Critical inter-defect distance that modulates strength and toughness in defective 2D sp2-lattice
Critical inter-defect distance that modulates strength and toughness in defective 2D sp2-lattice
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This study uncovers a critical separation distance (dc) that renders the elastic interactions between monovacancies in graphene or hexagonal boron nitride inconsequential for the strength and toughness of the defective lattice. The existence of a critical orientation angle of the defect pair (θc) further reveals distinctive mechanical behaviors, indicating that the crystallographic anisotropy has a weaker influence on toughness and strength compared to the anisotropy induced by the orientation angle itself. These findings highlight the localized nature of elastic fields around vacancy defects, offering crucial insights for understanding and manipulating the mechanical properties of 2D materials.
This study uncovers a critical separation distance (dc) that renders the elastic interactions between monovacancies in graphene or hexagonal boron nitride inconsequential for the strength and toughness of the defective lattice. The existence of a critical orientation angle of the defect pair (θc) further reveals distinctive mechanical behaviors, indicating that the crystallographic anisotropy has a weaker influence on toughness and strength compared to the anisotropy induced by the orientation angle itself. These findings highlight the localized nature of elastic fields around vacancy defects, offering crucial insights for understanding and manipulating the mechanical properties of 2D materials.
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(Left) Consider an atomistic configuration of a defective hexagonal boron nitride (hBN) lattice, which incorporates a pair of MV defects positioned along the Oa' line, separated by a distance denoted as 'd' and oriented at an angle θ=AOa' relative to the loading direction. The loading direction is visually represented by the red vertical line. Furthermore, the angle AOB denotes the chiral angle, defined as the angle between the armchair direction and the loading direction. The fracture planes, indicating the weakest planes, are delineated by the line mm', passing through the gulf-edges of the defects. The removed atoms are visually identified by the presence of filled red circles.
(Right) Plotting the virial stress field for four subsequent values of the separation distance 'd', it is observed that, beyond a critical separation distance, both toughness and strength become independent of the separation distance.
Mapping the virial stress field as a continuous scale surface for a constant chiral angle and three distinct values of θ, it is observed that in the left case, increasing the defect separation distance results in a decrease in both strength and toughness. In the middle case, an increase in the defect separation distance exhibits no discernible effect on its strength and toughness. Conversely, in the right case, augmenting the defect separation distance leads to an increase in both strength and toughness.
(a) The presence of a critical inter-defect distance, denoted as dc, is identified as a threshold beyond which a lattice featuring a substantial number of defects exhibits behavior analogous to that of a lattice with a singular vacancy. For both graphene (Gr) and hexagonal boron nitride (hBN), this critical distance is determined to be approximately 30 Å. This finding underscores the notably localized nature of the elastic field emanating from point defects and implies the potential for leveraging defect distribution as a potent tool for engineering the functional performance of graphene or hexagonal boron nitride, while concurrently upholding mechanical reliability.
(b) In instances where the separation distance between a pair of vacancy (MV) defects is less than the critical inter-defect distance (dc), the mechanical response of the defective lattice depends on the orientation of the defect pair relative to the loading direction. In such scenarios, a critical orientation angle, denoted as θc = 30 degrees, is identified. For orientation angles θ less than θc, the elastic interactions between the MVs result in an increased strength and toughness of the defective lattice compared to a lattice featuring non-interacting or isolated MVs. As the inter-defect separation distance diminishes, the lattice exhibits higher strength and toughness in contrast to a lattice containing non-interacting MVs. Conversely, for orientation angles θ greater than θc, a reduction in both strength and toughness is observed with decreasing inter-defect distance, demonstrating an exponential decline in mechanical properties.
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