Abstract
Topological grain forms in three dimensions are studied experimentally and by large-scale Potts model Monte Carlo simulation. Some new band-faced grain forms are firstly observed among 16,254 pure iron grains, yet none of them is found among 28,049 Monte Carlo simulation grains, which indicate that there is shorter residence times for band-faced grain forms in three dimensions. The combined curvature/topology analysis suggests a possible efficient way of topological transitions of grain forms which is different from the known transition paths.
Highlights
IntroductionThe 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
Schlegel diagram of a given grain has been proven to be a good description of the topological grain forms
In the analysis of grain form evolution via Schlegel tree, Patterson et al.[7] suggested 7 possible forms for 7-faced grains and 27 possible forms for 8-faced grains resulting from normal grain growth processes of face gain, loss and edge-switching events
Summary
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. T. Keller et al.[2] studied the dispersion in the distribution of edges per face for each grain form in different cellular structures. B.R. Patterson et al.[7] used Schlegel diagrams[8] to study the paths of evolution of topological grain forms and propose some possible forms for grains with 4–9 faces. Patterson et al.[7] used Schlegel diagrams[8] to study the paths of evolution of topological grain forms and propose some possible forms for grains with 4–9 faces Some of these grain forms are neither found in experiment nor in simulation. Since some topological forms for grains with 4–9 faces generated by either
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