2014
DOI: 10.1016/j.actamat.2013.11.039
|View full text |Cite
|
Sign up to set email alerts
|

Comparative grain topology

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
12
0

Year Published

2016
2016
2024
2024

Publication Types

Select...
6
1

Relationship

0
7

Authors

Journals

citations
Cited by 13 publications
(12 citation statements)
references
References 30 publications
0
12
0
Order By: Relevance
“…For comparison, some similar results are also included. The enumeration of 3-regular simple (3-connected) and band-faced (2-connected but not 3-connected) planar graphs using a Monte Carlo algorithm is done by Keller 15 . The number of our calculated grain forms with 3-connected Schlegel diagrams in this work is the same as Keller’s for grains with 13 and fewer faces, but more larger than Keller’s results for grains with 14 faces.…”
Section: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…For comparison, some similar results are also included. The enumeration of 3-regular simple (3-connected) and band-faced (2-connected but not 3-connected) planar graphs using a Monte Carlo algorithm is done by Keller 15 . The number of our calculated grain forms with 3-connected Schlegel diagrams in this work is the same as Keller’s for grains with 13 and fewer faces, but more larger than Keller’s results for grains with 14 faces.…”
Section: Resultsmentioning
confidence: 99%
“…The Schlegel diagrams of some grains, although not many in the system, are 2-connected but not 3-connected planar graphs 13 15 . The Weinberg vectors description is only suitable for grains with Schlegel diagrams being 3-connected planar graphs 10 , while not suitable for grains with Schlegel diagrams being 2-connected planar graphs.…”
mentioning
confidence: 97%
“…Voronoi constructions can produce grains with sharp points, wedge-shaped grains, or planar prismatic grains that are not observed experimentally. The grain topology of microstructures generated using PV has been shown to be significantly different than grain growth simulations and real systems [51]. Voronoi constructions also produce planar grain boundaries, while curved boundaries are common in experimentally observed microstructures.…”
Section: Introductionmentioning
confidence: 95%
“…Cellular structures are very common in nature, for example, polycrystals in materials, foams in physics, biological tissues in biology 1 . Although differences are clear among different cellular systems resulting from different formation or evolution processes, they shares many features in common 2,3 since they all belong to space-filling aggregates. Cellular networks are implicated in many, varied material properties at many different length scales, including lifetime properties such as fracture toughness, and functional properties such as electrical conductivity 4 .…”
Section: Introductionmentioning
confidence: 99%
“…Grain forms consist of the information of number of faces, edges per face and face arrangements, i.e., the refined/detailed grain topology. The topological viewpoint of grain growth describes the process as the decomposition of grains through decreasing numbers of faces toward the end state of a tetrahedral grain that disappears at a quadruple point 2 . The study on the paths of evolution of grain forms during grain growth is urgently need for describing the mechanism of grain growth from topological viewpoint.…”
Section: Introductionmentioning
confidence: 99%