November 17, 2015

A new symmetry underlies the search for new materials

Each diffusion path for an oxygen atom (red) moving across a graphene ring composed of carbon
atoms (gray ) is considered a “distortion” and is indexed by a unique “distortion symmetry group”
indicated below each image. The symmetry group contains all the essential information about the
properties of the material system as the diffusion occurs, including the ability to help determine the
minimum energy pathway. In this case, the minimum energy pathway is when oxygen moves
around the ring (right image) rather than across it (left image). Image: Penn State

(November 17, 2015)  A new symmetry operation developed by Penn State researchers has the potential to speed up the search for new advanced materials that range 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. Anything that can be done 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 explain how atoms can be arranged in space. These are symmetry "boxes" 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.

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