Uploaded by JUSTANEMONERD on 18.12.2012

Transcript:

PROFESSOR CIMA: So Bravais started thinking about--

OK, that's fine. This is what the unit cell has to look like.

Where did the atoms go? Am I free to put the atoms anywhere?

So he was concerned with what's called a lattice. And what does that mean?

Well, Bravais took a look at these simple shapes in two dimensions and

realized, well, that's pretty easy, at least for some of them.

If I put-- Look at the square one here.

If I put an atom, or I put a lattice point at each of the corners, I will--

Each lattice point is exactly the same as the other.

So here's my space filling unit cell. And I can arrange atoms at each of the corners

and it will fill space. And the same is true of the rectangle here.

Same is true there. Now here's an interesting one.

He said-- But it gets a little bit more complicated,

because I can't put a lattice point in the middle.

Why do these two differ? Well, this one, the four nearest neighbors

with different distances, right?

But here, one in the center, the four nearest neighbors of every lattice

point, are equal distant from each other. So in other words, from this one rectangular

space group-- I mean not space groups--

Lattice -- Oh, I'm going to be a careful.

OK. So from this one rectangular space filling

unit cell, I can put lattices on it, two different lattices on it, that

have the same symmetry. In other words, they're both rectangular space

filling unit cells, but one has got an atom centered in the center

and the other one doesn't. That's--

OK. So now let's go to three dimensions.

Oh, no. Sorry, here's another one.

So what do we put at those-- So what's so cool about these points?

What are at these points? Are the atoms?

Sometimes, they're atoms but other times they're not.

So before I go on to three dimensions, I want to look at this.

Here's another tile. And you want to look at this very carefully

and see. OK.

What is the unit cell? Well, the unit cell is just that one.

You can see this is repeated here, is repeated here, and is repeated here.

So this is our unit cell in this pattern. What's at this lattice point, though?

What's at that lattice point is that. See?

These eight tiles are all arranged associated with that lattice point.

And then when I go to this lattice point, which eight tiles is it?

Those. And what about this point?

Those. So we call this the basis.

It's the thing that's at the lattice point. And it doesn't necessarily need to be just

an atom. It could be a molecule.

So in this case the basis is actually these eight tiles, all associated with

that lattice point. So it's just easier to see it.

Before we get into three dimensions, you should understand the two

dimensional one. That's the basis.

Oh, this one's really wild. What's the basis here?

So there's the unit cell. It turns out the basis is that.

OK, that's fine. This is what the unit cell has to look like.

Where did the atoms go? Am I free to put the atoms anywhere?

So he was concerned with what's called a lattice. And what does that mean?

Well, Bravais took a look at these simple shapes in two dimensions and

realized, well, that's pretty easy, at least for some of them.

If I put-- Look at the square one here.

If I put an atom, or I put a lattice point at each of the corners, I will--

Each lattice point is exactly the same as the other.

So here's my space filling unit cell. And I can arrange atoms at each of the corners

and it will fill space. And the same is true of the rectangle here.

Same is true there. Now here's an interesting one.

He said-- But it gets a little bit more complicated,

because I can't put a lattice point in the middle.

Why do these two differ? Well, this one, the four nearest neighbors

with different distances, right?

But here, one in the center, the four nearest neighbors of every lattice

point, are equal distant from each other. So in other words, from this one rectangular

space group-- I mean not space groups--

Lattice -- Oh, I'm going to be a careful.

OK. So from this one rectangular space filling

unit cell, I can put lattices on it, two different lattices on it, that

have the same symmetry. In other words, they're both rectangular space

filling unit cells, but one has got an atom centered in the center

and the other one doesn't. That's--

OK. So now let's go to three dimensions.

Oh, no. Sorry, here's another one.

So what do we put at those-- So what's so cool about these points?

What are at these points? Are the atoms?

Sometimes, they're atoms but other times they're not.

So before I go on to three dimensions, I want to look at this.

Here's another tile. And you want to look at this very carefully

and see. OK.

What is the unit cell? Well, the unit cell is just that one.

You can see this is repeated here, is repeated here, and is repeated here.

So this is our unit cell in this pattern. What's at this lattice point, though?

What's at that lattice point is that. See?

These eight tiles are all arranged associated with that lattice point.

And then when I go to this lattice point, which eight tiles is it?

Those. And what about this point?

Those. So we call this the basis.

It's the thing that's at the lattice point. And it doesn't necessarily need to be just

an atom. It could be a molecule.

So in this case the basis is actually these eight tiles, all associated with

that lattice point. So it's just easier to see it.

Before we get into three dimensions, you should understand the two

dimensional one. That's the basis.

Oh, this one's really wild. What's the basis here?

So there's the unit cell. It turns out the basis is that.