Materials science is one field where structure makes all the difference in the world. Take carbon, for example—it has two crystalline forms, one of which is soft enough that it can be crumbled with your fingers, while the other is the hardest substance found in nature. The component atoms are identical, but the arrangement of those atoms determines whether they make common graphite or a sparkling diamond.
|A liquid can transition to a number of different crystalline solids, depending on
the conditions under which it solidifies.
Image Credit: Piaggi, Valsson, & Parrinello
While we typically think of the latter when we hear the word, crystals are everywhere—a crystal is anything with a repeating atomic structure, from table salt to aluminum cans to the silicon in the device that you’re reading this on.
The structure of a given crystal, along with the behavior of its component atoms, can imbue a material with unique and useful properties, allowing for the manufacture of things like transistors or ultra-high-strength glass. The wafer-thin semiconductor crystals that make LEDs light up with almost magical efficiency are rigorously engineered to give off certain wavelengths of light—and the creation of the blue LED was so arduous that the team which succeeded was awarded the Nobel Prize in physics a few years back. It’s no wonder that scientists want to understand the way atoms crystallize—being able to accurately predict crystal structures using computers would lay the groundwork for more efficient lasers, electronics, and more.
It’s a more difficult task than you might think, though. Crystal structure depends partly on the shape and behavior of a molecule’s electron cloud, but also on factors like atmospheric pressure and the rate of change in temperature as a substance transitions from liquid to solid. Ice, for example, can form more than 11 different structures, depending on the temperature and pressure that it’s frozen at—although we usually only encounter it in its hexagonal form.
|A phase diagram of water, showing the various crystalline phases
of ice that can form at different temperatures and pressures.
Image Credit: Wiki user cmglee, CC BY-SA 3.0
Current computer models of of crystallization are less than ideal for a variety of reasons. While it’s possible to simulate the behavior of a few atoms or molecules bonding together, this usually happens over such a short timescale that it makes it difficult to translate it to the behavior of a real-world system containing billions or trillions of particles. If two water molecules in your simulation latch together on a timescale where we can see it happen and account for all the forces involved, that means you’re stretching a process that might take a nanosecond in real life out into a full second of simulation-time. Suddenly, a glass of water freezing into ice—which might take a few hours in the freezer—means leaving the simulation running for something like a full year. A supercomputer could potentially run the simulation in fast-forward, but such powerful machines are almost never idle; someone always has data to analyze, and it’s just not worth the computational expense.
It’s sometimes possible to get around this long timescale by dropping the simulation’s temperature, so that all the atoms latch together in quick succession. However, this doesn’t always produce the results you’re looking for—notice how water forms a different kind of ice below -200°C in the phase diagram above.
Other techniques for modeling crystallization get around these difficulties by making simple assumptions about the bonds between atoms, but these assumptions can bias the results as well and reduce the likelihood that the method will produce the full range of possible crystal structures.
Despite the numerous challenges involved, a team of Swiss researchers has made significant progress in developing a computational model that will allow for the accurate simulation of crystallization behavior, according to a recently published paper in the journal Physical Review Letters. Their technique may circumvent many of the problems with modern simulations by using a model with only two variables to describe the collective behavior of the system—one for its enthalpy, which takes heat, potential energy, pressure, and volume into account—and the other for entropy, which represents the amount of disorder in a system. The interplay between these two quantities is what governs the process of crystallization, so the new approach lets the researchers accurately simulate the processes they’re studying. The results of their method were promising, properly reproducing the lattice structures of sodium and aluminum in their lowest free energy states.
While the development of these techniques is only the first step, the road it may lead down is an exciting one—efficient simulations of crystallization could help create the next generation of solar panels, computer chips, and more exotic metamaterials.