Spatio-temporal symmetry - crystallographic point groups with time translations and time inversion.

The crystallographic symmetry of time-periodic phenomena has been extended to include time inversion. The properties of such spatio-temporal crystallographic point groups with time translations and time inversion are derived and one representative group from each of the 343 types has been tabulated. In addition, stereographic symmetry and general-position diagrams are given for each representative group. These groups are also given a notation consisting of a short Hermann-Mauguin magnetic point-group symbol with each spatial operation coupled with its associated time translation.

Emergent Low-Symmetry Phases and Large Property Enhancements in Ferroelectric KNbO3 Bulk Crystals.

The design of new or enhanced functionality in materials is traditionally viewed as requiring the discovery of new chemical compositions through synthesis. Large property enhancements may however also be hidden within already well-known materials, when their structural symmetry is deviated from equilibrium through a small local strain or field. Here, the discovery of enhanced material properties associated with a new metastable phase of monoclinic symmetry within bulk KNbO3 is reported. This phase is found to coexist with the nominal orthorhombic phase at room temperature, and is both induced by and stabilized with local strains generated by a network of ferroelectric domain walls. While the local microstructural shear strain involved is only ≈0.017%, the concurrent symmetry reduction results in an optical second harmonic generation response that is over 550% higher at room temperature. Moreover, the meandering walls of the low-symmetry domains also exhibit enhanced electrical conductivity on the order of 1 S m-1 . This discovery reveals a potential new route to local engineering of significant property enhancements and conductivity through symmetry lowering in ferroelectric crystals.

The antisymmetry of distortions.

Distortions are ubiquitous in nature. Under perturbations such as stresses, fields or other changes, a physical system reconfigures by following a path from one state to another; this path, often a collection of atomic trajectories, describes a distortion. Here we introduce an antisymmetry operation called distortion reversal that reverses a distortion pathway. The symmetry of a distortion pathway is then uniquely defined by a distortion group; it has the same form as a magnetic group that involves time reversal. Given its isomorphism to magnetic groups, distortion groups could have a commensurate impact in the study of distortions, as the magnetic groups have had in the study of magnetic structures. Distortion symmetry has important implications for a range of phenomena such as structural and electronic phase transitions, diffusion, molecular conformational changes, vibrations, reaction pathways and interface dynamics.

Nano-sized Superlattice Clusters Created by Oxygen Ordering in Mechanically Alloyed Fe Alloys.

Creating and maintaining precipitates coherent with the host matrix, under service conditions is one of the most effective approaches for successful development of alloys for high temperature applications; prominent examples include Ni- and Co-based superalloys and Al alloys. While ferritic alloys are among the most important structural engineering alloys in our society, no reliable coherent precipitates stable at high temperatures have been found for these alloys. Here we report discovery of a new, nano-sized superlattice (NSS) phase in ball-milled Fe alloys, which maintains coherency with the BCC matrix up to at least 913 °C. Different from other precipitates in ferritic alloys, this NSS phase is created by oxygen-ordering in the BCC Fe matrix. It is proposed that this phase has a chemistry of Fe3O and a D03 crystal structure and becomes more stable with the addition of Zr. These nano-sized coherent precipitates effectively double the strength of the BCC matrix above that provided by grain size reduction alone. This discovery provides a new opportunity for developing high-strength ferritic alloys for high temperature applications.

Double antisymmetry and the rotation-reversal space groups.

Rotation-reversal symmetry was recently introduced to generalize the symmetry classification of rigid static rotations in crystals such as tilted octahedra in perovskite structures and tilted tetrahedra in silica structures. This operation has important implications for crystallographic group theory, namely that new symmetry groups are necessary to properly describe observations of rotation-reversal symmetry in crystals. When both rotation-reversal symmetry and time-reversal symmetry are considered in conjunction with space-group symmetry, it is found that there are 17,803 types of symmetry which a crystal structure can exhibit. These symmetry groups have the potential to advance understanding of polyhedral rotations in crystals, the magnetic structure of crystals and the coupling thereof. The full listing of the double antisymmetry space groups can be found in the supplementary materials of the present work and at http://sites.psu.edu/gopalan/research/symmetry/.

Crystallographic data of double antisymmetry space groups.

This paper presents crystallographic data of double antisymmetry space groups, including symmetry-element diagrams, general-position diagrams and positions, with multiplicities, site symmetries, coordinates, spin vectors, roto vectors and displacement vectors.