And then, what we'll do is to finish up by describing other types of materials and

how we might be able to extend what we've learned in this very simple system.

If we start out with our Na+ and our Cl-, and

we consider what happens as those two ions become closer and

closer, we follow the dotted line as indicated on the screen.

What you're seeing is a plot of the exponential behavior

of the attractive force associated with the positively charged sodium and

the negatively charged chlorine.

And so that becomes then our force of attraction.

And we can describe that force of attraction using a very simple equation

that relates the charge and the distance of separation between the two ions.

And here, that force of attraction is going

to be inversely related to the square of the distance between them.

And so that relationship gives us the calculated plot that we see in blue.

Now, we also have to consider these two ions can't go into one another,

because if they do, then they'll begin to violate Pauli's Exclusion Principal.

So as a consequence, we have to have a short reign force of repulsion

that is associated with that behavior.

So what I've done here is to plot in that blue dotted line

going down into the negative units.

So that's a force of repulsion.

And the behavior of that winds up controlling the behavior of the force

of attraction line, and

I can use a very simple relationship that's given as the force of repulsion.

In this particular case, I've lumped all of the variables and

the constants in the numerator, and

now what I'm going to do is to focus on the one over x to the m power.

And in order for us to be able develop this nice short range force that is

going to overcome the force of attraction, what we need to have is a value of m which

is going to be greater than the value of two in the force of attraction term.

And so when that happens, what we begin to see is a very rapid negative force or

force of repulsion associated with that positive force, and

the combination of those two then develops what we refer to as the net force curve.

What you can see is, first of all, that the force of attraction curve extends

over a long range, which is a long range force of attraction,

and it goes on out to infinity where the force is equal to zero.

And when we look at the force of repulsion, it's a short range force.

It doesn't really begin until the atomic clouds of the cation and

the anion get close to one another.

But what has to has happen is, as soon as they are in the proximity of one another,

then that behavior has to drop off very dramatically in order to create

the bond force curve, the net curve which results in a description

which is what we expect to see in terms of the behavior of this material.

So here is our cation and anion again.

There is our force of attraction curve and our force of repulsion curve.

And that solid line represents the net force that's operating on it.

And I said earlier that there is a relationship between the energy and

the force, and since we have the force curve, we can work backwards and

describe the energy behavior.

Because we know, at the equilibrium separation where the force of attraction

and the force of repulsion are equal to one another,

that describes our equilibrium position.

In terms of energy, that would represent a minimum in the energy, and

at the point where the crossover occurs in force, we're at an energy minimum,