Temperature Dependence Of Elastic Constants Research Articles

Pressure and temperature dependent ab-initio quasi-harmonic thermoelastic properties of tungsten

We present the ab-initio temperature and pressure dependent thermoelastic properties of body-centered cubic tungsten. The temperature dependent quasi-harmonic elastic constants (ECs) are computed at several reference volumes including both the phonon and the electronic excitations contribution to the free energy and interpolated at different temperatures and pressures. Good agreement with the experimental ECs on a single crystal at ambient pressure is found. The pressure and temperature dependence of the shear sound velocity measured on polycrystalline tungsten by Qi et al is also in agreement with theory. Some discrepancies are found instead for the compressional velocity at high temperature and this is attributed to the temperature derivative of the bulk modulus, higher in theory than in experiment. These conclusions are reached both by PBE and by PBEsol functionals. The two give elastic properties with a similar pressure and temperature dependence although the latter is closer to experiment at 0 K.

Accurate Surface and Finite-Temperature Bulk Properties of Lithium Metal at Large Scales Using Machine Learning Interaction Potentials.

The properties of lithium metal are key parameters in the design of lithium-ion and lithium-metal batteries. They are difficult to probe experimentally due to the high reactivity and low melting point of lithium as well as the microscopic scales at which lithium exists in batteries where it is found to have enhanced strength, with implications for dendrite suppression strategies. Computationally, there is a lack of empirical potentials that are consistently quantitatively accurate across all properties, and ab initio calculations are too costly. In this work, we train a machine learning interaction potential on density functional theory (DFT) data to state-of-the-art accuracy in reproducing experimental and ab initio results across a wide range of simulations at large length and time scales. We accurately predict thermodynamic properties, phonon spectra, temperature dependence of elastic constants, and various surface properties inaccessible using DFT. We establish that there exists a weak Bell-Evans-Polanyi relation correlating the self-adsorption energy and the minimum surface diffusion barrier for high Miller index facets.

Temperature-Dependent Elastic Properties of B4C from First-Principles Calculations and Phonon Modeling

Boron carbide plays a crucial role in various extreme environment applications, including thermal barrier coatings, aerospace applications, and neutron absorbers, because of its high thermal and chemical stability. In this study, the temperature-dependent elastic stiffness constants, thermal expansion coefficient, Helmholtz free energy, entropy, and heat capacity at a constant volume (Cv) of rhombohedral B4C have been predicted using a quasi-harmonic approach. A combination of volume-dependent first-principles calculations (density functional theory) and first-principles phonon calculations in the supercell framework has been performed. Good agreement between the elastic constants and structural parameters from static calculations is observed. The calculated thermodynamic properties from phonon calculations show trends that align with the literature. As the temperature rises, the predicted free energy follows a decreasing trend, while entropy and Cv follow increasing trends with temperature. Comparisons between the predicted room temperature thermal expansion coefficient (TEC) (7.54×10−6 K−1) and bulk modulus (228 GPa) from the quasi-harmonic approach and literature results from experiments and models are performed, revealing that the calculated TEC and bulk modulus fall within the established range from the limited set of data from the literature (TEC = 5.73–9.50 ×10−6 K−1, B = 221–246 GPa). Temperature-dependent Cijs are predicted, enabling stress analysis at elevated temperatures. Overall, the outcomes of this study can be used when performing mechanical and thermal stress analysis (e.g., space shielding applications) and optimizing the design of boron carbide materials for elevated temperature applications.

The thermoelastic properties of monolayer covalent organic frameworks studied by machine-learning molecular dynamics.

Two-dimensional (2D) covalent organic frameworks (COFs) are emerging as promising 2D polymeric materials with broad applications owing to their unique properties, among which the mechanical properties are quite important for various applications. However, the mechanical properties of 2D COFs have not been systematically studied yet. Herein, a machine-learned neuroevolution potential (NEP) was developed to study the elastic properties of two representative monolayer 2D COFs, namely COF-1 and COF-5. The trained NEP enables one to study the elastic properties of 2D COFs in realistic situations (e.g., finite size and temperature) and possesses greatly improved computational efficiency when compared with density functional theory calculations. With the aid of the obtained NEP, molecular dynamics (MD) simulations together with a strain-fluctuation method were employed to evaluate the elastic constants of the considered 2D COFs at different temperatures. The elastic constants of COF-1 and COF-5 monolayers were found to decrease with an increase in the temperature, though they were almost isotropic irrespective of the temperature. The thermally induced softening of 2D COFs below a critical temperature was observed, which is mainly attributed to their inherent ripple configurations at finite temperatures, while above the critical temperature, the damping effect of anharmonic vibrations became the dominant factor. Based on the proposed mechanisms, analytical models were developed for capturing the temperature dependence of elastic constants, which were found to agree with the MD simulation results well. This work provides an in-depth insight into the thermoelastic properties of monolayer COFs, which can guide the development of 2D COF materials with tailored mechanical behaviors for enhancing their performance in various applications.

Study on the Internal Stress and Thermal Anisotropy in Magnesium Alloys Using a Thermal Elastic Viscoplastic Self-Consistent Model.

A thermal elastic viscoplastic self-consistent model is utilized to examine the thermal stress induced by the thermal anisotropy of single crystals during heat treatments. This model considers temperature-dependent elastic constants and critical resolved shear stress associated with thermal dilation. Simulation results demonstrate that under cooling, the elastic lattice strain increases significantly when constrained compared to unconstrained cooling. The deformation mechanism observed under cooling with constraint resembles tension along the constrained direction at room temperature. Polycrystals offer more deformation mechanisms to accommodate thermal anisotropy compared to single crystals, resulting in lower applied stress at the constrained boundary. Among the various observed textures, the maximum amplitude of residual lattice strain follows the following order: rolled > extruded > random. Lower thermal anisotropy in the entire polycrystal structure leads to reduced internal stress. For a single crystal within aggregates, the {00.2} plane experiences tensile lattice strain, while the {10.0} and {11.0} planes undergo compressive lattice strain due to the greater contraction of single crystals along the <c> direction compared to the <a> direction during cooling.

A prediction of the thermodynamic, thermophysical, and mechanical properties of CrTaO4 from first principles

AbstractIt is reported that the self‐forming CrTaO4 oxide scale can protect refractory high‐entropy alloys from oxidation, superior to Cr2O3. In this paper, the phase stability, mechanical, and thermal properties of three polymorphous phases of CrTaO4 are systematically investigated from first‐principles density functional theory calculations. The mechanical properties predicted using the strain–energy methods indicated that all three phases are mechanically stable. The temperature dependence of elastic constants and polycrystalline moduli of three phases demonstrated the thermal softening as temperature increase. The Helmholtz‐free energies as a function of volume and temperature are derived from phonon dispersions within the quasi‐harmonic approximation at six strained volumes. The calculated apparent bulk coefficients of thermal expansion of these three phases are evaluated, the highest value approximately 13.4× 10−6 K−1 within a temperature range of 500–2000 K for the rutile I41md phase. The lattice thermal conductivity calculated by the Debye–Callaway model suggested that the rutile type I41md phase has the lowest value of approximately 2.1 W/m/K at 1800 K. The other two phases, C2/m and P2/c, exhibit higher values due to relatively lower Grüneisen parameters and larger phonon velocities. The melting point of CrTaO4 is predicted to be between 1975 and 2449 K using ab initio molecular dynamics simulations. This work provides a comprehensive theoretical understanding of the thermodynamic, mechanical, and thermal properties for the new material CrTaO4 and serves as an example of a viable computational design strategy for improved oxidation resistance of refractory alloys at high temperatures.

Elastemp — A workflow to compute the quasi-harmonic temperature dependent elastic constants of materials

Elastic constants characterize the stiffness of a material. A linear relationship between the stress and strain tensors in the limit of infinitesimal deformation is used to define and compute the elastic constants. Typically, this is computed at zero temperature by deforming the simulation box in one of the six directions and computing the stress tensor. Calculating elastic constants at finite temperature is more challenging owing to large fluctuations and thermal noise. Here, we introduce a semi-automated workflow — Elastemp, to obtain the quasi-harmonic elastic constants of materials as a function of temperature. The workflow integrates with electronic structure packages such as VASP and PHONOPY to get the quasi-harmonic energies. The workflow is capable of estimating the zero temperature elastic constants, thermal expansion coefficients of materials and temperature dependent elastic constants. The predictions for a set of representative test cases with different crystal symmetries (Al, Diamond, Titanium nitride (TiN) and α-Ti) are compared with experiments and used to demonstrate the efficacy of our workflow.

Ab initio prediction of temperature-dependent stability of heterogeneous B19′ phase in TiNi alloy using atomistically informed Eshelby’s ellipsoidal inclusion

In this study, we energetically predicted the temperature-dependent stability of the heterogeneous B19′ phase in the B2 matrix of TiNi alloys using density functional theory (DFT) and phonon analysis informed Eshelby’s ellipsoidal inclusion. The temperature-dependent eigenstrains and elastic constants for Eshelby’s ellipsoidal inclusion were calculated using DFT and phonon analysis under a quasi-harmonic approximation. The stable orientation of the disk-shaped B19′ phase in the B2 matrix and its total strains were evaluated with respect to temperature using Eshelby’s ellipsoidal inclusion analysis. Using the total strains, the elastically deformed atomic structure of the heterogeneous B19′ phase in the B2 matrix was determined, and its temperature-dependent free energy was calculated using DFT calculations and phonon analysis. Comparing the temperature-dependent free energies of the B2 and elastically deformed B19′ structures, we successfully predicted that the transformation between the two phases occurs at 300 K, which agrees with experimental observations. Moreover, it is shown that the temperature-dependent difference in the elastic constants between the B19′ phase and B2 matrix influences the phase transformation, which is the origin of the shape-memory effect of TiNi alloy.

Microscopic origin of the abnormal elastic behavior accompanying the superconducting transition in Nb3Sn crystals: An extended ab initio study

As a promising next-generation material for superconducting radiofrequency cavities, superconducting Nb3Sn, once developed for fabricating a high-field magnet, has attracted tremendous research interest due to the significant potential for both compact and large scale accelerator applications. However, the intrinsic physical origin, especially at atomic and electronic scale, of the abnormal elastic behavior accompanying the superconducting transition in Nb3Sn crystals is still controversial and not fully understood yet. Through an extended atomic and electronic modelling of electronic structure evolution arising from the perturbation of lattice strain and temperature, we proposed an analytical model for depicting the abnormal temperature-dependent elastic constants and transition resistivities of superconducting Nb3Sn. The extended ab initio modeling takes into account the interaction of the d electrons with the strain, the strain-modulated electronic structure evolution and the accompanied variations in the density of states at the Fermi level, and the competition between the lattice contribution and the electron contribution in governing the abnormal elastic response along with the superconducting transition of Nb3Sn. The model predictions of the elastic constants and the superconducting phase transition resistivities of single crystal and polycrystalline Nb3Sn qualitatively agree with the experimental observations. The extended ab initio studies indicate the abnormal changes in the elastic properties and the transition resistivity response characteristics are intrinsically correlated, the contribution arising from the d-band electrons determines the cross-scale abnormal elastic behavior accompanying the superconducting transition in Nb3Sn crystals.

Response embedded atom model potential of Pb at finite temperature: application on the dislocation mobility

Dislocation is a major carrier of plastic deformation for metal materials and are crucial. Understanding the mechanism of dislocation motion is beneficial for understanding the plastic deformation of materials under dynamic loading. In this work, a new response EAM (REAM) potential is developed for the applications under high pressure and finite temperature conditions. We use the REAM potential to investigate the behaviors of edge and screw dislocations in Pb by molecular dynamics (MD) simulations, and compare it with two commonly used EAM potentials. Specially, we examine the influence of the stacking fault energy and the temperature-dependent elastic constants on the dislocation motions. Our results show that the temperature-dependent elastic constants do not considerably affect the dislocation motion at the linear region of low stress, while the stacking fault energy plays a significant role. In the nonlinear region, the stacking fault energy and elastic constant together influence the dislocation motion. In subsonic and low transonic regimes, the dislocation width oscillates with time, but eventually fluctuates around equilibrium width.

First-principles calculations to investigate third-order elastic constant, anharmonicity and temperature dependent second elastic constant of thermoelectric materials Cu3MSe4(M = V and Nb)

The research on material‘s mechanics is critical in thermoelectric. Herein, we study the second(Cij), third(Cijk) order elastic constants, anisotropic and pressure and temperature dependent elasticity of Cu3MSe4(M = V and Nb) utilizing density functional theory. The elasticity of Cu3MSe4(M = V and Nb) is anisotropic. In addition, the calculated Cij suggests that these materials show relatively weak mechanical properties as thermoelectric device, and the ratio of bulk modulus(B) versus shear modulus(G) suggest that they are brittle. Cijk and pressure induced Cij reveal that Cu3NbSe4 has stronger anharmonic strength than that of Cu3VSe4. Finally, the thermal expansions are evaluated via quasi-harmonic approximation, and the temperature dependent elastic constants Cij indicate that Cu3NbSe4 has weak temperature dependent than that of Cu3VSe4. This research is dedicated to the design of thermoelectric devices and discovering novel thermoelectric materials with high performance in view of mechanical properties.

Ab initio thermo-elasticity of [formula omitted]-MH[formula omitted] (M[formula omitted]Zr, Ti)

In the present work, we report the results of a systematic ab initio study of the thermo-elastic properties of δ-MH1.5 (M=Zr, Ti). This investigation serves three purposes: (i) Elucidate the fully anisotropic temperature dependent elastic constants of hydrides, (ii) address discrepancies in thermal expansion data reported in the literature and (iii) provide input data for thermodynamic-based phase-transformation modelling. Due to a reduced contribution from the vibrational free energy to the strain energy, in agreement with experimental observations we find that the temperature dependent stiffness of hydrides vary to a much lesser degree than the matrix. For δ-ZrH1.5, we further find that Zener’s anisotropy ratio varies with temperature. Regarding the linear thermal expansion, our results indicate that it is highly temperature dependent. With the exception of a few outliers, our DFT data concurs well with experimental data, if the temperature range over which it was measured is taken into account.

First-principles study on the temperature dependent elasticity and thermodynamical properties of thermoelectric material NiSbS

The mechanical properties are critical factors in designing thermoelectric devices. In this work, the electronic structure, temperature dependent elasticity and thermodynamical properties of thermoelectric material NiSbS were investigated via quasi-harmonic approximation. Electronic structure calculation suggests that it exhibits metallic behavior with a band characteristic similar with that of n-type heavily doped semiconductor. The temperature-dependent elastic constants follow a normal behavior where these values decrease with the increase of temperature, and satisfy the stability conditions. The thermodynamical calculations suggest that NiSbS has weak expansion. Our calculation predicts that NiSbS has good mechanical property in application of thermoelectric device. NiSbS can be designed as thermoelectric device owing to its excellent mechanical property via DFT simulation

Integrating machine learning with mechanistic models for predicting the yield strength of high entropy alloys

Accelerating the design of materials with targeted properties is one of the key materials informatics tasks. The most common approach takes a data-driven motivation, where the underlying knowledge is incorporated in the form of domain-inspired input features. Machine learning (ML) models are then built to establish the input–output relationships. An alternative approach involves leveraging mechanistic models, where the domain knowledge is incorporated in a predefined functional form. These mechanistic models are meticulously formulated through observations to validate specific hypotheses and incorporate elements of causality missing from data-driven ML approaches. In this work, we demonstrate a computational approach that integrates mechanistic models with phenomenological and ML models to rapidly predict the temperature-dependent yield strength of high entropy alloys (HEAs) that form in the single-phase face-centered cubic (FCC) structure. Our main contribution is in establishing a quantitative relationship between the HEA compositions and temperature-dependent elastic constants. This allows us to improve the treatment of elastic constant mismatch to the solid solution strengthening effect in the mechanistic model, which is important for reliable prediction of yield strength. We accomplish this by combining Bayesian inference with ensemble ML methods. The outcome is a probability distribution of elastic constants which, when propagated through the mechanistic model, yields a prediction of temperature-dependent yield strength along with the uncertainties. The predicted yield strength shows good agreement with published experimental data, giving us confidence in applying the developed approach for the rapid search of novel FCC-based HEAs with excellent yield strength at various temperatures.

Temperature-dependent thermoelastic properties of GaSb and InSb semiconductors: Identification through ab initio DFT simulations

III–V semiconductors are extensively used in infrared sensor applications due to their superior structural and optical properties. Due to the extremes in the manufacturing and operating temperatures of the sensors, the knowledge of temperature-dependent elastic constants of these materials is of great importance. However, reliable measurements across a large range of temperatures prove difficult due to limitations of experimental setups. Density functional theory calculations present an affordable alternative. In this work, temperature-dependent elastic properties of InSb and GaSb are investigated using density functional theory within the quasiharmonic approximation. Calculated properties relevant for operation in a wide temperature range are presented including second order elastic constants, Young’s modulus (E), shear modulus (μ), Poisson’s ratio ν and the coefficient of thermal expansion (α). Our results are compared to available experimental values and good agreement is observed.

Thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity and nonlinear finite element analysis

In non-isothermal conditions, numerous experimental and theoretical investigations reveal that the elastic constants and thermal conductivity in piezoelectric solids depend on temperature distribution. This work aims to investigate thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity. The nonlinear time-domain finite element method is developed to directly solve nonlinear finite element governing equations, which maximally avoids the precision losses within the applications of the integrated transformation method. As a numerical example, the developed method is applied to analyze nonlinear transient thermo-electromechanical responses of a two-dimensional orthotropic piezoelectric plate of crystal class mm2. The achieved results reveal that temperature-dependent thermal conductivity and elastic constants remarkably affect the structural dynamic responses, whilst thermal wave or elastic wave will travel faster and the electrical energy harvesting ability is significantly elevated.

Finite-temperature atomic relaxations: Effect on the temperature-dependent C44 elastic constants of Si and BAs.

The effect of atomic relaxations on the temperature-dependent elastic constants (TDECs) is usually taken into account at zero temperature by the minimization of the total energy at each strain. In this paper, we investigate the order of magnitude of this approximation on a paradigmatic example: the C44 elastic constant of diamond and zincblende materials. We estimate the effect of finite-temperature atomic relaxations within the quasi-harmonic approximation by computing ab initio the internal strain tensor from the second derivatives of the Helmholtz free-energy with respect to strain and atomic displacements. We apply our approach to Si and BAs and find a visible difference between the softening of the TDECs computed with the zero-temperature and finite-temperature atomic relaxations. In Si, the softening of C44 passes from 8.6% to 4.5%, between T = 0 K and T = 1200 K. In BAs, it passes from 8% to 7%, in the same range of temperatures. Finally, from the computed elastic constant corrections, we derive the temperature-dependent Kleinman parameter, which is usually measured in experiments.

Temperature-Dependent Elastic Constants of Substrates for Manufacture of Mems Devices

We present a comparative computational study of temperature-dependent elastic constants of silicon (Si), silicon carbide (SiC) and diamond as substrates that are commonly used in the manufacture of Micro-Electromechanical Systems (MEMS) devices. Also mentioned is Cd2SnO4, whose ground-state elastic constants were determined just recently for the first time. Si is the dominant substrate used in the manufacture of MEMS devices, owing to its desirable electrical, electronic, thermal and mechanical properties. However, its low hardness, brittleness and inability to work under harsh environment such as high-temperature environment, has limited its use in the manufacture of MEMS like mechanical sensors and bioMEMS. Mechanical sensors are fabricated on SiC and diamond due to their high Young’s moduli as well as high fracture strength, while the bioMEMS are fabricated on polymers. The effect of temperature on the elastic constants of these substrates will help in giving insight into how their performance vary with temperature.

First principles calculations of structural, electronic, elastic and thermodynamic properties of ZnNi3X (X = N and C)

In this work, we investigated the structural, electronic, elastic and thermodynamic properties of ZnNi3X (X=C, N) based on density functional theory (DFT). Our results show that the two compounds ZnNi3N and ZnNi3C are stable in nonmagnetic configuration with metallic behavior. The analysis of the phonon curves and the elastic constants predict that these compounds are thermodynamically and mechanically stable. The obtained values of Pugh’s ratio are found higher than 1.75, which means that ZnNi3X (X=C, N) are ductile and have a metallic bond, furthermore, the ZnNi3N is more affected by the temperature compared to ZnNi3C, because the lattice parameter and the Poisson’s ratio increases more rapidly in ZnNi3N than ZnNi3C. We have also studied the temperature dependent elastic constants within quasi-static approximation in the range of temperature from 0 K to 800 K. The results show that these compounds maintain their mechanical stability.

Thermo-elastic behavior of hexagonal Sc–Ti–Zr–Hf high-entropy alloys

Recent advances in tuning the long-standing strength-ductility tradeoff have drawn attention to high-entropy alloys (HEAs), and the appearance of hexagonal close-packed (hcp) structures has been emphasized. However, few studies have explored the elastic moduli of hcp HEAs, which is of prime importance for improved understanding of the outstanding mechanical properties. In this work, we focus on a set of equiatomic rare-earth-free HEAs with hcp structures, i.e. ScTiZr, ScTiHf, ScZrHf, TiZrHf, and ScTiZrHf, and their thermo-elastic properties are studied using quantum mechanical first-principles methods. It is found that, for all considered HEAs, the hexagonal axial ratio shows a weak dependence on the temperature effect, and the thermal expansion coefficient remains almost unchanged above room temperature. From the calculated temperature-dependent single-crystal elastic constants, we analyzed the mechanical stability, elastic anisotropy, and derived polycrystalline moduli. Results indicate that the present HEAs exhibit rather high elastic isotropy and large elastic softening resistance. The ab initio predicted Young’s modulus, shear modulus, and specific modulus do not obey the rule of mixture, which indicates that there exists a strong intrinsic hardening effect in all of the considered HEAs. The calculated results are in good agreement with the available experimental measurements.