The antisymmetry of distortions.
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Distortions are ubiquitous in nature.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.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.
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Affiliation: Materials Research Institute and Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
ABSTRACT
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. No MeSH data available. Related in: MedlinePlus |
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Mentions: Next, we demonstrate a symmetry-based approach to testing the stability of a pathway and checking the results of numerical computations for accuracy. This is demonstrated in the NEB calculation of activation energy for an oxygen atom diffusing across a C6 ring on the surface of graphene (Fig. 3a,b). Although not typically thought of as a ‘distortion', this diffusion path is a distortion within the symmetry framework presented in this article. Linear interpolation from the state with oxygen on the right (λ=−1), to the state with oxygen on the left (λ=+1) creates a path with m*m2* symmetry with a high-activation-energy barrier (Fig. 3a,b); this is not an MEP. Typically, only the first and last images are specified when setting up a NEB calculation and a linear path, such as this would be constructed by default by the NEB implementation. For example, this is the case for VTST Tools for VASP and neb.x for Quantum Espresso (QE). Relaxing this path using NEB cannot and does not change the m*m2* symmetry, because every NEB iteration must conserve distortion symmetry (Fig. 3c,d; Supplementary Note 2; Supplementary Figs 2–5), since the forces are balanced by symmetry. Without understanding that the symmetry needs to be broken, one might incorrectly conclude that the activation barrier for oxygen diffusion on graphene is several times larger than it actually is. We can now systematically explore perturbations to this path by using the irreps of m*m2* summarized by the character table given in Table 1. |
View Article: PubMed Central - PubMed
Affiliation: Materials Research Institute and Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
No MeSH data available.