In this example, we're going to talk about various types of ceramic crystal structures. So bonding is everything. So if we talk about ceramic materials, we know we can have structures that come from elements that have large differences in electronegativity hence, they're going to have a substantial amount of ionic nature. We also can have ceramics that are close together. There, we'll see covalent bonding, especially in case of silicon carbide, we have directional or 3D covalent bonding, giving it a very, very high bond strength, high melting temperature. So the degree of ionic characteristics can be large, as we see in the ones that are made up of elements far apart in the periodic table. Or we can have small amount of ionic characteristic for elements that are close in the periodic table. So let's take a moment for inquiry. In this example, we are going to calculate the amount of ionic bonding characteristic. We utilize the electronegativity And then we take the equation here. So for alumina, we utilized electronegativity of aluminum and oxygen, for silicon carbide, silicon and carbon and for silica we use silicon and oxygen. In this structure, one of the most important things in the structure of ceramic materials is that you have to have, what we refer to as mechanical stability. And in that case, the ion has to reside in this space in a mechanically stable configuration, meaning it has to be stable or contiguous with the other ions. So it could be just fitting, or it could be larger, okay? But it cannot be smaller since [INAUDIBLE] in this interstitial position. So you want to maximize the number of oppositely charged neighbors, so it has to be mechanically stable hence, it has to be contiguous. The second feature is we have to be charged neutral, meaning the cation net charge has to equal that of the anion charge. So this +2 -2, add these together, it is neutral. So, the net charge has to be zero, and most often it will be reflected, the composition will be reflected in the chemical formula. So, for this calcium fluoride, calcium +2, the fluorine ion -1, so we need two of those. So Ca1 F2. Often we look at coordination number and the ratio of the radii. So here we take the cation ratio to that of the anion. As the coordination increases, this ratio will increase as well. So, how do we form a stable structure? And the ones that are most useful. Coordination four, meaning I'm in this tetrahedral, so the cation is sitting inside the tetrahedral. For coordination number of six, is sitting in the central of this octahedral and the coordination number of eight, [INAUDIBLE] in the queue. I'm based on where the cation is residing relative to the anion, it's going to tell us coordination number four, six or eight. But also we have a certain range in the ratio Based on this range and the coordination number, it will tell us what type of structure we'll have. We can have the zinc blend, in this particular case, The cation sitting in the tetrahedral, for sodium chloride structure is sitting in the octahedral and for the cesium chloride structure, the cations residing in the center of the cube. So based on, again, the coordination number and where the cation is sitting relative to the anion, where again, it's trying to maximize the coordination number and based on these ratios, it will determine what is our final structure. So let's take a moment for inquiry. Well, the stable ionic crystal, the net charge has to be zero, and what is the maximum ratio for the cesium chloride structure, again, is sitting in the cube, so the maximum value would have to be one.
