In the previous lessons, we've been describing the behavior of

the radius ratio and how that radius ratio ultimately leads to

the coordination number that occurs in materials in crystalline state.

I'd like to illustrate how we can understand the coordination number, and

how the coordination number relates to the radius ratio.

And then, to determine whether or

not we can understand the structures that we see in materials.

We're going to begin with the material cesium chloride.

We've talked about this material before.

The first thing that we're going to do is,

we're going to look at the radius of the cation.

Then we're going to look at the radius of the anion.

And we're going to make the ratio.

And that ratio turns out to be 0.912.

And when we consider the relationship between radius,

ratio, and coordination number,

we find that cesium chloride lies between 732 or

.732 which is the lower end of the radius ratio,

and up to 1 which is the, associated with a radius ratio

of the cation and the anion being equal to one another.

Therefore, this particular radius ratio that we have calculated for

cesium chloride, puts us in the middle there.

So what we expect to see in cesium chloride structure,

we expect to see a coordination number of 8.

Now let's go one more and let's take a look at sodium chloride.

We'll look at the radius ratio between the cation divided by the anion and

when we look at this radius ratio, we see that the Na+,

Cl- ratio of 0.541 puts us right in between

the radius ratio associated with 0.414 up to 0.732.

That means we're in the range of having a coordination number of 6.

I can make some illustrations of this,

using a three dimensional structure that we'll bring it,

let's return to the three dimensional model that we described before.

Where in this case we're going to be illustrating the relationship between

the radius ratio and the coordination number in a material like sodium chloride.

If we focus on the white ion that is sitting in the middle of the structure.

We'll let that represent a cation.

And that particular cation is surrounded by black anions.

And what we're seeing here is that that cation has a coordination number of six.

That is there are four black spheres that are in the plane of the white sphere.

And we have one directly above and directly below.

If we would move to a black position, we would see exactly the same result.

in other words, the coordination number would be six.

If we go back and review the description that we made with respect to radius ratio.

Looking at the radius of the cation divided by the radius of the anion for

sodium chloride, we see that that should lead to a coordination number of six and

indeed when we get to describing crystal structures in the next module,

we'll be looking at materials like sodium chloride and in fact the structure that we

see for sodium chloride is illustrated by the 3D model that I have in front of me.

Thank you.