Comparative grain topology

Trevor Keller; Barbara Cutler; Emanuel A. Lazar; Gregory Yauney; Daniel J. Lewis

doi:https://doi.org/10.1016/j.actamat.2013.11.039

Comparative grain topology

Trevor Keller, Barbara Cutler, Emanuel A. Lazar, Gregory Yauney, Daniel J. Lewis

Research output: Contribution to journal › Article › peer-review

Abstract

Space-filling polyhedral networks are commonly studied in biological, physical, and mathematical disciplines. The constraints governing the construction of each network varies considerably under each context, affecting the topological properties of the constituents. A method for mapping the topological symmetry of a space-filling population of polyhedra is presented, relative to all possible polyhedra. This method is applied to the topological comparison of populations generated by seven different processes: (i) natural grain growth in polycrystalline metal, ideal grain growth simulated by (ii) interface-tracking and (iii) phase-field methods, (iv) Poisson-Voronoi and (v) ellipsoid tessellations, and (vi) graph-theoretic and (vii) Monte Carlo enumerations of individual polyhedra. Evidence for topological bias in these populations is discussed.

Original language	English
Pages (from-to)	414-423
Number of pages	10
Journal	Acta Materialia
Volume	66
DOIs	https://doi.org/10.1016/j.actamat.2013.11.039
State	Published - Mar 2014
Externally published	Yes

Keywords

Computer simulation
Grain growth
Microstructure
Phase-field method
Topology

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Ceramics and Composites
Polymers and Plastics
Metals and Alloys

Access to Document

https://doi.org/10.1016/j.actamat.2013.11.039

Cite this

@article{1a9b84b8bd09449f9045b97a9a6ef0e3,

title = "Comparative grain topology",

abstract = "Space-filling polyhedral networks are commonly studied in biological, physical, and mathematical disciplines. The constraints governing the construction of each network varies considerably under each context, affecting the topological properties of the constituents. A method for mapping the topological symmetry of a space-filling population of polyhedra is presented, relative to all possible polyhedra. This method is applied to the topological comparison of populations generated by seven different processes: (i) natural grain growth in polycrystalline metal, ideal grain growth simulated by (ii) interface-tracking and (iii) phase-field methods, (iv) Poisson-Voronoi and (v) ellipsoid tessellations, and (vi) graph-theoretic and (vii) Monte Carlo enumerations of individual polyhedra. Evidence for topological bias in these populations is discussed.",

keywords = "Computer simulation, Grain growth, Microstructure, Phase-field method, Topology",

author = "Trevor Keller and Barbara Cutler and Lazar, {Emanuel A.} and Gregory Yauney and Lewis, {Daniel J.}",

note = "Funding Information: This work is supported by the NSF under Grant # 1056704 through the Metals and Metallic Nanostructures Program of the Division of Materials Research. The authors wish to thank David J. Rowenhorst (Naval Research Laboratory, Washington, DC) for access to the full -Ti dataset, and Martin E. Glicksman (Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL) for technical discussions on polyhedra and topology.",

year = "2014",

month = mar,

doi = "https://doi.org/10.1016/j.actamat.2013.11.039",

language = "الإنجليزيّة",

volume = "66",

pages = "414--423",

}

TY - JOUR

T1 - Comparative grain topology

AU - Keller, Trevor

AU - Cutler, Barbara

AU - Lazar, Emanuel A.

AU - Yauney, Gregory

AU - Lewis, Daniel J.

N1 - Funding Information: This work is supported by the NSF under Grant # 1056704 through the Metals and Metallic Nanostructures Program of the Division of Materials Research. The authors wish to thank David J. Rowenhorst (Naval Research Laboratory, Washington, DC) for access to the full -Ti dataset, and Martin E. Glicksman (Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL) for technical discussions on polyhedra and topology.

PY - 2014/3

Y1 - 2014/3

N2 - Space-filling polyhedral networks are commonly studied in biological, physical, and mathematical disciplines. The constraints governing the construction of each network varies considerably under each context, affecting the topological properties of the constituents. A method for mapping the topological symmetry of a space-filling population of polyhedra is presented, relative to all possible polyhedra. This method is applied to the topological comparison of populations generated by seven different processes: (i) natural grain growth in polycrystalline metal, ideal grain growth simulated by (ii) interface-tracking and (iii) phase-field methods, (iv) Poisson-Voronoi and (v) ellipsoid tessellations, and (vi) graph-theoretic and (vii) Monte Carlo enumerations of individual polyhedra. Evidence for topological bias in these populations is discussed.

AB - Space-filling polyhedral networks are commonly studied in biological, physical, and mathematical disciplines. The constraints governing the construction of each network varies considerably under each context, affecting the topological properties of the constituents. A method for mapping the topological symmetry of a space-filling population of polyhedra is presented, relative to all possible polyhedra. This method is applied to the topological comparison of populations generated by seven different processes: (i) natural grain growth in polycrystalline metal, ideal grain growth simulated by (ii) interface-tracking and (iii) phase-field methods, (iv) Poisson-Voronoi and (v) ellipsoid tessellations, and (vi) graph-theoretic and (vii) Monte Carlo enumerations of individual polyhedra. Evidence for topological bias in these populations is discussed.

KW - Computer simulation

KW - Grain growth

KW - Microstructure

KW - Phase-field method

KW - Topology

UR - http://www.scopus.com/inward/record.url?scp=84894904095&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.actamat.2013.11.039

DO - https://doi.org/10.1016/j.actamat.2013.11.039

M3 - مقالة

SN - 1359-6454

VL - 66

SP - 414

EP - 423

JO - Acta Materialia

JF - Acta Materialia

ER -

Comparative grain topology

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this