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A Simple Dry Sectioning Method for Obtaining Whole-Seed-Sized Resin Section and Its Applications

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Roundness of grains in cellular microstructures.

F H Lutz¹, J K Mason², E A Lazar³

¹Technische Universität Berlin, 10623 Berlin, Germany.

Physical Review. E

|September 28, 2017

Summary

This summary is machine-generated.

This study analyzes polyhedral cell structures, finding most grains are fundamental types. Vertex-truncated types decrease exponentially, explained by evolutionary processes eliminating unfavorable surfaces.

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Area of Science:

Materials Science
Computational Science
Geometry

Background:

Physical systems often comprise polyhedral cells with simple structures.
Understanding the combinatorial types of these cells is crucial for characterizing complex microstructures.
Grain growth microstructures serve as a relevant model for studying polyhedral cell distributions.

Purpose of the Study:

To determine the distribution of combinatorial types of polyhedral cells.
To introduce and apply the concepts of fundamental and vertex-truncated types.
To analyze grain growth microstructures and their topological properties.

Main Methods:

Classification of polyhedral cells into fundamental and vertex-truncated types.
Analysis of grain growth microstructures to observe combinatorial type frequencies.
Investigation of grain topology using combinatorial definitions of 'roundness'.

Main Results:

Most grains in microstructures belong to specific fundamental types.
The frequency of vertex-truncated types decreases exponentially with the number of truncations.
Grain types exhibit combinatorial 'roundness', lacking short separating cycles.

Conclusions:

The observed distributions are consistent with evolutionary processes in grain growth.
A Poisson-Voronoi derived microstructure shows a high proportion of round grains.
This rounder microstructure may possess greater resistance to topological change.