Structural and mechanical properties of monolayer amorphous carbon and boron nitride

Amorphous materials exhibit various characteristics that are not featured by crystals and can sometimes be tuned by their degree of disorder (DOD). Here, we report results on the mechanical properties of monolayer amorphous carbon (MAC) and monolayer amorphous boron nitride (maBN) with different DOD. The pertinent structures are obtained by kinetic Monte Carlo (kMC) simulations using machine-learning potentials with density-functional theory-level accuracy. An intuitive order parameter, namely, the areal fraction ${F}_{\mathrm{x}}$ occupied by crystallites within the continuous random network, is proposed to describe the DOD. We find that ${F}_{\mathrm{x}}$ captures the essence of the DOD: Samples with the same ${F}_{\mathrm{x}}$ but different sizes and arrangements of crystallites, obtained using two distinct kMC procedures, have virtually identical radial distribution functions as well as bond-length and bond-angle distributions. Furthermore, by simulating the fracture process with molecular dynamics, we found that the mechanical responses of MAC and maBN before fracture are mainly determined by ${F}_{\mathrm{x}}$ and are insensitive to the sizes and specific arrangements and to some extent the numbers and area distributions of the crystallites. The behavior of cracks in the two materials is analyzed and found to mainly propagate in meandering paths in the continuous random network region and to be influenced by crystallites in distinct ways that toughen the material. The present results reveal the relation between structure and mechanical properties in amorphous monolayers and may provide a universal toughening strategy for two-dimensional materials.