Calculation Of Elastic Constants Research Articles

Enhancing efficiency and scope of first-principles quasiharmonic approximation methods through the calculation of third-order elastic constants

A novel computational strategy is presented to calculate from first principles the coefficient of thermal expansion and the elastic constants of a material over meaningful intervals of temperature and pressure. This strategy combines a novel implementation of the quasiharmonic approximation to calculate the isothermal-isochoric linear and nonlinear elastic constants of a material, with elementary equations of nonlinear continuum mechanics. Our implementation of the quasiharmonic approximation relies on finite deformations, the use of nonprimitive supercells to describe a material, a recently proposed technique to calculate generalized mode Gr\"uneisen parameters, and the numerical differentiation of the stress tensor to calculate both second- and third-order elastic constants. The combination of this method with nonlinear continuum mechanics is shown to yield accurate predictions of lattice parameters and linear elastic constants of a material over finite intervals of temperature and pressure, at the cost of calculating isothermal second- and third-order elastic constants for a single reference state. Here, the validity and limits of our novel methods are assessed by carrying out calculations of MgO based on classical interatomic potentials. To demonstrate potential, our methods are then used in conjunction with a density functional theory approach to calculate thermal expansion and elastic properties of silicon, lithium hydrate, and graphite.

Pentaheptite diamond: a new carbon allotrope

The search for sp 3-hybridized carbon allotropes other than diamond has attracted extensive interest because of their fascinating properties. In this paper, an orthorhombic carbon phase in sp 3 bonding, named pentaheptite diamond, by combining the particle swarm optimization method with first-principles calculations has been predicted. The phonon spectra, total energy and elastic constants calculations of the pentaheptite diamond confirm its dynamical, thermal and mechanical stability at zero pressure, respectively. It possesses a high bulk modulus of 385 GPa and Vickers hardness of 72.6 GPa, comparable to diamond. Electronic band structure calculations show that the pentaheptite diamond has a direct band gap of 4.18 eV.

Exploring the structural, mechanical, electronic, and optical properties of double perovskites of Cs2AgInX6 (X = Cl, Br, I) by first-principles calculations

This article presents a comprehensive investigation of the structural, mechanical, electronic, and optical characteristics of double perovskite derivatives Cs2AgInX6 (X ​= ​Cl, Br, I) using first-principles calculations. Calculations of elastic constants are used to prove the mechanical stability of the three compounds. Based on the band structures, three Ag-based double perovskites appear to be direct bandgap semiconductors. The bandgap values range from 2.956 ​eV to 0.029 ​eV. We analyze the total and projected densities of states in order to determine the reason behind the bandgap variations. The HSE06 method has been used to explore the optical properties of these compounds in the UV and visible light regions. The optical absorption coefficients are very high for the three double perovskites within the order of 105 ​cm−1. According to our results, the Cs2AgInBr6 double perovskite has good physical properties and is suitable for photovoltaic applications.

Unusual crystal phases of noble metals Ir, Os, and hardness of Ir-Os systems from high throughput density functional calculations

The platinum-group elements (PGMs) owing their high chemical stability, and unique properties, have recently attracted great research interest in various promising applications. Herein using state-of-the-art first-principles evolutionary algorithms, we explore the thermodynamic and mechanical properties of Ir, Os, and their alloys. Hitherto unknown polytype-phases of Ir (6H, 4H, 2H) and Os (6H, 4H) have been predicted, two of these (4H-Ir, and 4H-Os) were recently observed experimentally. Os and, to more extent, Ir polytypes divulge weak thermodynamic instabilities. Phonon dispersion and elastic constants calculations were carried out to demonstrate the dynamical and mechanical stabilities of these phases. For the Ir-Os alloys, four ordered structures (Pm-3 m (IrOs3, Ir3Os), P-6 m2 (IrOs), P-3 m1 (IrOs2)) have been predicted, which are found mechanically and dynamically stables and manifest insignificantly thermodynamic instabilities. Furthermore, our obtained results show that Ir-Os systems evince outstanding mechanical properties, IrOs3 has high bulk modulus (∼421GPa), large shear modulus (∼266GPa), and Young’s modulus (659 GPa); whereas IrOs2 possesses a remarkable large elastic constants C11 (779GPa) and C33 (814GPa). The anisotropic calculations show that IrOs3 exhibits that greatest anisotropy in the universal elastic anisotropy index AU, shear modulus (AG) and Young’s modulus (AE); while IrOs2 has the smallest elastic anisotropy. Moreover, IrOs3 reveals distinguished hardness of 27.6GPa, which is 3% weaker than 2H-Os (28.6GPa), and is so far one of the hardest materials among the PGMs binary alloys.

P2221-C8: A novel carbon allotrope denser than diamond

We present a new superdense and superhard carbon allotrope with P2221 space group and 8 atoms in the unit cell, naming P2221-C8. The density of P2221-C8 is 3.579 g/cm3, which is denser than diamond and even BC8. The energetical, dynamical and mechanical stabilities of P2221-C8 are confirmed by the calculation of energy, phonon frequencies and elastic constants, respectively. The hardness ranges from 88 GPa to 94 GPa according to different models, which is comparable with that of the diamond. The bandgap is indirect with 4.475 eV, which is smaller than that of the diamond. In addition, the match between simulated X-ray diffraction (XRD) and detonation experiments shows a possible way to synthesis it.

Tetragonal distortion in magnetron sputtered bcc-W films with supersaturated carbon

Carbon has a low solid solubility in bcc tungsten at equilibrium. However, metastable supersaturated solid solutions can be synthesized with magnetron sputtering. Here, we present a systematic study on the phase stability and mechanical properties of such supersaturated W–C solid solutions. Θ–2θ scans show a split of the 200/020 and the 002 peaks for supersaturated films which is explained by a tetragonal distortion of the bcc structure. This split increases with increasing C content and is maximized at 4 at.% C, where we observe an a/b axis of 3.15–3.16 Å and a c-axis of 3.21–3.22 Å. We performed first-principles calculations of lattice parameters, mixing enthalpies, elastic constants and polycrystalline elastic moduli for cubic and tetragonal W–C solid solutions. Calculations show that tetragonal structure is more stable than the bcc supersaturated solid solution and the calculated lattice parameters and Young’s moduli follow the same trends as the experimental ones as a function of C concentration. The results suggest that supersaturated films with lattice distortion can be used as a design approach to improve the properties of transition metal films with a bcc structure.

ElasT: A toolkit for thermoelastic calculations

A toolkit that simplifies the calculation of solid-state elastic properties at finite temperatures to a one-shot task is developed. We report the improvement and automation of the stress-strain method, which relies on the averaged stresses from ab initio or classical calculations. Stresses obtained from strained crystal lattices at zero and finite temperatures can be directly extracted to fit the strain-stress relationship and get the elastic constants. Furthermore, the finite-temperature elastic constants can also be obtained by solving a system of overdetermined linear equations directly under constant pressure dynamics (NPT, NPH, etc.) within the stress-strain method, which does not require the equilibrated lattice as a prior condition. It is shown that the elastic constants converge quickly in constant pressure dynamics. This approach proves to be robust and can significantly reduce computational cost. Program summaryProgram Title: ElasT, VERSION 1.1CPC Library link to program files:https://doi.org/10.17632/cjrwdxvxcn.1Licensing provisions: GNU General Public License, version 3Programming language: FortranNature of problem: Calculations of the single-crystal elastic constants at finite temperature conditions.Solution method: Solve the stress-strain linear equations in constant volume or constant pressure ensembles.

Effect of stress regulation on electronic structure and optical properties of TiOCl<sub>2</sub> monolayer

Based on first-principles calculations, the electronic structure, the transport and optical properties of TiOCl<sub>2</sub> monolayer are systematically investigated. The vibrational, thermodynamic, and mechanical properties of TiOCl<sub>2</sub> monolayer are studied by phonon spectrum, molecular dynamics and elastic constants calculations. All these results indicate that the TiOCl<sub>2</sub> monolayer possesses good structural stability at room temperature and excellent mechanical properties. The electronic structure analysis shows that the TiOCl<sub>2</sub> is an indirect band gap (1.92 eV) semiconductor. Its band structure can be significantly affected by in-plane stress. Specifically, the TiOCl<sub>2</sub> monolayer undergoes an indirect-to-direct band gap transition under –4% uniaxial stress along the <i>a</i>-axis and the gap size decreases to 1.66 eV. Moreover, the TiOCl<sub>2</sub> monolayer exhibits obvious anisotropy characteristics, and its electron mobility is 803 cm<sup>2</sup>·V<sup>–1</sup>·s<sup>–1</sup> along the <i>b</i>-axis, whereas the hole mobility reaches 2537 cm<sup>2</sup>·V<sup>–1</sup>·s<sup>–1</sup> along the <i>a</i>-axis. The wave peaks (valleys) of the absorptivity, reflectivity and transmittance shift toward the violet part of the visible band by the stress. All these appealing properties make the TiOCl<sub>2</sub> monolayer a promising candidate for applications in optoelectronic devices.

A new direct band gap Si-Ge allotrope with advanced electronic and optical properties.

Direct-band silicon materials have been a sought-after material for potential applications in silicon photonics and solar cells. Accordingly, methodologies like nanostructure engineering, alloy engineering and strain engineering have been developed. In this work, the particle swarm optimization (PSO) algorithm is used to design direct-band Si-Ge alloys. The findings of phonon computations demonstrate that all these structures are dynamically stable. In addition, ab initio molecular dynamics and elastic constant calculations are carried out, with results indicating these structures are thermodynamically stable at 300 K, as well as being mechanically stable. All of these materials exhibit semiconductor behavior with band gaps of 1.03, 0.68 and 1.37 eV for α, β and γ phases, respectively, at the HSE06 level. The results of effective mass and mobility of carriers that are important in applications show that holes are more easily transported in all structures, with higher concentration of holes accompanied by lower carrier mobility. Different concentrations of holes nh lead to different limits in the scattering process. When nh is lower than the value of around 1016 cm-3, deformation potential scattering is dominant, while the ionized impurity scattering process limits overall mobility when nh is higher than such a value. Finally, the absorption spectra shows that both α and β phases have isotropic optical properties in the X- and Y-directions while strong anisotropy can be seen in the Z-direction. However, the γ phase exhibits no notable isotropy. This investigation finds three direct-band and potentially CMOS compatible materials, a finding which will benefit the development of high efficiency emitters or solar cells.

Micromechanical Analysis for Macroscopic Elastic Constants and Thermal Expansion Coefficients of Composite Materials Including Double Inhomogeneous Inclusions (2nd Report, Numerical Calculation of Macroscopic Elastic Constants)

Micromechanical Analysis for Macroscopic Elastic Constants and Thermal Expansion Coefficients of Composite Materials Including Double Inhomogeneous Inclusions (2nd Report, Numerical Calculation of Macroscopic Elastic Constants)

Pressure Induced Magnetic and Structural Transitions in Thmnasn: An Ab-Initio Study

In this work, we present first principles density functional study of magnetism and electronic structures of ThMnAsN at ambient as well as at high pressure. Magnetic ground state of ThMnAsN as resulted from our calculations, is C-type anti-ferromagnet which is consistent with the experiments. Our results also suggest that C-AFM ground states of ThMnAsN is insulating in nature with a small energy gap $\sim0.4$ eV (using GGA exchange-correlation functional) at the Fermi level. Applying hydrostatic pressure in ThMnAsN, we find that all the structural parameters show anomalies at 9 GPa pressure which is attributed to a structural phase transition from tetragonal to collapse tetragonal phase. Apart from that our elastic constant and electronic structure calculations clearly show a increment in the metallic behaviour at higher pressure accompanying with a magnetic phase transition at the vicinity of 9 GPa pressure. We also observe that electronic structure of ThMnAsN at high pressure (9 GPa) closely resembles with the electronic structure of Fe-based superconductors.

Modeling structural, elastic, electronic and optical properties of ternary cubic barium based fluoroperovskites MBaF3 (M = Ga and In) compounds based on DFT

This work presents in detail the Ab-initio computational research work on the structural, elastic, electronic, and optical properties of Perovskite-type (Halide-Perovskites) barium-based MBaF3 (M = Ga and In) compounds. The work is based on density functional theory (DFT) within WIEN2K. Structurally both GaBaF3 and InBaF3 based on optimization of Birch Murnaghan fit are found to be stable. The IRelast package for the calculations of elastic constants (ECs) is employed for the computation of elastic properties. Mechanically these compounds are identified to be ductile, hard to scratch, anisotropic, mechanically stable, and demonstrate strong resistance to plastic deformation. The precise modified Becke–Johnson (mBJ) potential is employed for electronic properties. Band structures of these compounds possess an insulating nature of direct wide energy band gap of 5 eV for GaBaF3 and 5.1 eV for InBaF3 from X-X symmetries points. To know the contribution of different electronic states to the band structures, the TDOS and PDOS i-e (total and partial density of states) are exploited. The insulating direct wide band gap energy nature presented a straightforward direction to study the optical properties of these compounds. The optical properties, of both the compounds, were studied deeply in the energy range from 0 eV to 40 eV. These compounds possess high absorption and optical conduction at high energy ranges. Both materials are transparent to incident photons at low energy ranges. We have concluded from the optical properties investigations that these compounds are suited for high-frequency UV device applications. To our deep knowledge, this is the first systematic theoretical computation of MBaF3 (M = Ga and In) with structural, elastic, electronic and optical, properties that have yet to be verified experimentally.

Novel Braceletlike BiSbX3 (X = S, Se) Monolayers with an In-Plane Negative Poisson's Ratio and Anisotropic Photoelectric Properties.

In this work, we predict two novel two-dimensional (2D) auxetic materials, BiSbX3 (X = S, Se) monolayers, through first-principles calculations. Attributed to their special braceletlike structure, the in-plane negative Poisson's ratio (NPR) of BiSbS3 and BiSbSe3 monolayers are as high as -0.25 and -0.26, respectively. The phonon dispersion calculations, ab initio molecular dynamics simulations, and elastic constants calculations demonstrate that these two monolayers possess excellent dynamic, thermal, and mechanical stabilities. The band gap values of BiSbS3 and BiSbSe3 calculated at the HSE level by considering the spin-orbit coupling (SOC) effect are 1.68 and 1.20 eV. The anisotropic carrier mobility and superior optical absorption indicate that they may shine in the next generation of electronic and optoelectronic devices. All of these discoveries not only enrich the types of auxetic materials but also provide a structural reference for designing new auxetic materials on the molecular level. Furthermore, they can provide theoretical guidance for future applications of BiSbX3 (X = S, Se) monolayers in various fields.

HSH-C10: A new quasi-2D carbon allotrope with a honeycomb-star-honeycomb lattice

Two-dimensional (2D) materials with honeycomb, kagome or star lattice have been intensively studied because electrons in such lattices could give rise to exotic quantum effects. In order to improve structural diversity of 2D materials to achieve unique properties, here we propose a new quasi-2D honeycomb-star-honeycomb (HSH) lattice based on first-principles calculations. A carbon allotrope named HSH-C10 is designed with the HSH lattice, and its mechanical properties have been intensively investigated through total energy, phonon dispersion, ab initio molecular dynamic simulations, as well as elastic constants calculations. Besides the classical covalent bonds, there is an interesting charge-shift bond in this material from the chemical bonding analysis. Additionally, through the analysis of electronic structure, HSH-C10 is predicted to be a semiconductor with a direct band gap of 2.89 eV, which could combine the desirable characteristics of honeycomb and star lattice. Importantly, by modulating coupling strength, a flat band near the Fermi level can be obtained in compounds HSH-C6Si4 and HSH-C6Ge4, which have potential applications in superconductivity. Insight into such mixed lattice would inspire new materials with properties we have yet to imagine.

Rational design of porous GeP2S6 monolayer for photocatalytic water splitting under the irradiation of visible light

Here, we predicted a novel compelling photocatalyst, the porous GeP2S6 monolayer. The stability of the GeP2S6 monolayer was examined via elastic constant calculations, vibratory phonon spectrum and ab initio molecular dynamics simulations. The electronic properties reveal that the GeP2S6 monolayer possesses a direct gap with the value of 2.06 eV. The photocatalytic properties analyses show that the band edges of the GeP2S6 monolayer meets the requirements of the photocatalytic decomposition water. Meanwhile, the GeP2S6 monolayer exhibits better optical absorption ability in the visible region. Additionally, high carrier mobility (electrons: 206.09 cm2/V·s and holes: 261.46 cm2/V·s) and strongly anisotropic transport properties lead to high solar energy conversion efficiency. Interestingly, the photocatalytic decomposition water in GeP2S6 monolayer is robust against compression strain, which will improve the activity of photocatalytic hydrogen evolution reaction. Our findings highlight the porous GeP2S6 monolayer as a good candidate material for electronics and photocatalytic applications.

Computational Prediction of New Series of Topological Ternary Compounds LaXS (X = Si, Ge, Sn) from First-Principles

Dirac materials and their advanced physical properties are one of the most active fields of topological matter. In this paper, we present an ab initio study of electronics properties of newly designed LaXS (X = Si, Ge, Sn) tetragonal structured ternaries, with the absence and presence of spin–orbit coupling. We design the LaXS tetragonal non-symophic p4/nmm space group (no. 129) structures and identify their optimization lattice parameters. The electronic band structures display several Dirac crossings with the coexistence of both type I and type II Dirac points identified by considering the effect of spin–orbit coupling toward the linear crossing. Additionally, we perform the formation energy calculation through the density functional theory (DFT) to predict the stability of the structures and the elastic constants calculations to verify the Born mechanical stability criteria of the compounds.

ElasTool: An automated toolkit for elastic constants calculation

We present the ElasTool package, an automated toolkit for calculating the second-order elastic constants (SOECs) of any two- (2D) and three-dimensional (3D) crystal systems. ElasTool uses three kinds of strain-matrix sets, i.e., the high-efficiency strain-matrix sets (OHESS), the universal linear-independent coupling strains (ULICS), and the all-single-element strain-matrix sets (ASESS), to calculate the SOECs automatically. ElasTool can efficiently compute both zero- and high-temperature elastic constants. We describe in detail the theoretical background and computational method of elastic constants, the package structure, the installation, and run, the input/output files, the controlling parameters, and two representative examples of how to use the ElasTool package. ElasTool is useful for either the exploration of materials' elastic properties or high-throughput new materials screening and design. ElasTool is freely available on GitHub: https://github.com/elastool Program summaryProgram Title: ElasToolCPC Library link to program files:https://doi.org/10.17632/ktvmxrdhpz.1Code Ocean capsule:https://codeocean.com/capsule/1893813Licensing provisions: GNU General Public License, version 3Programming language: Python 3External routines: NumPy [1], Spglib [2], ASE [3], Pandas [4]Nature of problem: The stress-strain method of elastic constants calculation depends on accurate stresses calculated with first-principles methods, such as the density functional theory (DFT). Compared to the energy-strain method, the stress-strain approach needs a smaller number of strain sets to solve the equation sets needed to deduce the elastic constants; it is also more straightforward to implement. However, accurate stresses take a lot of time to compute within DFT. Thus, a smaller number of strain sets and more efficient strain sets are urgently needed to improve the computational efficiency of elastic constants. An automated solution coupled with DFT is necessary for the exploration of materials' elastic properties and high-throughput new materials screening and design.Solution method: The solution to improve the computational efficiency of the stress-strain method is to decrease the number of strain-matrix sets and optimize the strain-matrix sets. We coupled our previously proposed high-efficiency strain-matrix sets (OHESS) with DFT and automated the processes of calculating the elastic tensor using the stress-strain method in the ElasTool package. ElasTool can also adopt the all-single-element strain-matrix sets (ASESS) and the universal linear-independent coupling strains (ULICS) approaches. It can deal with both zero- and high-temperature elastic constants of any crystal systems belonging to 2D or 3D. Having obtained the elastic moduli, ElasTool also gives other essential mechanical and elastic properties of materials such as Young's modulus, bulk modulus, elastic anisotropy, Debye temperature, and the sound velocities.Additional comments including restrictions and unusual features: Currently, this package interfaces with Vienna Ab initio Simulation Package (VASP) code as the stress tensors calculator. [5-7] Extension to other electronic structures is straightforward.

A novel two-dimensional boron–carbon–nitride (BCN) monolayer: A first-principles insight

The optical, electronic, and structural properties of a theoretically predicted new boron–carbon–nitride (BCN) two-dimensional monolayer have been explored using density functional theory calculations. The phonon dispersion, molecular dynamics simulation, the cohesive energy, and the Born criteria of elastic constant calculations of the BCN monolayer confirm its stability. The phonon spectrum illustrates an out-of-plane flexure mode with quadratic dispersion in the long-wavelength limit. The BCN monolayer is a semiconductor with a direct bandgap of 0.9 (1.63) eV determined via the Perdew–Burke–Ernzerhof (Heyd–Scuseria–Ernzerhof) functional. The same electron and hole effective masses and mobility values indicate the high recombination rate of electrons and holes. Meanwhile, the BCN monolayer can absorb ultraviolet radiation more effectively than visible light. Due to its interesting physical properties, the novel BCN monolayer could be a rather good candidate material for electro-optical applications.

Finite element modeling of elastic moduli and microstresses in textile carbon-carbon composites

sThe problem of detailed calculation of micro-stresses in textile composite materials under arbitrary types of loading is considered. A model for calculating the effective characteristics of textile composites considering the real complex curvilinear anisotropy of fibers in tissues is proposed. The model is based on the asymptotic homogenization method, whereby local problems of elasticity theory for a curvilinear anisotropic body are formulated. For the numerical solution of these problems, the finite element method is used. The implementation of the proposed method was carried out within the framework of the SMCM software package, developed at the Department of Computational Mathematics and Mathematical Physics of the Bauman Moscow State Technical University. The SMCM software package allows you to perform a full cycle of finite element modeling, including the stages of pre-processing and post-processing. An example of numerical modeling of a textile carbon-carbon composite of twill weaving is carried out. It is shown that the developed software package provides (a very high accuracy of calculations of the effective elastic properties of composites. The comparison was carried out with the calculations obtained using the ANSYS software, which was modified to provide the possibility of solving local problems, the relative deviation in the calculations of the effective elastic constants did not exceed (-7) degrees.

Calculation of elastic constants of embedded-atom-model potentials in the NVT ensemble

A method for the calculation of elastic constants in the NVT ensamble using molecular dynamics (MD) simulation with a realistic many-body embedded-atom-model (EAM) potential is studied in detail. It is shown that, in such NVT MD simulations, the evaluation of elastic constants is robust and accurate because it gives the elastic tensor in a single simulation which converges using a small number of time steps and particles. These results highlight the applicability of this method in (i) the calculation of local elastic constants of nonhomogeneous crystalline materials and (ii) the calibration of interatomic potentials, as a fast and accurate alternative to the common method of explicit deformation, which requires a set of consistent simulations at different conditions. The method is demonstrated for the calculation of the elastic constants of copper in the temperature range of 0-1000K, and results agree with the target values used for the potential calibration. The various contributions to the values of the elastic constants, namely, the Born, stress fluctuation, and ideal gas terms, are studied as a function of temperature.