In this lesson we're going to be describing some basic kinetics that we'll use through out this course. We can make a mechanical analog between a process that we're going be studying In terms of the behavior of a particular material. And what we're going to do is we're going to look at a block that is sitting stationary on a flat surface. And if we apply a force to the top end of this block, what we're going to see is that we can track the behavior of the center of gravity of this block, and we can follow it as we apply this force. And we see that associated with that application of the force. The block is beginning to tip on its side. And we're going from position one to position two. Position two represents our new center of gravity. If we continue through and we come to position number three, we see that that center of gravity is changing, it's going up. And as we continue through the process, we see that the center of gravity now is back down to where it was with respect to position two. And then ultimately, when we're in our state of equilibrium, which is position five, we're at an alternative state of equilibrium. And what we'll say then is that either one or five are equivalent to one another. And we're going to be introducing this as an analogy between a liquid and a solid, both being at the equilibrium melting temperature. So, we could represent the solid as one, and the liquid as five. And what that tells us is, because they are at the same position, they're at the same energy, those two phases can go back and forth, and the system is dynamic. It's changing from solid to liquid, but at any time they are always there. We can move away from equilibrium and we can describe what happens. Rather than having a square, we can have a rectangle. We're going to refer to this as metastable because you can already begin to see by looking at this figure that it is in a slightly less stable configuration then it would be in if the sides of the rectangle would both equal. So now what we're doing is we're going to continue the tipping of this block and we're going to follow the progress of the center of gravity as we tip over and now what we see is a difference between position one and position six. Position one is in a state of metastability and position six is in a state of equilibrium. And so we can go in one direction or the other. So this would be equivalent to say looking at our liquid at a temperature below the equilibrium melting temperature, and what that should tell us is that is not the stable state, it is the metastable state, and it ought to transform to an equilibrium state, which is the solid at a temperature below the melting temperature. So we can consider that in the next slide where we extend this process away from these simple mechanical analogs to a process like, solidification at, and melting at different temperatures. So, what we'll do is we'll talk about what happens when we are at the equilibrium melting temperature, so T is equal to T melting. And if we look at a potential energy diagram and I describe the configuration as the solid phase and the liquid phase and we're going to use a behavior that comes back to absolute rate theory. So what I've plotted on the left hand side is the energy of the system. And I have two local minima, one at the solid and one at the liquid configuration, so, both of those are equally probable. And if I look at the activation energy or the amount of energy that I have to overcome to go from state one to state two or from solid to liquid It makes no difference as to whether or not I'm going from solid to liquid or liquid to solid. And that turns out to be expressed in terms of Arrhenius equation. So I have the rate in the forward direction going from solid to liquid. And that's given in terms of this expression where Q represents the barrier to the process, and R and T have their usual symbols for the gas constant and the absolute temperature T. And I want to emphasize here when we're using an expression like the Arrhenius equation, we have to make sure because we're going to be doing division and taking exponentiation and logarithms of these terms, we have to be looking at an absolute unit. Okay, so, we then refer to this kind of behavior as the erroneous behavior. But this is now in the system where we have equilibrium between the two phases. Now what happens if we move away from equilibrium and we're going to be in a situation where we are above the melting temperature in the material. So now to describe this behavior, what I'm going to do is I'm going to have the energy of the solid phase at a slightly higher value. So this is our metastable phase, or non-equilibrium phase. Whereas our liquid phase is the stable phase, so it's going to be at the lower energy. So again T is greater than T melting. So now when I look at the activation energies that are associated with this process what I have is a reaction rate that I'm going to call Q f and that is going to be associated with the barrier that exists between the solid phase transforming to the liquid phase. And I'm going to write that in this way. Rate is going to be proportional to the exponent. Or the exponential of minus Q over RT. And we're looking at that barrier height as being Q in the forward direction. Now, when I go in the reverse direction, I have to go from the barrier of the minimum energy, which is at the liquid, all the way up to the height of the barrier, but this time, that barrier height is greater and now what I will have is an expression for the rate where the barrier is now in the reverse direction. And what I will see is a larger barrier that has to be overcome. So consequently, the rate in the forward direction will be different than the rate in the reverse direction. And that forward direction rate will overcome the reverse direction, and we will have a stable liquid phase. Now this ends our description of basic kinetics and how we can apply it to a process like melting. And in the next lesson, we're going to be finishing up with some concluding remarks that are associated with this particular module that we've been describing on atomic structure. Thank you.