In this lesson, we're going to be describing some basic differences between the homogeneous and the heterogeneous nucleation process. Let's make some comparisons of the two processes. When we talk about the nucleation event, it can either be homogeneous or heterogeneous. In terms of homogenous nucleation, that happens to be rarely encountered with respect to commercial type of processing. However, even though it doesn't occur much with respect to, say, solid to liquid transformation, it does provide us a development or a grounding where we can begin to talk about the process of heterogeneous nucleation. However, we will see opportunities where we have very common solid to solid nucleation, which is of the homogeneous nature. It also turns out, of course, that heterogeneous nucleation is very common, and in particular in the case of liquid to solid transformations, but it also occurs in solid to solid transformations. Now, when we look at the process, remember what we said was that a sphere minimizes the surface area. And what we wind up having is, a material will form a spherical structure when the interfacial energy is isotropic. Now, it should be pointed out that when we have nucleation, either homogeneous or heterogeneous, it usually is not in the case of a sphere. And the geometry can be very complicated. But by looking at the spherical case, we can begin to get some understanding of what happens in the nucleation events using a simple geometry. Increasing the amount of undercooling winds up decreasing the critical cluster size. And this is true with respect to both nucleation processes. The stability of the cluster during homogeneous nucleation is determined by the balance between the two factors of surface area and volume free energy. We also know that when we have a specific value of undercooling, the nucleation barrier is smaller for the heterogeneous process, and consequently that process will dominate if a site is present. So, in general, the heterogeneous nucleation process is ubiquitous and occurs quite significantly in a number of our processing, with respect to commercially processed materials. The heterogeneous nucleation process results in the elimination of a nucleation site, and it's the elimination of that nucleation site that helps provide some of the energy for the reaction. And since the critical radius is proportional to the interfacial energy, and the barrier is proportional to the cube of interfacial energy, the interfacial energy of a material is a very important property, and we'll be discussing more of that in the subsequent lecture. When we look at how much energy is released as a result of the nucleation process, and we examine free surfaces all the way through matrix, what we find is, the amount of energy decreases as we go from free surfaces to the matrix. And we also have an increase in the number of sites as we go from the free surface into the matrix. So both of these issues are important, that is, a decrease in energy, making homogeneous nucleation in the matrix the prevalent process, and what we find is a decrease in the number of sites in comparison from the matrix to the free surfaces. So matrix materials will have lots of sites, whereas the free surfaces in terms of those acting as nucleating sites will be smaller. We can use the equation at the bottom of the slide to help us understand the various nucleation processes and how they're affected by the presence of various sites. So what we're looking at is an equation that has the volume term, the surface area term, and there's also this that we refer to as the defect energy. And the defect is the energy that is released by the system that results in the elimination of that particular interface. So when we look at, for example, free surfaces, grain boundaries, and interfaces, and dislocations, when those are eliminated from the microstructure, they actually provide some free energy to the system. Now, when we look at the matrix, the matrix is typically what we have in terms of homogeneous nucleation. So in terms of looking at the equation that we have at the bottom of the page, what we're seeing is that as we go from free surfaces to the matrix, the defect energy that is released becomes smaller and smaller. Now, the other important idea is that as we go from free surfaces to the matrix, the number of sites where nucleation can occur winds up increasing. So at the free surface, it's just at the locations at the surface of the material, whereas again in the matrix, it's randomly distributed throughout the structure. So this gives us an idea or a way of thinking about the heterogeneous nucleation process and the free energy that becomes available as a result of the elimination of the defect free energy. Thank you.