Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids

Abstract

While the microscopic structure of defected solid crystalline materials has significant impact on their physical properties, efficient and accurate determination of a given polycrystalline microstructure remains a challenge. In this paper we present a highly generalizable and reliable variational method to achieve this goal for two-dimensional crystalline and quasicrystalline materials. The method is benchmarked and optimized successfully using a variety of large-scale systems of defected solids, including periodic structures and quasicrystalline symmetries to quantify their microstructural characteristics, e.g., grain size and lattice misorientation distributions. We find that many microstructural properties show universal features independent of the underlying symmetries.

Lattice Identification and Separation: Theory and Algorithm

“…Motivated by some of the current developments in material sciences [33,62] and crystalline material image analysis [7,8,12,30,40,70] , we focus on two dimensional lattice, which plays major roles in crystallography [23,60], sampling theory [50], ecology [66] and many others. For example, crystal structures of halite (NaCl) and gold (Au) have distinct scales (NaCl constant: 5.640Å [26]; Au constant: 4.065Å [19]), which explains their proprietary differences.…”