| Issue |
EPL
Volume 104, Number 5, December 2013
|
|
|---|---|---|
| Article Number | 56006 | |
| Number of page(s) | 4 | |
| Section | Condensed Matter: Structural, Mechanical and Thermal Properties | |
| DOI | https://doi.org/10.1209/0295-5075/104/56006 | |
| Published online | 06 January 2014 | |
Topological correlations of grain faces in polycrystal with experimental verification
1 School of Materials Science and Engineering, University of Science and Technology Beijing Beijing 100083, PRC
2 State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing Beijing 100083, PRC
3 Department of Chemical and Materials Engineering, University of Alberta - Edmonton, Alberta, T6G2V4, Canada
4 Center for Advanced Structural Materials, Department of Mechanical and Biomedical Engineering, City University of Hong Kong - 999077 Hong Kong, PRC
5 Department of Mathematics, Karakoram International University Gilgit- Baltistan - Gilgit 15100, Pakistan
(a) g.liu@ustb.edu.cn (corresponding author)
Received: 18 September 2013
Accepted: 4 December 2013
How grain faces are arranged in three-dimensional grain structures is one of the outstanding problems in physics, biology and materials science. Based on the topological analysis of 477 real pure iron grains and 6093 Monte Carlo simulated grains, two forms of topological correlations are studied. The first correlation is Rivier's relation (Philos. Mag. B, 52 (1985) 795), in which the average number of edges 
of faces neighboring to e-edged faces on f-faceted grains is related to e and f; and the second correlation is the one derived in the current paper, in which a typical e-edged face in a polycrystal is a function of the average number of edges of its neighboring faces M(e). Both correlations are verified by experimental and simulation data.
PACS: 64.30.Ef – Equations of state of pure metals and alloys / 81.10.Aj – Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation / 61.43.Bn – Structural modeling: serial-addition models, computer simulation
© EPLA, 2013
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