50 even though you had a passing grade going on the final, you're gone.

You are gone because that says to me you gave up; you stop learning at around Veterans Day. So, I think it's brinkmanship to decide you're going to go on the final and maybe just answer one or two questions and leave.

But, I leave the choice up to you. I don't tell people how to live their lives, but I will make you aware of the consequences of a really bad final. It doesn't look good. You can have your exam papers back.

We should have them graded. And you should have them available to you by Friday afternoon. Don't come and see us before then. We are busy grading. We are busy tabulating grades. There will be a grades meeting on Friday morning.

We'll discuss all the cases. I go through everything. There's no time limit for appeals, but I assure you, if someone is going to get a grade that's not going to pass them, I'm going to personally go through that paper, make sure there's no clerical errors, check the grading, work with the TA's; we're not going to fail somebody because, gee, I thought that was a three.

It looks like it's an eight. Oh, too bad. No, we're going to make sure it's done right. So, we will be very careful. And you can bring them back in the regrades if you want but I will put some security measures in place.

The practice of erasing answers and rewriting them is not a smart thing to do because what happens is, you have terrible taste. You have terrible taste. I'm drinking champagne. [LAUGHTER] [APPLAUSE] Now, I case of champagne, I would have said, quel finesse, but this, sauvage.

OK, so, to deal with the possible eventuality that somebody in a moment of weakness might erase something, we're going to indiscriminately photocopy about 5% of the exams. So, if you decide you want to erase something and bring it in and get it regraded, the question you've got to ask yourself is, do you feel lucky? [LAUGHTER] Do you? All right, so this is 3.091.

We've gone a long way, you know? We started a long time ago, bonding structure and went through the different types of bonding structure properties. A lot of learning went on in this class. Stability, instability, chemical reactions, diffusion, phase transformations, and now phase diagrams.

So, I want to make a few personal observations and say that you should be proud of what you've learned. This was an ambitious syllabus, and I'm convinced that people are going to have something that they can move on to their majors with next year.

Secondly, I want to wish you much success on the final. I'm not out to fail anybody. I love to pass everybody, but you've got to give me something to point to. And I've given you as much information as I can about how to succeed on the final.

But, if worse comes to worst and you don't make it, what's the worst thing that happens? You are required to withdraw from the Institute. So what? Remember one thing: that no grade that anybody gives you here is a commentary on your value as a human being.

Look, I have no degrees from this place. I feel great. The third thing I want to say is I've been teaching at MIT for 27 years. This is my 27th year, and I'd never enjoyed teaching as much as I had this year.

You've really been a joy to teach. I can't believe I said that with a straight face. [LAUGHTER] [APPLAUSE] I want to thank my staff, my TA is, my tutors, administrators. I had Hillary and Lori helping, Professor Ballinger who subbed for me when I had a chance to go up to Halifax and give a lecture about 3.091.

The audiovisual texts and the fellows outside from the academic media production group that takes the videos and gets them up on the web so that you can avoid coming to class, I mean, review what you failed to catch the first time round as you paid attention.

And, I guess the last thing I wanted to do before we can get to the champagne and the course evaluation is Dwayne Daughtry is here from my department's academic office. Actually, Dwayne, you're free to start distributing those forms.

There is one more chemistry lesson that we had to get to, and that is, we talked about four types of primary bonds: ionic, covalent, metallic, and van der Waals. Well, there is a fifth type of primary bond, and that's the kind of bond that's been forming in this room for the past 14 weeks.

As a bond between people, and it's a very special kind of bond because it has the property of, can never be broken. And, so you say, well that sounds kind of sappy and so on. Yeah, it does, because a student came up with it.

I didn't come up with it. I've been teaching a core graduate class in materials science for about ten years. I was at a conference and I saw these two people standing. One of them was from industry, and one of them I taught here at MIT.

It was an alum. I go up and say hello, and the fellow from industry says, hey, do you know so and so? And I said, yeah, of course. He was a student of mine at MIT. I was his kinetics professor. And, the student says, excuse me, Professor Sadoway, it's true.

You taught me kinetics, but please don't say you were my kinetics professor. You will always be my kinetics professor. And I went, whoa. [LAUGHTER] I mean, he came up with that. So, now the tables are turned, and now it's time for you to move on.

So, I know that you're going to do something remarkable in your professional lives. I hope it's remarkably wonderful and not remarkably stupid, but, you know, at some point people might ask you, where did you learn your chemistry? You'll have to say Sadoway at MIT.

So, whether you like it or not, I will always be your chemistry professor. And now I want to find out what's going on inside here. So, first, we have to open this. So, take the wire off, the mesh off, [LAUGHTER].

Tenure means never having to say you're sorry. [LAUGHTER] 27 years I've been doing this. Now, how many turns in a wire basket? One, two, three, four, five, six, always six. Six turns of the wire basket.

There's Vive Clicole. Her image is on the top in honor. We'll put it at a 45 degree angle and turn it ever so slightly. Beautiful. Soft, not this, vulgarity. That's what goes on in football locker rooms.

So, now, I've been waiting 14 weeks for this. So, this is the CO2 out gassing, you know that phase diagram. It's all about phase diagrams, put that back on ice. So, when Dom Perignon first drank champagne, he said, I feel as though I'm drinking stars.

He's right. Okay, the class is over. [APPLAUSE]

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