Higher Order Elastic Constants Research Articles

Temperature Dependent Behavior of Elastic and Ultrasonic Proprieties of Transition Metal Carbide Mo2C Superconductor

Abstract: Transition metal carbides exhibit peculiar chemical and physical properties, making them integral to industrial applications that demand performance under high temperatures In the case of the hexagonal transition metal carbide Mo2C superconductor, higher-order elastic constants were calculated to be temperature-dependent using an interactional potential model. Second-order elastic constants are used to determine other allied ultrasonic variables. Second-order coefficients are used to analyze the temperature variation of ultrasonic velocities along the z-direction of the superconductor. Furthermore, the temperature difference of Debye average velocity and thermal relaxation time are considered along the same direction. The temperature dependence of ultrasonic properties is explored in relation to thermal, elastic, and mechanical properties. Ultrasonic attenuation , resulting from phonon–phonon (p–p) interactions, is calculated at different temperatures .The study establishes that thermal conductivity is a core provider of the observed ultrasonic attenuation, particularly at higher temperatures. The mechanical and thermal properties of the Mo2C superconductor are superior at lower temperatures. Keywords:Transition metal carbide superconductor, Thermal conductivity, Ultrasonic properties, Elastic properties, Mechanical properties. PACS numbers: 43. 35. Cg; 62.20.Dc; 63.20.Kr.

Non-Linear Thermophysical Behaviour of Transition Metal Titanium

The propagation of ultrasonic waves in the hexagonal closed packed (hcp) structured lanthanide metal titanium has been investigated in the temperature range 300–1000 K. For this, initially the higher-order elastic constants (second-order elastic constants (SOECs) and third-order elastic constants (TOECs)) were computed using the Lennard-Jones interaction potential model. With the help of SOECs, other elastic moduli such as Young’s modulus (Y), bulk modulus (B), shear modulus (G), Poisson’s ratio (σ) and Pugh’s ratio (B/G) were computed using the Voigt-Reuss-Hill approximation. Three types of orientation-dependent ultrasonic velocities, including Debye average velocities, were evaluated using the calculated SOECs and density of titanium in the same temperature range. Thermophysical properties such as lattice thermal conductivity, thermal relaxation time, thermal energy density, specific heat at constant volume and acoustic coupling constant were evaluated under the same physical conditions. The ultrasonic attenuation due to phonon-phonon interaction is most significant under the chosen physical conditions. The ultrasonic properties of titanium are correlated with thermophysical properties to understand the microstructural features and nature of the material.

Symmetry constraints on the orientation dependence of high-order elastic constants for the hexagonal boron nitride monolayer.

Group theory is a powerful tool to explore fundamental symmetry constraints for the physical properties of crystal structures, e.g. it is well-known that only a few components of the elastic constants are independent due to the symmetry constraint. This work further applies group theory to derive constraint relationships for high-order elastic constants with respect to the orientation angle, where the constraint relationships are more explicit than the traditional tensor transformation law. These analytic symmetry constraints are adopted to explain the molecular dynamics simulation results, which disclose that the high-order elastic constants are highly anisotropic with an anisotropy percentage of up to 25% for the hexagonal boron nitride monolayer. The elastic constant is a basic quantity in the mechanics field, so its high anisotropy shall cause strong anisotropy for other mechanical properties. Based on the anisotropic high-order elastic constants, we demonstrate that Poisson's ratio is highly anisotropic for the hexagonal boron nitride at large strains. These findings provide fundamental insights into the symmetry dependence of high-order elastic constants and other mechanical properties.

Cross-modulation in guided wave propagation: how does it relate to the Luxemburg-Gorky effect?

The well-known Luxemburg-Gorky effect in radio waves has also been observed in elastic waves recently, which points to new possibilities for incipient damage detection. However, how the cross-modulation phenomenon of guided waves in a weakly nonlinear medium is related to the Luxemburg-Gorky effect remains an open question. This issue is investigated in this paper. Considering the third-order nonlinear elasticity of a plate waveguide, a theoretical framework is proposed to analyze the influence of the mode combination and mixing direction of a pair of single-frequency and modulated waves on the cross-modulated component generation. In particular, a codirectional shear-horizontal wave mixing scheme is highlighted which enables the generation of internally-resonant cross-modulated components at all frequencies. After verification by finite element simulation, mechanisms underpinning the cross-modulated components in the codirectional shear-horizontal wave mixing scheme are revealed through tactical tuning of the higher-order material elastic constants. Experiments are conducted to further confirm the phenomena and substantiate their relevance to the Luxemburg-Gorky effect. It is established that the cross-modulated components of guided waves can be generated and practically measured in a weakly nonlinear plate via both pure and mixed mechanisms as a result of the cubic nonlinearity instead of the quadratic nonlinearity. Compared with the conventional two-wave mixing methods based on quadratic nonlinearity, the cross-modulated components exhibit higher sensitivity to material microstructural changes, which is conducive to incipient damage detection. Although the observed nonlinear cross-modulation in guided waves shows similarities with the Luxemburg-Gorky effect, they stem from different mechanisms: the former from nonlinear elasticity and the latter nonlinear dissipation.

EFFECT OF PRESSURE ON ELASTIC CONSTANTS AND RELATED PROPERTIES OF RARE-EARTH INTERMETALLIC COMPOUND TBNIAL

The Lennard-Jones potential approach is used to investigate the effect of pressure on the ultrasonic and elastic properties of the rare-earth ternary TbNiAl intermetallic compound. The second- and third-order elastic constants of TbNiAl are considered using the potential model. The pressure-dependent higher-order elastic constants are studied, and it is observed that the elastic constants of the TbNiAl compound increased monotonously with pressure. The hexagonal TbNiAl compound is mechanically stable up to the pressure 20 GPa according to the Born elastic stability criteria. The Voigt-Reuss-Hill approach is used to compute such elastic parameters as Young’s modulus, bulk modulus, Poisson’s ratio, and shear modulus in the pressure range 0-45 GPa. Hardness, melting temperature, and anisotropy are also determined for the intermetallic TbNiAl compound. The pressure-dependent velocities and attenuation of ultrasonic waves in this ternary compound are evaluated. The computation results are also satisfactory in estimating the Debye temperature and thermal conductivity Kmin under different pressure. It is observed that TbNiAl has a significant anisotropy at zero pressure, which becomes stronger as the pressure increased. This ternary compound behaves as its purest form at higher pressure and is more ductile, which is demonstrated by the minimum attenuation.

Mechanical Stabilities and Properties of Graphene-like 2D III-Nitrides: A Review

Mechanical stabilities and properties are critical in real applications of materials, as well as material and machine design. With the success of graphene, graphene-like materials arose tremendous interest in the past few years. Different from bulk materials, two-dimensional (2D) materials have prominent non-linear elastic behaviors. Here, we briefly review the mechanical stabilities and properties of graphene-like 2D III-nitrides, including boron nitride (BN), aluminum nitride (AlN), gallium nitride (GaN), indium nitride (InN), and thallium nitride (TlN). These nitrides are excellent wide band gap semiconductors very suitable for modern electronic and optoelectronic applications. As a result, they play a central role in solid-state light-emitting devices. Their Young’s modulus, Poisson’s ratio, ultimate tensile strength, and elastic limits under various strains are extensively studied, as well as their high-order elastic constants and non-linear behaviors. These studies provide a guide for their practical applications and designs.

Temperature-Dependent Ultrasonic Properties of Semiconducting M<sub>2</sub>CO<sub>2</sub> (M= Ti, Zr, Hf) MXenes

Here, we have studied the elastic, ultrasonic, mechanical, and thermal behavior of temperature-dependent hexagonal oxygen-functionalized M2CO2 (M= Ti, Zr, Hf) MXenes. The higher-order linear and nonlinear elastic constants, viz., second-order (SOECs), and third-order (TOECs) have been computed using the Lenard Jones interaction potential model. For mechanical characterization, bulk modulus (B), shear modulus (G), Young's modulus (Y), Pugh's ratio (B / G), Poisson's ratio, and anisotropic index are evaluated using SOECs. Born's stability and Pugh's criteria are used to examine the nature and strength of the MXenes in all the temperatures. For the investigation of anisotropic behavior and its thermophysical properties, temperature-dependent ultrasonic velocities and thermal relaxation time have been calculated along with different orientations from the unique axis of the crystal. The ultrasonic attenuation (UA) of a longitudinal and shear wave due to phonon-phonon (p-p) interaction and thermoelastic relaxation mechanism were investigated for these oxygen-functionalized MXenes. Thermal conductivity is a principal contributor to the behavior of UA due to p-p interactions. Our analysis suggests that semiconductor Ti2CO2 MXenes show superior mechanical properties to other oxygen-functionalized MXenes. Computed elastic, ultrasonic, and thermal properties are correlated to evaluate the microstructural behavior of the materials useful for industrial applications.

A high-efficient strain-stress method for calculating higher-order elastic constants from first-principles

Though the method for calculating higher-order elastic constants (HOECs) have a long history, there still exist some unsolved issues (e.g. low efficiency), making the development of HOECs much slower than second-order elastic constants. In this paper, we present a general and efficient strain-stress method (SSM) for calculating HOECs from first-principles. In this method, the required number of strain modes is sharply cut down, which ensures a higher efficiency. The time spent on traditional methods is about 3-5 times that of SSM for calculating TOECs of diamond. By taking the HOECs into consideration, the convergence against maximum strain in SSM gets improved significantly, and the results of diamond, gold and magnesium obtained in SSM agree well with previous calculations by other methods. To accelerate the development of the calculation tools for HOECs, we present an algorithm, as well as an open source code, to deduce the strain modes and corresponding coefficients. Specially, we give an explicit expression of strain modes and corresponding coefficients for calculating TOECs in arbitrary symmetry and fifth-order elastic constants in CI (Laue group) symmetry. In addition, we make some extension, e.g. high-accurate numerical differentiation formula, of some existing methods.

Investigation of the Effect of Temperature on Ultrasonic, Mechanical and Thermal Properties in Single Silver Nanowire

The present paper reports the elastic, mechanical and thermophysical properties of silver nanowire (Ag NW) using ultrasonic techniques at temperature dependent. Higher order elastic constants are calculated using Coulomb and Born-Mayer potential up to second nearest neighbour. To compute mechanical parameters such as young modulus, bulk modulus, shear modulus tetragonal modulus, Poisson's ratio, fracture to toughness ratio and Zener anisotropy factor for finding imminent performance of the single silver nanowire at temperature dependent using second order elastic constants. The Ag NW is found to be brittle in nature at room temperature. Finally, we have evaluated the ultrasonic velocities, ultrasonic attenuation due to phonon–phonon interaction and thermoelastic relaxation for longitudinal wave and shear waves along <100>, <110> and <111> crystallographic directions in the temperature range 100-300K of silver nanowire using the higher order elastic constants. The attained results are discussed in correlation with available outcomes on these properties for the silver nanowire.

Volumetric and Ultrasonic Investigation of Acetamide in Aqueous Sodium Chloride

In present work, the Ultrasonic studies have been discussed for two different systems: 1) Acetamide + H2O and 2) Acetamide + H2O + NaCl (0.2 mol/kg) under different physical conditions like, temperature and concentration. Both the systems have been described in three phases of computation and discussion of a) Mechanical properties b) Ultrasonic velocity, density and thermal properties and c) Higher order elastic constants. These properties and constates provide the information about the intrinsic properties of the liquid system, for example information about bonding stability, kind of interaction etc. Therefore, this kind of study is worthwhile and interesting in view from number of aspects.

INVESTIGATION OF INTERMETALLIC GdFeAl TERNARY COMPOUND BY ELASTIC, THERMOPHYSICAL AND ULTRASONIC ANALYSIS

Higher order elastic constants were calculated of the intermetallic GdFeAl ternary compound using Lennard Jones potential approach. With the using of second order elastic constants (SOECs), other elastic moduli; shear modulus, bulk modulus, Young’s modulus, Pugh’s ratio, constants of elastic stiffness and Poisson’s ratio are estimated for mechanical and elastic characterization at room temperature. Born stability and Pugh's criteria are used to examine the nature and strength of the intermetallic ternary compound and found that it is mechanically stable compound. For the investigation of anisotropic behaviour and thermophysical properties, ultrasonic velocities and thermal relaxation time have been also calculated along with different orientations from theunique axis of the crystal. The temperature variation of ultrasonic velocities, Debye average velocity and thermal relaxation time along the z axis is evaluated using SOECs. The ultrasonic properties correlated with elastic, thermal and mechanical properties which is temperature dependent is also discussed. Ultrasonic attenuation was calculated at different temperatures due to phonon –phonon (p –p) interactions. The responsible reason of attenuation is p-p interactions; it was got that the thermal conductivity is a core contributor to the characteristic of ultrasonic attenuation as a role of temperature.GdFeAl ternary compound behave as its purest form at lower temperature and are more ductile demonstrated by the minimum attenuation

Nonlinear interaction of Rayleigh waves in isotropic materials: Numerical and experimental investigation

Surface treatment intensity monitoring is still an open and challenging nondestructive testing problem. For the estimation of residual stress with ultrasonic measurements, local linear and nonlinear elastic constants are needed as input. In this paper, nonlinear elastic-wave interactions (also called wave mixing or scattering) — namely, the generation of secondary ultrasonic waves in a nonlinear medium — are considered as a prospective means for near-surface nonlinear elastic parameter evaluation. The allowed interactions between bulk and surface waves, as well as the dependence of the scattering efficiency on the frequency and angle between source waves, were investigated through an analytical model, then compared with FEM simulations and experimental results. Finally, possible future steps for the development of the applied methods for the determination of near-surface higher-order elastic constants are discussed. In addition, several problem-relevant data processing procedures are presented.

Mechanical, Elastic and Thermal Properties of Hexagonal BC<sub>2</sub>N Superhard Material

The ultrasonic properties of the hexagonal BC2N superhard material were studied at temperature-dependent following the interaction potential model. Higher-order elastic constants are used for the determination of other ultrasonic parameters. The temperature variation of the ultrasonic velocities is evaluated along with different angles with z-axis (unique axis) of the crystal using the second-order elastic constants temperature variation of the thermal relaxation time, and Debye average velocities are also calculated along with the same orientation. The temperature dependency of the acoustic properties is discussed in correlation with elastic, thermal, and mechanical properties. It has been found that thermal conductivity and thermal energy density are the main contributors to the behavior of ultrasonic attenuation as a function of temperature. The responsible cause of attenuation is phonon-phonon interaction. Mechanical properties of BC2N superhard material at temperature 400K are better than at other temperatures because, at this temperature, it has low ultrasonic attenuation. Superhard material BC2N has many industrial and engineering applications.

Elastic, Mechanical and Thermophysical properties of Single-Phase Quaternary ScTiZrHf High-Entropy Alloy

Consequent to the interaction potential model, the high-order elastic constants at high entropy alloys in single-phase quaternary ScTiZrHf have been calculated at different temperatures. Elastic constants of second order (SOECs) helps to determine other ultrasonic parameters. With the help of SOECs other elastic moduli, bulk modulus, shear modulus, Young’s modulus, Pugh’s ratio, elastic stiffness constants and Poisson’s ratio are estimated at room temperature for elastic and mechanical characterization. The other ultrasonic parameters are calculated at room temperature for elastic and mechanical characterization. The temperature variation of ultrasonic velocities along the crystal's z-axis is evaluated using SOECs. The temperature variation of the average debye velocity and the thermal relaxation time (τ) are also estimated along this orientation axis. The ultrasonic properties correlated with elastic, thermal and mechanical properties which is temperature dependent is also discussed. The ultrasonic attenuation due to phonon – phonon (p-p) interactions is also calculated at different temperatures. In the study of ultrasonic attenuation such as a function of temperature, thermal conductivity appears to be main contributor and p- p interactions are the responsible reason of attenuation and found that the mechanical properties of the high entropy alloy ScTiZrHf are superior at room temperature.

Development of data-driven spd tight-binding models of Fe—parameterisation based on QSGW and DFT calculations including information about higher-order elastic constants

Quantum-mechanical (QM) simulations, thanks to their predictive power, can provide significant insights into the nature and dynamics of defects such as vacancies, dislocations and grain boundaries. These considerations are essential in the context of the development of reliable, inexpensive and environmentally friendly alloys. However, despite significant progress in computer performance, QM simulations of defects are still extremely time-consuming with ab-initio/non-parametric methods. The two-centre Slater–Koster (SK) tight-binding (TB) models can achieve significant computational efficiency and provide an interpretable picture of the electronic structure. In some cases, this makes TB a compelling alternative to models based on abstraction of the electronic structure, such as the embedded atom model. The biggest challenge in the implementation of the SK method is the estimation of the optimal and transferable parameters that are used to construct the Hamiltonian matrix. In this paper, we will present results of the development of a data-driven framework, following the classical approach of adjusting parameters in order to recreate properties that can be measured or estimated using ab-initio or non-parametric methods. Distinct features include incorporation of data from QSGW (quasi-particle self-consistent GW approximation) calculations, as well as consideration of higher-order elastic constants. Furthermore, we provide a description of the optimisation procedure, omitted in many publications, including the design stage. We also apply modern optimisation techniques that allow us to minimise constraints on the parameter space. In summary, this paper introduces some methodological improvements to the semi-empirical approach while addressing associated challenges and advantages.

Monitoring the Nonlinear Acoustic Behavior of Fresh Cementitious Materials during the Hardening Process Using Laser Doppler Vibrometry

A challenge in the field of material science and concrete technology is to associate material properties and behavior with changes in internal microstructure. A fundamental issue for planning, implementation, and quality control of construction projects is the fundamental understanding of the hardening process in freshly poured cement-based materials. Shortly after the mixing process, cementitious materials exhibit a substantial damping effect on ultrasonic wave propagation along with low-pulse velocity. The way a wave reflects and diffuses in the volume of a solid material can provide important information about internal heterogeneities. An important application of the wave propagation technique is the determination of layers within the material distinguished by unlike elastic properties. During the hardening process, the ultrasonic wave propagation exhibits a noticeable sensitivity at the point of phase change of the material, that is, the critical point at which the state of the suspension transforms from liquid to solid state. After that point, there is a continuous increase of pulse velocity and ultrasonic signal amplitude. The solidification point is of practical importance since at this point the load-bearing capacity of the composite material and its long-term behavior are based on the connectivity of the solid phase. This study aims to develop a nondestructive tool to monitor freshly poured cement-paste composites at early stages, during the hydration process, by means of nonlinear elastic waves. The measurement setup combined a contact ultrasonic transducer with a noncontact optical detection system, in which the principle of operation is based on the Doppler effect. This methodology enabled us to assess the amplitudes of harmonic vibrations of an acoustic wave propagating through the material with a specific fundamental frequency. This enabled the evaluation of important material properties, such as minute changes in the internal microstructure of fresh concrete during hardening, the evolution of nonlinearity parameters that relate to higher-order elastic constants of the material, as well as the ultrasonic wave velocity.

Interrogating the health condition of rails using the narrowband Rayleigh waves emitted by an innovative design of non-contact laser transduction system

The article reports an innovative optical system that is designed to interrogate the health condition of macroscopically intact rail specimens by measuring its inherent nonlinearity using the narrowband Rayleigh waves. A line-arrayed pattern is developed through the optical system that generates narrowband Rayleigh waves with high power on the surface of the rail. As a result of lattice-anharmonicity, a second harmonic is produced in the wave that is sensed by a scanning laser Doppler vibrometer. The spectral amplitudes of the first and generated second harmonics are used to calculate the inherent nonlinearity using an amplitude-based nonlinearity equation. These measurements are carried out on the head, web, and foot of the rail. The performance of the non-contact experiment is also compared with that of a contact experiment carried out using wedge transducers. The experimentally evaluated nonlinearity of the rail steel is further compared with that obtained using a physics-based nonlinearity equation that relies on the higher-order elastic constants. Agreement of the results shows that the new optical system is effective in generating Rayleigh waves in rails and thereby measuring the inherent nonlinearity of the rail track. The estimation of inherent nonlinearity may help in diagnosing the health status of the macroscopically intact rail specimens in terms of their microstructural consistency and level of dissolved impurities before fixing them on a track.

First-principles calculation of higher-order elastic constants using exact deformation-gradient tensors

We propose a general and easy-to-use method of the ab initio calculation of the higher-order elastic constants, which is based on the analytical formulas for the deformation-gradient tensors as functions of the Lagrangian strain. The method allows for elimination of the truncation errors in the Taylor expansion series of the deformation gradients and is particularly useful to calculate the fourth-order elastic constants, where large strains have to be applied. It also facilitates the calculation of the Lagrangian stress, which is helpful in determination of the strain-stress relations. To demonstrate the application of our approach, we derive the analytic formulas for the deformation gradients as functions of the Lagrangian strain tensors, which are used in calculations of the third-order elastic constants in trigonal crystals and the fourth-order elastic constants in cubic crystals. Then, we perform the ab initio calculations of the fourth-order elastic constants in face-centered-cubic aluminum. We discuss the results obtained using the strain-energy and strain-stress relations and analyze the errors of the fourth-order elastic constants which would be incurred when approximating the deformation gradients by the Taylor polynomials. We show that the relatively small truncation errors in the Taylor expansion series of the deformation gradients can cause significant deviations of the fourth-order elastic constants. This effect is larger for the strain-energy method than for the strain-stress approach. We find that in both methods, the deviations are particularly significant for the ${C}_{1155}$, ${C}_{1266}$, ${C}_{4455}$, ${C}_{1255}$, and ${C}_{1456}$ elastic constants and are mainly caused by the truncation errors in the nondiagonal elements of the Taylor expansion series of the deformation gradients.

Mechanical and thermophysical properties of high-temperature IrxRe1−x alloys

ABSTRACT The IrxRe1−x (0.1≤ x ≤0.7) alloys are hexagonal structured inclusion material used in an on-orbit communication satellite. The characteristic features of high-temperature alloys IrxRe1−x (0.1≤ x ≤0.7) are investigated by the theoretical evaluation of thermophysical and ultrasonic properties at room temperature. Initially, higher-order elastic constants of the alloys are calculated using the simple interaction potential model approach. With the help of this other elastic moduli, elastic stiffness constants and hardness parameters are estimated at room temperature for elastic and mechanical characterization. Later on, the ultrasonic velocity and thermal relaxation time of chosen alloys are evaluated utilizing calculated values of SOECs and lattice parameters within the same physical conditions. The orientation-dependent ultrasonic velocities and thermal relaxation time have been also evaluated for the determination of anisotropic behaviour and thermophysical properties. The obtained results are analysed to explore the inherent properties of IrxRe1−x alloys.

High-order nonlinear mechanical properties of g-SiC

Silicon carbide is one of the most important semiconductors with wide bandgaps and various applications including power electronics, nuclear fuel particles, hostile-environment electronics, and blue light emitting diodes. We investigate the nonlinear mechanical properties of a proposed graphene-like planar hexagonal silicon carbide (g-SiC) monolayer using first-principles calculations. The strength of g-SiC is about half that of graphene. The ultimate strain of g-SiC is 0.2, 0.25, and 0.19, in the direction of in armchair, zigzag, and biaxial, respectively. The Poisson’s ratio is 1.75 times of that of graphene. In the nonlinear elasticity regime, we obtain the high order elastic constants up to fifth order. The stiffness monotonically increases with pressure, has the same trend as that of second order elastic constants but opposes to that of Poisson’s ratio. There is a minimum at −4 GPa in the speed-pressure curve of compressive sound wave, different from the monotonic increment of shear waves. These theoretical mechanical properties provide elasticity limits for various applications of g-SiC.