We're going to be describing ionic bonds from the point of view of considering bond force and bond energy curves. The remaining part of lesson six will be given in lesson six B and C with a continuation in the concept of bond force and bond energy curves, and their applications. The first thing we'll do is to develop the bond force. And for ionic bonds, it's particularly easy. Because in this system, what we're going to do is to use a material like sodium chloride or cesium chloride, common salts. In this case, what we do is we take the sodium and the chlorine, and we create ions, so that's going to require some energy. We're going to separate those by a large distance and then we're going to allow the force of the traction associated with the positive cation and the negative anion. Once we've developed the bond force curve, then we're going to describe the bond energy curve based upon some important considerations between the relationship of force and energy. 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, which means that the derivative of that energy is going to be equal to zero or that's the force is equal to zero at that spacing that is associated with the equilibrium position. When we look at these curves, we want to pay some attention to the behavior of the attractive energy curves and we want to look at this as a function of energy that we're putting into the system by increasing the temperature. And as we increase the temperature, one of the things that we see is a shift in the location of that space that we're referring to as our equilibrium space. And as the amount of energy we put in increases, so increasing the temperature of the system, we wind up drifting slowly to the right, suggesting that that position is beginning to increase as a function of temperature. We might be able, therefore, to use this information to correlate it to a property such as thermal expansion. When we compare these two materials, material A and B, their behavior is slightly different. In case A, the energy of the bonds are stronger than they are in case B. And the thing that we also see is that the curves are more symmetric in the case of B than they are in A. We'll see how this behavior generates into some very interesting behaviors for materials. Now, when we look at that energy minimum, we see that the associated energy minimum and the minimum energy for B, the B is less energetic than the A, meaning that there's a stronger bond and we might be able to correlate that with melting temperature. And when we look at the two blue arrows indicating the asymmetry associated with the asymmetric behavior as the ions vibrate back and forth, we can see that the material that has the higher melting point will wind up having less asymmetry than does material B. And consequently, we can relate both the minimum energy to temperature and we can relate the asymmetry in the bond energy curve to the behavior that we referred to as the coefficient of thermal expansion. In the next module, we're going to be exploring how we might be able to apply completely the characteristic associated with the asymmetry in the curve and the melting temperature of the material. Thank you.