Elastic Stability Conditions Research Articles

On the possibility of low-symmetry structures in Zr2CoSi

First principles calculation shows that the energy difference between the cubic L21 and Hg2CuTi inverse structure for Zr2CoSi is 1.454 eV/f.u., indicating than the L21 structure is more stable. The density of states and band structure of Zr2CoSi in the L21 structure do not support the half–metallic state. Moreover, van Hove singularity involving partially occupied Co 3d eg states occurs in minority states at the Fermi level and the Zr2CoSi in L21 structure satisfies the preconditions to exhibit a cubic-to-tetragonal instability according to a band-Jahn-Teller mechanism. The computed total energy landscapes of the system shows that there are two tetragonal and one orthorhombic distorted phases of Zr2CoSi that are energetically favored over the undistorted cubic L21 structure. However, only one tetragonal phase of Zr2CoSi with c/a > 1.0 fulfills necessary and sufficient elastic stability conditions for both GGA and LDA exchange–correlation potentials.

Elastic stability criteria of seven crystal systems and their application under pressure: Taking carbon as an example

Elastic stability criteria are widely employed to prove the being of the lattice. Sin'ko and Smirnov have reported the applicable criteria under isotropic pressure and given the equations between the elastic constants C ~ i j and C i j under pressure. On this basis, the closed forms of necessary and sufficient conditions for elastic stability in all crystal classes have been presented, which are popular in normal pressure. However, the forms of elastic stability criteria under pressure are still fragmented in various literature studies. Carbon is an element with a rich variety of allotropes, and because of its excellent mechanical and electronic properties, it gains enduring and intense attention, while its phase diagram is poorly known. In order to systematically study the response of various carbon stabilities to pressure and offer some valuable insights into experimental exploration, we derive the total forms of mechanical stability criteria under isotropic pressure and calculate the mechanical stability of 46 carbon allotropes involving seven crystal systems under pressure.

Electronic, optical and thermoelectric properties of a novel two-dimensional SbXY (X = Se, Te; Y = Br, I) family: ab initio perspective.

Recent developments in the synthesis of highly crystalline ultrathin BiTeX (X = Br, Cl) structures [Debarati Hajra et al., ACS Nano 14, 15626 (2020)] have led to the exploration of the atomic structure, dynamical stability, and electronic, optical, and thermoelectric properties of SbXY (X = Se, Te; Y = Br, I) monolayers via density functional calculations. The calculated phonon spectrum, elastic stability conditions, and cohesive energy verified the stability of the studied SbXY monolayers. The mechanical properties reveal that all studied monolayers are stable and brittle. Based on PBE (PBE + SOC) functional calculations, the SbXY monolayers are semiconductors with indirect bandgaps. The calculated bandgaps using HSE (HSE + SOC) for SbSeBr, SbSeI, SbTeBr, and SbTeI monolayers are between 1.45 and 1.91 eV, which are appealing for applications in nanoelectronic devices. The signature of the Rashba effect appears in the SbXY monolayer. The SbXY monolayers are visible-light active. Hole doping can be an efficient way to increase the electricity production of SbXY monolayers from waste heat energy. This study suggests that SbXY (X = Se, Te; Y = Br, I) monolayers represent promising new electronic, optical, and energy conversion systems.

First principles comparative studies of thermoelectric and other properties in the cubic and hexagonal structure of CsCdCl3 halide perovskites

We present First-principles studies of cubic and hexagonal structured CsCdCl3, using Norm Conserving (PBE-NC) and Projected Augmented Wave (PBE-PAW) pseudopotentials. From our results, the hexagonal structure has direct bandgaps of 2.54 eV and 2.24 eV, within the PBE-PAW and PBE-NC pseudopotentials respectively. Whereas, the cubic structure possess bandgaps of 1.76 eV and 1.58 eV for PBE-PAW and PBE-NC pseudopotentials respectively. Also, from the elastic properties calculations, the results revealed higher values of Vicker's hardness, elastic constants C11 and C12, Young, Bulk and Shear moduli in the cubic structure than the hexagonal structure with the exemption in Pugh's ratio having a higher value in hexagonal structure. Further analysis of the calculated elastic properties reveals that CsCdCl3 is ductile and satisfied the conditions for elastic stability. Across calculated temperature range, the PBE-PAW pseudopotentials give higher electrical and thermal conductivity per relaxation time in the two structures, with a nearly linear increase in cubic and hexagonal structures. From 0 K up to the room temperature, the thermal conductivity per relaxation time in both pseudopotentials and crystal structures converged to the same values, while above 300 K the cubic phase has higher thermal conductivity per relaxation time. The hexagonal structure has a higher figure of merit with a significant peak located at 50 K with PBE-PAW and PBE-NC pseudopotential method. The work revealed that CsCdCl3 possess interesting thermoelectric properties and will be applicable as thermoelectric material.

First-Principles Calculations on Structural Property and Anisotropic Elasticity of γ₁-Ti₄Nb₃Al₉ under Pressure.

The effect of pressure on the structural property and anisotropic elasticity of -TiNbAl phase has been investigated in this paper by using first-principles calculations. The obtained bulk properties at zero pressure are in good agreement with the previous data. The structural property and elastic constants under pressures up to 40 GPa have been obtained. According to the elastic stability conditions under isotropic pressure, the phase is found to be mechanically stable under pressures up to 37.3 GPa. From the obtained elastic constants, the elastic moduli, anisotropic factors and acoustic velocities under different pressures have also been obtained successfully together with minimum thermal conductivities and Debye temperature. It is shown that the ductility of the phase is improved and its anisotropy and Debye temperature are enhanced with increasing the pressure.

Necessary and sufficient elastic stability conditions in 21 quasicrystal Laue classes

Abstract Mechanical stability is essential for solids and its stability criterion may date back to 75 years ago. Recently, the closed form necessary and sufficient conditions for elastic stability in all crystal classes have been investigated. Quasicrystals (QCs) are solids with long-range order and crystallographically forbidden rotational symmetries but without translational symmetry, attracting intense attentions in the last 30 years. In this work, we have explored the elastic constants and the elastic stability in detail for 1D, 2D and 3D QCs. All independent elastic constants and the closed form of necessary and sufficient conditions for elastic stability in all QCs classes are obtained, as a concise and pedagogical reference to stability criteria in aperiodic materials. Meanwhile, symmetry positions and stereographic projections of each QCs class are given as well.

Mechanical stability of Ni and Ir under hydrostatic and uniaxial loading

Two fcc crystals, Ni and Ir, are subjected to simulated isotropic and uniaxial tension along the direction. Their structural stability is assessed by analyzing phonon spectra that are calculated from first principles for different values of strain. A relevant analysis of elastic stability conditions is also performed. Predicted elastic instabilities correspond well to those associated with soft phonons with vanishing wavevectors. Although most of previous studies predicted that first instabilities in crystals correspond to macroscopic (elastic) instabilities, we found soft phonons of finite wavevectors at lower strains (and stresses) during both considered loadings in the crystal of Ir. Predicted instabilities were confirmed by our models of microscopic deformation.

Necessary and sufficient elastic stability conditions in various crystal systems

While the Born elastic stability criteria are well known for cubic crystals, there is some confusion in the literature about the form they should take for lower-symmetry crystal classes. Here we present closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in noncubic materials.

High pressure equation of state and ideal compressive and tensile strength of MgO single crystal: Ab-initio calculations

Ab-initio total energy calculations have been carried out on MgO single crystal as a function of hydrostatic compression to determine the 0 K isotherm, which is then utilized to derive the 300 K isotherm, isentrope, and Hugoniot of MgO. The theoretical isotherm, isentrope, and Hugoniot compare well with the experimental data. The shock parameters C0 and s obtained from theoretical Hugoniot are 6.74 km/s and 1.23 as compared to the experimental values of 6.87 km/s and 1.24, respectively. Having theoretically reproduced the various experimentally measured physical quantities at ambient conditions, the calculations have been extended to determine the ideal compressive and tensile strength of MgO single crystal subjected to uniaxial compressive and tensile loading along [001] direction under two deformation conditions, namely, “uniaxial strain condition” and “uniaxial stress condition.” Examination of elastic stability conditions suggests that for [001] compressive loading, the MgO single crystal will fail mechanically due to shear instability, whereas for expansion it will fail due to vanishing of tensile modulus. The ideal compressive strength under “uniaxial strain condition” and “uniaxial stress condition” is determined to be −283 GPa and −115 GPa, respectively. However, ideal tensile strength is evaluated to be 20 GPa and 11 GPa, respectively, for two loading conditions. Our results suggest that MgO single crystal will offer higher resistance against failure for compression as well as expansion along [001] direction under “uniaxial strain condition” than that for the “uniaxial stress condition.”

Symmetry breaking and other nonlinear elastic responses of metallic glasses subject to uniaxial loading

Topologically disordered metallic glasses (MGs) are known for exceedingly high elastic limit (2%–3%) and large local deformation at the onset of yielding in the form of shear banding. However, the manifestation of the large elastic deformation has not been taken into consideration in understanding the overall mechanical responses. By applying a finite deformation theory to initially isotropic solids under uniaxial loading, we investigate the nonlinear elastic behavior and its effects on mechanical properties. We take bulk metallic glass (BMG) Zr52.5Ti5Cu17.9Ni14.6Al10 as an example which is the only system by far with the experimentally measured nonlinear elastic constants up to the fourth order available for our theory. We show that the uniaxial loading breaks the isotropic symmetry of the MG and makes it transversely isotropic. We also predict the strain dependence of Poisson's ratio, Young's modulus, and anisotropic coefficients of the amorphous solids. Our work also gives the first estimate of the theoretical stress-strain relations and the elastic stability conditions under uniaxial loading from which we obtain the maximum tensile and compressive strengths and intrinsic deformation modes at the corresponding maximum stresses. Although depicting ideal scenarios, the theoretical results provide a useful reference for understanding mechanical response of MGs at large deformation.

Dynamic stability of fcc crystals under isotropic loading from first principles

Lattice dynamics and stability of four fcc crystals (Al, Ir, Pt and Au) under isotropic (hydrostatic) tensile loading are studied from first principles using the linear response method and the harmonic approximation. The results reveal that, contrary to former expectations, strengths of all the studied crystals are limited by instabilities related to soft phonons with finite or vanishing wavevectors. The critical strains associated with such instabilities are remarkably lower than those related to the volumetric instability. On the other hand, the corresponding reduction of the tensile strength is by 20% at the most. An analysis of elastic stability conditions is also performed and the results obtained by means of both approaches are compared.

Elastic stability ofβ-Tiunder pressure calculated using a first-principles plane-wave pseudopotential method

The elastic moduli ${c}^{\ensuremath{'}}$ and ${c}_{44}$ of $\ensuremath{\beta}\text{-Ti}$ with respect to external pressure $P$ (up to about 138 GPa) are calculated with a first-principles plane-wave pseudopotential method. The accuracy of the calculations regarding the plane-wave cut-off energy, $k$-point mesh, and transferability of the pseudopotentials is carefully tested. It is found that the critical pressure beyond which $\ensuremath{\beta}\text{-Ti}$ satisfies the elastic stability conditions is about 60 GPa. The Mulliken population analysis shows that both $s$ and $p$ electrons transfer to the $d$ orbitals with increasing pressure, however, the number of $s$ electrons starts to increase when the pressure exceeds about 70 GPa. The number of $d$ electrons at the critical pressure is about 2.96, in perfect agreement with the critical number of $d$ electrons for a stable bcc Ti-V alloy, which demonstrates the correlation between the stability of bcc metals and their $d$ orbital occupation. The bonding charge density calculations show charge accumulation on the $d\ensuremath{-}{t}_{2g}$ orbitals under high pressure, which may improve the elastic stability of $\ensuremath{\beta}\text{-Ti}$.

Thermal activation of shear modulus instabilities in pressure-inducedbcc→hcptransitions

Isostress molecular-dynamics (MD) simulations demonstrate that violations of the classical conditions for elastic stability predict the onset of $\mathrm{bc}\stackrel{\ensuremath{\rightarrow}}{c}\mathrm{hcp}$ transitions. Mechanical, geometric, and kinetic characteristics of the transitions are revealed in MD computations of shear moduli and the evolution of the crystal structure and its enthalpy. The transitions from bcc to hcp under isothermal-isobaric conditions are found to originate with thermally activated elastic instabilities that are associated with vanishing or diminishing shear moduli.

Covalent bond force profile and cleavage in a single polymer chain

We present here the measurement of the single-polymer entropic elasticity and the single covalent bond force profile, probed with two types of atomic force microscopes (AFM) on a synthetic polymer molecule: polymethacrylic acid in water. The conventional AFM allowed us to distinguish two types of interactions present in this system when doing force spectroscopic measurements: the first interaction is associated with adsorption sites of the polymer chains onto a bare gold surface, the second interaction is directly correlated to the rupture process of a single covalent bond. All these bridging interactions allowed us to stretch the single polymer chain and to determine the various factors playing a role in the elasticity of these molecules. To obtain a closer insight into the bond rupture process, we moved to a force sensor stable in position when measuring attractive forces. By optimizing the polymer length so as to fulfill the elastic stability conditions, we were able for the first time to map out the entire force profile associated with the cleavage of a single covalent bond. Experimental data coupled with molecular quantum mechanical calculations strongly suggest that the breaking bond is located at one end of the polymer chain.

Elastic stability for a discotic liquid crystal in the hexatic N+6 phase

The elastic stability of a discotic liquid crystal in the theoretically predicted hexatic N+6 phase against fluctuations of orientational order is tested. For this purpose, the author derives the elastic stability conditions for Frank constants of a discotic liquid crystal, and finds that the coupling constant gamma 3, which couples the director distortions to local rotations of the hexagonal two-dimensional lattice, is forced to be weak with respect to the other Frank constants, in order to preserve the long-range sixfold orientational order. He then shows that critical enhancements of Frank elastic constants, in the hexatic N+6 phase near the supposed continuous transition to the hexagonal discotic phase, fulfil the elastic stability conditions previously derived. Critical fluctuations of orientational order, therefore, are not able either to decorrelate the hexatic phase or to drive the transition to first order. Such a fluctuation-induced first-order transition, on the contrary, is known to play a role in smectic liquid crystals. We conclude that the N+6 phase remains orientationally correlated in the critical region, which proves the self-consistency of the model assuming such an intermediate phase, as yet experimentally undiscovered, between nematic and hexagonal discotic phases.

On the α-γ phase transition in solid nitrogen

The α-γ transition is discussed starting from the elastic stability conditions of the α-N2 phase. The α phase can be shown to become unstable on increasing pressure. The energy potential surface near the phase transition point has been calculated using an ab initio intermolecular potential. The probable path of the transition is traced on the surface.

Implications Of Hadamard's Conditions For Elastic Stability With Respect To Uniqueness Theorems

Introduction. The purpose of this paper is to discuss implications of Hadamard's condition for elastic stability (2, §269) with respect to uniqueness of solutions of boundary value problems in the theory of small deformations superimposed on large. We show that a slightly refined form of his condition implies a uniqueness theorem for displacement boundary value problems. We construct a counter-example showing that his condition does not imply uniqueness of solutions for one type of stress boundary value problem.