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/Å2 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.