Directional-dependent thickness and bending rigidity of phosphorene

Verma, Deepti; Hourahine, B.; Frauenheim, Thomas; James, Richard D.; Dumitrică, Traian

doi:10.1103/physrevb.94.121404

Cited by 19 publications

(11 citation statements)

References 41 publications

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“…For a single layer black phosphorus, the resistance to bending is highly anisotropic with the values for B of ~4.8 and ~7.9 eV for the direction perpendicular and parallel to the pucker, respectively [126], using the valence force field model to describe the atomic interactions. Similar results obtained by atomistic simulations and also deviations from the classical plate model were observed which is reflected into a directional dependent thickness [127]. For a monolayer of hBN, molecular dynamic simulations predict the bending stiffness to be 0.86 eV [128] and 1.54 eV [129], while values obtained by density functional theory are 0.95 eV [130] and 1.29 eV [131].…”

Section: Bending Rigiditysupporting

confidence: 80%

Tailoring the mechanical properties of 2D materials and heterostructures

et al. 2018

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The mechanical behavior of high quality two-dimensional (2D) crystals offers exciting opportunities for new material design, such as the combination of extremely high in-plane stiffness and bending flexibility, compared to existing three-dimensional (3D) material forms. By combining different 2D crystals vertically or by in-plane stitching, unusual properties can arise due to nonlinear mechanical interactions between them. Van der Waals forces between vertically stacked crystals give rise to a wide range of useful phenomena such as layer-number dependent friction, superlubricity, creasing, and spatial modulation of elastic properties through Moiré structures. In the present article, we review and explain the mechanical behavior of 2D materials and heterostructures (graphene, hexagonal boron nitride, transition metal dichalcogenides). Linear elastic properties of these 2D crystalline monolayers are well-studied using membrane nanoindentation towards their application in nano-electro-mechanical systems (NEMS) devices. On the other hand, a more thorough understanding of friction, fracture and stress transfer mechanisms between 2D layers and with the substrate or matrix is still lacking. More in-depth understanding of geometry-dependent behavior could enable the application of these materials in multi-functional composites. We discuss emerging opportunities achievable by assembling 2D heterostructures to tailor their mechanical behavior, and perhaps even break the traditional bounds limiting the properties of the bulk homostructures. Furthermore, to accelerate the design and discovery of the infinite combinations of new 2D heterostructures, we construct a crowd-sourced searchable online database to record and exploit the studies reporting on the complex arrangements of these crystals.

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Section: Bending Rigiditysupporting

confidence: 80%

Tailoring the mechanical properties of 2D materials and heterostructures

et al. 2018

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“…Comparisons for other directions cannot be made due to the unavailability of experimental/DFT studies in literature, as also noted in the introduction. In the case of phosphorene, there has been a recent study on its directiondependent bending modulus using the tight binding approximation [36]. While there is reasonable agreement in the qualitative features between [36] and the current work, there are significant quantitative differences, with values deviating by as much as 2 eV.…”

Section: Resultssupporting

confidence: 65%

“…These efforts have generally focused on tensile deformations, since bending requires sophisticated experiments with high accuracy in measurements [8];and ab initio DFT simulations are computationally intensive, scaling cubically with system size, which makes them nonviable at practically relevant bending curvatures [35]. Indeed, such studies can be performed using computationally cheaper alternatives such as tight binding [36][37][38] and classical force fields [39][40][41][42][43][44][45][46][47]. However, these methods typically lack the resolution required to study nanoscale systems such as monolayers, as is evident by the significant scatter in the reported bending moduli values for even elemental monolayers, e.g., 0.8 to 2.7 eV for graphene [39,46], and 0.4 to 38 eV for silicene [43,47].…”

Section: Introductionmentioning

confidence: 99%

On the bending of rectangular atomic monolayers along different directions: an ab initio study

Kumar¹,

Suryanarayana²

2022

Nanotechnology

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We study the bending of rectangular atomic monolayers along diﬀerent directions from ﬁrst principles. Speciﬁcally, choosing the phosphorene, GeS, TiS3, and As2S3 monolayers as representative examples, we perform Kohn-Sham density functional theory calculations to determine the variation in transverse ﬂexoelectric coeﬃcient and bending modulus with the direction of bending. We ﬁnd that while the ﬂexoelectric coeﬃcient is nearly isotropic, there is signiﬁcant and complex anisotropy in bending modulus that also diﬀers between the monolayers, with extremal values not necessarily occurring along the principal directions. In particular, the commonly adopted orthotropic continuum plate model with uniform thickness fails to describe the observed variations in bending modulus for GeS, TiS3, and As2S3. We determine the direction-dependent eﬀective thickness for use in such continuum models. We also show that the anisotropy in bending modulus is not associated with the rehybridization of atomic orbitals.

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“…In fact, abundant theoretical attempts have been done to explore these properties depending on the interlayer spacing or layer thickness besides the efforts experimentally, such as the bandgap engineering by vdW epitaxy, , the superlubricity triggered by pressure, , the adhesion and frictional force depends on the interface charge density . Even few literature reports , have pointed out that the existing definition of layer thickness is unsuitably extended to the nanosheets with single or several atomic layers. However, these efforts take only either the intralayer or the interlayer into account to analyze the major issue that they focused on due to the absence of a well-defined boundary between layer (intralayer/in-plane) and interlayer at the nanoscale.…”

Section: Introductionmentioning

confidence: 99%

First-Principles Delimitation of the Boundary between Intralayer and Interlayer in Two-Dimensional Structures

Cheng

Zhang

et al. 2019

J. Phys. Chem. C

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Acquiring how the performance depends on structure is the most pivotal step of material design, preparation, and application. In particular, it is extremely significant to figure out the correlation between structure and property for two-dimensional materials possessing abundant magical features due to their unique layered stacking. Here, we first reported a conceptually theoretical method to define the boundary between intralayer and interlayer of layered structures based on total electron density distribution. According to the concept, two-dimensional structures binding by the van der Waals force could be divided into layer thickness and interlayer interaction zones. Using 2D semiconductor hexagonal boron nitride (h-BN) and molybdenum disulfide (MoS 2 ) bilayers as model systems, we successfully applied the demarcation method into revealing the intrinsic relationship between bandgap fluctuation and potential energy surface (PES) landscape induced by the stacking configuration. The presented theoretical method enables the study of not only the correlation, depending on electronic redistribution, between PES and bandgap in h-BN and MoS 2 but also other analogous physical issues, such as microcontact, the sliding between surface/ interface, and the properties (heat conduction), which depend on the thickness of the 2D atomic layer.

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Directional-dependent thickness and bending rigidity of phosphorene

Cited by 19 publications

References 41 publications

Tailoring the mechanical properties of 2D materials and heterostructures

Tailoring the mechanical properties of 2D materials and heterostructures

On the bending of rectangular atomic monolayers along different directions: an ab initio study

First-Principles Delimitation of the Boundary between Intralayer and Interlayer in Two-Dimensional Structures

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