What Is a Crystal?

Not All Crystals Are Made Equal! Do You Know All Their Types?

A collection of crystals — some familiar some less. Image by Author via DALL-E.

We tend to think of crystals as “pretty, shiny rocks”, but crystals are much more than rubies and diamonds. The reality is that crystals come in countless different shapes and sizes and are literally everywhere. They are not just minerals and gems. They are in the clothes we wear (crystalline domains in cotton), in the food we eat (salt, sugar), even in the medicines we take (aspirin) — sometimes even when they shouldn’t!

For most compounds, crystallization is a way of life. Yet crystals hide fundamentally different mechanisms that allow them to develop the microscopic structure that gives rise to their own unique properties. But did you know that there are four major families of crystals sharing a lot of common features? In this story, I’ll walk you through what they are and we’ll discover what really holds them together.

The Beauty of Crystals

There are few things in nature more captivating and suggestive than crystals.

When our ancestors first encountered large crystal formations in caves, I imagine they must have felt a profound sense of awe. The intricate patterns and regular geometries of crystals infuse a sense of primordial order and timeless beauty in an otherwise pretty dull and irregular terrain. Especially gemstones, with their vivid colors and multifaceted reflections, almost look like a primitive form of life. It is no surprise, then, that humans have collected and jealously guarded crystals since the dawn of time, adorning themselves with them as symbols of status and power while attributing to them an astonishing array of mystical properties, from miraculous healing powers to deadly curses.

If you follow this blog, you know that besides their aesthetic qualities, crystals are a recurrent theme in condensed matter physics, too.

First of all, crystals are everywhere. In fact, most materials grow in a crystal structure. From a thermodynamic perspective, they are the default. When left to “relax” on their own, physical systems naturally look for the state with the lowest possible energy, a theorem known as **principle of minimum energy, **which is nothing but a reformulation of the second law of thermodynamics at fixed entropy. Periodic atomic arrangements are typically the configurations with the minimal free energy because they reduce the repulsion between positively charged atomic cores. That’s why minerals, metals, salts, gems, and ice all spontaneously crystallize when slowly cooled to solid form. During this relaxation process, nature is continuously solving an enormous optimization problem involving where to best place billions upon billions of atoms.

Another reason why crystals are so central to condensed matter physics is that they exhibit far richer and more robust phenomena than arbitrary collections of atoms. The reason is symmetry. Because the atoms repeat periodically in space, the physical landscape governing the motion of their electrons — and thus their quantum wave functions — repeats as well, a fact formalized by the famous Bloch’s theorem. Many crystals also possess additional symmetries, such as rotations, reflections, and inversion. These symmetries further restrict the number of allowed quantum states and the ways in which particles can evolve, enabling more structured behavior to emerge in the form of electricity, magnetism, or even superconductivity. In a sense, crystals represent the opposite of the highly chaotic and ergodic systems we discussed in previous stories.

Crystals are also much simpler to study. Since their translational symmetry drastically reduces the complexity of the problem through Bloch’s theorem, physicists are free to focus on understanding the behavior of a single repeating unit rather than billions of individual atoms. At low energies, the microscopic continuum can even be replaced by an effective lattice model, where electrons simply hop from one atomic site to another. In this description, the complicated physics of continuous space is condensed into a handful of parameters — such as the energy of each site and the probability of hopping between neighboring sites — making calculations vastly more tractable while faithfully capturing the essential crystalline behavior.

The largest crystal in the world. The largest natural crystals ever found are located in the (originally named) Cave of the Crystals in Mexico. They are giant selenite crystals, a mineral containing sulphur and calcium. Note the person in the bottom right corner for scale. Image Source: WikiMedia Commons.

Of course, not every material has a crystal structure. Amorphous (i.e. non-crystalline) solids certainly do exist — glass being perhaps the most common examples. However, they typically have a more violent origin. They are usually generated under out-of-equilibrium conditions that prevent atoms from reaching their preferred crystalline arrangement. This can happen when molten minerals cool so rapidly that atoms become frozen before they have time to organize into a regular lattice, as in volcanic eruptions that produce obsidian. Another pathway to the formation of glassy materials is the sudden release of energy, as when a lightning bolt melts silica-rich sand into glassy tubes known as fulgurites. In both cases, the rapid cooling traps the atoms in a disordered configuration that resembles the snapshot of a liquid much more than a regular crystal. Glassy states can be interesting on their own and understanding how they emerge remains one of the central challenges of non-equilibrium physics. In fact, there are many incredible parallels between the physics of glassy systems and the behavior of neural networks! But this is a story best left for another day…

Glass from lightning. Fulgurite is a glassy material produced when lightning strikes sand or rock. Image Source: WikiMedia Commons.

So, we’ve seen that the regular, repeating pattern of crystals is nature’s solution to a ubiquitous atom-packing problem that tries to constantly save energy. But this definition only tells us what a crystal looks like, not why or how it forms in the first place.

To understand what leads to a crystal in practice we need to explicitly consider the microscopic forces acting between the atoms.

Every atom consists of a positively charged nucleus surrounded by negatively charged electrons. These particles constantly attract and repel one another, and the delicate balance between these competing interactions determines how atoms organize themselves. Depending on how electrons are distributed between neighboring atoms, nature has developed several fundamentally different strategies for building stable crystals.

Ionic Crystals

Perhaps the simplest type of crystal is the ionic crystal. As the name suggests, an ionic crystal is a crystal made of ions, i.e. atoms that carry a net electric charge because their number of electrons differs from that of protons. An *anion (not to be confused with an [anyon](https://en.wikipedia.org/wiki/Anyon) — see my article about Microsoft’s quantum computer for more) is an atom that has gained one or more extra electrons, while a [cation](https://en.wikipedia.org/wiki/Ion#Anions_and_cations)* is an atom that has lost one or more electrons from its neutral configuration.

How do ions come about? Normally, atoms have an equal number of protons and electrons. Since protons and electrons carry opposite electric charges, having equal numbers of both guarantees that the atom as a whole remains electrically neutral. Sometimes, however, atoms donate or receive extra electrons when the conditions are right. This stems from the way quantum mechanics arranges electrons into shells around the nucleus. In that sense, electrons behave a bit like passengers boarding a plane by rows: they prefer to occupy complete shells whenever possible. The deeper reason is connected with quantum symmetry, but the end result is that atoms are most stable when their outermost electron shell is completely filled. This happens naturally for all *noble gases*, such as neon and xenon, making them remarkably stable and chemically inert, meaning that they rarely combine with other atoms to form compounds.

If the fully filled shell configuration of a noble gas is the most stable, it follows that the elements immediately preceding the noble gases in the periodic table (i.e. with fewer protons and electrons) are eager to capture additional electrons to complete their nearly filled outer shell. These include the group 17 elements — the *halogens — such as fluorine and chlorine, which need just one extra electron, and, to a lesser extent, the group 16 elements — the [chalcogens](https://en.wikipedia.org/wiki/Chalcogen) — such as oxygen and sulfur, which require two. On the other hand, atoms that follow the noble gases in the periodic table face the opposite situation. Their additional electrons occupy the next shell all by themselves and are therefore only weakly bound to the nucleus, making them easy to give away. The [alkali metals](https://en.wikipedia.org/wiki/Alkali_metal) in group 1, such as lithium and sodium, squarely belong to this category, as do, to a lesser extent, the [alkaline earth metals](https://en.wikipedia.org/wiki/Alkaline_earth_metal) *in group 2, such as magnesium and calcium.

The periodic table of the elements. Highlighted in red and blue are groups 1 and 2 (typical electron donors), and 16 and 17 (typical electron acceptors). Image Source: WikiMedia Commons.

Now, you can imagine what happens when an alkali metal atom encounters a halogen — a chemical match made in heaven! The alkali metal happily donates its outermost electron to the halogen, leaving behind a positively charged ion while the halogen becomes negatively charged. The resulting electrostatic attraction between these oppositely charged ions forms a strong ionic bond. Since opposite charges attract while like charges repel, the ions naturally like to arrange themselves into a highly regular three-dimensional crystal (usually cubic) to maximize attractive interactions while minimizing repulsive ones: this is an ionic crystal.

Sodium chloride, or NaCl, or “table salt” for friends, is the archetypal example of an ionic crystal. It consists of sodium atoms (an alkali metal) and chlorine atoms (a halogen) in a 1:1 ratio. Each sodium atom donates one electron to a chlorine atom, producing Na⁺ and Cl⁻ ions that alternate throughout the crystal. Many other salts, such as potassium chloride (KCl — table salt substitute), magnesium oxide (MgO — magnesia, anticake agent), and calcium fluoride (CaF₂ —used to manufacture windows and lenses), follow the same principle, and similar ionic structures are found in countless naturally occurring minerals.

Because the electrostatic forces between ions are extremely strong, ionic crystals tend to have high melting points and remarkable hardness. On the other hand, shifting one layer of ions relative to another often places like charges next to each other, creating enormous repulsive forces. Rather than bending, ionic crystals therefore tend to fracture suddenly, making them brittle. Another peculiar characteristic of ionic crystals is that they are electrical insulators in their solid form because the ions are locked into fixed positions within the crystal lattice and cannot move. Once the crystal is melted or dissolved in water, however, the ions become free to move and can carry their electric charge through the material, making it electrically conductive. That is why the salts dissolved in sports drinks help restore the body’s electrolyte balance after exercise!

Schematic illustration of an ionic crystal. Positively and negatively charged ions arrange themselves into a regular lattice that maximizes attractive interactions between opposite charges while minimizing repulsion between like charges. Image Source: WikiMedia Commons.

Covalent Crystals

Alkali metals and halogens occupy only a tiny fraction of all chemical elements. So what happens in solids composed of other elements that are neither particularly eager to gain electrons nor willing to give them away — for example, carbon? In this case, the ownership of electrons becomes more democratic. Instead of transferring electrons from one atom to another, neighboring atoms share them more or less equally. These shared electrons form highly directional chemical bonds that lock atoms into precise geometric arrangements when they crystallize. The result is a **covalent crystal **(often called also a network solid).

Because covalent bonds are highly directional, they can organize atoms into a variety of network geometries. As a result, the same chemical element can crystallize into completely different structures depending on external conditions such as temperature and pressure (which can be huge deep in Earth’s crust). These different crystal structures can exhibit incredibly different physical properties despite having exactly the same chemical composition.

Let us stick with carbon for a moment. Every carbon atom likes to share electrons with four neighbors, forming an extended three-dimensional network of exceptionally strong covalent bonds. When these bonds arrange themselves into a tetrahedral network, typically under extreme pressure, the result is diamond. Because this three-dimensional network is nearly isotropic, there is no preferred direction along which the crystal can be cleaved without breaking many strong covalent bonds simultaneously. The result is the hardest naturally occurring material. Diamond is so hard that it defines the maximum value on the Mohs hardness scale — a scale used by geologists to rank minerals according to their resistance to scratching.

However, change the atomic arrangement, and the mechanical properties change dramatically as well. Graphite consists of exactly the same carbon atoms, but arranged instead into stacked sheets of hexagons. Within each sheet, the covalent bonds remain exceptionally strong, yet neighboring sheets are held together only by much weaker forces. As a result, the crystal cleaves easily between adjacent layers, allowing them to slide over one another. This is precisely what happens when you write with a pencil: the friction against the paper peels off one graphite layer after another, depositing tiny flakes of carbon onto the surface and leaving behind a pencil mark.

A completely different crystal geometry gives rise to completely different physical properties.

Difference between diamond and graphite. These two materials have the same chemical composition, but a different atomic arrangement of their covalent network. The result is incredibly different mechanical, optical, and electrical properties. Image Source: WikiMedia Commons.

Molecular Crystals

The weak forces between the graphite layers might seem to play a secondary role at first when compared to the sheer stability and strength of ionic or covalent bonds, but in reality these types of interactions are among the most important ingredients in chemistry and biology. They are called van der Waals interactions and arise because the constantly fluctuating electron clouds surrounding atoms create tiny, short-lived electric dipoles that induce matching dipoles in neighboring atoms, producing a weak attraction that can bind even electrically neutral atoms and molecules.

Weaker intermolecular forces like the van der Waals interactions are responsible for stabilizing an entirely different class of crystals known as **molecular crystals*. Unlike ionic or covalent crystals, where chemical bonds extend throughout the entire material, molecular crystals are built from intact* molecules that remain chemically unchanged. The crystal is held together not by new chemical bonds between neighboring molecules, but almost exclusively by weak intermolecular forces. Besides the aforementioned van der Waals interactions, numerous other weak intermolecular forces can play this role, including hydrogen bonds (attractions involving hydrogen atoms), permanent dipole-dipole interactions, quadrupole interactions, and many more.

These weaker bonds give molecular crystals a very different character. They typically have much lower melting points, are softer, and are often poor electrical conductors. Dry ice (solid carbon dioxide), solid iodine, and many organic crystals all belong to this family. But perhaps the most familiar molecular crystal is ordinary ice. As in the case of diamond and graphite, ice can crystallize into many different geometric structures (dozens of them are known). In the most common form, known as ice Iₕ, each water molecule is held together by strong covalent bonds between its oxygen and hydrogen atoms, while neighboring water molecules attract one another primarily through hydrogen bonds. These interactions organize the molecules into the beautiful hexagonal lattice responsible for the characteristic sixfold symmetry of snowflakes. Although hydrogen bonds are much weaker than covalent bonds, billions of them acting together are strong enough to produce a remarkably stable crystal under everyday conditions.

Van der Waals forces at play. Van der Waals and London dispersion forces make iodine molecules condense into a molecular crystal at room temperature. Image Source: WikiMedia Commons.

Metallic Crystals

There is one last major crystal family that we have not yet covered, and that is crystals involving metals. Actually, most elements of the periodic table are metals (including the alkali metals and alkaline earth metals from earlier). This classification is best understood in terms of how these elements behave in their solid elemental form. When metallic atoms are brought close together, their electronic clouds overlap so strongly that the outermost electrons become delocalized and are shared collectively by the entire crystal. The positively charged atomic cores remain arranged in a regular lattice, while this mobile electron cloud permeates the material, acting as a kind of electronic glue that holds the crystal together.

This sea of electrons is responsible for many of the properties we naturally associate with metals. Because the electrons are free to move, metals are excellent conductors of both electricity and heat. At the same time, if one layer of atoms slides relative to another, the electron sea simply rearranges itself instead of allowing strong repulsive forces to build up. This makes metals pretty ductile and malleable: they can often be bent, rolled, or hammered into shape without shattering. Pure iron, silver, and gold all belong to the class of metallic crystals.

Some Crystals Are Even More Exotic…

For most of human history, the crystal families described above were essentially the only ones we could encounter and produce. Modern physics, however — and especially our ability to manipulate individual atoms in ultracold quantum systems — is revealing an entirely new planet of crystalline states.

These are systems in which the regular arrangement of atoms (or even electrons) is no longer tied to a particular type of chemical bond, but can instead be engineered by directly controlling how particles interact with one another. And once we learn to invent new ways for particles to repel one another, entirely new kinds of crystals emerge — some stabilized by magnetic dipoles, some by laser light, and some even by quantum statistics alone!

How can systems organize themselves into a crystal without sharing or exchanging a single electron? Well, that is a story for another time… Stay tuned!