Image related to Venkatraman Gopalan’s and Daniel Litvin’s research. Credit: Gopalan Lab |
A new way of understanding the
structure of proteins, polymers, minerals, and engineered materials will be
published in Nature Materials. The
discovery by two Penn
State researchers is a
new type of symmetry in the structure of materials, which the researchers say
greatly expands the possibilities for discovering or designing materials with
desired properties. The research is expected to have broad relevance in many
development efforts involving physical, chemical, biological, or engineering
disciplines including, for example, the search for advanced ferroelectric
ferromagnet materials for next-generation ultrasound devices and computers.
Before the publication of this
paper, scientists and engineers had five different types of symmetries to use as tools for understanding the
structures of materials whose building blocks are arranged in fairly regular
patterns. Four types of symmetries had been known
for thousands of years—called rotation, inversion, rotation inversion, and
translation—and a fifth type—called time reversal—have been discovered about 60
years ago. Now, researchers at Penn State Univ. have added a new, sixth, type,
called rotation reversal. As a result, the number of known ways in which the
components of such crystalline materials can be combined in symmetrical ways
has multiplied from no more than 1,651 before to more than 17,800 now.
“We mathematically combined
the new rotation-reversal symmetry with the previous five symmetries and now we know that symmetrical groups can
form in crystalline materials in a much larger number of ways,” said Daniel
B. Litvin, distinguished professor of physics, who coauthored the study with
Venkatraman Gopalan, professor of materials science and engineering.
The new rotation-reversal
symmetry enriches the mathematical language that researchers use to describe a
crystalline material’s structure and to predict its properties. “Rotation
reversal is an absolutely new approach that is different in that it acts on a
static component of the material’s structure, not on the whole structure all at
once,” Litvin said. “It is important to look at symmetries in materials because symmetry dictates all
natural laws in our physical universe.”
The most simple type of symmetry—rotation
symmetry—is obvious, for example, when a square shape is rotated around its
center point: the square shows its symmetrical character by looking exactly the
same at four points during the rotation: at 90 degrees, 180 degrees, 270
degrees, and 360 degrees. Gopalan and Litvin say their new rotation-reversal
symmetry is obvious, as well, if you know where to look.
The “eureka moment” of
the discovery occurred when Gopalan recognized that the simple concept of
reversing the direction of a spiral-shaped structure from clockwise to
counterclockwise opens the door to a distinctly new type of symmetry. Just as a
square shape has the quality of rotation symmetry even when it is not being
rotated, Gopalan realized that a spiral shape has the quality of
rotation-reversal symmetry even when it is not being physically forced to
rotate in the reverse direction. Their further work with this rotation-reversal
concept revealed many more structural symmetries
than previously had been recognized in materials containing various types of
directionally oriented structures. Many important biological molecules, for
example, are said to be either “right handed” or “left
handed,” including DNA, sugars, and proteins.
“We found that
rotation-reversal symmetry also exists in paired structures where the partner
components lean toward each other, then away from each other in paired patterns
symmetrically throughout a material,” Gopalan said. These “tilting
octahedral” structures are common in a wide variety of crystalline
materials, where all the component structures are tightly interconnected by
networks of shared atoms. The researchers say it is possible that components of
materials with rotation-reversal symmetry could be engineered to function as
on/off switches for a variety of novel applications.
The now-much-larger number of
possible symmetry groups also is expected to be useful in identifying materials
with unusual combinations of properties. “For example, the goal in
developing a ferroelectric ferromagnet is to have a material in which the
electrical dipoles and the magnetic moments coexist and are coupled in the same
material—that is, a material that allows electrical control of magnetism—which
would be very useful to have in computers,” Gopalan said. The addition of
rotation-reversal symmetry to the materials-science toolbox may help
researchers to identify and search for structures in materials that could have
strong ferroelectric and ferromagnetic properties.
Gopalan and Litvin said a goal of
their continuing research is to describe each of the more than 17,800 different
combinations of the six symmetry types to give materials scientists a practical
new tool for significantly increasing the efficiency and effectiveness in
finding novel materials. The team also plans to conduct laboratory experiments
that make use of their theoretical work on rotation-reversal symmetry. “We
have done some predictions, we will test those predictions
experimentally,” Litvin said. “We are in the very early stages of
implementing the results we have described in our new theory paper.”
Gopalan said, for example, that he has predicted new forms for optical
properties in the commonplace quartz crystals that are used widely in watches
and electronic equipment, and that his group now is testing these predictions
experimentally.
The National Science Foundation
provided financial support for this research through its Materials Research
Science and Engineering
Centers program.
