Lecture 21: Properties of Inorganic Glasses, Engineered Glasses

Slides (PDF)
Archived Notes (PDF)
Idle Mind Solutions (PDF)

A couple of announcements: tomorrow we will resume testing. We will have quiz eight based on the two versions of homework seven, one of which the second one, the beta version, I've relabeled homework eight.

And, it's posted on the Web as such. So that there's no confusion, there's a homework seven, second homework seven: one focused on x-ray diffraction, and the other one had x-ray diffraction and defects.

So, that's the subject matter for tomorrow's ten minute test. And, I think that's all I have by way of introduction. Anybody recognize the music? Philip Glass, yes. What else would you play if you are teaching amorphous solids? You could play something like Glass Onion by The Beatles if you can stand the Beatles.

But, I didn't want to do that. Oh yeah, there's people my generation, two categories: those who think the Beatles are great, and those who think they are just, ahem, and I'm in the second category.

They bore me. Anyways, this is what we were looking at. So, what we want to do today is continue the treatment of glasses. Last day, we saw that amorphous solids were formed under certain conditions.

And these were the three that we enunciated. Glass formation is enhanced. And here I'm talking about liquid to solid. We can also form glasses by vapor to solid. But, I'm talking about the dominant form of glass formation.

If we have a highly viscous liquid that is trying to rearrange itself to find a rather complex crystal structure in the solid, and the cooling rate is very, very rapid, those three factors together will make it difficult for the atoms to find their proper lattice sites.

And as a result, some of the disorder of the liquid will be quenched in. And the result will be a glass. And, today I want to study a particular form of glass which is the dominant one you know: silicate glasses.

And, these are based on silica. And, we are going to study their structure and their properties today. And so, the first thing we want to recognize is that we are talking about something that's inorganic and covalent.

It's covalent in both silicon and oxygen. We form sp3 hybrids. So, we have the capability of forming four bonds. And, obviously, oxygen forms two, and then two of its pairs of electrons are in non-bonding orbitals.

Silicon, on the other hand, has four electrons, each of which shares. And, the difference between what you're seeing here and what you are seeing in something like diamond is that in diamond or in crystalline silicon, all of the atoms on the board would be the same.

We'd have either all carbons sp3 hybridized, or all silicons sp3 hybridized. Here we've got silicons and oxygens. So, each silicon has four oxygens as nearest neighbors. And, if the atoms align perfectly, we will end up with something that is crystalline.

But, Tom, if we could go to the document camera and like to show what the basics of glass formation are. Consider the yellow atoms as being silicons and the gray atoms as being oxygen. So, you see, every silicon has four oxygen atoms.

And, every oxygen atom lies between two silicon atoms. And, these are both sp3 hybridized, but there's a difference. The difference is that in the case of silicon, all four bonds are specified in space.

But in the case of oxygen, this bond here, the bond that bridges the two silicons, it can maintain the 109° angle, but rotate because the other two orbitals are simply containing nonbonding electrons.

So, because this is free to rotate, we have the possibility that in the liquid state, it's twisting and turning every which way. And then, as the temperature drops, and the material is getting the signal, it's time to form the solid.

These have to twist around. They have to align themselves perfectly. If they do so, we'll end up with something that looks like this. Now, this, strictly speaking, is not crystalline quartz. It's a cousin of it.

It's a vertside structure. But again, you can see sp3 hybridized yellow atoms with bridging gray atoms. And, when everything lines up we end up with something that's a three-dimensional crystal. So, you see something that is net cubic.

You've got two atoms per lattice point and so on. There's an 001 plane, 002, and so on. Everything is making sense. And the same thing happens here. If this falls and forms on a line, then these three will line up as they do across this 011 face.

But, if the solidification occurs at a rate too rapid to allow everything to twist around, we end up with something that fails to achieve crystallinity. So, this is the origin of the crystal structure that we see here.

So, again, just to recap, the silicon bonds specified, they're fully specified. They are specified in three directions, whereas the oxygen bonds are specified only in two dimensions, and therefore, there is one degree of freedom.

And, this is where the cooling rate comes into play because the cooling rate can quench in the motion before everything has twisted to rearrange itself. So, the first thing to note, second thing is that we observed that this can continue without limit.

There's no reason for this to terminate. So, we have long chains here. So, this is, in essence, a polymer. This is a polymer, and SiO2 is the mer unit. You might say, well gee, I see four oxygens bonded to the silicon.

But each oxygen is shared by two silicons. So stoichiometrically, it's SiO2. It all comes out in the wash. So, you could think of this as long spaghetti. That's what we're looking at: molecules that are very long.

And, to make matters worse, they entangle in the liquid. So, they crisscross each other. And now, they have to disentangle and line up in such a way as to give us something that is crystalline. So, what about evidence of disorder? Tom, may we go to the computer graphic please? So, if we want to look for evidence of disorder, let's use some x-ray diffraction.

And here, you have two specimens. The upper one is cristobalite, which is one of the several crystalline forms of SiO2. And here you see this is intensity versus some function of angle. And, as you expect, if something is crystalline, you would get distinct peaks.

And those peaks come out of the selection rules, which you know on the basis of constructive and destructive interference. The lower trace is that of amorphous silica. Now, note carefully, it's not a featureless spectrum.

It has one feature. It has one feature. There's one broad peak. And why is there one broad peak as opposed to no peaks at all? Because in silica, there is short range order. I know what the local environment is around every silicon.

It's four oxygens. We know the silicon-oxygen bond distance, and we know that each of these is at 109° from the central silicon. And that gives rise to this one broad peak. After that, where the second nearest neighbors lie depends on how those backbones were twisted and turned at the time that motion ceased.

So, the point here is that in the glass, we have no long range order. But we do have short range order and the x-ray diffraction spectrum gives us that quite vividly. So, now, let's look at the energetics of this.

Let's look at energetics of glass formation. First of all, which do we expect to be lower energy, the crystalline form or the glassy form? Which one would be lower energy? Well, how do you attack a problem like that? Well ask yourself, what's the physical metric of energy in this system? It's bond formation.

We know that bond formation lowers the energy of the system, that is to say, makes it more negative. So, where do I form more bonds, when things are tightly packed in a crystalline array, or when they're loosely packed in this disordered glassy arrangement? Well, clearly the crystalline array gives us the most intimacy.

And so, therefore, we would argue that the crystalline solid is at lower energy. And, it achieves lower energy by forming more bonds via higher bond density. Well, higher bond density would mean that for a given mass of material, if I have a higher bond density it would be a more compact structure, more bonds per unit volume.

So, this leads to volume as a measure of disorder. So, I want to show you a trace that comes out of your reading. This is from the lecture notes, the archived lecture notes. And, what we're looking at here is volume on the ordinate as a function of temperature.

And, we're going to look at this in some detail. So, I'm going to spend a little bit of time on this because this teaches us what's going on in these systems energetically using a macroscopic measure, the volume.

It's trivial to measure volume. You could use Archimedean displacement. It's very easy to measure volume. All right, first of all, there's a typo in the book, excuse me, in the archive notes. I think it's pretty clear that when temperature falls, it's cooling.

So, just be mindful of that. So, the first thing I want to do is get you referenced against the crystal. So, I'm going to use T colors today, all right? So, let's start, since we're at MIT, we'll go on the red line.

OK, so here's the red line. We start up here. We have a given amount of silicate glass. And we decrease the temperature. That's what cooling means. We decrease the temperature, and if this is to form the crystal, in other words, I cool slowly enough that the atoms can rearrange, as is typical of crystalline solids, there is an abrupt change in volume at the freezing point.

The liquid turns to solid and the system contracts in a discontinuous manner. The volume of the liquid is substantially less than that of a solid typically. There's a few exceptions, and we know what some of them are such as ice, such as silicon, and a few other important substances.

But, the vast majority of substances pack more tightly in the solid state. So, here we have the volume of solidification, and then as we continue to decrease the temperature, the volume decreases. You know about thermal expansion, right? What's happening in thermal expansion? The atoms are moving about their rest positions, and so, here we finally get to a temperature at which we have enough energy to break the lattice energy.

And now, we does continuously jump up to the liquid state, and away we go. So, this is the reference. And by the way, notice one thing here, that the change in volume per unit change in temperature is much greater for a liquid than it is for a solid.

And, you can continue that. The unit change in volume per unit change in temperature is greater for a gas that it is for liquid. I mean, this is the basis for thermometry, right? If you've got mercury in a glass bulb, and temperature changes, what you are betting is that the unit change in liquid volume, which is pretty much constrained in one dimension because we have a very tiny cross sectional area, you are betting that the unit change in liquid volume is substantially higher than that of the unit change in the solid volume, in other words, if you will forgive me the term, the glass thermometer that contains the mercury.

It wouldn't do you any good if the mercury were expanding and the glass were expanding. That would be useless as a metric, wouldn't it? So, what we are betting is that the unit change in volume of the liquid is substantially greater than that of the solid.

And, you could see that that would be the slope of this line. This would be dV by dT. And, I've indicated this. This is the melting point. Now, let's go down the green line. Now we're going to go down the green line.

The Green line starts up with the same liquid, but we're cooling at a much more rapid rate. We're cooling so quickly that all of the atoms can't twist and turn and find their crystalline positions.

And so, we just go zooming right through the melting point with no substantial decrease in volume. We continue to cool, cool, cool. Down here, we're acting as a liquid below the normal melting point.

We have supercooled liquid. And, finally, we get to a temperature below which the change in volume levels out to that of what you would expect down here in the crystal. And, this knee in the curve is called the glass transition temperature.

So, above the glass transition temperature, this material is behaving as a liquid. And, you know that viscosity is strongly dependent upon temperature. So, I'm not saying that this is flowing like water.

It starts off flowing like honey, and down here, it's flowing like honey, the proverbial molasses in January. It is viscous, but very, very viscous. But finally, down here, at this lower temperature interval, it's immobile.

It's behaving as a solid. But the interesting thing here is that this knee in the curve is the function of the cooling rate. We have a rate dependent process. As you'd expect, if I cool more quickly, it's like musical chairs.

Instead of gradually decreasing the volume, I just cut the volume. So, let's do one more. So, by the way, what's the point of all this? I forgot. By the way, we said that volume is a measure of disorder.

So, if we use, let's say, this down here against the origin is room temperature. So, the projection of this lower line would be the unit volume of the crystal. And, you could see the projection of the upper line here is to a higher value.

And, that excess volume is some measure of how much disorder has been quenched in. If the crystal had truly formed, we would have the volume of the crystal. So, let's do it again, only this time we go much more slowly when we cool.

If we go more slowly, doesn't it stand to reason that the system will have more time to rearrange? And so, therefore, the amount of excess volume that quenches in is not as great. So, this excess volume is not anywhere nearly as great.

So, what have we shown? We've shown you a lot. We've shown you the dynamics of glass formation. So, let's write this all down. This is really good. What do we see? We're looking at liquid to solid transformation.

And, we have two possibilities. We can either make a crystal or we can make a glass. That is to say, it can be crystalline or amorphous. And, how do we indicate? We indicate solidification point.

The solidification, the metric that we're using for solidification is the knee in the curve of volume versus temperature because we say, we know we've achieved solidification on the basis of coefficient of thermal expansion.

Coefficient of thermal expansion of the solid is substantially less than the coefficient of thermal expansion of the liquid. So, if we're looking at V versus T, we define the temperature at which solidification has occurred when we switch from the high value of the liquid to the low value of the solid.

And the only difference between solidification to form a crystal, and solidification to form a glass is that if we look at V versus T for crystallization, I have a steep slope up here. I have a gentle slope down here, and I have an abrupt change.

I have an abrupt change, whereas in the case of glass formation, V versus T, this is glass formation. In that case, again I have the steep slope at high temperature. I have the shallow slope at low temperature.

But, there is no abrupt change. So, this is called the melting point, and this is called the glass transition temperature. In both cases, it is the coefficient of thermal expansion that clues you in, because a glass formation, there's no abrupt change in volume.

And, so this is going to be the lowest volume. And, this is the volume of the crystal. And, this is the volume of glass at some particular cooling rate. So, this is V1. And, just for reference, V crystal is down here, and this excess volume is the measure of disorder.

Excess volume is the measure of disorder. So, we're in good shape. Now, we can make the definitions. Let's make the definitions, the one, let's compare the two forms of solidification. So, the first one, crystallization.

In both cases we are going from liquid. In this case, we go from liquid to crystalline solid. And, this occurs at a temperature called the melting point. And, the melting point is not a function of cooling rate.

As we are going to learn later, it's a function of certain environmental constraints: pressure, composition, but it's not a function of the cooling rate. It doesn't matter if I cool water, which does not form glass.

If I cool water slowly, or if I cool it rapidly at one atmosphere pressure, 100% water should change from liquid to solid at zero degrees Celsius always. OK, so, the melting point independent of cooling rate.

Now, contrast that with what we've observed here for glass formation. This is, again, a form of solidification, but it's a different end result, same composition. So in this case, we have supercooled liquid.

It's liquid, but just to remind you, it's liquid that's cooled below the melting point, T less than melting point. And it transforms to glassy solid or amorphous solid. And, this occurs at a temperature known as the glass transition temperature T sub g.

And, unlike the melting point, T sub g is a function of the cooling rate. It's a function of the cooling rate. So, that's an engineering tool we can use. If we want to quench in more free volume, we cool at a higher rate.

If we want less free volume, we cool at a lower rate. So, this has to do with the intersection between the theory, and the process. So, that's what's going on in these silicate glasses. And, I don't want this to be so narrowly focused as only on silicates.

There are other such systems, in other words, inorganic, covalent networks. So, let's take a look at them, other glass forming oxides. What are we going to look for? We're going to look for oxides that have the capability of forming covalent bonds.

Covalent bonding of the metal atoms, of metal to metal, right, silicon is more metallic than oxygen. So, we have covalent bonding of metal to metal via bridging oxygen. Oxygen acts as the bridge between the metal ions.

So, we never have two silicons bonding to one another. We always have a silicon to silicon via the oxygen. So, let's look at them. Well, we've got silica. If we believe Mendeleev, then Germania should work.

GeO2 should work, so, germanate glasses. We can also look at group 3, B2O3. Boric oxide can form borate glasses. And, I think I've got a slide of that. Yeah, and on the left side, we see boron as group three.

It forms sp2 hybrids. So, sp2 hybrids will give you three bonds, 120° in the plane. So, this crystalline. This is crystalline B2O3 on the left side, whereas on the right side, you see that sometimes there is the freedom to twist.

And, as a result, this is not lying in the plane. It's hard to see this, but the right-hand image rises and falls above and below the plane of the projection. And, the result is we have disorder. And, you can see with the naked eye here.

Unit volume, if we say in round numbers we have the same number of atoms left and right, you can see that the volume of the glass is far in excess than the volume of the crystal. And, I could measure the change in volume between that of the disordered structure to that of the ordered structure and say the magnitude of that difference is a magnitude of glassiness.

If this is only a small volume larger, it's axiomatic. Then it must mean it's darn close to purely crystalline. So, you can see very nicely. So, this is borate glasses. And, we'll say something about those later.

We can go to group five, phosphate glasses, P2O5, vanadate glasses, arsenate glasses, and lastly, stibnate glasses. So, these are all elements that can form three-dimensional covalent networks via bridging oxygens.

Now, let's look at the properties. It's time to talk about properties. We know enough. Let's go. They are chemically inert. How did we conclude this? They are chemically inert. I've got strong covalent bonds, satisfied octet stability.

These things are not going to react with other compounds because they are stable the way they are, electrically insulating. How did I get that? Same thing. When you have strong bonds, whether it's strong ionic bonds as in sodium chloride, or strong covalent bonds as in SiO2 or diamond, strong bonds mean tightly held electrons.

Now, remember, all that glitters is not gold. But it must have free electrons. So, this will not be a good conductor of electricity. In fact, it is a good insulator. If you go out on the street and you see some of the old telephone poles, you'll see some of these silicate, they're typically brownish.

They are standoffs, where the wires hang from cross member to cross member. They're all made out of these materials. Mechanically brittle. Strong bonds, we don't have the shared smearing of orbitals as we do in metallic bonds.

We don't have that. We have things that are very strong, very directional, and so there's no possibility of glide, optically transparent. Yeah, I know because they are glasses, right? No, they are optically transparent.

Oxide glasses are optically transparent. Metallic glasses, not optically transparent. Why are they optically transparent? Strong covalent bonds. So therefore, the energy levels are far apart. And visible light, with its puny two to three electron volts per photon can't disturb the inner workings of the glasses.

And, they are visually arresting because they conform. And, they don't have to form sharp edges because they are amorphous. So, I showed you last day, here's some more of these Chihuly glasses. How do you get the color? Where does the color come from? Where you get color? How do you get the blue diamond? Well, if the band gap is like this, and photons of light are like this, I need to park some dopant in the band gap.

This is band gap engineering. OK, so those are the properties of the glasses. But, there's one property I've neglected to mention. With the strong bonds, what do you think their melting points are, high or low? They're high, and that's a problem because if I want to process these glasses, I have to go to really high temperatures.

For example, if you wanted to manufacture beer, I mean, soda bottles, you don't want to go up to 2,000°C to melt the glass. The energy costs are going to bury you. So, what could we do? If we were clever about the control of composition, maybe we could decrease the processing temperature.

And, indeed, that is the case. So, what I want to do is lower the processing temperature by weakening the bonds. Well, what are the bonds? They're strong covalent bonds. So, I'm going to weaken them.

What I'm going to do is add an ionic oxide. So, we want to lower processing temperature by weakening bonds. And, these are going to be the bonds along the backbone, silicon-oxygen bonds. So, the gambit is to add ionic oxides.

So, let's look at one. Here's a classic one: calcium oxide, calcium two plus, oxide two minus, good calciums from group two, oxygen from group 16. We want an oxide because we want something that's soluble.

So, let's go. Let's dissolve calcium oxide into silica. So, we dissolve, and calcium oxide is ionic. And it dissociates to give calcium cations and oxide anions. And then, the magic begins. Here's oxygen in a bridging position between two silicons.

And here's this free oxide ion. So, this is the ion. This is a bridging oxygen. And what happens is this oxide ion comes over here and says, I can lower the energy of the system by breaking this bond and turning that structure into the following one.

Instead, oxygen will insert itself. And so, now the chain has been cut here. The chain has been cut. This was a free oxygen. And now, the oxygen has attached itself to one side of the broken piece of chain, and the other oxygen remains attached.

And, now I've got charge neutrality. I've got a two minus here. So, I'll put one minus here and one minus here. So now, the chain has been cut, and just for grins and chuckles, we'll bring over calcium as a spectator to give us charge neutrality.

So, what's the effect here? The effect here is to shorten the chain. And, what happens if you shorten the chain? Well, look at our factors that promote glass formation: viscosity, complexity, cooling rate.

Which one of those is affected by shortening the chain? Viscosity. If you've got long spaghetti strands or short spaghetti strands, OK, spaghetti, macaroni, which one entangles? Which one's more difficult to move around? I know some of you haven't been in a kitchen in a while, but just imagine.

Studying pasta can teach you a lot about macromolecular behavior. All right, so clearly, these short chains now have higher mobility, lower viscosity. Well, if we have lower viscosity then that's equivalent to moving over to the left here.

That's going to decrease our glass transition temperature. So, this will help us process. So, this act is called chain scission. It gives us shorter chains, and the result is higher fluidity. And, with higher fluidity, we don't have the propensity to form glass at the same temperature as we otherwise would.

And so, this gives us the ability to process at lower temperatures. So, just to recap, the way to represent that reaction is to show this oxygen as a bridge. This is bridging oxygen plus free ion - ionic oxygen - gives us two terminal oxygens, terminal because each of these oxygens ends the chain segment that it's attached to.

And, it's got a little negative one charge associated with it. So, this is chain scission, and this lowers Tg. So, that helps us to process. So, what is the menu of oxides that we can use? I said we need something that's ionic so it will donate the O double minus.

If it doesn't donate O double minus, it won't help us with this reaction. So, there is a ton of oxides we can use. Group one, we can obviously use very metallic oxides, lithium oxide, sodium oxide, potassium oxide, etc.

We can pretty much use any group one oxide. I've shown you calcium oxide. If calcium oxide works, what's an even more strongly ionic oxide than calcium oxide out of group two? Magnesium. Of course, it's smaller, got a higher charge density, higher Madelung energy.

Doesn't that sound a little bit like quiz or test number two? Yeah. OK, so we could use any of the group two oxides. They would work in chain scission. How about group three? Any oxide donor, good oxide donor.

And, we use these. I'm going to show you examples in commerce where these are used, not the first one. Scandium oxide is not used. It's so, so expensive. But lanthanum oxide, maybe, but in your catalytic converter in the automobile, you have yttria-stabilized zirconia acting as the sensor.

And, we can use some group four. Group four we could use lead oxide. We'll see an example of that. Or, you could use tin oxide. This is the divalent oxide, and this is the tetravalent oxide of tin.

So, these are all oxide donors, and you will see various combinations of these added to glasses in order to achieve the kind of chain scission that we are looking for. And here's some really interesting data.

This is XPS data. This is XPS data. And, what we're looking at is sodium oxide. This is Na2O-SiO2. So, it's slightly modified. These materials, all of them, I forgot, I meant to give the term for all of these types of oxides, the ionic oxides that engage in chain scission, the term used for all of these oxides is network modifiers: to modify the network by cutting the chain length.

So these are called network modifiers. So this is a slightly modified network that these data come from. And, all of these are called network formers. Let's get that up there. These are all network formers.

Network formers, we form the network, we modify the network, and tailor the properties. So, this is a sodium oxide silica, and overlooking at is XPS of two different states. We're looking at the oxygen 1s electron in this particular system.

And the blue line is the raw data. So if you had that blue line, you'd say, gee, it doesn't have the shape you'd expect. It lacks symmetry. So, what you can do is imagine that the blue curve is, in fact, the sum of two separate curves.

And, there's a mathematical technique called deconvolution that says if the blue curve were the sum of two properly configured curves, what would they look like? And so, what you do is you deconvolve the blue curve into the red and green curve.

So, if there were a red curve of this magnitude, and a green curve of this magnitude, with the right symmetry, they would sum to give us the blue curve. And furthermore, we see that there's two curves that have been ascribed to bonding oxygen, or what we call bridging oxygen, and what I'm calling terminal oxygen for the red, or they're calling nonbridging oxygen.

So, you can actually tell the difference in energy states of those two oxygens because what you are looking at is - this is the bridging oxygen, and this is nonbridging oxygen. And, we're looking at not the valence electrons.

We're looking at the inner shell electrons, the 1s. And so, the presence of the silicon on either side, the presence on the silicon here on either side as compared to the presence of silicon only on one side has an effect on what the 1s electron in the two atoms senses in terms of nuclear charge versus screening of all the electronic charge.

Clearly, in this case, with the silicon, the silicon pulls the electrons farther out than they would be here because here you've got nonbonding electrons not having to go out. So, in this XPS spectrum, it's possible to see the subtle difference in the energetics of the two electronic states, which I think is just so cool.

It's very elegant. And so, let's keep going. What's the worst we can do to modify the network? I said this is a long chain. I keep cutting, and cutting, and cutting, until in the extreme I'm down to one unit.

I can't get any smaller than one unit. So, what's one unit? It's silicon with four oxygens: one, two, three, four. Silicons plus four: each of the oxygens is minus two, so this has a net charge of four minus.

So, it's just a single complex anion, right? It's just something with a net charge of minus four. And, this is called the orthosilicate anion. And, we could make a compound of this stuff. We need to balance it with some cation.

We can't just throw anions around. So, if you had Ca, calcium, you could take two times calcium, one times orthosilicate, this would be a salt. This would be analogous to sodium chloride or calcium fluoride, only here you've got silicate as your anion, and calcium, this stuff here does not form glass.

This behaves as a molten salt. So, it's very poor at glass forming, and will crystallize on cooling. Well, let's look at the compositions of some of these glasses now that we know we can engineer properties by playing with a mix of former and modifier.

There's a few of them worth looking at. The first one is window glass, soda lime. Well, it's soda lime because it contains soda, which is sodium oxide, and lime, which is calcium oxide. What are they doing? They are cutting the chains, making the chains shorter so that you don't have to heat window glass to 2,000°C to process it.

You can process this stuff down around 600-700°C. Let's see, what else do we have here? Borosilicate: this is the workhorse for Pyrex. You have two network formers. You have silica and B2O3, with a little bit of modifiers, sodium oxide and alumina.

Alumina is added to give thermal shock resistance. And, thermal shock resistance comes from a third category called an intermediate. And, an intermediate improves thermal and mechanical behavior by adding void space.

And it does this because of forms, these are covalent. I'm going to show you these are covalent. They are covalent compounds but with a different coordination number. In fact, their coordination number is higher.

Their coordination number is greater than the coordination number of the host network. So, for example, you see up here alumina, the typical ones are alumina, titania, or zirconia. And these typically have coordination numbers on the order of six to eight, whereas silica has a coordination number of four.

So, by having the higher coordination number, when you have rapid thermal change the system doesn't shock and shatter. Instead, there's room for flexure. This allows for some flexure because, remember, plastic deformation is out of consideration here.

There's no opportunity for such things. So, you can see evidence of that. Here's some light flint optical glass, 37% lead oxide. So, what's the lead oxide doing? Two things: first of all, lead oxide up here is a modifier.

So, it's breaking the chains. And secondly, lead is one of the heaviest naturally occurring elements. So, it's got a lot of electrons. So, lead oxide is going to have a very, very high index of refraction.

And, in fact, if you put more than 24 weight percent lead oxide into silica, you have enough chain scission that when you cut that glass, it will look as though it is crystalline. And, that's the basis for lead crystal.

It's lead oxide-modified silicate glass. And, here, they want to use it for high index of refraction optics so that you don't have to wear eyeglasses the shape of Coke bottles. You can now have something that's very, very thin.

And now, they've been able to do this and polymers to allow you to get the performance that you need. So now, here we look at, this is the other curve from the reading. It shows viscosity as a function of temperature, and as I mentioned earlier, very strong temperature dependence.

But what you can see it is, here's pure silica, SiO2. And, if you're going to work with the glass, you have to get the viscosity down to about ten to the fifth poise. Just for reference, water is ten to the minus two poise.

It's one centipoise. So, this stuff is very, very viscous. And, it becomes more and more viscous going through the softening point and finally annealing and strain. And on the next slide are these definitions.

And they are posted at the website. So, you can go through. They are also in the readings. And all they're doing is defining these different points in terms of the change in viscosity. In other words, it is a measure of how quickly the atoms can rearrange as a function of temperature that defines these different breakpoints.

And these are not exact. In other words, it's not as though the working point is ten to the fifth poise. If it's two times ten to the fifth, you can't work with it. It just becomes more and more difficult to work with.

So, if you see people downstairs in the basement of building four in the glass shop, when they're taking something out of the lair, the furnace, when they take the glass out and it's glowing red heat, then it's up here in the regime of working point.

And, as the glass radiates and the temperature is falling, they have a certain time window during which they can form the glass. And if the temperature gets below the softening point, at that point they are not going to be able to shape the glass.

So, this is what you're seeing on this slide. And, you can see how the addition of various elements, if you take a constant value, let's say, take the working temperature, which is in round numbers, ten to the fifth poise, so for pure silica, we'd have to be up here at around 2,000°C.

But if we add B2O3, and some Na2O, now we are operating at around 1,000 degrees. And, if the ads of calcium oxide, lime, now you're able to operate down around 800°. So, you can see how by changing composition, through this mechanism you can dramatically alter the processing temperatures of the various glasses.

And that's exactly what we're doing. So, last thing to talk about is strengthening of glass, how to strengthen glass. Glass is not too bad in compression, but is very weak in tension. So, two ways of doing it.

First is to thermally treat the glass. We are going to exploit the fact that glass has this dependence of quenched in volume on temperature. So, let's go back to this. What we do is, in this case, imagine we are going to treat the windshield of an automobile.

So, we want to make it more resistant to cracking if a stone should hit it. So, this is not to scale, of course. This is glass that's being processed. It's in. It's above its softening point. Rather than just let it cool, and cool very slowly, what we can do is send an air jet along the surface.

And what that will do, what the air jet will do is cause the surface to cool more rapidly than the center. We know that glass is a poor conductor of heat so we're not going to expect to this going to be isothermal.

So, I'm going to break this in half, and then I'm going to take this part and expand it, OK? And, I'm going to divide the top into two zones. So, this is fast cooling. And, the center is slow cooling.

And, likewise on the bottom side. So, what happens? If you look on this trace, it says fast cooling gives me high excess volume. So, I could say that when this is finished, I could characterize it as follows: that because the upper portion cooled quickly, it should occupy a large volume.

And, the lower portion cooled slowly. It wants to occupy a smaller volume. But, they are joined. So, what does that require? It requires it all be one volume. So, that means the lower part is going to force the upper part in.

So, when the thing, in fact, looks like this, we know that the upper part is on the influence of strong compressive stresses. And as a result, if a stone hits this, instead of simply having to break the bonds, it has to overcome all of the bonds plus the added stress that has been, the material is pre-stressed.

So, now, in order to break this, I have to break both the bonds plus pre-stress. And, again, if you study this V versus T curve, you can convince yourself that high cooling on the outer edge will give you a higher volume.

But, the material is not allowed to delaminate. So, in fact, the surface has a compressive stress that is built-in. OK, well, there are other ways to strengthen it. Let's see, here's one. There's the ability to recrystallize glasses.

In this case, what is done is to introduce crystalline material into the glass during the cooling process. So, now we're going to combine the properties of crystals with glasses. And, this is work that began back in the 50s at Corning under Stookey.

And, what they did was they added nucleating agents to the glass melt. And, these nucleating agents do not dissolve. They are floating around like grains of sand in honey. And, they cause the honey to crystallize out.

And the result is that when this thing grows to completion, what we have is a material that is, these are the various grains. During solidification, these start to solidify, nucleate crystalline glass.

When these grow to impingement, we have something that is in many instances 95% crystalline. And the only glass is this mortar in between, 5% glassy. And, these are the glass ceramics which if you go to grandma's house, you'll see this stuff here.

Remember these? This is Pyroceram glass. It's 95% crystalline, the grain size of about 1 micron, which is large enough to scatter light. And that's why it's white because this is a high band gap material.

It should all be transparent to visible light. But this is white for the same reason that table salt is white. A large single crystal of sodium chloride is transparent. But if you crush it up in a fine powder it appears white because of the scattering.

That's what you see here. And this was designed by Corning, which by the way doesn't make Corning Ware anymore. They moved into optoelectronics and so on, fiber optics. So anyways, if you see this on eBay, you know that this is Pyroceram.

It has amazing toughness. I used to have a demonstration. I had one of these, a sauce pan, and I hold up a 2 x 4 and drive a roofing nail into the 2 x 4 using the PyroCeram saucepan as the hammer. These things have enormous strength, and they are also transparent in the microwave region.

They are great in the thing, and I'm not trying to do a cooking show here. I'm just telling you that these are engineered materials. All right, now, next one is visions. This is visions. Maybe you've seen some of that around.

The only difference between visions is that the crystallites are submicron size. And so, now, they remain transparent to visible light, and they index match them so that the index of refraction of the glassy mortar is the same as the index of refraction of the crystalline material.

And then, they dope with transition metal so that it looks sort of like the old copper, elegant, chi-chi upscale cookware. And, also you can charge a premium over plain, clear, colorless Pyrex. And so, all of this is done by engineering of the molecular architecture.

I'll see you on Wednesday.