Tilt grain boundaries of hexagonal structures: a spectral viewpoint

TL;DR

This paper introduces a spectral approach to analyze tilt grain boundaries in hexagonal structures, revealing key spectral contributions and proposing a new definition for interface width that aligns with visual estimates.

Contribution

It presents a novel spectral viewpoint for quasiperiodic grain boundaries and demonstrates its effectiveness in extracting boundary features and defining interface width.

Findings

Few spectra dominate grain boundary formation

Spectral intensities relate linearly to bulk spectra

Proposed interface width matches visual estimates

Abstract

We propose a spectral viewpoint for grain boundaries that are generally quasiperiodic. To accurately capture the spectra computationally, it is crucial to adopt the projection method for quasiperiodic functions. Armed with the Lifshitz-Petrich free energy, we take the spectral viewpoint to examine tilt grain boundaries of the hexagonal phase. Several ingredients of grain boundaries are extracted, which are not easy to obtain from real-space profiles. We find that only a few spectra substantially contribute to the formation of grain boundaries. Their linear relation to the intrinsic spectra of the bulk hexagonal phase is independent of the tilt angle. By examining the feature of the spectral intensities, we propose a definition of the interface width. The widths calculated from this definition are consistent with visual estimation.