Based on first-principles calculations, we resent a method to reveal the elastic properties of recently synthesized monolayer hydrocarbon, graphane. The in-plane stiffness and Poisson's ratio values are found to be smaller than those of graphene, and its yielding strain decreases in the presence of various vacancy defects and also at high ambient temperature. We also found that the band gap can be strongly modified by applied strain in the elastic range.
In this Letter, we investigate the strain-induced band-gap modulation of both armchair and zigzag graphane nanoribbons based on the first-principles calculations. Within the elastic range, the band gap changes linearly with the uniaxial strain, where the band-gap of graphane nanoribbonsis more sensitive to compressive than tensile deformation. The band-gap deformation mainly originates from the shift of valence band edge of graphane nanoribbons under stain. Our results imply the great potential of graphane nanoribbons in the pressure sensor and optical electronics applications.
Strain effects on the stability, electronic structure, and hydrogen storage capacity of lithium-doped graphane (CHLi) have been investigated by stateof-the art first principle density functional theory (DFT). Molecular dynamics MD) simulations have confirmed the stability of Li on graphane sheet when it is subject to 10% of tensile strain. Under biaxial asymmetric strain, the binding energy of Li of graphane (CH) sheet increases by 52% with respect to its bulk's cohesive energy. With 25% doping concentration of Li on CH sheet,the gravimetric density of hydrogen storage is found to reach up to …
We have studied the mechanical properties and phonon dispersions of fully hydrogenated borophene (borophane) under strains by first principles calculations. Uniaxial tensile strains along the a- and b-direction, respectively, and biaxial tensile strain have been considered. Our results show that the mechanical properties and phonon stability of borophane are both highly anisotropic. The ultimate tensile strain along the a-direction is only 0.12, but it can be as large as 0.30 along the b-direction. Compared to borophene and other 2D materials (graphene, graphane, silicene, silicane, h-BN, phos…
In this paper we present a new general framework for anisotropic elastoplasticity at large strains. The new framework presents the following characteristics: (1) It is valid for non-moderate large strains, (2) it is valid for both elastic and plastic anisotropy, (3) its description in rate form is parallel to that of the infinitesimal formulation, (4) it is compatible with the multiplicative decomposition, (5) results in a similar framework in any stress-strain work-conjugate pair, (6) it is consistent with the principle of maximum plastic dissipation and (7) does not impose any restriction on…
The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This…
Coupling between axial and torsional degrees of freedom often modifies the conformation and expression of natural and synthetic filamentous aggregates. Recent studies on chiral single-walled carbon nanotubes and B-DNA reveal a reversal in the sign of the twist-stretch coupling at large strains. The similarity in the response in these two distinct supramolecular assemblies and at high strains suggests a fundamental, chirality dependent non-linear elastic behaviour. Here, we seek the link between the microscopic origin of the non-linearities and the effective twist-stretch coupling using energy …
Materials under complex loading develop large strains and often transition via an elastic instability, as observed in both simple and complex systems. Here, we present Si I under large strain in terms of Lagrangian strain by an $5^{th}$-order elastic potential found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress-Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including elastic instability driving Si I$\rightarrow$II phase transformation (PT) and the shear instabilities. PT conditions for Si I$…
In this study, thin elastic films supported on a rigid substrate are brought into contact with a spherical glass indenter. Upon contact, adhesive fingers emerge at the periphery of the contact patch with a characteristic wavelength. Elastic films are also pre-strained along one axis before initiation of contact, causing the fingering pattern to become anisotropic and align with the axis along which the strain was applied. This transition from isotropic to anisotropic patterning is characterized quantitatively and a simple model is developed to understand the origin of the anisotropy.
A precisely selected elastic strain can be introduced in submicron-thick single-crystal SrTiO3 sheets using a silicon nitride stressor layer. A conformal stressor layer deposited using plasma-enhanced chemical vapor deposition produces an elastic strain in the sheet consistent with the magnitude of the nitride residual stress. Synchrotron x-ray nanodiffraction reveals that the strain introduced in the SrTiO3 sheets is on the order of 10 4, matching the predictions of an elastic model. This approach to elastic strain sharing in complex oxides allows the strain to be selected within a wide and c…
We present a study of the local strain effects associated with vacancy defects in strontium titanate and report the first calculations of elastic dipole tensors and chemical strains for point defects in perovskites. The combination of local and long-range results will enable determination of x-ray scattering signatures that can be compared with experiments. We find that the oxygen vacancy possesses a special property -- a highly anisotropic elastic dipole tensor which almost vanishes upon averaging over all possible defect orientations. Moreover, through direct comparison with experimental mea…
The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, we obtain exact analytical solutions for the stress and strain fields of dislocatio…
The influence of elastic strain on the lithium vacancy formation and migration in bulk LiCoO2 is evaluated by means of first-principles calculations within density functional theory (DFT). Strain dependent energies are determined directly from defective cells and also within linear elasticity theory from the elastic dipole tensor (Gij) for ground state and saddle point configurations. We analyze finite size-effects in the calculation of Gij, compare the predictions of the linear elastic model with those obtained from direct calculations of defective cells under strain and discuss the differenc…
The influence on macroscopic work hardening of small, spherical, elastic particles dispersed within a matrix is studied using an isotropic strain gradient plasticity framework. An analytical solution, based on a recently developed yield strength model is proposed. The model accounts for random variations in particle size and elastic properties, and is numerically validated against FE solutions in 2D/3D material cell models. Excellent agreement is found as long as the typical particle radius is much smaller than the material length scale, given that the particle volume fraction is not too large…
Elastic interactions play an important role in controlling irradiation damage evolution, but remain largely unexplored experimentally. Using transmission electron microscopy (TEM) and high-resolution on-axis transmission Kikuchi diffraction (HR-TKD), we correlate the evolution of irradiation-induced damage structures and the associated lattice strains in self-ion irradiated pure tungsten. TEM reveals different dislocation loop structures as a function of sample thickness, suggesting that free surfaces limit the formation of extended defect structures found in thicker samples. HR-TKD strain ana…
In this paper, we did a systematic comparative study on the accuracy of two computational methods of elastic constants combined with the density functional theory (DFT), the stress-strain method and the energy-strain method. We took metal Ru as a prototype to compare its high-pressure elastic constants calculated by our present stress-strain method with the previous energy-strain results by others. Although the two methods yielded almost the same accuracy of high-pressure elastic constants for Ru, our stress-strain method directly based on the Hooke's law of elasticity theory is much straightf…
We depict the use of x-ray diffraction as a tool to directly probe the strain status in rolled-up semiconductor tubes. By employing continuum elasticity theory and a simple model we are able to simulate quantitatively the strain relaxation in perfect crystalline III-V semiconductor bi- and multilayers as well as in rolled-up layers with dislocations. The reduction in the local elastic energy is evaluated for each case. Limitations of the technique and theoretical model are discussed in detail.
We derive the Green tensor of Mindlin's anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient elastic constants in the general case of triclinic media. In contrast to its classical counterpart, the Green tensor is non-singular at the origin, and it converges to the classical tensor a few characteristic lengths away from the origin. Therefore, the Green tensor of Mindlin's first strain gradient elasticity can be regarded as a physical regularization of the classical anisotropic Green tensor. …
Criteria of selecting strain and fitting schemes are proposed for the calculation of higher-order elastic constants more efficiently, robustly and accurately. As demonstrated by the third-order elastic constants (TOECs) of diamond, the proposed method is 3-5 times faster than existing methods, and the range of strain for getting correct TOECs is expanded. In addition, our result provides an evidence for the inaccuracy of some previous experiments caused by higher-order effect, and the difference among experiments and several different theoretical methods is resolved. Finally, we give the recom…
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we…
The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of $α$-iron is investigated using \textit{ab initio} density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisot…
Using the notion of eigenstrain produced by the defects formed in a material exposed to high energy neutron irradiation, we develop a method for computing macroscopic elastic stress and strain arising in components of a fusion power plant during operation. In a microstructurally isotropic material, the primary cause of macroscopic elastic stress and strain fields is the spatial variation of neutron exposure. We show that under traction-free boundary conditions, the volume-average elastic stress always vanishes, signifying the formation of a spatially heterogeneous stress state, combining compr…
In this paper we present thorough experimental observation of the process of shock wave transformation into a bulk strain solitary wave in a nonlinearly elastic solid bar made of polystyrene. A theoretical model based on the describing propagation of a plane elastic wave in a bar is developed with account made for material nonlinearity and viscosity. Numerical modeling performed on the base of the developed model with and without regard to viscosity demonstrated formation of a long stable disturbance at proper account made for viscoelastic properties of the bar material.
Strain-based theory on elastic instabilities is being widely employed for studying onset of plasticity, phase transition or melting in crystals. And size effects, observed in nano-materials or solids under dynamic loadings, needs to account for contributions from strain gradient. However, the strain gradient based higher order elastic theories on the elastic instabilities are not well established to enable one to predict high order instabilities of solids directly at atom level. In present work, a general continuum theory for higher order elastic instabilities is established and justified by d…
Understanding the role of elastic strain in modifying catalytic reaction rates is crucial for catalyst design, but experimentally, this effect is often coupled with a ligand effect. To isolate the strain effect, we have investigated the influence of externally applied elastic strain on the catalytic activity of metal films towards the hydrogen evolution reaction (HER). We show that elastic strain tunes the catalytic activity in a controlled and predictable way. Both theory and experiment show strain controls reactivity in a controlled manner consistent with the qualitative predictions of the H…
Indentation experiments on graphene membranes pre-stressed by hydrostatic pressure show an increase in effective elastic modulus from 300 N/m in non pressurized membranes to 700 N/m for pre-strains above 0.5 %. This pronounced dependence of the stiffness of graphene with strain is attributed to its high anharmonicity and the great influence of out of plane corrugations of this atomic thick membrane in its mechanical properties. Our experimental findings imply that graphene measured stiffness is highly influenced by the presence of corrugations and that the in plane elastic modulus correspondin…
The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and …
A Twinning Induced Plasticity (TWIP) steel with a nominal composition of Fe-16.4Mn-0.9C-0.5Si-0.05Nb-0.05V was deformed to an engineering strain of 6\%. The strain around the deformation twins were mapped using the 4D-STEM technique. Strain mapping showed a large average elastic strain of approximately 6\% in the directions parallel and perpendicular to the twinning direction. However, the large average strain comprised of several hot spots of even larger strains of up to 12\%. These hot spots could be attributed to a high density of sessile Frank dislocations on the twin boundary and correspo…
The effect of interstitial hydrogen on the elastic properties of $α$-iron is investigated using \textit{ab initio} density functional theory. We find that while the overall strength properties are reduced by H, the effects are mainly due to the resulting local volume expansion. We use these concentration-dependent elastic moduli to model the effects of homogeneous strain fields on H solubility and make extrapolations to H-solubility in the spatially-varying strain fields of realistic dislocations. We find that H is strongly trapped by dislocations of both the edge and screw variety, leading to…
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical (2nd-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products …
Young's modulus determines the mechanical loads required to elastically stretch a material, and also, the loads required to bend it, given that bending stretches one surface while compressing the opposite one. Flexoelectric materials have the additional property of becoming electrically polarized when bent. While numerous studies have characterized this flexoelectric coupling, its impact on the mechanical response, due to the energy cost of polarization upon bending, is largely unexplored. This intriguing contribution of strain gradient elasticity is expected to become visible at small length …
We report on quantification and elastic strain mapping in two artificial BaZrO3/BaTiO3 (BZ/BT) superlattices having periods of 6.6 nm and 11 nm respectively, grown on (001) SrTiO3 single crystal substrate by pulsed laser deposition technique. The methodology consists of a combination of high-resolution scanning transmission electron microscopy and nanobeam electron diffraction associated with dedicated algorithm for diffraction patterns processing originally developed for semiconductors to record the strains at atomic scale. Both in-plane and out-of-plane elastic strains were then determined a…
Strain gradient elasticity and nonlocal elasticity are two enhanced elastic theories intensively used over the last fifty years to explain static and dynamic phenomena that classical elasticity fails to do. The nonlocal elastic theory has a clear differentiation from the classical case by considering stresses in a point of the continuum as an integral of all stresses defined in the treated elastic body. On the other hand, strain gradient elasticity is characterized as a non-classical theory because considers both potential and kinetic energy densities as not only functions of strains and veloc…
Transformer-based prediction of two-dimensional material electronic properties under elastic strain engineering
School of Materials Science and Engineering, Beijing Institute of Technology（北京理工大学材料学院）；School of Chemistry and Chemical Engineering, Beijing Institute of Technology（北京理工大学化学与化学工程学院）
An extended elastic eigenvector approach for adatom interactions is applied to elastically isotropic substrates. The oscillating interactions between adatom monomers or dimers are caused by strain fields in the substrate. Expansive or contractive strain fields are surrounding adatoms in form of quasi circular rings. The exact shape of the ring structure depends on the elastic constants of the substrate and especially on the surface Brillouin zone. Interactions on isotropic substrates are depicted and compared with an anisotropic example. Overlays of 2-D plots can help to identify adatom struct…
Synchrotron Laue microdiffraction and Digital Image Correlation measurements were coupled to track the elastic strain field (or stress field) and the total strain field near a general grain boundary in a bent bicrystal. A 316L stainless steel bicrystal was deformed in situ into the elasto-plastic regime with a four-point bending setup. The test was then simulated using finite elements with a crystal plasticity model comprising internal variables (dislocation densities on discrete slip systems). The predictions of the model have been compared with both the total strain field and the elastic str…
In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of $N$ slow kinks in the sine-Gordon model were calculated analytically (for $N=1,2$, and 3) and numerically (for $4\le N\le 7$). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the …
We discuss the roles of continuum linear elasticity and atomistic calculations in determining the formation volume and the strain energy of formation of a point defect in a crystal. Our considerations bear special relevance to defect formation under stress. The elasticity treatment is based on the Green's function solution for a center of contraction or expansion in an anisotropic solid. It makes possible the precise definition of a formation volume tensor and leads to an extension of Eshelby's result for the work done by an external stress during the transformation of a continuum inclusion (P…
The Landau theory was applied to treat the phase diagrams for a multiferroic with two second order phase transitions taking into account the coupling of the primary order parameters with strain. Two order parameters are coupled biquadratically which corresponds to the magnetoelectric materials. The coupling with strain is assumed to be linear in strain and quadratic in order parameters. Three ordered phases are discussed. Analytic relationships were obtained for the phase transition temperatures and for elastic modulus changes through the phase transitions. Strong influence of the coupling wit…
A 3D unit cell model containing eight different spherical particles embedded in a homogeneous strain gradient plasticity (SGP) matrix material is presented. The interaction between particles and matrix is controlled by an interface model formulated within the higher order SGP theory used. Strengthening of the particle reinforced material is investigated in terms of the increase in macroscopic yield stress. The results are used to validate a closed form strengthening relation proposed by the authors, which suggests that the increase in macroscopic yield stress is governed by the interface stren…
The influence of elastic strains on the adsorption of H, O, and OH on the (111) surfaces of 8 fcc (Ni, Cu, Pd, Ag, Pt, Au, Rh, Ir) and on the (0001) surfaces of 3 hcp (Co, Zn, Cd) transition metals was analyzed by means of density functional theory calculations. To this end, surface slabs were subjected to different strain states (uniaxial, biaxial, shear, and a combination of them) up to strains dictated by the mechanical stability limits indicated by phonon calculations. It was found that the adsorption energy followed the predictions of the d-band theory but -- surprisingly -- the variation…
We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite strain tensor. It reflects the Eulerian structure of the continuum models and correctly describes the strain dependence of the stiffness. In general, the relevant strain tensor is related to the left Cauchy-Green deformation tensor. In isotropic one- and two-dimensional situations the elastic energy can be expressed equivalently through the right deformation t…
We employ three dimensional x-ray coherent diffraction imaging to map the lattice strain distribution, and to probe the elastic properties of a single crystalline Ni (001) nanowire grown vertically on an amorphous Si02 || Si substrate. The reconstructed density maps show that with increasing wire width, the equilibrium compressive stress in the core region decreases sharply while the surface tensile strain increases, and gradually trends to a nonzero constant. We use the retrieved projection of lattice distortion to predict the Young's Modulus of the wire based on the elasticity theory.
We investigate the elastic properties of selected zincblende III-V semiconductors. Using hybrid functional density functional theory we calculate the second and third order elastic constants, and first and second-order internal strain tensor components for Ga, In and Al containing III-V compounds. For many of these parameters, there are no available experimental measurements, and this work is the first to predict their values. The stricter convergence criteria for the calculation of higher order elastic constants are demonstrated, and arguments are made based on this for extracting these const…
Elastic effects due to lattice strain modify the local equilibrium condition at the solid-solid interface compared to the classical dendritic growth. Both, the thermal and the elastic fields are eliminated by the Green's function techniques and a closed nonlinear integro-differential equation for the evolution of the interface is derived. In the case of pure dilatation, the elastic effects lead only to a trivial shift of the transition temperature while in the case of shear transitions, dendritic patterns are found even for isotropic surface energy.
Flexible strain sensors are critical to several potential intelligent applications, such as human-machine interfaces, soft robotics, human motion detection, and safety monitoring of components. Stretchable functional materials are important components of strain sensors, and they are still major challenges for high performance strain sensors. Herein, we demonstrate a novel strategy of designing and optimizing flexible strain sensor by developing topological structure modulated high permittivity elastic nanocomposite. The topological structure with three-phase percolative nano-nanonetworks produ…
The coalescence in dense arrays of spontaneously formed GaN nanowires proceeds by bundling: adjacent nanowires bend and merge at their top, thus reducing their surface energy at the expense of the elastic energy of bending. We give a theoretical description of the energetics of this bundling process. The bending energy is shown to be substantially reduced by the creation of dislocations at the coalescence joints. A comparison of experimental and calculated x-ray diffraction profiles from ensembles of bundled nanowires demonstrates that a large part of the bending energy is indeed relaxed by pl…
Within the framework of Landau-Ginzburg-Devonshire (LGD) theory we studied the role of the flexocoupling between the order parameter and elastic strain gradients in the stability of a spatially-modulated phase (SMP) in ferroics with commensurate and incommensurate long-range ordered phases under the presence of squired elastic strain gradient. The squired elastic strain gradient is required for the free energy stability to arbitrary strain gradients. Obtained analytical expressions showed that the fundamental upper limit for the magnitude of the static bulk flexoelectric effect strength, estab…
Thermodynamics of crystalline materials is analyzed using strain volumes, an incremental tensorial state variable which is the volume per unit mass multiplied by the incremental strain.
We show how the St.Venant compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric strain tensor. The compatibility constraints generate an anisotropic long-range interaction in the order parameter (deviatoric strain) components. In contrast to two dimensions, the free energy is characterized by a "landscape" of competing metastable states. We find a variety of textures, which result from the elastic frustration due to the effects of comp…
The effect of elastic strain on catalytic activity of platinum (Pt) towards oxygen reduction reaction (ORR) is investigated through de-alloyed Pt-Cu thin films; stress evolution in the de-alloyed layer and the mass of the Cu removed are measured in real-time during electrochemical de-alloying of (111)-textured thin-film PtCu (1:1, atom %) electrodes. In situ stress measurements are made using the cantilever-deflection method and nano-gravimetric measurements are made using an electrochemical quartz crystal nanobalance. Upon de-alloying via successive voltammetric sweeps between -0.05 and 1.15 …
The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model for binary alloys. By surveying the dependence of the elastic energy on chemical composition and lattice misfit, we propose a lattice strain coefficient λ*. Applying to several high-entropy alloys and superalloys, we found that most solid solution alloys are stable when λ*<0.16, analogous to the Hume-Rothery atomic-size rule for binary alloys. We also reveal that the polydispersity index δ, frequently used for describing strain in multi-component alloys, is directly relate…
