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.

中文翻译：

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单层无定形碳和氮化硼的结构和机械性能

非晶材料表现出晶体所没有的各种特性，有时可以通过其无序度 (DOD) 进行调整。在这里，我们报告了具有不同 DOD 的单层非晶碳 (MAC) 和单层非晶氮化硼 (maBN) 的机械性能结果。相关结构是通过使用具有密度泛函理论级精度的机器学习势的动力学蒙特卡罗 (kMC) 模拟获得的。直观的阶参数，即面积分数$F_{\mathrm{X}}$被连续随机网络内的微晶占据，被提议用来描述 DOD。我们发现$F_{\mathrm{X}}$抓住了国防部的本质：具有相同的样本$F_{\mathrm{X}}$但是使用两种不同的 kMC 程序获得的不同尺寸和排列的微晶具有几乎相同的径向分布函数以及键长和键角分布。此外，通过分子动力学模拟断裂过程，我们发现MAC和maBN断裂前的力学响应主要由下式决定：$F_{\mathrm{X}}$并且对微晶的尺寸和具体排列以及在某种程度上的数量和面积分布不敏感。对两种材料中的裂纹行为进行了分析，发现裂纹主要在连续随机网络区域中的蜿蜒路径中传播，并以不同的方式受到微晶的影响，使材料增韧。目前的结果揭示了非晶单层结构和机械性能之间的关系，并可能为二维材料提供通用的增韧策略。