Theory of Finite-Length Grain Boundaries of Controlled Misfit Angle in Two-Dimensional Materials

Grain boundaries in two-dimensional crystals are usually thought to separate distinct crystallites and as such they must either form closed loops or terminate at the boundary of a sample. However, when an atomically thin two-dimensional crystal grows on a substrate of nonzero Gaussian curvature, it can develop finite-length grain boundaries that terminate abruptly within a monocrystalline domain. We show that by properly designing the substrate topography, these grain boundaries can be placed at desired locations and at specified misfit angles, as the thermodynamic ground state of a two-dimensional (2D) system bound to a substrate. Compared against the hypothetical competition of growing defectless 2D materials on a Gaussian-curved substrate with consequential fold development or detachment from the substrate, the nucleation and formation of finite-length grain boundaries can be made energetically favorably given sufficient substrate adhesion on the order of tens of meV/Ų for typical 2D materials. New properties specific to certain grain boundary geometries, including magnetism and metallicity, can thus be engineered into 2D crystals through topographic design of their substrates.