Sixth type of symmetry discovered
April 4, 2011 by Editor
A lattice composed of columns of squares representing repeating molecular structures, one rotated clockwise (colored blue) and another counterclockwise (colored orange) with respect to each other (credit: Penn State University, Gopalan lab, Ryan Haislmaier)
Researchers at Penn State have discovered a sixth type of symmetry in the structure of materials called rotation reversal.
Rotation-reversal symmetry enriches the mathematical language that researchers use to describe a crystalline material’s structure and predict its properties. The research is expected to have broad relevance in many development efforts involving physical, chemical, biological, and engineering disciplines, such as the search for advanced ferroelectric ferromagnet materials for next-generation ultrasound devices and computers.
A lattice composed of two repeating squares that represent molecular structures (credit: Penn State University, Gopalan lab, Ryan Haislmaier)
Four types of symmetries (rotation, inversion, rotation inversion, and translation) have been known for thousands of years. A fifth type, time reversal, was discovered about 60 years ago. As a result of the discovery of the new sixth type, the number of known ways in which the components of crystalline materials can be combined in symmetrical ways has multiplied from 1,651 to more than 17,800.
A goal of the 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 researchers see immediate applications in the search for structures in materials that could have strong ferroelectric and ferromagnetic properties (allowing the electrical control of magnetism in computers), and in quartz crystals that are used widely in watches and electronic equipment.
Ref.: Venkatraman Gopalan & Daniel B. Litvin, Rotation-reversal symmetries in crystals and handed structures, April 3 online edition, Nature Materials
Topics: Nanotech/Materials Science