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PROFESSOR CIMA: So if that's the case, I mean, there's all these advantages
to adding network modifiers. Why would you ever not do it?
And there's a cost to everything. And the cost has to do with the thermal expansion.
Remember, we talked about this last time. The thermal expansion coefficient is a measure
of just how fast the volume changes as I increase the temperature.
And its origin is in the bonding. So let's look at an individual bond between
two atoms. And we know that that can stretch and contract.
And it costs you energy to do that. In fact, we studied this.
If that's the separations between the atoms, and this is the energy, we have
a curve that kind of looks like this. It kind of looks like that.
Now, the important point for thermal expansion is
that this is not symmetric. So I know at a given temperature, this thing
will oscillate back and forth. It's vibrating.
And let's say at temperature T1, it vibrates between these two positions.
So that's T1. And if I go to a higher temperature, it'll
vibrate between these positions. And that's T2.
Now if I look at the average position, the length of this bond, because of
the fact that this is not symmetric, you'll see that the average position
in the bond has changed. And that delta x, or delta r, I guess you
should say, delta r is at the heart of thermal expansion.
That's when we heat it. As we heat things up, they get spread out.
And that's why this is generally a positive number.
So why do I bring that up? Well, here's what happens to thermal expansion
when I add network modifiers.
So here, you can see this is for silicate glass.
And you can see here, this is alpha. It's got units of generally PPM.
1 times 10 to the minus 6. So generally, this is a small effect.
1 times 10 to the minus 6 per degree. And you can see, silica glass starts out here
down below 1. And as I add network modifier, it goes up.
In fact, you get out here to 20%, it's up well over an order of magnitude.
Now, why is that bad? Can anybody tell me why that would be bad?
Anybody at all? Take a guess.
Perfect. Yes?
STUDENT: Thermal shock. PROFESSOR CIMA: Exactly.
Thermal shock. So you take a piece of glass.
Here's my hunk of glass. And you put it on a hot plate.
And it's hot down here. And that means this side is hot, and this
side's still cold. This wants to expand.
In fact, it's got a large alpha. So it wants to expand a lot.
The top's not expanding. Guess what you get?
You get stress, right? You get the strain energy is one half sigma
epsilon. So you get this stress building up.
Some strains taking place. This energy, and as soon as this energy gets
big enough to generate a crack, boom, it breaks.
So the key cost of putting all this stuff into the glass to make a working
temperature work, right? So that you can make things at low temperatures
is that the properties are less of a problem.
Now, I can take fused quartz, and I can put it in that hydrogen flame, and
put it in a bucket of water, and it stays in one piece.
Try that with soda-lime glass. It would be a mess.
OK. Here's some thermal expansions.
These are good things to know. Thermal expansion coefficients.
See, for metals, they're generally in the 10s, or, oh, are they?
I think that's right. I think that should be 8.9, I'll check that.
And 4.9. 4.5.
That can't be right. Something got garbled there.
I'll fix that. But you can see for quartz, its way down here.
0.5 or 0.6, fused quartz. Now, we talked about the confusion between
quartz crystal. It's different than crystalline quartz.
Quartz crystal is what? Who can tell me?
You know, the fancy wine glasses and stuff? Yeah, it's the network modifier in silica
is lead. So it's lead crystal.
And why do they use lead? Anybody can tell me?
Certainly doesn't improve the thermal expansion. You can't put them in the dishwasher, that's
for sure. Not cheap.
It's actually more expensive. Why?
What do you notice about quartz crystal? You take a soda-lime glass and a quartz crystal,
and you put them next to one another, and they look different.
Index and refraction, that's right. Lead, because of its larger number of electrons
in it, gives it a much higher index of refraction.
So they've sacrificed the properties. In other words, you can't put in the dishwasher.
But the index of refraction is more like, it's getting closer to diamond.
It's not diamond, but it has a very high index of refraction.
And that's what gives it that beautiful color.