Geometric and topological properties of the canonical grain growth microstructure

TL;DR

This paper investigates the geometric and topological features of steady-state microstructures resulting from isotropic grain growth in polycrystalline materials, providing insights into their physical properties through large-scale simulations.

Contribution

It presents a detailed analysis of the geometric and topological properties of canonical grain growth microstructures using extensive simulations.

Findings

Characterization of microstructure geometry and topology

Insights into the physics of polycrystalline materials

Large-scale simulation data of steady-state microstructures

Abstract

Many physical systems can be modeled as large sets of domains "glued" together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of a simple energy, directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady-state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through large, accurate simulations of isotropic grain growth.