And this time what we're going to do is reposition the atoms.

So the atoms now are located at the titanium at the corners.

And when we start looking at the calcium, it lies in the center.

And those two, then, are just simply interchanged and consequently,

we maintain the one to one relationship between titanium and calcium.

All right, now let's take a look at the oxygens.

Because of our new origin, the oxygens are not located on the faces,

but now they're located on the edges.

So let's do a little bit of counting here.

It turns out that we're dealing with a queue,

which means that we're going to have a total of 12 edges.

When we look at each one of those edges wherein oxygen is occupied.

Then what we find is,

each one of those oxygens is contributing a total of one quarter.

So hence, when we sum up all the edges and the one quarter contribution,

we'll get a total then of 12 divided by three or

four which is ultimately going to give us three.

So now we go back and we see the structure of calcium titanate.

Again, one titanium, one calcium and three oxygen.

So everything is consistent here.

If we were to go down the column of the periodic chart and replace calcium with

barium, we would come up with a structure barium titanate.

When we look at the structure of barium titanate,

it's similar to what we saw with calcium titanate with the exception that

the titanium is now displaced in the center of the unit cell.

As a result of that displacement, what we see is on the diagram to the right,

we see that the titanium has been moved up relative to the oxygen.

And then what we find is as a consequence of that charge displacement,

we develop a dipole that's associated with the structure now.

So we have a dipole.

And what does that mean?

Well, what happens in this particular case.

If we were to take this unit so and compress it along the C direction or

the Z direction, what we could do is to move the titanium back into

the center of the cell and the dipole then winds up the superion.

Well it turns out that there is a very fascinating material that can be

developed as a consequence of utilizing this structure, and that is we can produce

a material which can take electrical energy and mechanical energy,

or mechanical and electrical, and go back and forth between those two.

And this then becomes the basis for

something that we refer to as a transducer.

The last structure that I want to introduce in this lesson

is that associated with a crystalline polyethylene.

And remember we can begin to think about these polymer chains as spaghetti.

And what we've done in this particular case is to align each one of those

change in such a way that we produce this unit cell that happens to be orthogonal.

So the a, b and c have different dimensions but

again all of those interaxial angles are 90 degrees.

So you can begin to see as we move away from some of these simple structures and

we come in to these more complicated structures that we can still begin to

analyze the individual crystal structures of the various materials.

It just takes a lot more detail in order to do that.

Thank you.