Symmetry guides search for new materials

A new symmetry operation developed by Penn State researchers has the potential to speed up the search for new advanced materials ranging from tougher steels to new types of electronic, magnetic, and thermal materials. With further developments, this technique could also impact the field of computational materials design.

"In the physical sciences, making measurements can be time consuming and so you don't want to make unnecessary ones," said Venkat Gopalan, professor of materials science and engineering. "This is true for any material property – mechanical, electrical, optical, magnetic, thermal or any other. Knowing the symmetry group of a material can greatly reduce the number of measurements you have to make. "

Symmetry is pervasive throughout the physical universe and underlies the basic laws of physics. Gopalan gives a simple but scientifically accurate definition: "Symmetry is when doing something looks like doing nothing."

A circle has perfect symmetry, because if you rotate it by any number of degrees it will look the same. Similarly, rotating a hexagon by sixty degrees leaves it exactly the same, but rotating it by a different amount does not. Any action that leaves an object looking the same is a symmetry operation.

In crystals, atoms are arranged in symmetrical patterns, like a cube of salt or a crystal of sugar or quartz. Symmetry groups tell scientists in how many different ways atoms can arrange in repeating patterns. If they know which symmetry group a material falls into, they already know a great deal about the properties – mechanical, thermal, electrical and so forth – that material will have.

There are precisely 230 groups that detail how atoms can be arranged in space; these are symmetry "boxes" that a material will fit into. If scientists are looking for a material with a certain property, such as the ability to be electrically polarized, they can look at materials only in that symmetry box and ignore all the boxes that cannot possibly contain polar materials.

Another symmetry operation, called time reversal, adds to the number of symmetry boxes available, and applies specifically to magnetic materials. Time reversal simply says that if time runs backwards a material will either look the same or it won't.

In a paper published in Nature Communications, Gopalan and his co-author and former PhD student Brian VanLeeuwen report a new set of boxes called distortion symmetry groups. These boxes describe what happens when physical systems are perturbed by stresses, electric and magnetic fields, or other forces, and change from one state to another.

"Distortions are the most common phenomenon in nature," Gopalan said. "A chemical reaction is a distortion, diffusion is a distortion, and a change in the atomic positions and electronic clouds within a material is a distortion. The symmetry that Brian and I discovered is like recording a movie of atoms and looking at its symmetry, whereas most symmetry operations are looking at one frame of a movie.

"We show that there is a huge family of problems that this will apply to, such as phase transitions – for example, water changing from a liquid to a solid or vibrations in molecules and solids. You will see symmetries you couldn't easily see before. Then we can quickly reduce the number of experiments we have to run or the number of computations that have to be done to find how a material will change under the effect of distortions."

VanLeeuwen and Gopalan's operation is already being applied by colleagues at Penn State working in computational materials design. One group is using the technique to understand and model the diffusion of hydrogen atoms in steel. Another group is incorporating it into a powerful computer code called Quantum Espresso, used by modelers around the globe.

"The first question we like to ask when a new material is discovered is how the atoms are arranged in space," said Ismaila Dabo, assistant professor of materials science and engineering, and one of the developers of Quantum Espresso. "Symmetries provide a powerful language to explain such atomic arrangements and their distortions close to equilibrium. But when the distortions are so large that they bring the atoms far away from equilibrium, there was no clear way to describe materials transformation, making it difficult to classify critical phenomena like phase transitions or grain boundary motions. This work gives an admirably elegant and much needed answer to that question."

VanLeeuwen said that many technologies that are currently limited by materials properties could benefit by applying this method to the search for new materials. These materials include stronger and lighter alloys for space exploration and fuel efficiency, better sensors for healthcare, and more efficient turbines for energy production.

"Nature always takes the path of least resistance. Knowing this path allows us to calculate tremendously important materials properties. These properties are critical to the function of a very wide range of technologies, from making it possible for an ultrasound to detect a life-threatening heart condition to preventing nuclear reactors from melting down," VanLeeuwen said.

This story is adapted from material from Penn State, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.