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Generalized high-fidelity closed-form formulae are developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach. Hexagonal nano-structural forms (top view) are common for nanomaterials with monoplanar (such as graphene, hBN) and multiplanar (such as stanene, MoS2) configurations. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. Shear modulus assumes an important role in characterizing the applicability of different two-dimensional nanomaterials and heterostructures in various nanoelectromechanical systems such as determining the resonance frequency of the vibration modes involving torsion, wrinkling and rippling behavior of two-dimensional materials. We have developed mechanics-based closed-form formulae for the shear modulus of monolayer nanostructures and multi-layer nano-heterostructures. New results of shear modulus are presented for different classes of nanostructures (graphene, hBN, stanene and MoS2) and nano-heterostructures (graphene-hBN, graphene-MoS2, graphene-stanene and stanene-MoS2), which are categorized on the basis of the fundamental structural configurations. The numerical values of shear modulus are compared with the results from scientific literature (as available) and separate molecular dynamics simulations, wherein a good agreement is noticed. The proposed analytical expressions will enable the scientific community to efficiently evaluate shear modulus of wide range of nanostructures and nanoheterostructures.

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Content uploaded by Tanmoy Mukhopadhyay

Author content

All content in this area was uploaded by Tanmoy Mukhopadhyay on Feb 07, 2018

Content may be subject to copyright.

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... Shear modulus assumes a vital role in characterizing the applicability of dierent lattice metamaterials in various multi-functional systems such as deformation under shear and torsional modes, and vibrational behaviour involving torsion, wrinkling and rippling eects. Moreover, due to the absence of thermoelastic loss, torsional modes have been claimed to have advantages over exural modes, resulting in improved mechanical quality factors and device sensitivity [17]. Keeping such importance of non-normal modes of deformation, the focus of this article is concentrated on characterizing and enhancing the mechanical properties under the shear mode. ...

... Estimation of eective elastic properties is a key research area on regular honeycomb lattices [19,21,25,17,27,28]. Other frequently reported research areas include responses of honeycomb lattices under crushing, buckling, low-velocity impact, dynamics, and wave propagation, etc. [22,23,24,26,29,30,31,32,33,34,35]. ...

Shear modulus assumes an important role in characterizing the applicability of different materials in various multi-functional systems and devices such as deformation under shear and torsional modes, and vibrational behaviour involving torsion, wrinkling and rippling effects. Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. In general, the lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt initially straight beams. While shear modulus and multiple other mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. In this article, we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing shear modulus in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective shear modulus of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the complementary deformed shapes of cell walls of honeycomb lattices under anti-clockwise or clockwise modes of shear stress as the initial beam-level elementary configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode of shear stress, leading to increased effective shear modulus. Within the framework of a unit cell based approach, initially curved lattice cell walls are modeled as programmed curved beams under large deformation. The combined effect of bending, stretching and shear deformation is considered in the framework of Reddy’s third order shear deformation theory in a body embedded curvilinear frame. Governing equation of the elementary beam problem is derived using variational energy principle based Ritz method. In addition to application-specific design and enhancement of shear modulus, unlike conventional materials, we demonstrate through numerical results that it is possible to achieve non-invariant shear modulus under anti-clockwise and clockwise modes of shear stress. The developed physically insightful semi-analytical model captures nonlinearity in shear modulus as a function of the degree of anti-curvature and applied shear stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattices would introduce novel exploitable dimensions in mode-dependent effective shear modulus modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.

... These materials have tunable mechanical properties as the global-level physical behavior is not only dependent upon the intrinsic material, but the microstructural geometry of the periodic units also. The macro-scale lattice properties like Young's moduli [13,14], Poisson's ratio [15] and shear moduli [16] are largely dependent upon the geometric congurations of the periodic unit cells [17,18]. In most cases, the unit cells can be imagined as a network of beam-like solid elements. ...

Architected lattice materials, realized through artificial micro-structuring, have drawn tremendous attention lately due to their enhanced mechanical performances in multi-functional applications. However, the research area on the design of artificial microstructures for the modulation of mechanical properties is increasingly becoming saturated due to extensive investigations considering different possibilities of lattice geometry and beam-like network design. Thus there exists a strong rationale for innovative design at a more elementary level. It can enhance and grow the microstructural space laterally for exploiting the potential of geometries and patterns in multiple length scales, and the mutual interactions thereof. We propose a bi-level design where besides having the architected cellular networks at an upper scale, the constituting beam-like members at a lower scale are further topology-engineered for most optimum material utilization. The coupled interaction of beam-level and lattice-level architectures can enhance the specific elastic properties to an extreme extent (up to $\sim$ 25 and 20 times, depending on normal and shear modes respectively), leading to ultra-lightweight multi-functional materials for critical applications under static and dynamic environments.

... Formulas for the shear modulus of hexagonal nanostructures were derived based on a physically motivated model [43]. In the works [44][45][46], concrete examples of materials with unusual properties are considered, and the origin of these properties at the discrete level is described. ...

Stanene, composed of tin atoms, is a member of 2D-Xenes, two-dimensional single element materials. The properties of the stanene can be changed and improved by applying deformation, and it is important to know the range of in-plane deformation that the stanene can withstand. Using the Tersoff interatomic potential for calculation of phonon frequencies, the range of stability of planar stanene under uniform in-plane deformation is analyzed and compared with the known data for graphene. Unlike atomically flat graphene, stanene has a certain thickness (buckling height). It is shown that as the tensile strain increases, the thickness of the buckled stanene decreases, and when a certain tensile strain is reached, the stanene becomes absolutely flat, like graphene. Postcritical behaviour of stanene depends on the type of applied strain: critical tensile strain leads to breaking of interatomic bonds and critical in-plane compressive strain leads to rippling of stanene. It is demonstrated that application of shear strain reduces the range of stability of stanene. The existence of two energetically equivalent states of stanene is shown, and consequently, the possibility of the formation of domains separated by domain walls in the stanene is predicted.

... With signicant potential for a wide range of engineering applications, mechanical metamaterials form a domain of cutting-edge research in the present age [4,5,6,7,8]. One of their many dening features is the denition of mechanical properties of the material at a global scale through geometric attributes of the microstructure, rather than only intrinsic material properties of constituent members [9,10,11,12,13,14]. This enables meeting specic engineering demands and achieving unusual (not attainable in orthodox natural materials) yet useful mechanical properties, proving benecial for various multifunctional systems [15,16,17]. ...

This paper develops kirigami-inspired modular materials with programmable deformation-dependent stiffness and multidirectional auxeticity. Mixed-mode deformation behaviour of the proposed metastructure involving both rigid origami motion and structural deformation has been realized through analytical and computational analyses, supported by elementary-level qualitative physical experiments. It is revealed that the metamaterial can transition from a phase of low stiffness to a contact-induced phase that brings forth an extensive rise in stiffness with programmable features during the deformation process. Transition to the contact phase as a function of far-field global deformation can be designed through the material's microstructure. A deformation-dependent mixed-mode Poisson’s ratio can be achieved with the capability of transition from positive to negative values in both in-plane and out-of-plane directions, wherein it can further be programmed to have a wide-ranging auxeticity as a function of the microstructural geometry. We have demonstrated that uniform and graded configurations of multi-layer tessellated material can be developed to modulate the constitutive law of the metastructure with augmented programmability as per application-specific demands. Since the fundamental mechanics of the proposed kirigami-based metamaterial is scale-independent, it can be directly utilized for application in multi-scale systems, ranging from meter-scale transformable architectures and energy storage systems to micrometer-scale electro-mechanical systems.

... In the present study, in addition to the lattice geometry, another design parameter is proposed in terms of pre-existing stress in the constituting beam elements. A unit cell based approach is followed here for deriving the lattice level eective elastic properties [38,39,40,41,42,43,44,45]. ...

Characterization of the effective elastic properties of lattice-type materials is essential for adopting such artificial microstructures in various multi-functional mechanical systems across varying length-scales with the requirement of adequate structural performances. Even though the recent advancements in manufacturing have enabled large-scale production of the complex lattice microstructures, it simultaneously brings along different aspects of manufacturing irregularity into the system. One of the most prevailing such effects is the presence of intrinsic residual stresses, which can significantly influence the effective elastic properties. Here we have proposed closed-form analytical expressions for the effective elastic moduli of lattice materials considering the influence of residual stresses. Besides characterization of the effect of manufacturing irregularities, the presence of such prestress could be viewed from a different perspective. From the materials innovation viewpoint, this essentially expands the design space for property modulation significantly. The proposed analytical framework is directly useful for both property characterization and materials development aspects. The numerical results reveal that the presence of residual stresses, along with the compound effect of other influencing factors, could influence the effective elastic moduli of lattices significantly, leading to the realization of its importance and prospective exploitation of the expanded design space for inclusive materials innovation.

... In a periodic structure, one unit cell (i.e. repeating units) can be analyzed with appropriate periodic boundary conditions to obtain the global behaviour of the entire lattice [67,68,69,70,71,72,73,74,75,76,77,78,79,80,81]. Figure 1(A) shows the schematic diagram of the parent 3DCDL unit cell. It has two planar rings (loops) in two orthogonal planes with four connected beams. ...

If we compress a conventional material in one direction, it will try to expand in the other two perpendicular directions and vice‐versa, indicating a positive Poisson’s ratio. Recently auxetic materials with negative Poisson’s ratios, which can be realized through artificial microstructuring, are attracting increasing attention due to enhanced mechanical performances in multiple applications. Most of the proposed auxetic materials show different degrees of in‐plane auxeticity depending on their microstructural configurations. However, this restricts harnessing the advantages of auxeticity in 3D systems and devices where multi‐directional functionalities are warranted. Thus, there exists a strong rationale to develop microstructures that can exhibit auxeticity both in the in‐plane and out‐of‐plane directions. Here we propose generic 3D connected double loop (3DCDL) type periodic microstructures for multi‐directional modulation of Poisson’s ratios. Based on the bending dominated behaviour of elementary beams with variable curvature, we demonstrate mixed‐mode auxeticity following the framework of multi‐material unit cells. The proposed 3DCDL unit cell and expanded unit cells formed based on their clusters are capable of achieving partially auxetic, purely auxetic, purely non‐auxetic and null‐auxetic behaviour. Comprehensive numerical results are presented for the entire spectrum of combinations concerning the auxetic behaviour in the in‐plane and out‐of‐plane directions including their relative degrees. This article is protected by copyright. All rights reserved.

Severe competition between nanolubricant additives and polar lubricating oil molecules for the formation of lubricant films has been hindering the progress of green and advanced lubricants. In this work, based on the tautomerism of cyanuric acid molecule (trione and triol configurations), two kinds of triazine-based covalent-organic frameworks (COFs), that is, Ton-COFs and Tol-COFs, were synthesized as additives of the polar PEG 400 oil, realizing compromise between them by providing delicate interactions. The triazine matrix bonding with intense polar groups in the framework of additives offers more powerful interactions to competitively form the adsorbed lubricant film on the surface of the metal substrate over PEG 400 oil and also bolts PEG 400 oil molecules by the hydrogen bonding inside the pore of the framework to cooperatively bear against the load. Molecular quantum chemical calculations further confirm that Ton-COFs can produce a more intense interaction with Fe atoms in the form of coordination and ions···π than Tol-COFs, far beyond PEG 400, and the cross-sectional profile of the worn surface definitely exhibits a protective lubricant film only composed of Ton-COFs. Consequently, at the low concentration of 0.3 wt %, the excellent friction reduction (41.2%) and antiwear property (97.4%) are achieved for the Ton-COFs compared to pure PEG 400 oil; moreover, 28.6% and 79.0% for Tol-COFs at the essential concentration of 0.7 wt % are achieved. This finding provides a novel insight from molecules to materials into guiding the development of additives for advanced lubricants.

Two-dimensional chalcogenide-based materials of group 14 elements are predicted as potential thermoelectric (TE) materials, though the figure of merit (ZT) obtained requires improvement to be commercially accessible. Herein, we have computationally modeled synthesized γ-GeSe and reduced-dimension 2D layers (monolayer, bilayer, trilayer, and quad-layer) and subjected them to first-principles calculations to extract essential properties pertaining to TE. The ZT values obtained for the considered systems are found to be remarkably high (quad-layer: 2.8; trilayer: 3.1; bilayer: 3.8), even at a high temperature of 900 K. The dimensionality reduction (3D to 2D) as well as reducing layers (quad-layer to bilayer) improved the ZT considerably in comparison to that of bulk γ-GeSe (0.8 at 900 K). Even though the power factor decreases with decreasing layers, ultralow lattice thermal conductivities (kL) are responsible for the high ZT. Ultralow kL (>1 W m–1 K–1) was observed in 2D γ-GeSe at all temperature ranges, with the lowest kL observed in the bilayer (0.15 W m–1 K–1) and trilayer (0.17 W m–1 K–1) at 900 K. The low kL is also supported by the presence of high anharmonicity, high phonon scattering rates, low elastic constants, low group velocity, and low Debye temperature. We envisage that these findings will motivate investigations on similar low-dimensional materials for improved thermoelectric performance

The present article outlines a probabilistic investigation of the uniaxial tensile behaviour of twisted bilayer graphene (tBLG) structures. In this regard, the twist angle (θ) and temperature (T) are considered as the control parameters and the ultimate tensile strength (UTS) and failure strain of the tBLG structures are considered as the responses. It is observed that with the increase in twist angle (θ) of tBLG; the fracture responses exhibit a declining trend deterministically. The tBLG twisted with the magic angle (θ = 1.08o) results in around 7% decrease in UTS and nearly 24% decrease in failure strain, when compared with normal BLG (θ = 0̊). The Monte Carlo simulation (MCS) based random sampling is performed for the considered control parameters, wherein θ is varied from 0o to 30o, and temperature is varied from 100 K to 900 K. Within such bounds of the input parameters, the training (64 samples) and validation (8 samples) sample spaces are constructed. In the next step, molecular dynamics (MD) simulation of uniaxial tensile deformation of the modelled tBLG structures is carried out for each instance of the sample space. The dataset is subsequently used to form and validate the artificial neural network (ANN). The computationally efficient machine learning (ML) model is further utilized to perform the detailed investigation of fracture behaviour of the tBLG structures in the probabilistic framework. Such analysis captures all the possible instances of variation in the input parameters and leads to deep insights in the material behaviour, which would have otherwise remained unnoticed due to the prohibitive nature of conducting a large number of MD simulations. The novelty of the present study lies in the probabilistic interpretation of the tensile behaviour of tBLG structures subjected to variation in twist angle (θ) and temperature (T). The preparation of nano-scale samples with the exact design specifications such as twist angle is often extremely difficult, which leads to inevitable stochastic system disorders. The current article essentially proposes a probabilistic avenue of quantifying the effect of such disorders on the failure properties of tBLG.

Molecular dynamics (MD) simulations have emerged to be a vital tool for the analysis of nanoscale materials like graphene. However, reliability of the results derived from MD simulations depends on the adopted inter-atomic potential (IP), which is mathematically fitted to the data obtained from first principle approaches or experiments. There exists a significant scope of uncertainty associated with the IP parameters. Such internal uncertainties, together with the effect of stochastic external parameters like temperature and strain rate can trigger an augmented random deviation in the output mechanical responses. With the aim of developing an inclusive analysis and design paradigm, we have systematically quantified the effect of uncertainties associated with the internal parameters (Tersoff IP parameters) and external parameters (temperature and strain rate) individually, and their compound effect on the mechanical properties of graphene. In establishing the complete probabilistic descriptions of the response quantities corresponding to different levels of source uncertainties, we show that a coupled machine learning-based Monte Carlo simulation approach could lead to significant computational efficiency without compromising the accuracy of results. The study reveals that internal parameters are more sensitive compared to the external parameters in general. Among the inter-atomic parameters λ1 and λ2 are found to be the most sensitive, while the temperature is found to be more sensitive than the strain rate among the external parameters. Cohesive energy is noted to be dependent only on the inter-atomic potential parameters, while fracture strength depends on both the internal and external input parameters. The numerically quantifiable outcomes of this study would improve and bring new perspectives in the inclusive analysis and design of various graphene-based devices and systems, including the effect of inherent uncertainties and their relative sensitivity.

Two-dimensional and quasi-two-dimensional materials are important nanostructures because of their exciting electronic, optical, thermal, chemical and mechanical properties. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. For example, transition metal dichalcogenides such as MoS2 show promising electronic and piezoelectric properties, but their low mechanical strength is a constraint for practical applications. This barrier can be mitigated by considering graphene-MoS2 heterostructure, as graphene possesses strong mechanical properties. We have developed efficient closed-form expressions for the equivalent elastic properties of such multi-layer hexagonal nano-hetrostructures. Based on these physics-based analytical formulae, mechanical properties are investigated for different heterostructures such as graphene-MoS2, graphene-hBN, graphene-stanene and stanene-MoS2. The proposed formulae will enable efficient characterization of mechanical properties in developing a wide range of application-specific nano-heterostructures.

The stochastic dynamic stability analysis of laminated composite curved panels under non-uniform partial edge loading is studied using finite element analysis. The system input parameters are randomized to ascertain the stochastic first buckling load and zone of resonance. Considering the effects of transverse shear deformation and rotary inertia, first order shear deformation theory is used to model the composite doubly curved shells. The stochasticity is introduced in Love’s and Donnell’s theory considering dynamic and shear deformable theory according to the Sander’s first approximation by tracers for doubly curved laminated shells. The moving least square method is employed as a surrogate of the actual finite element model to reduce the computational cost. The results are compared with those available in the literature. Statistical results are presented to show the effects of radius of curvatures, material properties, fibre parameters, and non-uniform load parameters on the stability boundaries.

An analytical framework is developed for investigating the effect of viscoelasticity on irregular hexagonal lattices. At room temperature many polymers are found to be near their glass temperature. Elastic moduli of honeycombs made of such materials are not constant, but changes in the time or frequency domain. Thus consideration of viscoelastic properties are essential for such honeycombs. Irregularity in lattice structures being inevitable from practical point of view, analysis of the compound effect considering both irregularity and viscoelasticty is crucial for such structural forms. On the basis of a mechanics based bottom-up approach, computationally efficient closed-form formulae are derived in frequency domain. The spatially correlated structural and material attributes are obtained based on Karhunen-Loève expansion, which is integrated with the developed analytical approach to quantify the viscoelastic effect for irregular lattices. Consideration of such spatially correlated behaviour can simulate the practical stochastic system more closely. The two effective complex Young’s moduli and shear modulus are found to be dependent on the viscoelastic parameters, while the two in-plane effective Poisson’s ratios are found to be independent of viscoelastic parameters and frequency. Results are presented in both deterministic and stochastic regime, wherein it is observed that the amplitude of Young’s moduli and shear modulus are significantly amplified in the frequency domain. The response bounds are quantified considering two different forms of irregularity, randomly inhomogeneous irregularity and randomly homogeneous irregularity. The computationally efficient analytical approach presented in this study can be quite attractive for practical purposes to analyse and design lattices with predominantly viscoelastic behaviour along with consideration of structural and material irregularity.

An analytical framework is developed for predicting the effective in-plane elastic moduli (longitudinal and transverse Young's modulus, Poisson's ratios and shear modulus) of irregular hexagonal lattices with generalized form of spatially random structural geometry. On the basis of a mechanics based bottom-up multi-step approach, computationally efficient closed-form formulae are derived in this article. As a special case when there is no irregularity, the derived analytical expressions reduce to the respective well known formulae of regular honeycombs available in literature. Previous analytical investigations include the derivation of effective in-plane elastic moduli for hexagonal lattices with spatially random variation of cell angles, which is a special case of the generalized form of irregularity in material and structural attributes considered in this paper. The present study also includes development of a highly generalized finite element code for obtaining equivalent elastic properties of random lattices, which is employed to validate the proposed analytical formulae. The statistical results of elastic moduli obtained using the developed analytical expressions and using direct finite element simulations are noticed to be in good agreement affirming the accuracy and validity of the proposed analytical framework. All the in-plane elastic moduli are found to be significantly influenced by spatially random irregularity resulting in a decrease of the mean values for the two Young's moduli and two Poisson's ratios, while an increase of the mean value for the shear modulus.

With the aim of manipulating the mechanical properties of the recently discussed two-dimensional material MXene, we investigate the effect of alloying. We consider substitutional doping of B and V at Ti and C sites of Ti2C. Calculations of quantities such as in-plane stiffness, Young's modulus, and critical strain through rigorous first-principles technique establish that B doping is highly effective in improving the elastic properties. Oxygen passivation of B-doped Ti2C in addition to improved elastic properties also exhibits reasonably high critical strains making them ideally suited for applications in flexible devices. Our study further reveals the presence of strong spin-phonon coupling in unpassivated Ti2C compounds which influences the mechanical behavior. The damage of Ti2C in its magnetic ground state of A-type antiferromagnetic structure is found to occur at much higher strain than that of the nonmagnetic Ti2C.

In this paper, the interlayer sliding between graphene and boron nitride (h-BN) is studied by molecular dynamics simulations. The interlayer shear force between h-BN/h-BN is found to be six times higher than that of graphene/graphene, while the interlayer shear between graphene/h-BN is approximate to that of graphene/graphene. The graphene/h-BN heterostructure shows several anomalous interlayer shear characteristics compared to its bilayer counterparts. For graphene/graphene and h-BN/h-BN, interlayer shears only exit along the sliding direction while interlayer shear for graphene/h-BN is observed along both the translocation and perpendicular directions. Our results provide significant insight into the interlayer shear characteristics of 2D nanomaterials.

Recent studies showed that the in-plane and inter-plane thermal conductivities of two-dimensional (2D) MoS2 are low, posing a significant challenge in heat management in MoS2-based electronic devices. To address this challenge, we design the interfaces between MoS2 and graphene by fully utilizing graphene, a 2D material with an ultra-high thermal conduction. We first perform ab initio atomistic simulations to understand the bonding nature and structure stability of the interfaces. Our results show that the designed interfaces, which are found to be connected together by strong covalent bonds between Mo and C atoms, are energetically stable. We then perform molecular dynamics simulations to investigate the interfacial thermal conductance. It is found surprisingly that the interface thermal conductance is high, comparable to that of graphene-metal covalent-bonded interfaces. Importantly, each interfacial Mo-C bond serves as an independent thermal channel, enabling the modulation of interfacial thermal conductance by controlling Mo vacancy concentration at the interface. The present work provides a viable route for heat management in MoS2 based electronic devices.

The effect of a MoS2 substrate on the structural and electronic properties of stanene were systematically investigated by first-principles calculations. The Brillouin zone of isolated stanene has a Dirac cone at the K point. MoS2 helps to open an energy gap at the K point, whereas contributes no additional transport channels near the Fermi level. Our results suggest that the carrier mobility remains large, which makes the stanene/MoS2 heterostructure a competitive material for electronic applications. Subsequently, strain engineering study by changing the interlayer spacing between stanene and MoS2 layer and changing lattice constants indicates that the energy gap at K point can be effectively tuned to meet the demands of experiments and device design in nanoelectronics. Moreover, a large enough strain leads to a metal–semiconductor phase transition to make the intrinsic semiconductor turn into self-doping phase. Our study indicates that MoS2 is a good substrate to promote the development of Sn-based nanoelectronics.

Graphene and other two-dimensional materials have been proved to be able to supply low friction. Here we assembled van der Waals heterostructures with graphene and molybdenum disulphide monolayers. The Raman spectrum together with a modified linear chain model indicate a two-orders-of-magnitude decrease in interlayer lateral force constant, as compared with their homogeneous bilayers, indicating a possible routine to achieve superlubricity. The decrease of interlayer lateral force constant is consistent with the ultrasmooth potential energy corrugation during sliding, which is derived from density functional theory calculations. The potential energy corrugation is found to be determined by the sliding-induced interfacial charge density fluctuation, suggesting a new perspective to understand the physical origin of atomic scale friction of two-dimensional materials.

Recently, flexible electrodes with biaxial/omnidirectional stretchability have attracted significant attention. However, most existing pliable electrode materials can be only stretched in one direction. In this work, an unexpected isotropic van der Waals (vdW) heterostructure is proposed, based on the assembly of two-dimensional crystals of anisotropic black phosphorene (BP) and transition metal carbide (TiC2). Using vdW-corrected density functional theory calculations, the BP/TiC2 vdW heterostructure was predicted to have excellent structural and mechanical stability, superior electrical conductivity, omnidirectional flexibility, and a high Li storage capacity. We have unraveled the physical origin of the excellent stability, as well as the Li adsorption preferences of the lithiated heterostructure, based on a three-step analysis of the stability of the Li-adsorption processes. In addition, the BP/TiC2 vdW heterostructure can also be applied as the anode material for flexible Na-ion batteries because of its high Na storage capacity and strong Na binding. However, compared with Na adsorption, the capacity is higher, and the adsorption energy is more negative for Li adsorption. Our findings provide valuable insights into the exploration of a rich variety of vdW heterostructures for next-generation flexible energy storage devices.
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