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The antisymmetry of distortions.

VanLeeuwen BK, Gopalan V - Nat Commun (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

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

Four different example distortions in crystals and their distortion symmetry groups.Each panel depicts the superimposed structures through a distortion from λ=−1 to λ=+1 so that the movement of the atoms appears in the form of a blur. (a) A distortion pathway between two domain variants of a right-handed alpha quartz, passing through beta quartz at λ=0, with a distortion group of P6422. (b) A distortion of ferroelectric PbTiO3 created by a linear interpolation between opposite (180°) polarization states; the pathway has a symmetry of P4/mmm. (c) A distortion of YMnO3 between opposite ferroelectric domain variants with a distortion symmetry of P63/mcm. (d) A B1u normal mode of YBa2Cu3O6.5 with a distortion symmetry of Pmmm.
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f5: Four different example distortions in crystals and their distortion symmetry groups.Each panel depicts the superimposed structures through a distortion from λ=−1 to λ=+1 so that the movement of the atoms appears in the form of a blur. (a) A distortion pathway between two domain variants of a right-handed alpha quartz, passing through beta quartz at λ=0, with a distortion group of P6422. (b) A distortion of ferroelectric PbTiO3 created by a linear interpolation between opposite (180°) polarization states; the pathway has a symmetry of P4/mmm. (c) A distortion of YMnO3 between opposite ferroelectric domain variants with a distortion symmetry of P63/mcm. (d) A B1u normal mode of YBa2Cu3O6.5 with a distortion symmetry of Pmmm.

Mentions: The ubiquitousness of distortion symmetry is further illustrated in Fig. 5 with four examples. Each panel depicts the structures from λ=−1 to λ=+1 superimposed so that the movement of the atoms appears in the form of a blur. A common piezoelectric crystal quartz (SiO2) is depicted in Fig. 5a, where a distortion from one domain of right-handed alpha quartz (at λ=−1) through beta quartz (at λ=0) to another domain of right-handed alpha (at λ=+1) exhibits the distortion symmetry of P64*22* (with point group 6*22*). Supplementary Note 4 and Supplementary Fig. 7 shows how there is an equivalent pathway in left-handed quartz with P62*22* symmetry, as well as the symmetries of paths between left- and right-handed quartz. More generally, one can find distortion groups describing transformation between any two enantiomorphic structures (related by mirror) by choosing an appropriate parent that is intermediate between the two. Multiple such parents are possible, in principle. These ideas are also applicable to liquid crystals that can switch between left- and right-handed enantiomorphs under an electric field, a property that is utilized in display technologies.


The antisymmetry of distortions.

VanLeeuwen BK, Gopalan V - Nat Commun (2015)

Four different example distortions in crystals and their distortion symmetry groups.Each panel depicts the superimposed structures through a distortion from λ=−1 to λ=+1 so that the movement of the atoms appears in the form of a blur. (a) A distortion pathway between two domain variants of a right-handed alpha quartz, passing through beta quartz at λ=0, with a distortion group of P6422. (b) A distortion of ferroelectric PbTiO3 created by a linear interpolation between opposite (180°) polarization states; the pathway has a symmetry of P4/mmm. (c) A distortion of YMnO3 between opposite ferroelectric domain variants with a distortion symmetry of P63/mcm. (d) A B1u normal mode of YBa2Cu3O6.5 with a distortion symmetry of Pmmm.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4660051&req=5

f5: Four different example distortions in crystals and their distortion symmetry groups.Each panel depicts the superimposed structures through a distortion from λ=−1 to λ=+1 so that the movement of the atoms appears in the form of a blur. (a) A distortion pathway between two domain variants of a right-handed alpha quartz, passing through beta quartz at λ=0, with a distortion group of P6422. (b) A distortion of ferroelectric PbTiO3 created by a linear interpolation between opposite (180°) polarization states; the pathway has a symmetry of P4/mmm. (c) A distortion of YMnO3 between opposite ferroelectric domain variants with a distortion symmetry of P63/mcm. (d) A B1u normal mode of YBa2Cu3O6.5 with a distortion symmetry of Pmmm.
Mentions: The ubiquitousness of distortion symmetry is further illustrated in Fig. 5 with four examples. Each panel depicts the structures from λ=−1 to λ=+1 superimposed so that the movement of the atoms appears in the form of a blur. A common piezoelectric crystal quartz (SiO2) is depicted in Fig. 5a, where a distortion from one domain of right-handed alpha quartz (at λ=−1) through beta quartz (at λ=0) to another domain of right-handed alpha (at λ=+1) exhibits the distortion symmetry of P64*22* (with point group 6*22*). Supplementary Note 4 and Supplementary Fig. 7 shows how there is an equivalent pathway in left-handed quartz with P62*22* symmetry, as well as the symmetries of paths between left- and right-handed quartz. More generally, one can find distortion groups describing transformation between any two enantiomorphic structures (related by mirror) by choosing an appropriate parent that is intermediate between the two. Multiple such parents are possible, in principle. These ideas are also applicable to liquid crystals that can switch between left- and right-handed enantiomorphs under an electric field, a property that is utilized in display technologies.

Bottom Line: 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.

View Article: PubMed Central - PubMed

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