Second-order Elastic Constants Research Articles

Comprehensive investigation of half Heusler alloy: Unveiling structural, electronic, magnetic, mechanical, thermodynamic, and transport properties

This study employs density functional theory (DFT) using Wien2k to comprehensively analyze the essential properties of two half-Heusler alloys, KCrSi and KCrGe. Our findings demonstrate that the ferromagnetic Type 2 configuration exhibits superior stability over non-magnetic and antiferromagnetic states for all KCrZ (Z = Si, Ge) alloys. These alloys exhibit complete spin polarization and half-metallic character, with calculated magnetic moments of 3 μB for both KCrSi and KCrGe. The Curie temperature (TC) is determined using the mean field approximation. Mechanical stability is assessed through second-order elastic constants (SOECs), and electronic properties are analyzed using local spin density approximation (LSDA), Perdew-Burke Generalized Gradient Approximation (PBE-GGA), and Tran-Blaha modified Becke-Johnson (TB-mBJ) schemes, confirming the retention of the half-metallic nature. The negative enthalpy of formation (ΔH) suggests material stability. The use of semi-classical Boltzmann theory, incorporated through the sophisticated scheme of BoltzTraP, explores transport coefficients. High pressures and temperature discrepancies in thermodynamics are considered by implementing the quasi-harmonic Debye approximation to illustrate stability. Finally, optical properties are summarized to assess the applicability of this alloy for optoelectronic applications. The overall characteristics of these particular alloys suggest potential applications in sustainable thermoelectric and optoelectronic features.

Elastic properties of TiC and TiN crystals in high temperature range

The elastic properties of crystals at high temperature are of significant interest as they affect the mechanical stability and performance of materials at elevated temperatures. In present study a theory for evaluating the temperature variation of second third and fourth order elastic constants for face centred cubic crystal structure solids is used on the basis of Coulomb and Born-Mayer potential using nearest-neighbour distance and hardness parameter. The theory is first applied to get the second order elastic constants (SOECs) and third order elastic contants (TOECs) for TiC and TiN crystals at different temperatures up to 500 K. In addition, the elastic constants thus obtained are used to evaluate the first order pressure derivatives (FOPDs) SOECs and TOECs. The elastic properties of these crystals at high temperature are of significant interest and are related to other important material properties such as thermal expansion, thermal conductivity, phase transformations, creep behaviour, oxidation resistance, and high-temperature strength.The results obtained show that the second order elastic constants and third order elastic constants of TiC are highest, so mechanical properties of TiC will be better than TiN, which makes it stiffer and more resistant to deformation under an applied load. These properties make TiC a popular material for cutting tools, wear-resistant coatings, and other high-performance applications.

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.

Ultrasonic non-destructive evaluation of w-GaSe at different temperatures

ABSTRACT The present work includes non-destructive evaluation of mechanical, thermal and ultrasonic properties of inorganic semiconducting wurtzite gallium selenide (w-GaSe) material using Lenard Jones’s potential approach at different temperatures. For elastic and mechanical properties, second-order elastic constants (SOECs), elastic moduli, anisotropy factors are estimated within the temperature range of 300-1500K. The ultrasonic and thermo-physical properties are calculated within the same temperature range utilising estimated SOECs, density and lattice parameters of the chosen material. The elastic, mechanical, and ultrasonic properties of the chosen semiconducting material have been found to decrease with an increase in temperature. The obtained results have been compared and analysed for justification and to explore the inherent properties of GaSe for semiconductor manufacturing industries.

ElasTool v3.0: Efficient computational and visualization toolkit for elastic and mechanical properties of materials

Efficient computation and visualization of elastic and mechanical properties are crucial in the selection of materials and the design of new materials. The ElasTool v3.0 toolkit marks a significant advancement in the computational analysis and visualization of elastic and mechanical properties of materials, essential in material selection and design. This enhanced version extends beyond standard calculations like elastic tensor, Young's modulus, bulk modulus, and Poisson's ratio. It introduces capabilities for computing minimum thermal conductivity, linear compressibility, rendering the Christoffel equation, and elastic energy density. Notably, it integrates advanced visualization tools, including compatibility with Plotly and Elate web platforms for interactive web-based property exploration. A key feature of ElasTool v3.0 is the implementation of second-order elastic constants (SOECs) for tubular 2D-based nanostructures and nanotubes. Leveraging high-efficiency strain-matrix sets (OHESS), the toolkit now facilitates efficient computation of elastic constants and mechanical properties at both zero and finite temperatures for 1D, 2D, and 3D dimensions. ElasTool is openly accessible on GitHub: https://github.com/elastool. Program summaryProgram Title: ElasTool v3.0CPC Library link to program files:https://doi.org/10.17632/9hpgmspfmk.1Licensing provisions: GNU General Public License, version 3Programming language: Python 3Nature of problem: A computational toolkit that can efficiently compute the elastic and mechanical properties of materials using ab initio methods and provide advanced visualization capabilities is crucial to accurate material analysis.Solution method:ElasTool addresses this need by incorporating high-efficiency strain-matrix sets that require only small strain sets with ab initio methods such as density functional theory and molecular dynamics. This package is versatile and adept at calculating elastic constants for both 2D and 3D structures, including tubular 2D-based nanostructures and nanotubes and 1D nanoribbons at zero and finite temperatures. Beyond basic elastic moduli, ElasTool now boasts advanced visualization capabilities and computes additional critical properties such as minimum thermal conductivity, elastic energy density, and linear compressibility. This enhancement transforms ElasTool into a comprehensive tool for accelerated material design and modeling, and advanced visualization, offering both efficiency and depth in material property analysis.Additional comments including restrictions and unusual features:ElasTool is currently integrated with the Vienna Ab initio Simulation Package (VASP). Adapting to other electronic structures is straightforward.ElasTool offers serial and parallel execution. Depending on the system size, the number of strains, the nature of the calculations (zero or finite temperature), and the computing architecture, the computing time can vary from a minute to as long as 15 hours.

Topological semimetals in the ZrB5 (B = Se, Te) material class: Weyl points and electronic properties

In the present work, the electronic structure, elastic parameters, density of states (partial and total), optical properties, and charge density of ZrB5 (B = Se, Te) have been investigated by means of first principles calculations. The generalized gradient approximation has been used for modeling the exchange-correlation effects. It has been observed that the calculated lattice parameter values are in agreement with the values in the literature. The second-order elastic constants were calculated, and the other related quantities have also been estimated. The electronic band structures and the partial density of states corresponding to these band structures of ZrSe5 and ZrTe5 are examined, and it is understood that ZrTe5 and ZrSe5 are narrow band semiconductors or semimetals. Finally, the electron energy loss function (ELS) spectra and charge density of ZrB5 are calculated and interpreted.

A critical comparative review of generalized gradient approximation: the ground state of Fe3Al as a test case

Quantum-mechanical calculations have become an indispensable tool for computational materials science due to their unprecedented versatility and reliability. Focusing specifically on the Density Functional Theory (DFT), the reliability of its numerous implementations was tested and verified mostly for pure elements. An extensive testing of binaries, ternaries and more-component phases is still rather rare due to a vast configurational space that is nearly infinite already for binaries. Importantly, there are well known cases of theoretical predictions contradicting experiments. In this paper, we analyze the failure of theory to reproduce correctly the ground state of the Fe3Al intermetallic compound. Namely, most exchange-correlation (xc) energies within the generalized gradient approximation (GGA) predict this material in the L12 structure instead of the experimentally found D03 structure. We test the performance of 36 combinations of 6 different GGA parametrizations and 6 different Fe and Al potentials. These combinations are evaluated employing a multi-dimensional multi-criteria descriptor {, a, {}, {C ij }} consisting of fundamental thermodynamic properties (energy difference between the D03 and L12 structures), a structural aspect (lattice parameter a), electronic-structure related magnetic properties (local magnetic moments of Fe atoms {}) and elastic properties (a complete set of second-order elastic constants {C ij }). Considering the thermodynamic stability as the most critical aspect, we identify the Perdew–Wang (1991) GGA xc-functional parametrization as the optimum for describing the electronic structure of the Fe3Al compound.

Large difference of lattice thermal conductivity between thermoelectric compounds Cu3VSe4 and Tl3VSe4: Elasticity, anharmonicity and chemical bonding from first-principles calculation

The elasticity has a great impact on thermoelectric efficiency and working service life as thermoelectric device. In this work, the large difference of lattice thermal conductivity (κL) between thermoelectric materials Cu3VSe4 and Tl3VSe4 was investigated by calculating their second-order (Cij) and third-order elastic constants (Cijk). The mechanical properties and thermal expansion coefficients were also evaluated. These results show that Cij of Cu3VSe4 and Tl3VSe4 are relatively overall weak. Particularly, in contrast to Cu3VSe4, Tl3VSe4 displays larger negative Cijk, revealing its stronger intrinsic anharmonicity. The relatively smaller elasticity of Tl3VSe4 derives from its weaker Tl-Se and V-Se chemical bonds as compared with that of Cu3VSe4. Finally, the increased anharmonicity results in a non-linearly mechanical behavior and reducing the κL with the rise of temperature. The research provides insight into the relationship of elasticity, anharmonicity and thermal expansion and κL in view of elasticity and will be useful for designing and optimizing of thermoelectric materials with high performance.

Investigating elastic constants across diverse strain-matrix sets

Elastic constants and mechanical properties play a pivotal role across multiple disciplines and engineering applications. We introduced the optimized high-efficient strain-matrix set (OHESS) that determines the second-order elastic constants of materials using the stress–strain method. Herein, we systematically investigate the computational efficiency of OHESS across a broad range of crystal systems and compare it with other notable stress–strain approaches, such as the single-element strain-matrix sets and the universal linear-independent coupling strains. Notably, our data affirm the superior efficacy of OHESS among the strain-matrix sets under consideration. We believe OHESS will markedly improve computational efficiency in determining the elastic constants and mechanical properties, becoming an indispensable tool for material research, design, and high-throughput screening.

Elastic and thermodynamic properties of B2-MgX intermetallics: A high throughput first-principles investigation

Precipitation strengthening is an effective approach in Mg alloys, and hence, it is worthwhile investigating the properties of the Mg-containing intermetallics. In the present work, the thermodynamic and mechanical properties of B2-MgXs (69 different elements) are calculated by high-throughput first-principles calculations. The static properties, including equilibrium volume, equilibrium energy, and bulk modulus, and thermodynamic properties, including linear thermal expansion coefficient (LTEC), are predicted. Meanwhile, the second-order elastic constants (SOECs) and third-order elastic constants (TOECs) are calculated using an efficient strain-stress method. The consistency between our results and the limited experimental or previous theoretic work confirms the high reliability of the present work. Using SOECs and equilibrium energy, the stability of MgXs is assessed from mechanics, energy and lattice dynamics, and 33 (out of 69) stable compounds are screened out. According to Young's and shear modulus, the MgXs are divided into four classes, and the first two classes present high modulus, high ductility, and reasonable anisotropy, equipping those compounds as promising candidates for precipitation strengthening in Mg alloys. In addition, the pressure and temperature dependence of SOECs is estimated using TOECs and LTEC. Furthermore, the present work provides abundant fundamental data for the design of new Mg alloys.

Theoretical investigation on the elastic and mechanical properties of high-entropy alloys with partial replacement of Sc in Hf0.25Ti0.25Zr0.25Sc0.25−x Al x (x ≤ 15 %)

Abstract The theoretical assessment of mechanical and elastic properties is used to analyze the distinctive properties of high entropy alloys (HEAs) at room temperature. Using Lennard–Jones potential model, the second order elastic constants (SOECs) and third order elastic constants (TOECs) have been determined for the HEAs Hf0.25Ti0.25Zr0.25Sc0.25−x Al x (x ≤ 15 %) in their hexagonal close-packed (hcp) phases. SOECs have been used to calculate mechanical constants, Poisson’s ratio, Pugh’s ratio, Kleinman’s parameter. In order to determine the anisotropic behaviour of the selected HEAs, the elastic anisotropy has also been computed at room temperature. All the HEAs under consideration have anisotropy parameters that are not equal to one, indicating anisotropic behaviour. Later, the Grüneisen parameters were estimated for the chosen HEAs Hf0.25Ti0.25Zr0.25Sc0.25−x Al x (x ≤ 15 %) along longitudinal and shear modes of wave propagation. Analysis of the research results reveals the inherent properties of HEAs.

Discovery of new MAX-phase-like layered ternary carbide V8P6C: Crystal structure, thermal expansion, and elastic properties

Due to the laminated structure, MAX phases and MAX-phase-like compounds possess outstanding damage tolerance capability with good thermal/electrical conductivity and other charming functional properties, showing a bright future for structural-functional uses. Here, a new MAX-phase-like ternary carbide V8P6C with layered characteristics was discovered. Contrary to the alternate stacking of hexagonal-arranged M/A/X atom layers in MAX phases, V8P6C has a layered structure formed by a repeated stacking of the slabs consisting of V6C-octahedrons and VP6-distorted-octahedrons in three-atomic layers thick. The thermal expansion anisotropy was revealed, with the thermal expansion coefficients (TECs) along a-axis, c-axis, and the average value, equal to αa=8.55(5) μK−1, αc=10.23(5) μK−1, and αL=9.14(5) μK−1, respectively. The dilation along the c-axis was mainly dominated by out-plane V-P bonds between layered slabs. According to the pressure-dependent lattice parameters, the polycrystalline bulk modulus (B0 = 185(9) GPa) and high compressibility anisotropy factor (Ba/Bc = 1.64) was found. Meanwhile, the second-order elastic constants were calculated, and the elastic moduli, E=303 GPa, B=198 GPa, G=122 GPa, and ν = 0.246, were obtained. And the weak connection between layer slabs by out-plane V1-P bond was revealed by the bond stiffness model, with a bond stiffness close to the M-A bond in MAX phases. Furthermore, good damage tolerance capability was predicted according to Paugh's ratio (G/B=0.616) and Cauchy pressure (Pa = 0 GPa, Pc = -7.5 GPa), even better than those of typical MAX phases. The discovery of V8P6C provides a new member of MAX-phase-like damage-tolerant ceramic with relatively low density, moderate thermal expansion, and anisotropic compressibility, and the unique layered structure is inspiring for exploring new layered ternary ceramics.

Comment on: “The structural, elastic, electronic and optical properties of MgCu under pressure: A first-principles study”

Rahman et al. [International Journal of Mod. Phys. B 30, 1650199 (2016)] found that MgCu intermetallic compound with CsCl-type (B2) structure becomes unstable under pressure at about 15[Formula: see text]GPa. This prediction has been made using an elastic instability condition for second-order elastic constants given by Born. They determined the elastic constants using Hooke’s law for the linear stress–strain relationship which does not hold good at high pressures. It has been shown here that the values of elastic constants for MgCu at high pressures determined by Rahman et al. are not consistent with the values of bulk modulus computed from the Birch–Murnaghan equation of state (BM-EOS). We have used the Tallon formulation based on the thermodynamics of elastic deformation to estimate elastic constants which yields results for the bulk modulus of MgCu at different pressures in good agreement with those determined from the BM-EOS. It has been found that MgCu remains stable up to about 20 GPa which is significantly higher than the limit of elastic stability predicted by Rahman et al.

A comment on the paper “The structural, elastic, electronic and optical properties of MgCu under pressure: A first-principles study”

Rahman et al. [International Journal of Mod. Phys. B 30, 1650199 (2016)] found that MgCu intermetallic compound with CsCl-type (B2) structure becomes unstable under pressure at about 15[Formula: see text]GPa. This prediction has been made using an elastic instability condition for second-order elastic constants given by Born. They determined the elastic constants using Hooke’s law for the linear stress–strain relationship which does not hold good at high pressures. It has been shown here that the values of elastic constants for MgCu at high pressures determined by Rahman et al. are not consistent with the values of bulk modulus computed from the Birch–Murnaghan equation of state (BM-EOS). We have used the Tallon formulation based on the thermodynamics of elastic deformation to estimate elastic constants which yields results for the bulk modulus of MgCu at different pressures in good agreement with those determined from the BM-EOS. It has been found that MgCu remains stable up to about 20 GPa which is significantly higher than the limit of elastic stability predicted by Rahman et al.

Ab Initio Studies of Structural and Mechanical Properties of NH3, NO, and N2O Hydrates.

The investigation on the mechanical properties of clathrate hydrate is closely related to the exploitation of hydrates and gas transportation. In this article, the structural and mechanical properties of some nitride gas hydrates were studied using DFT calculations. First, the equilibrium lattice structure is obtained by geometric structure optimization; then, the complete second-order elastic constant is determined by energy-strain analysis, and the polycrystalline elasticity is predicted. It is found that the NH3, N2O, and NO hydrates all have high elastic isotropy but are different in shear characteristics. This work may lay a theoretical foundation for studying the structural evolution of clathrate hydrates under the mechanical field.

Mech2d: An Efficient Tool for High-Throughput Calculation of Mechanical Properties for Two-Dimensional Materials.

Two-dimensional (2D) materials have been a research hot topic in the passed decades due to their unique and fascinating properties. Among them, mechanical properties play an important role in their application. However, there lacks an effective tool for high-throughput calculating, analyzing and visualizing the mechanical properties of 2D materials. In this work, we present the mech2d package, a highly automated toolkit for calculating and analyzing the second-order elastic constants (SOECs) tensor and relevant properties of 2D materials by considering their symmetry. In the mech2d, the SOECs can be fitted by both the strain-energy and stress-strain approaches, where the energy or strain can be calculated by a first-principles engine, such as VASP. As a key feature, the mech2d package can automatically submit and collect the tasks from a local or remote machine with robust fault-tolerant ability, making it suitable for high-throughput calculation. The present code has been validated by several common 2D materials, including graphene, black phosphorene, GeSe2 and so on.

DFT-continuum characterization of third-order elasticity of sI methane hydrates under pressure

Methane gas hydrates (GHs) are polyhedral crystalline guest-host materials found under high pressure and low-temperature conditions, which can serve as an energy source. Previous work on methane GH material physics was limited to simple linear models, which only involves second-order elasticity. However, this is not fully suited to high-stress load conditions in technological applications and fundamental material physics. For other material systems, it has been demonstrated that third-order elasticity and pressure derivatives of second-order elasticity have a strong and hence significant correlation. To narrow a critical theory-simulation gap in gas hydrates materials research, in this work we expand prior work from second-order elastic constants (SOECs) to third-order elastic constants (TOECs). By using the open-source Python tool Elastic3rd and the DFT calculation software Vienna Ab initio Simulation Package (VASP), we found that the non-linear fitting involving TOECs gave a better overall prediction and a smaller root-mean-square deviation on pressure-strain evaluation when compared with linear fitting. In addition, the non-linear fitting provides robust results on the piezo-effect on the shear constant C44 and the ductile-to-brittle transition (P = −0.5 GPa). These results are not achievable from previous work based on a linear model and these findings prove that non-linear models, including TOECs, are needed under high pressures. In addition, this research includes a detailed analysis of the calculation of TOECs and mechanical properties to study pressure stability limits and ductile-brittle transitions. Together the results, findings, and analyses from this work are a novel and significant contribution to the material physics knowledge of gas hydrates and hydrogen-bonded crystalline materials.

Ab-initio study of C2/c, Cmca-12, Pbcn and P6122 phases of solid hydrogen

We investigate structural, electronic, phononic and mechanical properties of the C2/c, Cmca-12, Pbcn and P6122 phases of solid hydrogen in the 100–300 GPa pressure region using ab-initio methods. The computed structural parameters, PV-equation of states (EOSs), electronic and phononic properties show a good agreement with the earlier values. By computing second-order elastic constants, we establish the mechanical stability of all phases in the studied pressure region and these values were used to compute the average sound velocities and Debye temperatures. All these quantities exhibit usual pressure behaviour. Further, we found that at 100 GPa, C2/c and P6122 phases are dynamically unstable and Pbcn phase is unstable in the entire pressure region. The effect of vdW corrections is also tested for C2/c and P6122 phases at 100 GPa.

Pressure Dependent Elastic and Thermo-Physical Properties of U Ternaries with ZrNiAl Structure Compounds

bstract: The Thermophysical and ultrasonic aspects of U- ternaries are examined theoretically under high pressure. In order to determine the second- and third-order elastic constants of U- ternaries (URhAl and ThRhAl) compounds under pressure conditions (0-45GPa), the potential model technique has been used. The assessed second-order elastic constants are used along with the pressure-dependent ultrasonic velocities, thermal relaxation time, and other significant and important thermophysical data to determine the orientation. It is observed that thermal relaxation time and mechanical & thermal properties exhibit an increasing trend with increasing pressure for U-ternaries URhAl and ThRhAl compounds. The effect of increasing pressure on the URhAl and ThRhAl compounds shows up as an increase in elastic constants, ultrasonic velocities, ultrasonic attenuation, and Debye temperature. The ratio B/G increases with pressure which indicates that the materials are ductile in nature. We have used the approximate values of SOECs, density, and lattice properties in calculating the melting point, ultrasonic velocity, and thermal conductivity.

Theoretical study of second and third order elastic constants of β-SiC

First principles calculations of the second and third order elastic constants of the cubic silicon carbide β-SiC have been accomplished using the density functional theory within the local density approximationand the pseudopotential plane-wave method with the Hartwigsen Goedecker Hutter scheme. The secondorder elastic constants Cij compared fairly well with those previously measured by one of us using theBrillouin light scattering technique (P. Djemia) [1]. The ab-initio calculations include parameterspressure dependence determinations in relation with the structural transformation from a zinc Blende toa rocksalt structure. The transition pressure at which arises elastic instabilities is found to be Pt = 113GPa. Also, we investigate the effects of anharmonicity by calculating the third order elastic constantsC_ijk . The experimental values are still unknown and comparisons with our calculations are suitable in thefuture.