In this lecture, we're going to discuss in more detail how bonding actually impacts the melting temperature, as well as the modulus of elasticity coefficient thermal expansion, and look how we can describe or predict the type of bonding by looking at the potential wealth and bonding force curves. Very fundamental elasticity. We have Hooke's Law. It basically says, hey, if I take a solid and I deform it in a elastic region. When I talk about elasticity I mean the elastic region. That means that work is reversible. If I take a solid, I compress it with a force. If I remove the force, it goes back to it's original shape. If I pull it and elongate it and I remove the load, it returns back to its original shape. Hooke's law, we have a force and then we apply, or we move it over a distance, whether it's negative or positive, and then this coefficient here is just Hooke's coefficient or spring constant. Oh, and make sure we have our units forces is Newton's elongation, Delta L is in centimeters, and then we have the spring constant is Newtons over centimeter. Now if we talk about some stress, that's the force over the initial cross-sectional area. We normalize the elongation. That gives us strain, and finally, I'll stress we use Pascal's strain is Delta centimeters over centimeters. Hence is unitless. If we look at our stress, it is proportional to strain, and the proportionality constant is the modulus of the elasticity, which is in Pascal, often referred to as Young's modulus as well. Now if we look at the case where we again deform our solid. If I relate it back or normalize it to convert it to stress strain. When I'm in the elastic region, I have this linear dependence on relationship between stress and strain. When I'm positive, That's elongation. I can also do it in compression that's going to be on the negative side. But this slope in the elastic region, meaning it's reversed, the work is reversible. I remove the load, it goes back to the original shape. In this particular case, the slope of this line is the modulus of elasticity. Coefficient of thermal expansion. We're interested in how the length per unit length changes with temperature. We're going to take tether these things. Kelley, those peer's not working so cool. Now T_1, now in this particular case, T_1 is less than T_2. We got to heat it up and we get some expansion , coefficient thermal expansion. Now this is macroscopic, but we've always said any material property on the microscopic scale has to translate to the macroscopic scale. Let's look at what happens. Well, I heat it up, it expands my Delta L. Now I have Delta L, L naught, and now it's going to be proportional to the change in temperature. Strain is going to be proportional to Delta T and that proportionality constant is going to be the coefficient of thermal expansion. You can see here, Delta Lo divided by Delta T will give you the coefficient thermal expansion. Now how can we determine that? Well, we take our sample in a furnace, we heat it up, and we just measure Delta L. We know L naught, we divided it by L naught Delta T, and then I look at this coefficient of thermal expansion, typically parts per million per degree C. Reason we use that, we come up with some nice friendly numbers. If I look at silicon and aluminum, I see those. If I look at some, let's go polymers. If I look at the difference, small number, big number. So right off hand, it tells us in strongly bonded materials is going to have a small coefficient thermal expansion. In weakly bonded materials, there have a high coefficient of thermal expansion, and metals which we know have an intermediate type of bonding, they will reside somewhere in the middle, and later on when we get to looking at glasses, you like, hey, glass is a ceramic. But it has a high coefficient of thermal expansion. This is a type of glass, especially when we add dopants on network modifiers, such that it makes the melting temperature and glass transition temperature lower than say of just alumina. Heat, you're able to process it much easier because you're processing it at a lower temperature. Let's take a moment for inquiry. Based on the information provided, the largest coefficient of thermal expansion is associated with what type of bonding and the smallest coefficient is associated with which type of bonding? Well, if you were paying attention earlier, you would see that silicon, which is directional and covalent bonding or 3D covalent bonding, it's going to have the smallest because that's the strongest type of bonding, and if I look at the largest is going to be associated with the polymers because it has the weakest total bonding.
