Deformation pathway and defect generation in crystals: a combined group theory and graph theory description

Gao, Yipeng; Wang, Yunzhi; Zhang, Yongfeng

doi:10.1107/S2052252518017050

Title: Deformation pathway and defect generation in crystals: a combined group theory and graph theory description

Abstract

The generation and motion of crystalline defects during plastic deformation are critical processes that determine the mechanical properties of a crystal. The types of defect generated are not only related to the symmetry of a crystal but also associated with the symmetry-breaking process during deformation. Proposed here is a new mathematical framework to capture the intrinsic coupling between crystal symmetry and deformation-induced symmetry breaking. Using a combination of group theory and graph theory, a general approach is demonstrated for the systematic determination of the types of crystalline defect induced by plastic deformation, through the construction of a crystal deformation group and a deformation pathway graph. The types of defect generated in the deformation of a face-centered cubic crystal are analyzed through the deformation pathway graph and compared with experimental observations.

Authors:: Gao, Yipeng; Wang, Yunzhi; Zhang, Yongfeng

Publication Date:: Tue Jan 01 00:00:00 EST 2019

Research Org.:: Idaho National Lab. (INL), Idaho Falls, ID (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1617920

Alternate Identifier(s):: OSTI ID: 1561227

Report Number(s):: INL/JOU-18-45559-Rev000
Journal ID: ISSN 2052-2525; IUCRAJ; PII: S2052252518017050

Grant/Contract Number:: SC0001258; AC07-05ID14517

Resource Type:: Published Article

Journal Name:: IUCrJ

Additional Journal Information:: Journal Name: IUCrJ Journal Volume: 6 Journal Issue: 1; Journal ID: ISSN 2052-2525

Publisher:: International Union of Crystallography (IUCr)

Country of Publication:: United Kingdom

Language:: English

Subject:: 36 MATERIALS SCIENCE; Crystalline materials; Deformation; Crystalline defects; group theory; graph theory

Citation Formats


                    Gao, Yipeng, Wang, Yunzhi, and Zhang, Yongfeng. Deformation pathway and defect generation in crystals: a combined group theory and graph theory description.  United Kingdom: N. p., 2019. 
Web.  doi:10.1107/S2052252518017050.

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                    Gao, Yipeng, Wang, Yunzhi, & Zhang, Yongfeng. Deformation pathway and defect generation in crystals: a combined group theory and graph theory description.  United Kingdom.  https://doi.org/10.1107/S2052252518017050

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                    Gao, Yipeng, Wang, Yunzhi, and Zhang, Yongfeng. Tue .  
"Deformation pathway and defect generation in crystals: a combined group theory and graph theory description".  United Kingdom.  https://doi.org/10.1107/S2052252518017050.

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@article{osti_1617920,

  title        = {Deformation pathway and defect generation in crystals: a combined group theory and graph theory description},

  author       = {Gao, Yipeng and Wang, Yunzhi and Zhang, Yongfeng},

  abstractNote = {The generation and motion of crystalline defects during plastic deformation are critical processes that determine the mechanical properties of a crystal. The types of defect generated are not only related to the symmetry of a crystal but also associated with the symmetry-breaking process during deformation. Proposed here is a new mathematical framework to capture the intrinsic coupling between crystal symmetry and deformation-induced symmetry breaking. Using a combination of group theory and graph theory, a general approach is demonstrated for the systematic determination of the types of crystalline defect induced by plastic deformation, through the construction of a crystal deformation group and a deformation pathway graph. The types of defect generated in the deformation of a face-centered cubic crystal are analyzed through the deformation pathway graph and compared with experimental observations.},

  doi          = {10.1107/S2052252518017050},

  journal      = {IUCrJ},

  number       = 1,

  volume       = 6,

  place        = {United Kingdom},

  year         = {Tue Jan 01 00:00:00 EST 2019},

  month        = {Tue Jan 01 00:00:00 EST 2019}

}

Copy to clipboard

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Works referencing / citing this record:

Computational and materials structural science
journal, June 2019

Catlow, C. Richard A.
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DOI: 10.1107/s2052252519009114

Phase Transformation Graph and Transformation Pathway Engineering for Shape Memory Alloys
journal, February 2020

Gao, Yipeng; Yu, Taiwu; Wang, Yunzhi
Shape Memory and Superelasticity, Vol. 6, Issue 1
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Title: Deformation pathway and defect generation in crystals: a combined group theory and graph theory description

Abstract

Citation Formats

Crystal symmetry and the reversibility of martensitic transformations journal, March 2004

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The crystallography and core structure of twinning dislocations in H.C.P. metals journal, December 1988

The bain strain, lattice correspondences, and deformations related to martensitic transformations journal, May 1972

Interphase-boundary dislocations and the concept of coherency journal, December 1979

On the elasticity of monatomic crystals journal, July 1976

High-resolution electron microscopy of grain boundaries journal, January 1995

Crystal symmetry and physical properties: application of group theory journal, March 1949

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High-resolution transmission electron microscopy of grain boundaries in aluminum and correlation with atomistic calculations journal, March 1992

A Revisit to the Notation of Martensitic Crystallography journal, August 2018

Dissociation and faceting of asymmetrical tilt grain boundaries: Molecular dynamics simulations of copper journal, October 2007

Angular distortive matrices of phase transitions in the fcc–bcc–hcp system journal, June 2016

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The mechanism of crystal deformation journal, September 2015

A universal symmetry criterion for the design of high performance ferroic materials journal, April 2017

On the mechanism of {332} twinning in metastable β titanium alloys journal, June 2016

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups journal, March 2006

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3 n grain boundaries journal, December 2006

Computer simulation of extrinsic grain-boundary defects in the ∑11, 〈101〉{131} symmetric tilt boundary journal, March 1999

Variational methods for elastic crystals journal, September 1987

High-resolution electron microscopy of interfaces in fcc materials journal, August 1991

Low-energy configurations of symmetric and asymmetric tilt grain boundaries journal, February 1992

Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool journal, December 2009

Deformation twinning journal, January 1995

Some phase transitions in crystals journal, January 1980

The symmetry of martensites journal, July 1977

A Variational Model for Reconstructive Phase Transformations in Crystals, and their Relation to Dislocations and Plasticity journal, April 2004

Group theory description of transformation pathway degeneracy in structural phase transformations journal, May 2016

Self-organized multigrain patterning with special grain boundaries produced by phase transformation cycling journal, July 2018

Reconciliation of local and global symmetries of crystals journal, June 1984

Grain boundary character distribution of CuNiSi and FeNi alloys processed by severe plastic deformation journal, April 2015

The crystallography of martensite transformations I journal, January 1954

Computational and materials structural science journal, June 2019

Phase Transformation Graph and Transformation Pathway Engineering for Shape Memory Alloys journal, February 2020

Crystal symmetry and the reversibility of martensitic transformations
journal, March 2004

Atomistic modeling of interfaces and their impact on microstructure and properties
journal, February 2010

The topological theory of defects in ordered media
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The crystallography and core structure of twinning dislocations in H.C.P. metals
journal, December 1988

The bain strain, lattice correspondences, and deformations related to martensitic transformations
journal, May 1972

Interphase-boundary dislocations and the concept of coherency
journal, December 1979

On the elasticity of monatomic crystals
journal, July 1976

High-resolution electron microscopy of grain boundaries
journal, January 1995

Crystal symmetry and physical properties: application of group theory
journal, March 1949

Desiderata and Suggestions: No. 2. The Theory of Groups: Graphical Representation
journal, January 1878

High-resolution transmission electron microscopy of grain boundaries in aluminum and correlation with atomistic calculations
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A Revisit to the Notation of Martensitic Crystallography
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Dissociation and faceting of asymmetrical tilt grain boundaries: Molecular dynamics simulations of copper
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Angular distortive matrices of phase transitions in the fcc–bcc–hcp system
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Boundary energies of Σ11 [110] asymmetric tilt boundaries in Cu determined from the shape of boundary silica particles
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On the mechanism of {332} twinning in metastable β titanium alloys
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Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3 ⁿ grain boundaries
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The symmetry of martensites
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Group theory description of transformation pathway degeneracy in structural phase transformations
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