  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 (MLP) with density-functional-theory (DFT)-level
accuracy. An intuitive order parameter, namely the areal fraction Fx occupied
by crystallites within the continuous random network, is proposed to describe
the DOD. We find that Fx captures the essence of the DOD: Samples with the same
Fx but different sizes and distributions of crystallites have virtually
identical radial distributions 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 solely determined by Fx and are insensitive to the sizes and
specific arrangements of the crystallites. The behavior of cracks in the two
materials is analyzed and found to mainly propagate in meandering paths in the
CRN 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 2D materials.
