Line-defect orientation- and length-dependent strength and toughness in hBN
Line-defect orientation- and length-dependent strength and toughness in hBN
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In the domain of defective 2D hexagonal boron nitride, classical molecular dynamics simulations unveil a pivotal "transition angle" (θt=2.47 degrees), where both toughness and strength become impervious to the finite length of the line defect in an infinite domain. Below this threshold (θ < θt), an increase in defect length enhances both toughness and strength, while above it (θ > θt), the opposite trend emerges. The stress-field analysis underscores that θ-dependent variations in stress localization and symmetry-breaking with respect to the defect axis dictate these divergent behaviors. Additionally, a critical defect length (λc = 60 Å) below which strong θ-dependent variations in elastic interactions significantly impact strength and toughness is identified. Conversely, for λ > λc, elastic interactions saturate, rendering both strength and toughness insensitive to changes in the defect length.
In the domain of defective 2D hexagonal boron nitride, classical molecular dynamics simulations unveil a pivotal "transition angle" (θt=2.47 degrees), where both toughness and strength become impervious to the finite length of the line defect in an infinite domain. Below this threshold (θ < θt), an increase in defect length enhances both toughness and strength, while above it (θ > θt), the opposite trend emerges. The stress-field analysis underscores that θ-dependent variations in stress localization and symmetry-breaking with respect to the defect axis dictate these divergent behaviors. Additionally, a critical defect length (λc = 60 Å) below which strong θ-dependent variations in elastic interactions significantly impact strength and toughness is identified. Conversely, for λ > λc, elastic interactions saturate, rendering both strength and toughness insensitive to changes in the defect length.
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A defective hexagonal boron nitride (hBN) lattice with dimensions Lx and Ly, a line defect denoted as OM is present, oriented at an angle θ relative to the y-direction or the loading direction. The dashed line mm' signifies the weakest plane crossing the bonds with the maximum direction cosine. The bonds denoted as p, q, r, and s represent the critical bonds nearest to the edges of the line defect. Specifically, the edge proximate to the M point is referred to as the "cove" edge, while the edge near the O point is termed the "gulf" edge. The length of the line defect is defined by the distance OM = λ, where the line defect assumes the character of a monovacancy (MV) when λ = 0.
The color-coded contours depict a continuum-scale mapping of the stress field, σyy (x, y), measured in GPa units. These contours illustrate the stress fields surrounding the line defect under conditions of 5% strain for the AC lattice and 10% strain for the ZZ lattice. In the initial and subsequent rows, corresponding to the 0-degree orientation for the AC and ZZ lattice, respectively, it is observed that the maximum stress diminishes with an increase in defect length. Conversely, in the third and fourth rows, representing the 90-degree orientation for the AC and ZZ lattice, respectively, the observed behavior is reversed.
(a) Depictions of atomistic configurations capture segments of the lattice housing a line defect of finite length λ with the minimum achievable width, demonstrating diverse chiralities of the lattice. Dashed lines demarcate the weakest plane, anticipating rupture. (b) Bond deformation maps, coded by color in Angstrom units, illustrate localized and anisotropic deformation patterns at a 4% macroscopic strain state. Bonds denoted by the letter "T" represent those with the greatest length, correlating higher bond strain with earlier bond ruptures. (c) Bonds are color-coded to represent the stress field σyy in GPa units, revealing a direct coupling between maximum stress and maximum bond deformation in the lattice. Furthermore, an increase in the angle corresponds to a higher maximum stress at the edge of the line defect.
Schematics are employed to compare the strength and toughness of four defect configurations, representing: (a) a line defect with a length λ1 exceeding λc and an orientation θ smaller than θt, (b) a monovacancy with a diameter d much smaller than λc, (c) a line defect with a length λ1 greater than λc and an orientation θ equal to θt, and (d) a line defect with a length λ1 exceeding d and an orientation θ greater than θt. Configuration (a) exhibits superior toughness and strength compared to configuration (b), while configuration (b) is equivalent to configuration (c) in terms of toughness and strength. Configuration (c) surpasses configuration (d) in both toughness and strength. For uniaxial loading along the y direction, configurations (b) and (c) demonstrate equivalent toughness and strength, irrespective of the line-defect length, while configuration (a) is 5.28 times stronger and 31 times tougher than configuration (d).
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