Single-crystal Elastic Constants Research Articles

The Structural, Elastic, and thermodynamic properties of Sr2P7Br Double Zintl salt with heptaphosphanortricyclane configuration

We investigated the effects of externally applied pressure on the Sr2P7Br compound’s properties, specifically its crystalline structure, elasticity, and thermodynamics. This investigation was carried out using the pseudopotential plane wave method within the framework of density functional theory. We used the well-known PBEsol variant of the exchange–correlation general gradient approximation specifically designed for solid-state analysis. This is the first endeavor to investigate the effects of pressure on the Sr2P7Br material using a theoretical approach. The computed equilibrium structural parameters closely match the relevant experimental counterpart values. The determined elastic constants, obtained under both ambient pressure and hydrostatic pressures up to 18 GPa, satisfy the mechanical stability requirements. Based on the computed Pugh’s ratio, Cauchy pressure, and Poisson’s ratio, it can be concluded that the Sr2P7Br compound exhibits ductile behavior. The polycrystalline elastic moduli, including the isotropic bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio, at ambient pressure and under pressure effects, were derived from the single-crystal elastic constants. Additionally, associated parameters, such as average sound velocity, Debye temperature, minimum thermal conductivity, and Vickers hardness, were examined under pressure influences. The quasi-harmonic Debye approximation was used to investigate the relationship between temperature and some macroscopic physical parameters, such as lattice parameter, bulk modulus, Debye temperature, volume thermal expansion coefficient, and isobaric and isochoric heat capacities, at fixed pressures of 0, 4, 8, 12, and 16 GPa. The results derived from the elastic constants exhibit substantial concordance with those computed using the Debye quasi-harmonic model, thereby validating the reliability of our findings.

Inverting Single Crystal Elastic Constants of Polycrystals with Metallographic Measurement and Modified Ultrasonic Backscatter Mode

Inverting Single Crystal Elastic Constants of Polycrystals with Metallographic Measurement and Modified Ultrasonic Backscatter Mode

Insight into the influence of X (X = Cu, Mg and Zn) alloying on the mechanical and electronic properties of orthorhombic Ti3Sn compound by first-principles investigation

The mechanical properties and electronic structures of X (X = Cu, Mg and Zn) alloyed orthorhombic Ti3Sn compounds have been carried out by using first-principles calculations. It is revealed from formation energy that the all X-alloyed compounds are thermodynamically stable. According to the results of site occupancy energy, the X atom prefers to occupy the Ti 8g site of orthorhombic Ti3Sn compound. The calculated single crystal elastic constants showed that Ti47Sn16CuTi8g and Ti47Sn16ZnTi8g possess the largest resistance to shear deformation in (100) crystal plane and the most compressible compound along c-axis, respectively. It is found that the mechanical properties of Cu-alloyed orthorhombic Ti3Sn compound are stronger than that of Mg- and Zn-alloyed. It can be revealed from electronic structures that the Ti–Sn, Ti–Cu and Cu–Sn covalent bonds in Ti47Sn16CuTi8g are attributed to the hybridization of Cu-3d, Ti-3d and Sn-5p orbitals, while some ionic bonds and antibonding states are existed in Ti47Sn16MgTi8g and Ti47Sn16ZnTi8g.

Electronic, elastic, and thermodynamic properties of complex hydrides XAlSiH (X = Sr, Ca, and Ba) intended for hydrogen storage: an ab-initio study

The mechanical and thermodynamic properties of polyanionic hydrides XAlSiH (X = Sr, Ca, and Ba) were evaluated using density functional theory (DFT). The thermal parameters of XAlSiH hydrides, such as the Grüneisen parameter γ, heat capacity, and thermal expansion coefficient, were computed for the first time. The quasi-harmonic Debye model was used to determine these parameters over a range of pressures (0–40 GPa) and temperatures (0–1000 K). The gravimetric hydrogen storage capacities for BaAlSiH, SrAlSiH, and CaAlSiH were found to be 0.52%, 0.71%, and 1.05%, respectively. The hydrogen desorption temperatures for these compounds were also simulated at 748.90 K, 311.57 K, and 685.40 K. Furthermore, semiconducting behavior with an indirect bandgap value between 0.2 and 0.7 eV was exhibited by these compounds using the GGA and LDA approximation, and between 0.7 and 1.2 eV using the mBJ-GGA and mBJ-LDA approximation. Accurate elastic constants for single crystals were obtained from the calculated stress–strain relationships. The elastic constants for the XAlSiH compounds were significantly higher than those for other hydrides. The [001] direction was more compressible than the [100] direction in the hexagonal structure of XAlSiH. A lower bulk modulus than metallic hydrides was exhibited by these materials, indicating that XAlSiH compounds (X = Sr, Ca, and Ba) were highly compressible. The melting temperature for CaAlSiH was higher than that for SrAlSiH and BaAlSiH. Consequently, the decomposition temperature for XAlSiH (X = Sr and Ba) at which hydrogen was released from a fuel cell was lower than that for CaAlSiH. The bonding behavior of CaAlSiH was more directional than that of SrAlSiH and BaAlSiH. Brittle materials were XAlSiH (X = Sr, Ca, and Ba). Our PBE calculations yield linear compressibility and orientation-dependent Young’s modulus. Materials composed of hexagonal XAlSiH (where X represents Sr, Ca, or Ba elements) exhibit anisotropy in Young’s modulus but isotropy in bulk modulus.

Computational investigation of the structural, elastic, electronic, and thermodynamic properties of chloroperovskites GaXCl3 (X = Be, Ca, or Sr) using DFT framework

In this study, we employed the pseudopotential plane wave approach to examine the influence of the X atom (X = Be, Ca, or Sr) on the physical properties of isostructural chloroperovskites GaXCl3. The GGA-PBEsol functional was employed to simulate the exchange–correlation interactions. The computed equilibrium lattice parameters exhibit a high level of concordance with the existing theoretical findings. The cohesion energy and enthalpy of formation were computed to verify the energetic stability of the materials under consideration. The determined values of the single-crystal elastic constants (Cij) indicate that GaBeCl3 remains mechanically stable up to a hydrostatic pressure of 18 GPa. Similarly, GaCaCl3 preserves its stability up to 5 GPa, while GaSrCl3 remains mechanically stable up to 1.25 GPa. The projected Cij values were used to estimate several elastic moduli and related properties, including the shear and bulk moduli, sound wave speeds, Young’s modulus, Poisson’s ratio, and Debye temperature. The energy band structures of the studied compounds, as predicted by the HSE06 functional, demonstrate their wide bandgap semiconductor nature. Specifically, GaBeCl3 demonstrates an indirect bandgap of 3.828 eV, while GaCaCl3 reveals an indirect bandgap of 4.612 eV and GaSrCl3 has an indirect bandgap of 4.405 eV. The quasiharmonic Debye approach was employed to examine various thermal parameters, including the temperature dependence of the unit cell volume, bulk modulus, expansion coefficient, Debye temperature, isochoric and isobar heat capacities, Grüneisen parameter, and entropy function. It has been shown that GaBeCl3 demonstrates a lower thermal expansion coefficient and a higher Debye temperature in comparison to GaCaCl3 and GaSrCl3.

DFT insights into i-MAB phase, Mo4Y2Al3B6: a potential thermal barrier coating and solar heat reducing material

We have investigated the physical properties of the i-MAB: Mo4Y2Al3B6 phase via the density functional theory (DFT) approach. The optical properties, thermal properties, and Vickers hardness of the compound Mo4Y2Al3B6 have been studied theoretically for the first time. The correctness of the fine-tuned structural parameters is confirmed by their close match with experimental results. The compound’s metallic nature is established by an analysis of its electronic band structure, which is demonstrated by the overlap of the valence and conduction bands at the Fermi level. The mechanical and dynamic stability of the compound is supported by the single crystal elastic constants and computed phonon dispersion curve. The brittleness and machinability index has been studied to predict its usefulness in any form/shape. The compound’s ability to be exfoliated into 2D nanosheets has been proven by the f-index value. The obtained Vickers hardness value indicate the materials’ softness and ease of machining, aligning with the experimental findings. The thermodynamic properties are evaluated through phonon dispersion curves, including Debye temperature, free energy, enthalpy, entropy, and specific heat capacity. The potential of Mo4Y2Al3B6 as a thermal barrier coating (TBC) material is demonstrated by its low minimum thermal conductivity (K min), low volume expansion coefficient and high melting temperature (T m ). Key optical parameters, including dielectric functions, refractive index, photoconductivity, reflectivity, absorption coefficient, and loss function, have been computed and analyzed. The reflectivity spectrum suggests that the titled compound acts as a promising coating material for mitigating solar heating.

In-Situ synchrotron investigation of elastic and tensile properties of oxide dispersion strengthened EUROFER97 steel for advanced fusion reactors

The augmentation of mechanical properties of reduced activation ferritic martensitic steels through the introduction of creep resistant nano-oxide particles produces a class of oxide dispersion strengthened steels, which have attracted significant interest as candidates for first wall supporting structural materials in future nuclear fusion reactors. In the present work, the effect of temperature on the elastic properties and micro-mechanics of 0.3 wt% Y2O3 oxide dispersion strengthened steel EUROFER97 is investigated using synchrotron high energy X-ray diffraction in-situ tensile testing at elevated temperatures, alongside the non-oxide strengthened base steel as a point of comparison. The single crystal elastic constants of both steels are experimentally determined through analysis of the diffraction peaks corresponding to specific grain families in the polycrystalline samples investigated. The effect of temperature on the evolving dislocation density and character in both materials is interrogated, providing insight into deformation mechanisms. Finally, a constitutive flow stress model is used to evaluate the factors affecting yield strength, allowing the strengthening contribution of the oxide particles to be assessed, and correlation between the thermally driven microstructural behaviour and macroscopic mechanical response to be determined.

Properties of Erythritol Tetranitrate from Molecular Dynamics Simulation.

The nonpolarizable force field for alkyl nitrates developed by Borodin et al. [J. Phys. Chem. B, 2008, 112, 734-742] has been employed to calculate selected properties of crystalline and liquid erythritol tetranitrate (ETN). The set of partial charges proposed by Borodin for pentaerythritol tetranitrate (PETN) was used except for a small correction to the H atom charges to ensure charge neutrality owing to the absence of the neopentyl carbon in ETN. The force field was used to compute the isothermal compression curve, lattice parameters, heat capacity, thermal expansivity, single crystal elastic constants, and Gruneisen parameters of crystalline ETN. The density- and temperature-dependent viscosities of liquid ETN are also reported. We anticipate that these data will be of some utility to the development of equations of state and thermomechanical models for ETN.

Cohesive, elastic and anisotropic properties of s-, p- and d-block fission metals substituted Fe–Zr intermetallics

Density functional theory (DFT) based calculations are performed to study cohesive, elastic and anisotropic properties of c-Fe2Zr, t-FeZr2 and o-FeZr3 phases in the presence of s-, p- and d-block fission metals (FMs), viz. Rb, Sr, Cs, Ba, In, Sn, Sb, Te, Y, Nb, Mo, Tc, Ru, Rh, Pd, Ag and Cd. The FM substituted intermetallics are found to be thermodynamically stable owing to their negative formation energy. The Gibbs free energy of mixing is calculated to find the solubility of these FMs in these intermetallics. The calculated single crystal elastic constants suggest that all the FM substituted phases are mechanically stable. We also report the change in polycrystalline elastic moduli, viz. bulk, shear and Young moduli of the pristine intermetallics on incorporation of these FMs. The substitution of FMs in the FeZr2 phase increases its intrinsic ductility; while that in FeZr3 phase decreases it. The degree of anisotropy exhibited by the intermetallics follow the order FeZr2> FeZr3> Fe2Zr. The substitution of FMs does not affect the anisotropic behavior of Fe2Zr and FeZr2 phases, but slightly changes that of FeZr3 phase. Finally, the potential of these intermetallics to incorporate the FMs is discussed.

First-principles analysis of the structural, thermodynamic, elastic and thermoelectric properties of LuXCo2Sb2 (X = V, Nb and Ta) double half Heusler alloys

We used the pseudopotential plane wave approach, as implemented in the Quantum Espresso program, to investigate the impact of X atoms (V, Nb, and Ta) on the physical properties of LuXCo2Sb2 double half Heusler alloys. We determined the equilibrium structural parameters, including the crystal lattice parameters, atomic position coordinates, and bulk modulus, with and without including the spin-orbit effects. The predicted single-crystal elastic constants (Cij) show that the title compounds are mechanically stable with a pronounced elastic anisotropy. The bulk modulus, shear modulus, Young's modulus, Poisson coefficient, Debye temperature, and Vickers hardness coefficient were deduced from Cij via the Voigt-Reuss-Hill approximations. We also determined the variations of some macroscopic physical parameters as functions of temperature and pressure, namely the thermal expansion coefficient, lattice thermal conductivity, heat capacity at constant volume, Debye temperature and entropy. The considered alloys demonstrate special thermal properties under pressure and heat conditions, specifically, their low thermal expansion coefficient and lattice thermal conductivity; their thermal expansion coefficient is lower than 4.5 × 10−5 K−1 at 1000 K, and lattice thermal conductivity don’t exceed 1 W.m−1 K−1 for temperatures higher than 300 K. Furthermore, we investigated the temperature and charge carrier concentration dependencies of some thermoelectric coefficients. The results of this study reveal the potential of the considered compounds for achieving a figure of merit greater than 0.5 at a temperature of 500 K and a doping concentration of 1020 cm−3.

Physical properties of Be-based fluoroperovskite compounds XBeF3 (X = K, Rb): a first-principles study

In this study, we used the ab-initio computational tools as implemented in the CASTEP code to explore the effects of pressure on the structural, elastic, electronic, thermodynamic and optical properties of the fluoroperovskite compounds XBeF3 (X = K, Rb) based on Being. Exchange–correlation interactions were modeled using the GGA-PBEsol functional. The ground state of the title materials was characterized by calculating the optimized lattice parameter, the bulk modulus B and its pressure derivative, and the Goldsmith tolerance factor. These materials exhibit structural stability in the cubic structure even when subjected to significant pressure levels, extending up to 18 GPa. The analysis of numerical assessments of single-crystal elastic constants (Cij ), polycrystalline elastic moduli, namely shear modulus (G), Young’s modulus and Poisson’s ratio, as well as the anisotropy factor (A), highlights the mechanical stability, elastic anisotropy and ductility of considered the compounds. The thermodynamic properties of these materials were studied through the Debye quasi-harmonic model. Analysis of energy band structures and density of states spectra shows that XBeF3 (X = K, Rb) is insulating in nature, with band gaps of 7.99 and 7.26 eV, respectively. Additionally, we calculated the linear optical spectra, including dielectric function, absorption coefficient, refractive index, optical reflectivity, and energy loss function. Based on the results obtained, these materials could be used in various optoelectronic devices operating in the UV spectrum and in energy storage devices.

Elastic behaviour of orientation-correlated grains in multiphase aggregates.

Diffraction elastic constants (DEC) describe the elastic response of a sub-set of orientation correlated grains which share a common lattice vector. DEC reflect the elastic behaviour of the single crystal constituents through their dependence on grain orientation. DEC furthermore depend on the behaviour of the polycrystal aggregate both through the dependence on preferred orientation and through the average elastic interaction of the grains in the sub-set with their surroundings. The latter is also known as grain-matrix interaction which is grain shape dependent. Both dependencies can make the DEC uniquely sensitive to the elastic effects of the grain shape, texture, and phase composition. Several micro-mechanical models are explored with respect for use both in calculating diffraction elastic constants and overall elastic constants. Furthermore, it is shown how discrete data from electron backscatter diffraction on grain shape, grain orientations, and neighbouring grains can be used for DEC calculations. Lastly, the inverse problem of calculating single crystal elastic constants from DEC is discussed in detail. All calculations discussed in this work can be verified using the freely available computer program IsoDEC.

On the statistical behavior of homogenized properties and ultrasonic phase velocities in random polycrystals

Most theoretical studies on homogenized properties of polycrystals consider infinite textureless media with orientations characterized by independent Euler angles. However, microstructural analyses of polycrystals reveal spatially correlated orientations of grains whose sizes often follow lognormal distributions. Moreover, experimental investigations show that the single-crystal elastic constants (SEC) in the crystallite’s local coordinates could exhibit variabilities. To the best of our knowledge, in the context of our study, these have never been considered in the literature. In this paper, the crystal orientations are simulated using random fields (RFs) with different correlation parameters. A maximum entropy principle is used to simulate realizations of the local stiffness matrices. Numerical results indicate that generating Euler angles using independent random variables is legitimate when correlation lengths of orientations are close enough to the average grain size. Analytical formulas are derived to estimate the statistical behavior of effective elastic moduli and the phase velocities considering either unimodal or bimodal grain size distributions and fluctuations in local tensors for both two- and three-dimensional polycrystals. The former highlight the important roles of the coefficient of variations of the grain sizes and that of the elastic constants. This work contributes to microstructural characterization research associated with ultrasonic phase velocity measurements.

The lattice vibration, mechanical anisotropy, stress-strain behavior and electronic properties of ZrxCuySiz intermetallics: A first-principles study

In recent years, ternary metal silicides have attracted more and more interests because of their excellent physical and chemical properties. The mechanical properties, electronic structures and thermal properties of ZrCuSi, ZrCuSi2, Zr3Cu4Si2, Zr3Cu4Si4 and Zr6Cu8Si12 ternary silicide were calculated by first-principles methods. The formation enthalpies, phonon dispersions and single-crystal elastic constants reveal that ZrCuSi, ZrCuSi2, Zr3Cu4Si2, Zr3Cu4Si4 and Zr6Cu8Si12 are thermodynamically, dynamically and mechanically stable. According to the analysis of the enthalpy of formation, ZrCuSi is the most thermodynamically stable intermetallics. Besides, Push's ratio (BH/GH), Poisson's ratio v, hardness and elastic anisotropic were investigated. The results indicated that ZrxCuySiz intermetallics show brittle properties and elastic anisotropy. Cu–Si bonds can be formed in ZrxCuySiz intermetallics due to the strong hybridization between Cu-3d and Si-3s states. The analysis of the electronic properties confirms that ZrxCuySiz intermetallics show the metallic behavior. The stability and mechanical properties are further explained by Debye temperature and electronic properties.

Hydrogen storage: Investigation of the elastic properties of Mg7NbH16 hydride

Structural, mechanical and electronic structure properties of Mg7NbH16 were investigated using the norm-conserving pseudo-potentials and plane waves (PP-PW) within the general gradient approximation (GGA) in the frame of density functional theory (DFT). The computed equilibrium lattice constants are in excellent agreement with the available experimental and theoretical data. The elastic constants Cij of Mg7NbH16 were calculated for the first time. The Mg7NbH16 compound is found to be mechanically stable. The bulk modulus of single crystals has been derived using elastic constants. The results are discussed and compared with the calculated bulk modulus reported in the literature. The polycrystalline elastic moduli (namely: the shear modulus, Young's modulus, Poisson's ratio, Lamé's coefficients, sound velocities and the Debye temperature) were derived from the obtained single-crystal elastic constants. According to the obtained results, Mg7NbH16 can be classified as ductile material. The shear anisotropic factors and the elastic anisotropy are also discussed. A Debye temperature of 619 K was also determined using theoretical elastic constants.

Ab initio predictions of pressure-dependent structural, elastic, and thermodynamic properties of CaLiX3 (X = Cl, Br, and I) halide perovskites

In this comprehensive investigation, we undertook an ab initio exploration of the pressure-dependent structural, elastic and thermodynamic attributes of lithium-based halide perovskite compounds, namely CaLiCl3, CaLiBr3 and CaLiI3. Our analytical approach encompassed a diverse set of parameters, and the main conclusions and implications of our study are summarized as follows: (i) Calculated values of formation enthalpy and cohesion energy were determined for these perovskite compounds. Our results notably affirm the structural and thermodynamic stability of these materials in their cubic lattice configuration. (ii) Our optimized network parameters, derived from ab initio calculations, demonstrated commendable congruence with previously established theoretical predictions. This agreement strengthens the credibility of our conclusions. (iii) Using strain-constraint methodology, we successfully estimated the single-crystal elastic constants (Cij) of these compounds. This data served as the basis for further analysis. (iv) Using the obtained Cij values, we calculated a complete suite of elastic moduli for CaLiX3 (X = Cl, Br and I) in polycrystalline aggregates. This encompassed bulk modulus, Young's modulus, shear modulus, Lame coefficients, Poisson's ratio and Debye temperature, thus providing valuable information on the mechanical behavior of materials. (v) Using Debye's quasi-harmonic approach, we systematically investigated the temperature dependencies of several essential thermodynamic properties. These include the lattice parameter, thermal expansion coefficient, bulk modulus, Debye temperature, and isochoric and isobaric heat capacities. These analyzes covered a wide temperature range while maintaining fixed selected pressures. Overall, our study aims to provide the scientific community with a robust and comprehensive dataset regarding the structural, elastic, and thermodynamic attributes of CaLiX3 perovskite compounds.

Ab initio investigation of structural, elastic, and thermodynamic characteristics of tetragonal XAgO compounds (X = Li, Na, K, Rb)

The present research utilizes ab initio computations to examine the thermodynamic, structural, and elastic characteristics of XAgO ternary oxides, where X signifies Li, Na, K, and Rb.The GGA-PBE and GGA-WC functionals were used to calculate the ground-state lattice parameters and atomic position coordinates of the title materials. The calculated results were in good agreement with both experimental measurements and theoretical predictions. This suggests that the GGA-PBE and GGA-WC functionals are accurate for describing the structural properties of the material under study.This study offers computational predictions for the elastic properties of monocrystalline structures and polycrystalline aggregates of XAgO compounds. These predictions encompass various key parameters, including single-crystal elastic constants, Young’s modulus, bulk modulus, Lame coefficients, Poisson’s ratio, shear modulus, and Debye temperature. Additionally, the quasi-harmonic Debye approximation is utilized to explore the temperature-dependent behavior of bulk modulus, Debye temperature, volume thermal expansion coefficient, and isobaric and isochoric heat capacities over an extensive temperature range, while maintaining constant pressures. The results obtained from this model are found to be highly successful in accurately predicting the behavior of these properties.

Determination of diffraction and single-crystal elastic constants of laser powder bed fused Inconel 718

High energy X-ray synchrotron diffraction is used to investigate the elastic anisotropy of the nickel-based superalloy IN718 produced by laser powder bed fusion (PBF-LB). This material is characterized by a columnar grain morphology with some crystallographic texture. The material is subjected to elastic loading to determine the diffraction elastic constants (DECs). Furthermore, the single-crystal elastic constants (SCEC) are refined from these experiments using different micromechanical models. The results show that each micromechanical model predicts a specific set of SCEC that well describes the elastic anisotropy of PBF-LB/IN718.

The physical properties of Sc2PbC: A first-principles calculations

The structural, electronic, elastic, hardness, fracture toughness, and thermodynamic properties of the newly synthesized MAX phase Sc2PbC were studied for the first time through the first-principles calculations. The optimized lattice parameters are in agreement with the experimental data. The thermodynamic and mechanical stability of Sc2PbC is verified based on the formation enthalpy and single-crystal elastic constants. By analyzing the polycrystalline elastic moduli, it is found that Sc2PbC is brittle, very soft, easily machinable, and exhibits elastic anisotropy. Finally, thermodynamic properties such as Debye temperatures, thermal conductivity, melting temperature, and the temperature dependence of heat capacity are investigated.

The dependence of X-ray elastic constants with respect to the penetration depth.

X-ray diffraction techniques are widely used to estimate stresses within polycrystalline materials. The application of these techniques requires the knowledge of the X-ray elastic constants relating the lattice strains to the stress state. Different analytical methods have been proposed to evaluate the X-ray elastic constants from the single-crystal elastic constants. For a given material, such methods provide the bulk X-ray elastic constants but they do not consider the role of free surfaces. However, for many practical applications of X-ray diffraction techniques, the penetration depth of X-rays is the same order of magnitude as the grain size, which means that the influence of the free surface on X-ray elastic constants cannot be excluded. In the present work, a numerical procedure is proposed to evaluate the surface and bulk X-ray elastic constants of polycrystalline materials. While the former correspond to the situation where the penetration is infinitely small in comparison with the grain size, the latter are representative of an infinite penetration depth with no free-surface effect. According to numerical results, the difference between surface and bulk X-ray elastic constants is important for strongly anisotropic crystals. Also, it is possible to propose a relation that allows evaluating X-ray elastic constants as a function of the ratio between the penetration depth and the average grain size. The corresponding parameters of such a relation are provided here for many engineering materials.