By Walt Mills

Symmetry is a concept that we have recognized throughout history, says Penn State materials scientist Venkatraman Gopalan. We see symmetry in snowflakes, hear it in music, and admire it in a human face. Many types of materials, particularly crystals, grow symmetrically.

In materials science, structure and properties are related. According to Neumann’s Principle, if a crystal’s elements are arranged in a symmetrical fashion, its properties will reflect those symmetries. That is, if you know the structure and symmetry of a material, you can determine the form of all its properties. “It’s powerful,” Gopalan says. “It allows a physical scientist to make say two measurements to determine all the components of a specific material property instead of 20 or more.

In the search for new materials with unusual properties, a set of rules that can help scientists and engineers narrow their search to a few among hundreds of possible materials would be welcome. The field of symmetry helps achieve exactly that. In a paper published online in the journal Nature Materials, Gopalan and coauthor, Penn State physicist Daniel B. Litvin, introduce a new type of spatial symmetry to be discovered in materials in more than 50 years.

A lattice composed of columns of squares that represent repeating molecular structures, one rotated clockwise (colored blue) and another counterclockwise (colored orange) with respect to each other -- such structures have many more symmetries than had been recognized before the paper by Gopalan and Litvin (May 2011, Nature Materials). Such new symmetries also arise in helical structures such as DNA, proteins, and sugar crystals. These new symmetries lead to the prediction of new properties of these crystals that relate to these rotations, called "roto properties." Applications range from the discovery of materials that allow electrical control of magnetism to new insights into well-known crystals such as quartz and organic crystals.

Credit: Penn State University, Gopalan lab, Ryan Haislmaier

Called rotation reversal, it applies to crystals and materials that have what is called handedness – such as your left versus right hands, which are mirror images of each other. It also applies to materials with static rotations, where both clockwise and counterclockwise rotations are present, often called antidistorted structures. “This new operation flips the switch between clockwise and counterclockwise directions of static rotations. A clockwise motion becomes counterclockwise, and vice versa,” Gopalan says. With the addition of rotation reversal, the number of possible symmetry groups has increased dramatically, from 90 to 624 point groups that describe symmetry around a point, and from 1421 to 17,807 space groups that describe symmetry repeated in space.

Gopalan says that rotation reversal has similarities to, but is distinct from the last discovered type of symmetry, time reversal, pointed out by Landau and Lifshitz in 1958, which reverses the sense of time and is applied primarily to describe the symmetries in magnetic crystals. “Like time reversal, the idea of rotation reversal is simple,” he remarks. “But it applies only to static objects. There are a lot of crystals that have static rotations that do not change with time.”

A lattice composed of two repeating squares that represent molecular structures, one rotated counterclockwise (color coded blue) and another clockwise (color coded orange) with respect to each other -- such structures have many more symmetries than had been recognized before the paper by Gopalan and Litvin (May 2011, Nature Materials). Such new symmetries also arise in helical structures such as DNA, proteins, and sugar crystals. These new symmetries lead to the prediction of new properties of these crystals that relate to these rotations, called "roto properties." Applications range from the discovery of materials that allow electrical control of magnetism to new insights into well-known crystals such as quartz and organic crystals.

Credit: Penn State University, Gopalan lab, Ryan Haislmaier

The practical consequence of their discovery is that more symmetry reduces the amount of information needed to construct a structure from scratch and aids in predicting the form of its properties. That means fewer measurements, less costly experimentation, and a clearer understanding of the many minerals and biological materials that display handedness, including DNA and protein crystals. In fact, Gopalan is now applying his new symmetry to the study of protein crystals grown by molecular biologists Neela and Hemant Yennawar of the Huck Institutes of the Life Sciences.
“Symmetry, when it is present or broken, is a powerful way to understand our physical world, such as understanding why matter exists and predicting how it behaves” says Gopalan. “This new symmetry element could help in such pursuits.”

“Rotation-reversal symmetries in crystals and handed structures” by Venkatraman Gopalan, professor of materials science and engineering, and Daniel Litvin, professor of physics, Penn State Berks. Contact Prof. Gopalan at vgopalan@psu.edu.
 

More information about the ZnSe core optical fiber can be found here, and in the attached articles below.