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!

Thinking About Collections of Atoms

On a basic level, science is about asking why the world is the way it is, and engineering is about asking, how can we use that to better our condition? There is certainly a lot of interplay between the two; they inform each other and rely on each other. And in my mind, a good scientist should always be a reasonable engineer, and vice versa. So if we want to understand what the science is that underpins a lot of our current technology, we first have to ask a lot of “why” questions about the world around us. Such as, why do different objects and materials have different properties? Why are there different forms that matter can take? Why do some forms appear on Earth and some don’t? Then, once we know what makes materials different from each other, we can start talking about how to use that to do something useful.

So what is the difference between the atoms in a metal table, the atoms in a cup of coffee, and the atoms in our hands? There are two major differences that are relevant: first, the atoms themselves come in a wide variety of types, and second, they can be arranged with other atoms in many unique ways that affect the property of the resultant material. The image below shows how we can arrange the same silicon and oxygen atoms in a random way or an ordered way, to get either silica or quartz. This change in ordered affects the physical properties of the resultant material.

We touched on the many types of atoms before when we discussed the number of protons in an atom. Proton number affects electron number, because of the attractive force between protons and electrons due to their opposite charge. So, for a given number of protons, an atom will end up with a similar number of electrons. How many electrons an atom has is very important, because the cloud of electrons is much larger than the compact nucleus which contains the neutrons and protons, so electrons are the primary means by which an atom interacts with the world.

What “the world” means here is primarily other atoms. So to assemble a solid, we have lots of atoms whose electron clouds are interacting with each other. Atoms can share electrons, they can be attracted to each other if they have opposite charges, and they can form three-dimensional structures to allow many atoms to interact . These interactions are all based around electronic forces, which stem from charge as we discussed earlier. Different kinds of atoms will experience different forces in different environments, so we end up with a whole slew of ways to assemble atoms. We can pack carbon into sheets and get pencil lead, we can jam it together with no ordering and get charcoal, we can compress it until it has a dense, flawless periodic structure and get diamond, or we can mix it with hydrogen to get the long hydrocarbon chains that crude oil is made of. And that’s just carbon!

Now, the obvious question to ask here is why atomic species and ordering vary, and why those variations lead to different material types. We’ll get into the first question shortly, but the second will take a lot longer to answer.