Method Of Homogeneous Deformation Research Articles

First-principles calculations to investigate electronic band structure, optical and mechanical properties of new CaFCl monolayer

Two-dimensional materials present new opportunities to venture into largely unexplored areas of material property space. They are appropriate for several electronic powers, photonics, and sunlight device applications. In this framework, leveraging density functional theory and even beyond, we investigate the structural, vibrational, electronic, optical, and elastic properties of novel CaFCl thin film. We have found that the CaFCl sheet is dynamically stable because its spectrum contains no imaginary frequencies. The direct band gap energy value of our GW findings is around 9.10 eV, which really is higher than the band gaps of ScOI and InOF oxyhalides thin films. We have found that the external electric fields immediately affect the structure of the layer. The band gap of the CaFCl structure is reduced rapidly by increasing the strength of the electric field. Additionally, our Bethe–Salpeter theory calculations demonstrate that when the excitation light rate is greater than the resonance frequency (8.00 eV), the substance becomes translucent. We have also used the method of homogeneous deformation, which is coupled with density functional theory and random phase approximation total-energy computations to produce a comprehensive scheme for studying the second-and third-order elastic constants for the CaFCl layer. A polynomial fit to the estimated energy-strain connection yielded these constants. Our results reveal that this 2D monolayer is a promising material for nanophotonics and optoelectronics.

Electronic, Optical, and Elastic Properties of CaFI Monolayer and Acoustic Phonon Dispersion at Hypersonic Frequencies Using Density Functional Theory and beyond with Random Phase Approximation and Bethe-Salpeter Equation.

The extraordinary properties of graphene have motivated us to investigate a novel 2D compound. In this framework, we study the structural, vibrational, electronic, optical, and elastic properties of a new two-dimensional CaFI monolayer, using DFT, GW, RPA, and BSE methodologies. The phonon dispersion curve of the CaFI monolayer exhibited no unstable phonon modes, confirming that this 2D sheet is dynamically stable. Our GW calculations show that the indirect bandgap energy value of CaFI is 6.52 eV. Interestingly, the bandgap rapidly decreased by improving the electric field value. Our BSE computations indicate that this monolayer becomes translucent when the incident light frequency exceeds the plasma frequency (6.50 eV). Also, we have computed the second and third elastic constants of CaFI by combining the DFT and RPA approaches with the homogeneous deformation method. Additionally, the longitudinal acoustic phonon dispersion of CaFI was studied. We have determined that the longitudinal acoustic wave velocity in our sheet is higher than the LA wave velocity of germanium measured using Brillouin or ultrasonic techniques.

First‐Principles Calculations to Investigate the Third‐Order Elastic Constants and Mechanical Properties of Mg, Be, Ti, Zn, Zr, and Cd

We present theoretical studies for the third‐order elastic constants of Mg, Be, Ti, Zn, Zr, and Cd with a hexagonal‐close‐packed (HCP) structure. The method of homogeneous deformation combined with first‐principles total‐energy calculations is employed. The deformation gradient Fij is applied to the crystal lattice vectors ri, and the elastic strain energy can be obtained from the first‐principles calculation. The second‐ and third‐order elastic constants are extracted by a polynomial fit to the calculated energy‐strain results. In order to assure the accuracy of our method, we calculated the complete set of the equilibrium lattice parameters and second‐order elastic constants for Mg, Be, Ti, Zn, Zr, and Cd, and our results provide better agreement with the previous calculated and experimental values. Besides, we have calculated the pressure derivatives of SOECs related to third‐order elastic constants, and high‐pressure effects on elastic anisotropy, ductile‐to‐brittle criterion, and Vickers hardness are also investigated. The results show that the hardness model is more appropriate than for HCP metals under high pressure.

Determination of second- and third-order elastic constants for energetic materials

Accurate calculations of second-order elastic constants (SOECs) and third-order elastic constants (TOECs) are important for energetic materials to describe the linear and nonlinear mechanical responses quantitatively. Homogeneous deformation method combined with first-principles total energy calculations are performed to calculate a complete set of SOECs and TOECs for cyclotrimethylene trinitramine (RDX), pentaerythritol tetranitrate (PETN) and cyclotetramethylene tetranitramine (δ-HMX). The computed SOECs for RDX, PETN and δ-HMX agree well with previous experiments and theoretical calculations. Bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio deduced from SOECs reveal quantitatively the anisotropic mechanical properties along different crystal orientations. TOECs of these three energetic materials, which can be used to construct constitutive equations and provide input parameters for mesomechanics model and macroscopic simulations, are predicted. In particular, the TOEC results provide guidance for future experimental measurements and lay the foundation for more accurate calculations.

ANÁLISE NUMÉRICA E ANALÍTICA DA CARGA NO PROCESSO DE ROLAMENTO

The rolling process is of great importance to the industry and the understanding is a fundamental function for its design and use. Currently there are two traditional processes for steel rolling: Hot rolling (from 1300 ⁰C to ⁰700 C) and cold rolling (at room temperature). The process consists in reducing the cross section of a billet by means of compressive forces, applied by rolling rolls, mounted in a rolling mill. In order to control the efforts in the mill, the billet usually passes several times between the rollers, with a thinner thickness each time less. Between each rolling, annealing processes may be applied to recover the ductility of the reduced metal by the scrubbing and pickling to remove the oxide layer formed on the surface. A good calibration of the rolling mill and material is important to avoid rolling defects, generating products with imprecise dimensions and undesirable deformations. Two mathematical models can be presented: Homogeneous Deformation Method and Equilibrium Method. A case study is proposed. The study consists in calculating the efforts required to laminate a defined steel billet, comparing both analytical formulations to the results obtained by Finite Element Method developed in ABAQUS software. The results of the analytical path are compared with the simulation results. Finally, the difference of the presented results can be explained by the consideration of the increase of the tension for plastic deformation due to the hardening by ABAQUS software.

Revisiting the Criterion for Mechanical Supression of Dendrites at the Li/Electrolyte Interface

Large-scale adoption of electric vehicles has been challenging due to the high energy density required to achieve a reasonable driving range. One route to increasing the energy density has been to develop “beyond Li-ion” chemistries1 like Li-air and Li-S. Another route is to use Li metal anode coupled with a traditional Li-ion cathode since lithium metal electrode possesses a very high theoretical specific capacity (3860 mAh g-1) and low reduction potential.2 Both routes require a Li metal anode which can reversibly cycle without forming dendrites. Mechanical suppression of dendrite growth through solid or polymer electrolytes has shown potential for alleviating the problem. It has been suggested by treating the electrode and electrolyte as isotropic materials that a solid polymer electrolyte that has roughly a shear modulus twice that of lithium can suppress dendrite growth.3 One potential issue relates to the assumption of isotropic materials as Li metal is highly anisotropic with a drastically different shear and elastic moduli depending on the crystal orientation. This further dictates that the nature of dendrite growth will be affected by the crystal orientation of Li metal in contact with the electrolyte. In this work, we aim to fill the gaps in our current understanding of the mechanical suppression of dendrite growth at electrode-electrolyte interfaces by explicitly accounting for the anisotropic effects. We impose a periodic deformation at the interface and solve two-dimensional linear elasticity equations to get the resulting periodic deformation at the anisotropic electrode-electrolyte interface. We use the full elastic tensor of Li metal anode and solid electrolyte calculated from first-principles density functional theory calculations for the constitutive stress-strain relationship of each material. The elastic tensor was calculated based on the method of homogeneous deformations of the unit cell followed by fitting the energies of the strained cell to energy-strain relationship. Using the calculated deformation, we obtain the stresses at the interface and study their role in the amplification of surface roughness using a kinetic model.4 Our anisotropic model enables us to study the effect of different crystal orientations of Li metal anode and solid electrolyte on the dendrite growth.

Third-order elastic constants of ZnO and size effect in ZnO nanowires

Higher order elastic constants are very useful in understanding the anharmonicity of ZnO due to finite strain. The third-order elastic constants of zinc oxid (ZnO) and the size effect of the strain dependent Young's moduli of ZnO nanowires have been studied by first-principles calculations and molecular mechanics methods. The whole set of the third-order elastic constants were obtained for the first time for ZnO with homogeneous deformation method. The Young's modulus along the [0001] direction is evaluated to be Y=142.4−173.4ξ (GPa). Strain dependent Young's moduli were obtained for [0001] oriented ZnO nanowires with diameter ranged from 1.8 nm to 6.0 nm. The constant term of Young's moduli of ZnO NWs is smaller than those of the bulk, and it decreases from 121.5 to 96.7 GPa as the diameter decreases. The linear term increases rapidly as the diameter decreases and changed from negative to positive when the diameter is 3.6 nm. The linear term was −124.4 GPa when diameter is 6.0 nm, and it reached 248.8 GPa when the diameter is 1.8 nm. The mechanics of the size effect in ZnO nanowires is discussed. The obtained results will be helpful to get some insight on the elastic properties of ZnO nanowires.

Nonlinear Elastic Properties of Superconducting Antiperovskites MNNi3 (M =Zn, Cd, Mg, Al, Ga, and In) from First Principles

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Gruneisen constants of long-wavelength acoustic modes by using the calculated TOECs.

Non-linear elastic behavior of hexagonal silicon carbide

The full sets of non-vanishing second- and third-order elastic constants (SOEC and TOEC) in 2H-SiC have been determined by the method of homogeneous deformation with interactions extending upto fourth neighbors using the sublattice displacement to the first degree in strains. The effective SOEC are obtained in terms of SOEC and TOEC. The aggregate elastic moduli and its pressure dependence have been studied. In 2H-SiC, the value of , showing the compressibility along the ab-plane to be larger, reducing the system more anisotropic, which is corroborated in the pressure derivatives of SOEC. TOEC of the shear modes, like and have smaller values than their longitudinal counterparts like and , uantifying the effect of pressure on the longitudinal wave velocity to be greater. Absolute value of , predicting anisotropy along ab-plane to be more pronounced than c-axis. The pressure derivatives for the longitudinal moduli ( and ) are positive while the shear moduli ( and ) are negative, consistent with the pressure derivatives of the bulk modulus () and shear modulus () of polycrystalline 2H-SiC. The elastic shear softening predicts the B4 -to-B1 structural phase transformation in 2H-SiC.

Non-linear elastic behaviour of hexagonal cadmium sulfide single crystals

Elastic characterization of wide direct band gap semiconductor cadmium sulfide has been studied using finite strain elasticity theory. The complete sets of second and third order elastic constants are obtained using the method of homogeneous deformation for single crystal cadmium sulfide in hexagonal wurtzite phase. All the third order elastic constants are negative; indicating an increase of vibrational frequencies under stress, giving rise to an increase in the strain energy. The longitudinal wave velocities C 111, C 222 and C 333 in the single crystal cadmium sulfide is greater than the shear wave velocity. The six first order pressure derivatives of the second order elastic constants obtained indicate the higher compressibility of the cadmium sulfide crystal along the c-axis. The generalised Gruneisen parameters of the acoustic waves and the low temperature limit of lattice thermal expansion are determined. The obtained results are compared with the available reported values.

ELASTIC PROPERTIES OF GROUP IV SEMICONDUCTORS BY PSEUDOPOTENTIAL APPROACH

The higher-order perturbation theory based on pseudopotential approach is used to investigate few elastic and vibrational properties of Group IV semiconductors. The homogeneous deformation method is used to calculate elastic constants. To consider electron-ion interactions, our own proposed potential is employed to investigate such properties of Si , Ge and α- Sn . The potential contains only single parameter and its value is determined by fitting experimental value of bulk modulus. The calculated physical properties like elastic constants, pressure derivatives of the bulk modulus, pressure derivatives of elastic constants, Young's modulus and Poisson's ratio etc., of Si , Ge and α- Sn are in good agreement with available experimental and other available theoretical results. The deviation of the present calculations using our potential with respect to experimental data is found to be less than 10% in most of the calculated physical properties. To consider the exchange and correlation effect, five different local-field correction functions are incorporated in the present investigations. From the present study, it can be observed that incorporation of local-field correction and the covalent-correction term are important in such type of investigations.

The stability and the nonlinear elasticity of 2D hexagonal structures of Si and Ge from first-principles calculations

By using the first-principles calculations based on the density-functional theory (DFT), we study the stability and the nonlinear elasticity of two-dimensional (2D) hexagonal structures of Si and Ge. The reproduced structure optimization and phonon–dispersion curves demonstrate that Si and Ge can form stable 2D hexagonal lattices with low-buckled structures, and provide a good agreement with the previous DFT calculations. The second- and third-order elastic constants are calculated by using the method of homogeneous deformation. The present results of the linear elastic moduli agree well with the previous results. In comparison with the linear approach, the nonlinear effects really matter while strain is larger than approximately 3.5%. The force–displacement behaviors and the breaking strength of 2D hexagonal Si and Ge are discussed using the nonlinear stress–strain relationship. By using the available results of graphene, we reasonably demonstrate that the radius of the atom increases and breaking strength of this element decreases for 2D hexagonal structures of group IV-elements.

Nonlinear elasticity of monolayer zinc oxide honeycomb structures: A first-principles study

We present the second- and third-order elastic constants and discuss the nonlinear elasticity for monolayer zinc oxide (ZnO) with honeycomb structure. Density functional theory (DFT) within generalized-gradient-approximation (GGA) combining with the method of homogeneous deformation is employed. The predictions for the elastic constants are obtained from the nonlinear least-squares polynomial fit to the calculated strain-energy relations from first-principles total-energy calculations. In comparison with the linear approach, the nonlinear effects really matter for strain larger than approximately 3.0%. We discuss how internal relaxation acts on the elastic properties, and internal relaxation displacements for the corresponding applied strain are obtained. Our results show that internal relaxation is important for the values of elastic constants, and especially influence the third-order elastic constants. Finally, we discuss force–displacement behavior and the breaking strength of monolayer ZnO within a framework of nonlinear stress–strain relationship. Monolayer ZnO exhibits very high ductility, in our study exceeding 20% ductility in tension, and the elastic response will exhibit highly nonlinear while the third-order effects really matter.

Ab initio calculations on the third-order elastic constants for selected B 2–MgRE (RE = Y, Tb, Dy, Nd) intermetallics

We present the third-order elastic constants for the magnesium-rare-earth alloys MgY, MgTb, MgDy, and MgNd with CsCl-type B2 structure. Density functional theory (DFT) within generalized-gradient-approximation (GGA) combining with the method of homogeneous deformation is employed. The predictions for the elastic constants are obtained from the nonlinear least-squares polynomial fit to the calculated strain–energy relation from first-principles total-energy calculations. To judge that our computational accuracy is reasonable, we compare the ab initio calculated results for the third elastic constants with experimental data and previous theoretical results for Si. Our calculated second-order elastic constants for the selected magnesium-rare-earth alloys agree well the previous calculations and the experiments. The third-order effects really matter when the finite strains are larger than approximately 2.5%.

On third-order elastic constants for ductile rare-earth intermetallic compounds: A first-principles study

We present the unknown third-order constants of ductile rare-earth intermetallic compounds YAg and YCu with CsCl-type B2 structure. Density functional theory (DFT) within generalized-gradient-approximation (GGA) combining with the method of homogeneous deformation is employed. The predictions for the elastic constants are obtained from a polynomial fit to the calculated strain–energy relation from first-principles total-energy calculations. Calculated second-order elastic constants are consistent with the previous calculations and the experiments. The third-order effects really matter when the finite strains are larger than approximately 3.0%. The relation between the third-order elastic constants and pressure derivatives of the second-order elastic constants has also been discussed.

First-principles calculations on third-order elastic constants and internal relaxation for monolayer graphene

The method of homogeneous deformation is combined with first-principles total-energy calculations on determining third-order elastic constants and internal relaxation for monolayer graphene. We employ density functional theory (DFT) within generalized-gradient-approximation (GGA). The elastic constants are obtained from a polynomial fitted to the calculations of strain–energy and strain–stress relations. Our results agree well with recent calculations by DFT calculations, tight-binding atomistic simulations, and experiments with an atomic force microscope. The internal relaxation displacement has also been determined from ab initio calculations. The details of internal lattice relaxation by first principles are basically consistent with the previous molecular dynamics (MD) simulation. But for tiny deformation, there is an anomalous region in which the behavior of internal relaxation is backward action. In addition, we have also demonstrated that the symmetry of the relationship between the internal displacement and the infinitesimal stains can be satisfied.

DFT study on elastic and piezoelectric properties of tetragonal BaTiO 3

A theoretical method for studying the mechanism of the piezoelectric effects in crystals from first-principles calculations is described and applied for tetragonal BaTiO 3 in the present work. The elastic constants of tetragonal BaTiO 3 are calculated by using the homogeneous deformation method in the scheme of density-functional theory and the generalized gradient approximation. The bulk modulus and the Debye temperature are also calculated from the elastic constants and found to be in good agreement with corresponding experimental values.

Thermo-mechanical stability and strength of peptide nanostructures from moleculardynamics: self-assembled cyclic peptide nanotubes

Peptide nanostructures present a wide range of opportunities for applications inbiomedicine and bionanotechnology; hence experimental and theoretical studies aiming atdetermination of thermo-mechanical stability of peptide-based nanostructuresare critical for the design and development of their technological applications.Here, we present a homogeneous deformation method combined with the finiteelasticity theory and molecular dynamics simulations (MD) for the calculation ofsecond-order anisotropic elastic constants for a membrane model made up ofself-assembled cyclic peptide nanotubes. We have computed the values of all anisotropicelastic constants at 300 K. The value of the engineering Young’s modulus (in thez direction) is 19.6 GPa. We observed a yield behavior in thez direction for a strain value of 6%. Furthermore, we also report calculated heat capacity,thermal expansion coefficient and isothermal compressibility of the system under study.

First-principles calculations of second- and third-order elastic constants for single crystals of arbitrary symmetry

The method of homogeneous deformation was combined with first-principles total-energy calculations to provide a general method for determining second- and third-order elastic constants for single crystals of arbitrary symmetry. Lagrangian strain tensors characterized by a single strain parameter are applied to the crystal lattice and the elastic strain energy is calculated from first principles. Second- and third-order elastic constants are obtained from a polynomial fit to the calculated energy-strain relation. Fitting the energy-strain relation, rather than the stress-strain relation, provides a more robust procedure and enables the use of certain first-principles codes where the stress tensor cannot be determined directly. To illustrate the method and to compare with previous work, we calculated the complete set of second- and third-order elastic constants for silicon (cubic lattice). Our results provide better agreement with experimental data than results from previous first-principles calculations. To demonstrate the use of the method for lower-symmetry crystals, second- and third-order elastic constants for $\ensuremath{\alpha}$-quartz (trigonal lattice) were calculated and reasonable agreement was obtained with experimental results. Our method is general and can be applied to crystals with low symmetry and/or low yield strength where experimental determination of the third-order elastic constants is difficult.

Formal elasticityof four carbon allotropes: II. The anatomy of the macroscopic elasticconstants, compliances, and pressure derivatives and a generalizedmethod of homogeneous deformation

The formal contributions of inner elastic constants to themacroscopic second- and third-order elastic constants of fourdiamond and graphite allotropes of carbon are analysed. Second-and third-order compliances and compressibilities, effectiveelastic constants, and pressure derivatives of the second-orderconstants are also presented. A generalized method ofhomogeneous deformation is developed to relate thecomputationally friendly infinitesimal strain approach to thethermodynamically rigorous finite-strain formalism.Computational protocols, involving up to nine distinctshape-changing deformations, are developed to facilitate thedetermination of all second- and third-order elastic and innerelastic constants, and hence of all derived quantities.