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welcome to our first example video. Looking at Bonds in condensed matter physics. In this video, we're going to consider how we can approximate what's known as the Madelon constant. Remember the Madeleine Constant was this factor Alfa, which multiplied our electric electrostatic potential term in orders to give us a total electrostatic potential for a particular Adam. So, uh, considered down here we have a sodium atom, which has six chlorine atoms that air a distance are away. These will be called the six nearest Neighbors, and then we have 12 next nearest neighbors, which are a distance route to our away, which are all going to be so Diem's. It's an interesting activity to draw out this entire box. I've only done part of the box here in order to not destroy the perspective, but try to do it on your own and help yourself count all of the different atoms and figure out the distances between them. Now, how are we going to do this? What we're going to do is we're going to add up the electrostatic potential from our nearest neighbors, plus the electrostatic potential from our next nearest neighbors, and hopefully that will get us close to the Maddalone constant. So here's our electrostatic potential term from our nearest neighbors. Noticed that is going to be a negative because we have opposite signs of charge. But our next news neighbors. It's the same sign of charge, so this term will be positive. It also has a different distance down here now when we put these two together and try to solve for our constant Alfa, what we come up with is negative 2.49 which is not even close. It's not even the right sign. So what's happening here? Well, what's happening is we're not taking into account the effects of enough of the neighbors if we consider the second nearest neighbor or rather the second next nearest neighbor. What we're going to see then is that this glory or this sodium is going to be a distance of Route three are from a diagonal chlorine atom here, so if I were to draw that, it would be a distance. Route three are, and this chlorine would be directly above this. Sodium and Route three are will be the distance there, and it will be that far from eight total chlorine atoms which means we can add in a third term of positive eight over Route three. When we put that in, we end up with an Alfa equal to 2.13 which is closer to the eventual value will find for N A, C. L or any ionic crystal of 1.748 Now you can do this with other types of crystals, though it's a little more difficult. You have to keep track exactly of what the different charges are. Um, it's pretty simple. With Ionic crystals. You just need to know the distance between them and you'll be able to calculate the total potential of the crystal.

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