In this lesson, we're going to talk about structures in which we have two ions or

two different atoms per lattice point.

What I've illustrated up here is the Cesium Chloride Structure.

And when you first look at the cesium chloride structure on the left,

what it appears to be is body center cubic.

However, we need to go back and

consider exactly what we mean by the Concept of a Lattice Point.

Remember if it's body-centered cubic, then we have two equivalent lattice points.

All those that lie on the corners and

the one that lies wholly in the interior of the unit cell.

Now, if you stand at a lattice point and you move to another lattice point,

the environment that you see around that new lattice point

has to be exactly the same as the environment that you saw in the first.

However, in the case of the cesium chloride structure,

when you're standing on the corner, what you see is the open circle whereas when

you're sitting at the open circle, what you see is that filled in black circle.

So consequently, those are two different environments, so

rather than referring to this as a Body Center Cubic unit,

what we do is we refer to it as a Simple Cubic Structure

in which we have two ions, one cesium ion and one chlorine ion.

And those two ions move together as we translate the unit cell in the X,

Y, and Z directions.

Now there's an alternative way that we can look at the cesium chloride structure.

And we can look at it in terms of having two different

simple cubic lattices that interpenetrate one another.

So for example, if we look at the filled in circles,

we're going to refer to those as the B ions and the open circles as the A ions.

And each of those on the corners has eight

corner positions in one eighth therefore a total of one lattice point for the blue.

And one lattice point to the associated black.

And so consequently we're dealing with two ions per lattice point.

Now, as I say, cesium chloride is the characteristic that we

usually refer to these structures by, by calling them cesium chloride.

But it turns out that there are other systems.

For example, in the metallurgy community, when we look at copper zinc alloys,

which are the bases of brasses, what we have is a structure where

when the material goes through a particular type of transformation,

the copper sits at one of those positions and the zinc sits at the other position.

So once again, it's a simple cubic structure.

Now what we can do is also because we have the relationship between the radius and

the body diagonal of the unit cell, we can actually therefore go through and

make a calculation for the density for example.

So here is the cesium chloride structure.

We have two different atoms or two different ions.

In this case, one at the positions 0,0,0.

And the other one at one-half, one-half, one-half.

Now what we need to do is to turn our attention to what is the diameter or

what is the radius of these two ions?