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ROFESSOR CIMA: And this graph is just what I've just drawn on the board,
except this is a real one. This one shows--
I don't have a pointer. Yeah, here it is.
And you can see that at low temperatures, it's all solid, and
they're completely miscible. Copper can sit on a nickel site in the nickel
crystal, and the nickel can sit on a copper site in the copper crystal.
So why is that? Let's look at some properties of copper and
nickel. So copper and nickel--
structure, size-- these will be in angstroms--
electronegativity, delta H of vaporization, molar volume, and I'll
get to the last one. So here's some properties.
What's the crystal structure of copper? It's on the right hand side of the transition
series. All of those are pretty much--
FCC, thank you. What about nickel?
It's also FCC. That's good, right?
Because if I started dissolving-- let's say copper was BCC, and I started putting
nickel in it and nickel was FCC--
then at some point, I have to change crystal structure.
So one of the requirements for full solubility, across the phase diagram,
is that they have-- each end member has the same crystal structure.
Size. Here's the metallic radius from your periodic
table, 1.28 angstroms and 1.25, pretty close.
Electronegativity, 1.90 and 1.91. Heat of vaporization, 304.6 kilojoules per
mole and 371. And molar volume is 7.11 grams per cc and
6.59. Now, why'd I do these?
What's heat of vaporization related to? We've talked about this numerous times.
Heat of vaporization. What does it take--
all this is is taking an atom in a crystal and making a vapor molecule,
or atom in this case. Well, what do I have to do to do that?
Break some bonds, right. So this is somehow proportional to the bond
energy. And I don't have a good feel to know whether
these are similar or not. But one way people normalize these is to divide
this by this because these are, basically, the bond energy per unit volume.
And that's a good way to compare these two materials.
And so if you do that, you'll have something that has units of energy
divided by volume. Does anybody know what that ends up being,
energy divided by volume? Turns out it's units of pressure.
So this is called the internal pressure. It's not really a physical pressure, it just
basically has units of pressure.
But it's something-- you can think of it, it's like the pressure holding
this thing together. Well, these end up being about 42.8 here and
56.4. So this ends up being about 2.3% different
with the size, and about 24% different here.
And apparently, everything else here looks close enough.
Well, 24%, I don't know how to put that in scale.
But I can tell from the experiment that it didn't matter, at least in
these temperature ranges. So that's the first thing.
So maybe it doesn't surprise us, because of the similarity between
copper and nickel, that you can completely dissolve one in the other.