# Tag Archives: bragg reflection

## Crystal Lattices and Atomic Ordering

Back when we talked about the polymorphism of chocolate, we mentioned crystal phases, which are the differing configurations that atoms can take in order to make a solid. As we saw with chocolate, what crystal phase a material has can greatly affect its properties. If we want to know whether a material can conduct electrons, looks shiny, or is optically transparent, then it’s useful to know how its atoms are assembled.

Let’s start simple, with a solid composed of only a single element. How many ways are there to arrange identical atoms in three-dimensional space? We can do it randomly, so that there is no regular relationship between the positions of various atoms. This is called an amorphous, meaning not shaped, or glassy solid. Many materials (such as glass!) are amorphous, but often it’s more energetically favorable for there to be some kind of order in the arrangement. Remember that each atom has an electron cloud with a specific shape and orientation, and thus if we align the cloud shapes in some clever way, we may be able to fit more atoms into a given space. This is sometimes called a ‘close-packing’ problem, because of the similarity to packing M&Ms into a jar, dice into a container, and other practical mathematics problems.

Depending on the character of the electron cloud of the atom in question, there may be a specific distance between atoms that’s energetically preferred, or an angle between chemical bonds which yields the lowest energy configuration. These atomic traits largely dictate the crystal structure, but as it turns out if you want to create a repeating pattern in three dimensions there are only fourteen ways to do it. These possible lattices are often called the Bravais lattices, and some straightforward examples include the cubic lattice and the hexagonal lattice, pictured below. Most of the Bravais lattices are found in nature, but the denser lattices tend to be a lot more common.

Does the exact same lattice type continue throughout an entire solid, such as a metal table? Well, if it is the lowest energy configuration, yes! But what can happen is that one part of the table has the same lattice type, but slightly rotated from the part next to it. This could occur during solidification if crystal lattices begin growing at two points in a liquid, and gradually expand until they meet. The point where they meet is called a grain boundary, and because the crystal order is disrupted there, it’s usually a point of mechanical instability in the solid. For example, dropping something heavy onto a table is most likely to break the table if the heavy object lands on a grain boundary, and if the table is made of something which can corrode, that’s most likely to begin at a grain boundary. Grain boundaries are also really important in magnetism, which we’ll discuss in more detail another time.

But,  given a sample of some material, how can we find out what crystal structure it has? Well, these days there are some very powerful microscopes which can actually see the arrangement of individual atoms. But long before the development of those microscopes in the 1980s, the Braggs, a father and son physics team in the early 1900s,  thought of another way to verify crystal structure. With a lattice of atoms that repeats periodically, from some angles there will appear to be a series of planes. X-rays, very high energy photons, have a wavelength which is similar to the spacing between these planes. So when x-rays are sent into the sample, they will reflect off the planes of atoms, and along some angles these reflections will add up to give a strong scattered x-ray signal. This phenomena is known as Bragg reflection, and is the basis of x-ray diffraction, a family of very common techniques to determine the structure and composition of materials. As you can see from the example below, typical x-ray diffraction patterns have a lot of symmetry, but the locations of the bright spots can be used to mathematically calculate what the crystal structure of the sample is.

Although the discussion above focused on materials made from a single element, it is also possible to have a periodic crystal whose building blocks have multiple elements, or even complicated organic structures like DNA. Now that we’ve seen how material response to external probing can depend on crystal structure, and how material strength can be affected by breaks in structure. But there are many other properties that are affected by which crystal lattice a material assumes, such as whether it is a metal, an insulator, or a solid. More next time!