The amorphous-structure conundrum in two-dimensional materials: Monolayer amorphous carbon versus boron nitride*

The structure of amorphous materials – continuous random networks (CRN) vs. CRN with crystallites – has been debated for decades. In two-dimension (2D), this question can be addressed more directly. Recently, atomic-resolution imaging revealed that monolayer amorphous carbon (MAC) is a CRN containing random graphene nanocrystallites. For another prototypical 2D material – h-BN, the existence and structure of its amorphous counterpart is unknown. Here we report kinetic Monte Carlo simulations of the formation and structure evolution of monolayer amorphous boron nitride (ma-BN) and demonstrate that it has a purely CRN structure. The key difference between MAC and ma-BN is that, at low temperatures, C atoms easily form canonical hexagons, whereas the probability to form canonical B-N-B-N-B-N hexagons is very low. It is the binary nature of BN that generates insurmountable steric constraints for the formation of h-BN crystallites. However, ma-BN contains pseudocrystalline nano regions comprising noncanonical hexagons, analogs of MAC's graphene nanocrystallites. Therefore, two distinct amorphous structures are possible in 2D. The ma-BN is stable and insulating, and the thermal conductivity is two orders of magnitudes smaller than h-BN due to vibrational-mode localization.