And now we're going to go down to the plain that is three-quarters

of the way up or a quarter of the way down, and that's our plain.

And on that plain I'm going to put the next atom.

And so now I have two of my atoms so far included into this structure.

And now we'll go down to 0.50.

And when I do that, my position, according to the structure to the left,

the atom position actually sits on the face.

But now what we're really trying to do, is to develop a relationship that will take

us back and forth between the radius of the atoms and the edges of the unit cell.

So in order to do that, we need to calculate how many atoms we actually have

moving from z down to the front corner of the cell.

So as a consequence, what I'm going to do is, I'm going I'm going to imagine that

atom actually sits here and it's going to be right there along that body diagonal.

So it doesn't exist there.

But there is in fact a space that would be equal to

the dimensions of the atom that is at the face centering operation.

Now what I'm going to do is, I'm going go down to 25% up the z-axis or

a quarter the way up the z-axis.

And that's my plan of interest.

And the position of the atom that I have on that particular plane lies

where the atom has just appeared.

And in order to get it a long the body diagonal of the cube,

what I'm going to do is just displace it.

And so now I have a body diagonal for that.

Now remember, the atoms don't actually exists at this points,

but I've included those atoms there, so

that they actually are controlling the spacing between the blanks.

Now, the last plane that I'll look at is the z = 0,

so now I have an atom at that front corner.

So I'll draw my line that goes between the position at z = 1,

all the way down to the position at z = 0.

And now what you see is, those atoms are sitting at the particular positions that

are equivalent to those positions that lie along the body diagonal of the cube.

And I'm doing this primarily because I'd like to be able

to develop this relationship between a0 and r.

If I look at the atoms, and those atoms are, in effect,

tightly packed along that body direction, I would have a total of eight of those.

And when I look at those 8 radii,

I can relate the line a0 onto the square root of 3,

which is that magnitude of the body diagonal to the value 8r.

So now what I've done, I've come up with a relationship between a0 and r.

I can use that relationship in the following way.

I can describe all of the structures that are of the type of diamond cubic.

Where I have 2 atoms per lattice point and they're the same, and

let's consider what materials they are.