Lecture 20: Crystal Defects: Interfacial Defects, Voids, Amorphous Solids, Glass Formation

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OK. Let's settle down. Settle down. A couple of announcements. You got the test back. This is what it looked like. These are the very nice Gaussian. You see it goes up and down. And the average was 54 with a standard deviation about 15.

We have a high here of 95. We had a number of people in the 80s and 90s. We had a number of people that were in the 50s and 60s on the first test who moved to the right, and we had also some people that were up here who moved to the left.

Far more moved to the left than moved to the right. I talked to the TAs and we put a fair bit of care into preparing the test that no one felt that it was atypically difficult. But somehow people didn't do as well.

I have been getting emails from people asking about a makeup. Yeah, there is a third test on the 17th of November. We are not going to allow you to retry until you get a score that you like because there is no point in doing that.

You know what the rules of engagement are. I don't ask much of you. But, if you fail to give seven hours a week, you are not going to pass this class. There was nothing there that was out of the ordinary.

Nothing tricky. Just asking you to answer a few skill-testing questions. I am very happy to talk to anybody about his or her performance. I know my TAs are willing to do the same. We have tutorial assistance available at no charge, but there is no substitute for your making the investment in time.

And I think that perhaps some people are lulled into complacency because I don't require you to hand in monster problem sets, because I think that is childish. I think that you should take ownership of your learning.

I treat you as adults. But if you think because I am not there looking over your shoulder whether you are doing your work or not, I don't have to. I just look at this. I would warmly recommend that if you want to pass this class, and I told you everyone in this room should pass this class.

I want to fail nobody. But if you don't demonstrate basic proficiency, I cannot do it. It is intellectually dishonest on my part. You wouldn't want that. You want to know the truth, so I will tell you if you are not doing the basics.

And we will have a chance to get back into the swing of things. There will be a quiz on Tuesday. And I goofed. I issued two problem sets in a row both called Homework 7. Just to be clear, I fixed this one and reposted it on the Web.

It is the same questions, but basically you will be looking at the x-ray diffraction questions and the questions on defects. That is where we are going to be for Tuesday. And that is good news because, those of you who had trouble on the test this past Wednesday, we are going to be moving into some new topics so you get a chance to start over.

Towards the end there is some integration, but at least it is not so strictly lock step that if you didn't do well on Wednesday then you are hopelessly behind. Again, I mean it when I say this. I want everyone to succeed here, but you have to invest.

You have to invest. Last day we were looking at defects. We looked at point defects and line defects. Today I want to continue and look at surface defects and volume defects and ultimately go to something that is so defective it lacks order.

We will move from surface to volume to disordered solids. Let's look at what makes surfaces special. What makes surfaces special is that the coordination number is different at the surface from what it is inside the material.

What I am showing here is the free surface of the material. And here is one region of the material where the atoms are lined up in this manner. And here is another region of the material where the atoms are lined up in this manner, because they grew from the melt starting from different starting points from different nuclei.

And, when they impinge, this plane does not line up with this plane. And there is a boundary along here. We have two types of surfaces here. We have a free surface and we have an internal surface.

I am going to talk about both of them. The thing they have in common is that if we look at an atom down here in the center, if this is an FCC structure, an atom here in an FCC structure has 12 nearest neighbors.

An atom here at the free surface cannot have 12 nearest neighbors. It has fewer than 12 nearest neighbors. And we know that systems form bonds maximally to lower their energy. Therefore, if I have fewer than the maximum number of bonds, this is not at as low an energy at the free surface as it would be were it inside the material.

Because at the free surface it has fewer than 12 nearest neighbors. That means that surfaces are higher energy. They are higher energy regions in the crystal. And that can be good or it can be bad.

If we want something high energy that is good if we are looking for catalysis. We will talk about catalysis later, but catalysis occurs at the free surface. By definition, you need to have those broken bonds.

Catalysis is good, but it also means things are highly reactive sometimes undesirably. And that can lead to corrosion which is undesirable. Where is corrosion going to occur? This material is not uniform in its properties.

The corrosion resistance of an atom deep inside the crystal is different from the corrosion resistance on the free surface, which is different from the corrosion resistance along this internal surface.

Each of these regions is called a grain. The grain is a virtual single crystal. It is a single crystal. We have a polycrystalline material consisting of a tapestry of single crystals called grains.

And this internal surface is called a grain boundary. Both of these are defects. What does the grain boundary do? Well, the grain boundary does several things. First of all, the grain boundary acts as a trap for impurities.

That can be good or it can be bad. If all the impurities collect at the grain boundaries, and those impurities embrittle the material, it doesn't matter what ductility the grains have, the material will fail at the grain boundary.

It would be as though you had bricks that are very strong held together by a weak mortar. The grain boundaries act as that mortar, but they have beneficial effects. Imagine a dislocation sliding in one grain.

It wants to rip through the entire material. That misregistry of atoms at the grain boundary stops the dislocation so it can act as a site for arresting dislocations. It arrests dislocations. I talked to you last day about the management of defects.

If we want to have a material that has high strength and is not going to easily slip, do we want a material that has coarse grains or fine grains? We want to have fine grain material. Grain boundary engineering is important in the management of the mechanical properties of material.

And I want to show you several things. First of all, here is a cartoon just to get you, again, onto the page of what is happening. These different grains began from the melt at different sites in the liquid, grew to impingement.

And you can see these atoms cannot ever perfectly align with the atoms growing from the adjacent grain. And so this zone of misregistry, it is the void here which is called the grain bound. Now, this is showing it in terms of cross-hatching.

The cross-hatching is tilted in different ways. And the gaps between the cross-hatching are termed grain boundaries. This is a piece of polycrystalline copper that has actually been polished and then etched.

And because their different grains are presenting different crystal densities, atom densities, these grains etch differently. They etch at different rates in the same acid. And, after a while, they will actually be tilting at slightly different angles.

And then when we illuminate this with polarized light and look at it under a simple optical microscope we see different colors. And these are the different grains. Each one of these you can consider a single crystal that has just the normal atoms in their FCC lattice throwing in some vacancies and some dislocations.

And now they impinge along these different boundaries. And this is a field ion microscope image of a tungsten bicrystal. And right along the lower right corner you can see the edge. This is the grain boundary, so there is a single crystal to the lower right and the rest is a single crystal to the upper left.

Grain boundaries. And also I can show you again, we will go to the document camera and go back to our pal the atom mix here and see if we can zoom in. That is too much zoom. Now auto focus. Auto focus off.

Auto focus on. That's a so-so auto focus, but if we had a manual. Oh, that's better. Now you can see how things align. You can see zones here, perfect, and then you can see there are some vacancies.

And you see along here? These atoms are moving sort of towards 2 o'clock and these atoms are moving here. And then, when they try to align, there is the grain boundary. That auto focus is really going nuts.

Isn't it fun to see the machine struggle? I just laugh. Laugh at it. It is a stupid machine. Look at this. There are grain boundaries, and then the free surface up here of course. These are both high energy regimes.

And we can anneal this. If we anneal it we can try to get a more coarse grain structure. Now I have a single grain. There was the original grain boundary, there was one in here and now we have a larger regime.

Let's go back to the computer. Now let's look at three-dimensional defects. Three-dimensional defects, there are really two types, being and void, things that are missing and things that are there.

So, what is there and void. I will talk first about the three-dimensional voids. Voids are simply coalesced vacancies. The vacancies will eventually come together and coalesce. And so this clearly weakens the material mechanically.

Mechanical properties are degraded by the presence of what looks like blowholes on the micron scale. And then there are three-dimensional defects consisting of matter. And the most injurious is called the inclusion.

And the inclusion is simply trapped foreign matter. It is trapped foreign matter. Why is it trapped? Because it is insoluble in the parent matrix. And this can lead to deleterious mechanical properties.

And I will show you an example immediately following. And then there is a desirable form of three-dimensional defect which is called the precipitate. And the difference between the precipitate and the inclusion is that the inclusion is never soluble.

The inclusion is something that is foreign matter that got trapped during the melting process or the vapor deposition process when the solid was formed. The precipitate sometimes is put there by designation.

It is something that was dissolved at one point and then made to come out of solution, so it is exsolved matter, formerly dissolved. And the reason that both of these are so injurious is that they represent separate phases.

And what do we have at the interface between one phase and the other phase? Well, we have the same issue as an interface. Not only do we have the bad mechanical properties of the precipitate or the bad mechanical properties of the inclusion, but we also have an interface.

These things do double injury. And the other point is that most typically the exsolved material or the inclusion has a different density. And so when it comes out of solution there is a volume change.

And that either leads to a compressive stress or a tensile stress. There is a volume difference with the parent or the host matrix. This all leads to trouble. Now, I showed you that carbon in iron is strengthening the iron to make steel because it is a little bit larger than its interstitial site in iron.

And there are examples. When you fly on an airplane, you're flying on something that is largely made of aluminum. And one of the elements that goes in there is copper. And it goes in at a level that causes precipitation of aluminum copper compounds called Guinier-Preston zones.

These are precipitates that raise the strength of aluminum beyond what you would have if you had essentially pure aluminum. You do not want to be flying in an airplane made out of something that has this level of ductility.

I mean, I love dislocations, but there is a time and a place. We don't want that. Let me show you an extreme example of what happens with inclusions. Yes, the Titanic sank because of these three-dimensional defects called inclusions.

And this is some data taken recently down at the National Institutes of Standards and Technology in Gaithersburg. This is Tim Fecke who is a metallurgist who did a lot of the work. This is a rivet.

And you can see the actual size of it in his hand. These are very, very large rivets. And these are the rivets that were in the hull. What has happened is they have cut the rivets, polished them and put them in an optical microscope.

And here is what you see. If you look inside, you see these dark zones. These dark zones are inclusions of slag. And how did they get there? Well, in those days, we're talking around 1910. The way steel was made was in a unit called the open hearth furnace.

And the open hearth furnace was the invention of Siemens, one of his many inventions. And the way the open hearth furnace works -- This is not to scale. What I am going to show you is a vessel that would have a floor about the size of the entire front of 10-250.

Actually, many times larger. But this gives you a sense of the scale. And you have two layers here. Two liquids that are insoluble in one another as salad oil and water. The lower layer is iron, it is a metallic layer, and the above layer is slag.

And the slag basically consists of things like silica, calcia, alumina. It is all oxides so it is sort of the equivalent of what you know to be window glass or bottle glass. And it lies in a giant pool on top of a pool of metal.

And what is going on in here is that the iron has come out of the blast furnace, it contains far too much carbon and it contains impurities, things like silicon and manganese at too high a level. And the process was called open hearth steelmaking.

You had a vessel about the size of the front of this room. And, to keep it molten at 1300 degrees C, you had to giant burners at either end. And these things would be like dragons shooting flames across and keeping everything molten.

It was all contained in brickwork. And the idea here is that over time the impurities will rise out of the metal and move into the slag layer. For example, carbon in the iron will react with some oxygen in the iron to form carbon monoxide and bubble away.

But, more importantly, things like manganese in the iron will react with oxygen in the iron to form manganese oxide which is not soluble in the iron, and it goes into the slag. This process, in those days, took about 12 hours.

For 12 hours you kept the steel sitting at about 1300 degrees C. And you want good mixing so there is a far bit of turbulence here. And, towards the end, you stopped the turbulence and let things separate.

Just as after you have shaken salad dressing. You have oil. In an aqueous phase vinegar. And then you watch. Slowly the bubbles start to rise and so on, the globules of oil. Well, clearly what happened on the day they made the heat for this vessel, rivets, somebody got greedy and tapped the metal too soon.

With the result, there was still a lot of this glassy slag-like material in the metal. Then the ingots were poured. And then from the ingots they made the rivets. Well, when they make rivets they draw them.

And so, instead of having little globules of glass, which would have been bad but not super bad, by drawing them, can you see from the center of the rivet, these globules have turned into long stringers.

Now, instead of having the strength of steel across the cross-section, it is as though you have these perforations. If you cut the cross-section the other way and look down, it would look like mortadella luncheon meat.

There is meat and globules of fat. That is what this thing would look like. And then down here at the bottom, see, there are stringers everywhere. Now, this thing does not have the strength anymore.

When it hit the iceberg, what should have happened is that there would have been damage in the hull in that local region, it would have been taking up water, and there would have been time for five or six hours before the rescue vessels arrived.

Instead what happens was these rivets were so weakened by the presence of the inclusions that they broke. But, as they broke, it was just like a zipper unzipping. It just went down the entire hull, opened up, water rushed in and the vessel didn't last very long.

It stayed afloat too short a time. And, of course, there were not enough life vessels on it and so on. You know the rest of the story. Anyway, it started with a bad metallurgical heat which gave us the trapped foreign matter which is insoluble and so on.

Before leaving, this is pretty much the catalog of defects, I want to return to something I hinted at last day. I want to be clear with you about the chemical origins of mechanical behavior. And this is a part of 3.091 that sets it apart from a classical chemistry subject, because what we have been looking at is how electronic structure informs chemical bonding.

Well, that is no surprise. You would expect to get that in chemistry class. But then chemical bonding informs atomic arrangement, and that is where the rubber meets the road when it comes to mechanical behavior.

You have to know where the atoms are. I want to talk about deformation. That is what makes metals in particular so useful. That is why they have been historically utilized by humans going back to prehistory, because they have the special property of ductility.

We can take them in the solid form and have them change shape. And the reason they can change shape has to do with, first of all, their electronic structure which leads to metallic bonding which gives us these cubic crystalline arrangements.

And then we introduce dislocations and things slip. I want to talk about two types of deformation. First of all, I want to look at elastic deformation. And this is deformation that is reversible. It is characterized by its reversibility.

And the simplest way to define it is strain. That is strain only under stress. Release the stress, the material relaxes back to its initial state. Only under stress. Or, if you want, you could say displacement only under the action of applied force.

And Hooke's Law applies for this. And I want to show you the chemical origin of Hooke's Law. We saw, when we looked at the force curves that defined the equilibrium separation of two atoms, regardless of the type of bonding, that we could plot energy as a function of interatomic separation.

And we find that we have some kind of a repulsive energy up here and we have some kind of an attractive energy down here. And we went through the strict derivation for ionic crystals, but analogous derivations exist for other types of crystals.

And if we go through we find that there is a minimum energy which defines this r naught which is the equilibrium interatomic separation. And this is E minimum. Well, I can keep going. What I can do is look at the derivative of that and show you where you get Hooke's Law.

If I look at the derivative of this then that will give me force, because I know if I plot force which is equal to dE by dr, the derivative of the energy with respect to displacement. And right here about r naught you can see that the curve is positive slope to the right, negative slope to the left and is flat at the origin.

I am exaggerating this over a wider range, but it is fair to say that about r equals r naught, F is linear in r. Well, doesn't that remind you of this from physics where you have a spring and you hang a mass on a spring, and that mass on a spring in a gravitational field gives rise to a force? And you can look at the displacement versus an initial displacement.

Here is an x and here is an x naught with no mass. And I think you have seen this. You've seen that some constant times x minus x naught is force. That's Hooke's Law, that there is a linear relationship between applied force and the displacement of the string.

And that is the same thing happening with atoms. For a tiny force I get a tiny displacement, for a larger force I get a larger displacement, and if I relax the force the atom springs back to its rest position.

What you are seeing on a macro scale here is what is being played out at the nanoscale here. Hooke's Law is related directly to the linearity in the force curve as a function of position. And, by the way, here is how he published Hooke's Law in 1676.

It was first published as follows. That is Hooke's Law as he first published it. This is an anagram and it is in Latin. Hooke was a wise guy, to be sure. He was a contemporary of Newton. They hated each other's guts.

They fought bitterly. Three years later he published the solution to this, Ut tensio, sic uis. As the extension, thus the force. He was quite a guy. There it is. That is elastic deformation. Now let's look at plastic deformation.

Plastic deformation is the other form, and that is permanent deformation. Plastic deformation is permanent. Let's look at the chemical origins of that. And now we will do another experiment. Instead of a spring this is a wire.

This is a wire and we hang a mass on it. And this mass is very, very heavy so that the force here is great enough to actually cause elongation. We have elongation of the wire here. Let's make this a simple copper wire.

It is pure copper FCC. The only thing we have in there is it has high purity copper. There are vacancies, there are grain boundaries and there are dislocations. Let's look at this a little bit more carefully.

Here is the wire, and we are going to make it polycrystalline. I am going to indicate polycrystalline as follows. Different grains have different orientations of the atoms. And I am applying a force in the vertical direction.

The question is how does this deform? If we go down to the next level, I will take a look over here on the right side. And I can imagine that I have here atoms touching as follows. It is in an FCC lattice, but I am pulling in the vertical direction.

Now, maybe around the early 1800s we might argue that the atoms start off as spherical and then they become elongated under the action of a force. But I think that is kind of goofy so we are going to turn that one down.

Instead what we are going to do is say, well, we know about dislocations and we know that dislocations allow atoms to glide over one another. So what is the problem here? The problem is that the atom planes are lined up on a 45 degree angle.

What the system does is it reforms. It reconstitutes the applied stress and resolves it into a resolved sheer stress that moves along the componentry of the atoms. What happens is this atom plane underneath slides down to the lower right.

The next plane slides to the upper left. And, from a distance, we see that the wire is becoming narrower and longer, but it is happening thanks to the atom slip. And we went through the reasoning last day of what the slip systems will be.

The atoms are going to slip in such a way that preserves the strength of the planes. The planes that will slip over one another are the planes that have the tightest binding. And the tightest binding comes from neighboring atoms.

The planes that have the tightest binding are the planes that have the highest populations. That would be the planes of highest packing. We have gone through this. And just to return. The planes that have the highest packing are the ones that have the highest atom density, and that is going to be the highest binding.

The highest density plane in FCC is {111}. And then the plane will slip along the direction that has the highest density. Because what we are thinking of are rigid rafts and rigid rods. To make the most rigid raft you have the highest density of bonds.

And once you are in the plane, how do you slip? Are you going to push a wet noodle or are you going to push something that is rigid? The highest rigidity comes from the direction where the atoms touch.

And so all of this goes back right to the very beginning and explains how slip systems work. And so slip systems operate in close packed planes along close packed directions with the aid of dislocations.

Which provide for the ability to move in permanent displacement at stresses that are less than what is critical. Now, what I would like to do is show you something that comes from a bubble raft model that was constructed by Krystyn Van Vliet as part of her PhD.

She is now a faculty member in our department. This is a bubble raft model that represents the movement of atoms under an applied stress. Let's look at the first one here. What you are going to see is -- -- the application of stress, you will see the grain boundary, and then you will see a dislocation here.

And you will see the atom squirt up. The force is being applied from top to bottom but the atoms are on an angle, so there is a dislocation that issues from this triple junction. And now it is up in here and is getting ready to squirt up to this side.

You can see how the atoms are moving side-by-side on a 45 degree angle in order to allow for what, in essence, has to be compression in the vertical direction. I will show you another one that involves a single crystal and the same thing.

The pressure gets high enough that finally a dislocation originates in the center of a single crystal, the dislocation shoots up to the surface, and now you have a step at the surface. Now we have a single crystal.

You are going to see a dislocation originate right in here. There it is. You see it squirt. And now there is a step here. This side of the surface is one atom step higher. We will see it one more time.

It will originate right down in here. There it goes. The atoms are slipping over the highest population. Now you know the origins of mechanical behavior. Now I want to talk about the ultimate defect, which is total disorder.

And so what we are going to look at is a loss of crystallinity and go to amorphous materials. I will take you back to the big picture, which was about a week or so ago, where we looked at how we got to solids.

And we said there are two types of solids. We saw that we have ordered solids, and that is what we have been talking about for the last week or so. And now I want to get over here to disordered solids.

These are solids that lack long-range order. There is a little bit of short-range order. Amorphous solids. And the colloquial word for them is glasses. Amorphous solids or glasses. And these are solids that lack long-range order.

What kind of solids can form glasses? Well, anything that is capable of being solidified in a way that prevents crystallization. I can show you inorganic glasses such as the silicates that sank the Titanic and are also used in everything from window glass to beverage containers and so on.

These are made of SiO2, and we are going to return to that as a prototypical system to study very shortly. There is organic glasses, the most common being polymers. For example, the polymethylmethacrylate that we use in such applications as substitution for window glass, the polymethylmethacrylate you use in your eye glasses, this material is all disordered.

And we even have elements that have certain features. For example, sulfur. Sulfur typically when it solidifies does not form a crystal but rather forms a glass. It is an amorphous material when it solidifies.

The point here is that we do not classify things as amorphous based on their chemical composition but rather based upon atomic order. And specifically here the lack of long-range order. And some do both.

For example, SiO2, silica, silicon oxide. If it forms a crystal, we call it quartz. And the quartz crystal in our watches is made of high purity SiO2 which has been hydrothermally processed to give it a high degree of crystallinity.

And it has a very characteristic vibrational frequency from which we derive the ability to set the time. But we can also have amorphous SiO2. And this is the only time you are going to see me use this term as the general public uses it.

It gives you glass, as you know glass. Window glass, bottle glass and so on. But only when I put quotation marks am I using this vernacular, this vulgar term. When I use the term glass up here, I mean no long-range order.

And so I think just to get some nomenclature here so that you will know, you have silicon which is the metal. The oxide is silica, SiO2. And the anion is silicate. And so we will refer to silicate glasses.

SiO4 four minus is the maximum coordination. You can go through. You have aluminum. Al2O3 is alumina, AlO3 is aluminate and so on. I thought, since it is Friday and people are kind of in a festive mood after the quiz on Wednesday, I would take a look at the geography here.

I think we can learn a little bit here. This is Si. I am going to now look at oxides. This is silica, so this would be Germania. GeO2 would be Germania, which is Latin for...Germania. I wonder what the Latin is.

How about Germany? Maybe Germany. Gallium, the oxide is Gallia. What is Gallia? France. France lies to the west of Germany. See, that is making sense. In 203 would be India. India is south of France.

This is the oxide of Polonium, so that would be Polonia. That is Poland. Poland is east of Germany. It is not south of India so it is not so good. This is Francia, which is France. So France is twice on the table here.

We have got to do something about that. This is Ruthenia, which could be Russia, more properly Ukraine. Scandia, well, it is almost Scandinavia, not quite. Hafnia, hafnium was discovered in Copenhagen under the direction of Niels Bohr.

It was an impurity in zirconium. Hafnia is the Latin name for Copenhagen. Holmia is Stockholm. Lutecia is the Latin name for Paris. If you go surfing, you go to Cf 3, California. While we are on the Periodic Table, copper is also geography.

It is a corruption of the ancient word for Cyprus. Cyprus and copper have the same root because copper was mined in Cyprus. Strontium, that comes from the Latin for Scotland. That should cheer the hearts of McDonald and McTavish and so on.

Hesse is the province where Darmstadt is located in Germany where they have that accelerator. So that's Hassium, Dubnium is for Dubna in former Soviet Union. And Berkeley is where we have the accelerator in the United States.

If you had the oxide of Americium, it wouldn't quite be America. It is Americia. There is Europia. Terbia. One town in Sweden is called Ytterby. And we get yttrium, ytterbium, erbium and terbium.

Four elements from one little town. What do you think is in that town? There must be a resource of minerals from which all of these elements were discovered. What else is up here? People. Rutherfordium.

Seaborgium. This is Niels Bohr, Bohrium. This is Elisa Meitner. And now we have our pal Roentgen. He looks like he is going to go on 111. There are Curies, Einstein, Fermi, Mendeleev, Nobel and Lawrence.

E.O. Lawrence was the designer of the accelerator that was put at Berkeley. That is why you have the Lawrence Berkeley Laboratory. There is astronomy here, too. Did you see the lunar eclipse the other night? Tellus is the earth and Selene is the moon.

The moon is above the earth. That is good. Mercury is a fast running planet and it is a liquid metal. Pallas and Ceres are asteroids. And there is the outer reaches of the solar system, Uranus, Neptune and Pluto.

There is so much information. Can you believe it? Enough fun. Now let's look at the conditions that stabilize glasses. And I am going to look at it from the perspective of solidification. Liquid goes to solid.

And I want to ask why something would decide to solidify as an amorphous solid rather than a crystalline solid. And so there are basically three factors to consider. The first one is -- Let's do it in an analogy.

Suppose you were thinking about a game that your younger siblings play, musical chairs. Musical chairs involve moving around while music is playing, and then there is a rush to get to a certain site, a certain chair.

So the chairs are the lattice sites and the people are the liquid in motion. What is going to enhance the ability to get to the lattice site? In other words, to crystallize? Mobility is an issue.

Mobility of atoms in the liquid is going to enhance the ability to crystallize. What is another factor? Well, the arrangement of the chairs. If the chairs are simply arranged, it is easy to get to them.

If the chairs have complexity in their arrangement then it is more difficult. Let's liken that to the complexity of the crystal lattice, complexity of the solid crystal structure. Systems that have complex crystal structures are more apt to form glasses than systems that have simple crystal structures.

And then the last thing is how you're told to race for the chairs. Normally the music is shut off abruptly, but suppose I had a turn on the volume. In some cases, I turn the volume down slowly and in other cases I turn the volume down quickly.

That is your cue to start moving to the lattice site. And the analogous quantity in the basic physics is temperature, so cooling rate has an effect. High cooling rates are apt to quench in the liquid disorder.

High complexity of the solid is apt to make it difficult to make a solid crystal. High mobility is in favor of crystallinity, so I am going to replace mobility with the analogous quantity so that when all of these are high I do not form a crystal.

The inverse of mobility, at the liquid level, would be viscosity of the liquid. Highly viscous liquids that have very complex solid state crystals that are cooled very rapidly will form glasses. And we will look at that in a little more detail next day, but here is what I would like to do, show you something very interesting.

And I said anything could be made noncrystalline. And the one I am going to show you here comes from 1959 when somebody decided I am going to make a metallic glass. And what happened here is Pol Duwez at Caltech, not far from some of the places we just looked at on the chart, decided to cool a gold silicon, drop the temperature down very, very low where he could get down to hundreds and hundreds of degrees below the normal solidification temperature, put it on a water-cooled copper wheel, cooled at a rate succeeding a million degrees per second and quenched in the disorder of the liquid state.

So this is metallic glass. This has no long-range order. This is one giant amorphous mess. There are no grain boundaries. There are no grains. There are no dislocations. Listen to this. It doesn't have the ductility of aluminum.

It is very, very different. We will talk a little bit more about that, but I have to do something special today because Sunday is Halloween and I cannot have you all coming to my place. Oh, I forgot to show you this.

Somebody sent me this. Natalia Cherenkov sent me this. This was late in the game on Wednesday. Did you catch this? [APPLAUSE] See, we are everywhere. 3.091 is everywhere. I am going to show you some beautiful glasswork of Dale Chihuly from Seattle.

And then what we are going to do is do some trick or treating here. Do you think we could dim the lights a little bit? I think it is a little bit too bright for this sort of thing. What we are going to do is share.

[APPLAUSE] I don't want to hit one of those cameras, though, because I don't have insurance like that. What we are going to do is cheat a little bit and come up here and throw some up this way and up this way and up that way and over there.

Now, you have to open them up and share. You're supposed to be very group-oriented here. And those who don't get any, they're bad for your teeth anyway. Who didn't get anything? Oh, you didn't? Who is sharing here? Come on.

If you didn't get the handout, raise your hand. You guys got about four bags and you are asking for more. One last one. Where is it going to go? I've thrown about five bags up there, so I am going to put this one and you can share.

All right. Stay out of trouble this weekend. I will see you Monday.

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