Welcome back. In this lesson we're going to be describing the concept of the driving force. Let's take the simple concept that we have introduced previously. We're going to be looking at a pure substance. And remember that a pure substance is a material that melts at a single temperature for a fixed pressure. I've indicated on this diagram that's up on the screen, two phases. A blue which represents the solid, and the red, which represents the liquid state. And what we've done is to plot them in a way such that their behavior reflects the behavior of the change in free energy of each of the two phases. Now, one of the things that's important is that, at the equilibrium melting temperature, the free energy of the two phases are equal to one another. So that point becomes fixed. In addition, when we look to the right of the melting temperature, that is to higher temperatures, what we will see is that the phase that is the stable phase is the liquid phase. And you can see that and notice that by recognizing that the free energy of the liquid lies below the free energy of the solid, which is represented by the blue line. Now, when we take a look to the left, what we're now looking at is the stability of the microstructure, which is the solid. And what we see, of course, is that the blue line lies below the red line, meaning that we have a stable microstructure in the case of the solid. I've also indicated the term delta T, which represents undercooling. And we talk about undercooling, it's the temperature below the melting temperature. So when we define delta T in this way, what we're actually saying is below the equilibrium melting temperature, the undercooling, delta T is positive. Now, we start out with the free energy of the two phases being equal at the equilibrium melting temperature. And as a consequence of that, the change in free energy associated with a particular volume of material for the liquid to solid change is going to be equal to zero. And what we can do is we can substitute that into the entropy relationship. And basically what it says on the left hand side is that the entropy when we go form the liquid to the solid is going to be equal to the change in the enthalpy for that process divided by the equilibrium melting temperature. Now one thing we should point out here is if we look at the signs of the two expressions, the one on the left and the one on the right. In the case of delta V for entropy, we know that the entropy of the solid is below the entropy of the liquid. Therefore that term is going to be negative. And what that implies is what has to be true on the right hand side is that the delta H of liquid going to solid must be also negative, which means we're dealing with an exothermic reaction. So the solidification, or the development of a solid phase from a liquid is going to be an exothermic process. Now what we can do is we can take a look at any temperature now and consider what the free energy would be. And the way we're going to do this is to assume that the heat capacities of the solid and the liquid are the same. That's just the simple approximation that we can use in the vicinity of the melting temperature. When we do that, and we substitute that into our Gibbs free energy equation, which relates the free energy to the enthalpy and the entropy. What we wind up is that the change in free energy of liquid going to solid per unit volume is going to be proportional to the change in the enthalpy divided by the melting temperature, times the amount of undercooling. So, those terms, delta H per volume, divided by TM, those are all positive terms. And what we have with respect to the positive undercooling is another term which is positive. So what that is in effect doing is it's showing us that the free energy change of liquid going to solid is going to be negative, or hence, exothermic. And it's going to be controlled by the value of delta T. Again we take a look at the two phases, the liquid and the solid. And when the liquid is cooled from below the equilibrium melting temperature there's a driving force for solidification, and that's indicated by the red circle. So going from the liquid to the solid phase, the more material we transform, the lower that free energy will become. And so we can see how that behaves with respect to the change of going from solid to liquid. Now, when we take a look at what happens when we go to the solid phase, we're in a condition where the solid has a lower free energy than does the liquid phase, and that's what's driving the reaction. So homogeneous nucleation, and what we mean by the term homogeneous is the fact that this process is going to be occurring randomly throughout the structure. So it's not going to occur specifically at interfaces like the mold wall that separates the exterior from the interior liquid that's being solidified. So what's happening then is that the solidification process is occurring throughout the liquid, but it's occurring in a random way. We'll be describing more of this as we go further into this module. Thank you.