Hi, and welcome again to my series of videos for physical chemistry 2. For the next few videos, we'll be talking about much larger systems than the single atoms in molecules we've been looking at so far in the course. The next few videos are all about crystals, and a good place to start might be to ask, but exactly makes a crystal different from any other collection of solid phase molecules. In a crystal, the atoms or molecules are packed in such a way that the potential energy of the system is at a minimum, which makes it the most stable configuration for the molecules. The minimized potential energy is mostly a result of the balance between the electrostatic attractions and repulsions between the molecules. The resulting configuration of molecules usually results in a highly ordered repeating pattern called a lattice. The smallest repeating unit in a crystal is called a unit cell or sometimes a primitive cell. For example, this figure represents a tiny portion of a sodium chloride crystal. In reality, a crystal like this would continue for trillions of atoms in every direction. However, even in this tiny fragment of a crystal, you can see the repeating pattern in the lattice. The unit cell is the smallest repeating unit, which would be this part. So a crystal is built by simply repeating the unit cell in every dimension. The overall shape of the resulting large crystal is called the lattice type. It might seem like there would be a nearly infinite number of possible lattice types, but surprisingly, all lattice types fall into one of only seven different categories, which means that most crystals have one of seven general shapes. The lattice type depends on the lengths of the edges of the unit cell, which are called A, B, and C, and the angles between the edges of the unit cell, which are alpha, beta, and gamma. Let's look at each of the seven lattice types. The simplest one is called a cubic lattice, and as the name suggests, all three edges of the unit cell are equal to one another, and the angles between the edges are all 90 degrees. For that reason, both the unit cell and the resulting crystals are cubes. Notice that because flaws developed in a crystal as it grows, most of the real minerals we look at won't be perfect. That's a normal result of crystal growth. The next lattice type is called a tetragonal lattice. In this one, the angles are all 90 degrees again, but only two edges of the unit cell have the same length. The third edge can be longer or shorter than the other two. The third lattice type is called an orthorombic lattice, and it's another one that has 390 degree angles. This time, each of the three edges of the unit cell has a different length. The fourth lattice is called rhombohedral. Like the cubic lattice, the edges in this one all have equal lengths. The angles are all equal, too, but this time, they aren't 90 degrees. The next lattice is the monoclinic lattice type, in which the edges all have different lengths, and two of the three angles are 90 degrees. The sixth lattice type is tri-clinic, in which each edge has a different length, and in each angle is also different, and none of the angles are 90 degrees. The last of the seven lattice types is the hexagonal lattice. This one's distinctly different than the other ones at first glance. In this one, two of the angles are 90 degrees, and the third is 120 degrees. Two of the edges of the unit cell have the same length, but the third is different, and maybe shorter or longer than the other two. You've probably seen examples of this one before, as quartz crystals have a hexagonal unit cell. At normal pressures, ice also forms a hexagonal lattice, which is in part responsible for the familiar six-sided shapes of snow crystals. Well, that's all for today. This was a pretty short lesson, but that's because next we'll talk about the instrumental technique called x-ray crystallography. It's one of the most powerful ways of determining the structure and chemical composition of a crystal, and it's commonly used to determine the three-dimensional structures of proteins. It was even used to determine the structure of DNA. I hope you'll join me for that. But until then, have a good week.