Elastic Constants C11 Research Articles

Synthesis and thermal expansion of chalcogenide MAX phase Hf2SeC

Thermal expansion of MAX phases along different directions tends to be different because of the anisotropy of hexagonal crystals. Herein, a new Hf2SeC phase was synthesized and confirmed to be relatively isotropic, and the coefficients of thermal expansion (CTEs) along a and c directions were determined to be 9.73 μK−1 and 10.18 μK−1, respectively. The strong MS bond endowed Hf2SC and Zr2SC lower CTEs than those of Hf2SeC and Zr2SeC. The relationship between the thermal expansion anisotropy and the ratio of elastic stiffness constant c11 and c33 was established. This straightforward approximation can be used to roughly predict the thermal expansion anisotropy of MAX phases.

Physical Properties Investigations of Ternary-Layered Carbides M2PbC (M = Ti, Zr and Hf): First-Principles Calculations

We investigated structure optimization, mechanical stability, electronic and bonding properties of the nanolaminate compounds Ti2PbC, Zr2PbC, and Hf2PbC using the first-principles calculations. These structures display nanolaminated edifices where MC layers are interleaved with Pb. The calculation of formation energies, elastic moduli and phonons reveal that all MAX phase systems are exothermic, and are intrinsically and dynamically stable at zero and under pressure. The mechanical and thermal properties are reported with fundamental insights. Results of bulk modulus and shear modulus show that the investigated compounds display a remarkable hardness. The elastic constants C11 and C33 rise more quickly with an increase in pressure than that of other elastic constants. Electronic and bonding properties are investigated through the calculation of electronic band structure, density of states, and charge densities.

A density functional theory approach to the effects of C and N substitution at the B-site of the first boride MAX phase Nb2SB

MAX phases have diverse physical properties and as such are an important research field linked to numerous applications. The recent addition of boride member to the MAX family has further extended the physical properties and diversity of these compounds. In this study, the structural, electronic, mechanical, thermal and optical properties were investigated using the density functional theory (DFT) for Nb2SB. The effects of C and N substitution at the B-site of Nb2SB are also investigated. To do so the conventional carbide and nitride counterparts of Nb2SB have also been calculated. In most cases, the first boride MAX phase Nb2SB is mechanically stronger than its carbide and nitride counterparts. Its elastic constants C11 and C44, elastic moduli G and E, Vickers hardness HV, Debye temperature θD, lattice thermal conductivity κph, minimum thermal conductivity κmin, and melting temperature Tm are higher than those of Nb2SC and Nb2SN. Nb2SB is brittle in nature, whereas Nb2SC and Nb2SN are ductile. Non-central forces are dominant in Nb2SB while the central forces are dominant in Nb2SC and Nb2SN. Nb2SB is more covalent and more resistant to shear deformation than its carbide and nitride counterparts. Elastically and optically, Nb2SB is less anisotropic than its carbide and nitride counterparts. Data availabilityData will be made available upon reasonable request.

Pressure dependent structural phase transition and observation of Dirac-like dispersions in CaTe and SrTe

At ambient pressure both CaTe and SrTe are known to exist in NaCl type structure (B1 phase) and undergo structural transition at high pressure to CsCl type structure (B2 phase). Most theoretical studies presented regarding the structural transition from B1 to B2 phase are based upon enthalpy comparisons. In this paper, we have computed elastic constants C11, C12, and C44 for both phases at various pressures and used Born stability conditions to compare the relative mechanical stability of both phases with pressure. The dynamical stability of these structures has been investigated using phonon dispersion calculations at different pressures. Our study finds that phonon dispersion calculations match well with enthalpy based predictions for the transition from B1 to B2 phase. Moreover, the Born stability conditions are necessary but not sufficient conditions to predict the structural stability of a crystal. Both CaTe and SrTe are 3D Dirac metals in the B2 phase and exhibit linear dispersions of electronic states near the Fermi level.

Anomalous elastic behavior of tantalum at high pressures: Experimental and theoretical studies

Elastic wave velocities of polycrystalline tantalum have been measured up to 13.6 GPa at room temperature using ultrasonic interferometry technique in a multi-anvil apparatus. The bulk and shear moduli, as well as their pressure derivatives are obtained using Eulerian 3rd order finite strain equations, yielding KS0 = 193.9(29) GPa, G0 = 69.3(10) GPa, KS0′ = 3.18(5) and G0′ = 0.88(1). The Steinberg-Guinan yield stress model is examined using the current shear modulus and its pressure derivative, where a slightly lower A0 = 0.0127 GPa−1 compared to previous studies is obtained. First-principles calculations on the elasticity of tantalum have also been performed up to 200 GPa. Anomalous softening of the elastic shear constant C44 and shear wave velocity VS is observed between 80– 180 GPa, whereas the anisotropy shows a softening-stiffening behavior with increasing pressure and reaches a minimum at around 150 GPa. Such anomalies might commonly originate from the nesting of Fermi surface for Group VB metals.

Physical properties of YB66 and consideration of possible use for high-resolution X-ray optics

A combined microscopic, i.e., powder and single crystal x-ray diffraction and inelastic x-ray scattering, and macroscopic, i.e., heat capacity, characterization was carried out on YB66 between 10 and 400K. The system crystallizes in a rather large unit cell with a lattice parameter of about 23.4Å at room temperature. The volume thermal expansion coefficient is found to be 3.9×10−5K−1 at 295K. A high Debye temperature above 1000K was determined using several methods, 1043(25)K, from heat capacity measurements, 1430(59)K, from elastic constants measurements, and 1690(198)K, from thermal expansion measurements. The thermal transport is modeled as a collection of Einstein oscillators with an Einstein temperature of 194(2)K. The C11 and C44 elastic constants are above 400 and 150GPa, respectively. The average speed of sound in YB66 is estimated to be 9631(380)m/s, similar to the average speed of sound in corundum, 10000m/s. The large volume of the unit cell and the stiffness of the crystal structure make YB66 a promising candidate for high-resolution x-ray monochromatization applications. Candidate reflections for high-resolution resonant inelastic x-ray scattering are indicated and potential pitfalls relevant to the quality of crystals and multi-beam cases are mentioned.

Combining the Mie-Lennard-Jones and the Morse Potentials in Studying the Elastic Deformation of Interstitial Alloy AGC with FCC Structure under Pressure

In this study, the mean nearest neighbor distance between two atoms, the Helmholtz free energy and characteristic quantities for elastic deformation such as elastic moduli E, G, K and elastic constants C11, C12, C44 for binary interstitial alloys with FCC structure under pressure are derived with the statistical moment method. The numerical calculations for interstitial alloy AGC were performed by combining the Mie-Lennard-Jones potential and the Morse potential. Our calculated results were compared with other calculations and the experimental data.

The Influence of Pressure on Structural, Elastic, Piezoelectric and Dielectric Properties of R3c‐BiAlO3 Based on Ab Initio Calculations

AbstractIn this paper, we deal with a theoretical and predictive study of the influence of the applied pressures on the structural, elastic and piezoelectric properties of the rhombohedral BiAlO3 perovskite (R3c space group) phase by combining both the density functional theory (DFT) and the density functional perturbation theory (DFPT) included in the ABINIT code. The results indicate a decrease in structural cell volume and the elastic constants appear to be more intense as the applied pressure increases. Due to the increase in the direct piezoelectric coefficient (e33) and the decrease of the elastic constant (c33), the converse piezoelectric coefficients (d33) tend to improve with increased pressure applied. At a pressure of 10 GPa, the value of the direct piezoelectric constant reached 6.23 C/m2 which becomes an indirect competitor to lead zirconate titanate (PZT). The dielectric constants and born effective charge at high pressure have been calculated. Our results agree well with the available experimental and theoretical results. Our findings, especially piezoelectricity, can help in various applications of high‐pressure devices such ultrasonic transducer.

STUDY ON ELASTIC PROPERTY OF STAINLESS STEEL UNDER PRESSURE

The paper presents analytic expressions of the Helmholtz free energy and characteristic elastic deformation quantities such as the elastic moduli E, K, G and the elastic constants C11, C12, C44 for BCC interstitial and substitutional alloy with four components are determined by the statistical moment method. The obtained elastic quantities depend on temperature, pressure, the concentration of interstitial atoms, and the concentration of substitutional atoms. This is the elastic deformation theory of BCC interstitial and substitutional alloy with four components published for the first time. The elastic deformation theories of BCC metal, BCC binary interstitial alloy, BCC binary substitutional alloy, and BCC ternary interstitial and substitutional alloy are limit cases of the elastic deformation theory of BCC substitutional and interstitial alloy with four components. Our numerical calculations of the obtained theoretical results for metal Fe and alloy FeSi are in good agreement with other calculations and experiments. Other numerical calculations for alloys FeCr, FeNi, FeCrSi, FeNiSi, FeCrNiSi (some atoms Fe are substituted by atoms Cr and some other atoms Fe are substituted by atoms Ni) called stainless steels predict and orient experimental results in the future. Our numerical calculations for alloy FeCrNiSi are published for the first time.

Study of half metallic ferromagnetism, transport and mechanical properties of X0.9375Ti0.0625Te (X = Ca, Sr, and Ba) alloys: for spintronics application

The diluted magnetic semiconductors (DMS) are emerging materials for spitronic applications. Therefore, X0.9375Ti0.0625Te (X = Ca, Sr, and Ba) Alloys for electronic, magnetic, and transport properties while 25% doping of Ti for elastic properties have been elaborated. The band structures and density of states ensures the half metallic ferroamgneitsm (HMF) and 100% spin polarization has been ensured by Heisenberg classical model. The quantum ferromagnetism has been disccused in terms of double exchange mechanism, crystal field energy Ecry, and exchange energies and The negative pd exchange energy, and exchange constants guarantee the ferromagnetism is due to quantum exchange of electrons rather than clustering. The effect of electrical and thermal conductivities of electrons quantum, potential gradient effect and power factors are elaborated by BoltzTraP code. The elastic properties are elucidated by elastic constants C11, C12, C44, elastic moduli, Pugh’s (B/G), and Poisson’s (υ) ratios. Therefore, the studied alloys are taken as potential materials for spintronic.

DEPENDENCE OF PHYSICAL PROPERTIES OF PIEZOELECTRIC ALUMINUM-SCANDIUM NITRIDE ON SCANDIUM CONCENTRATION

In this work the physical properties of the piezoelectric aluminum-scandium nitride (ASN) solid solution as a function of scandium concentration were studied using the density functional theory and experimental methods. The phase transition from the wurtzite phase to the rock salt phase at a Sc concentration of 43% was shown. The barriers of transformation from the wurtzite phase to the rock salt phase for various Sc concentrations were obtained. The behavior of the ASN piezoelectric constant d33 calculated by the piezoelectric constants e33, e31, and e15 shows a sharp increase with increasing Sc concentration compared to aluminum nitride AlN. The relationship between the increase in the piezoelectric response of ASN and the softening of the lattice, accompanied by a decrease in the main elastic constants C11, C33, C44 and C66, as well as a decrease in the c/a ratio with increasing Sc concentration, is shown. ASN films with a predominance of the crystal orientation (00·2) were obtained experimentally by magnetron sputtering. The structural properties of the films were studied by X-ray diffraction analysis. A comparison of the experimentally obtained dependence of the c/a ratio on the Sc concentration with the theoretical values showed a good correspondence. Studies of the physical properties of ASN thin films were performed using microwave multi-overtone composite resonators on diamond substrates with a longitudinal bulk acoustic wave (BAW) as the operating mode in the range of 0.5 – 20 GHz. The frequency dependences of the Q-factor of BAW-resonators with different ASN films were obtained, and the frequency dependences of the square of the modulus of the form factor as |m|2 were calculated. The dependences of the elastic constant С33 and the piezoelectric constant e33 for the ASN films with different Sc concentrations were calculated. The calculated and measured values of these constants are agreed within the experimental error.

Giant heterogeneous magnetostriction induced by charge accumulation-mediated nanoinclusion formation in dual-phase nanostructured systems

The fundamental origin of giant magnetostriction in dual-phase nanostructured systems is still under debate in recent years. Previous studies have revealed that the formation of tetragonal nanoinclusions induced the enlargement in local magnetocrystalline anisotropy, leading to a strengthened magneto–elastic coupling coefficient, which was considered to promote magnetostriction. Another key factor of magnetostriction, the influence of the nanoinclusions on the elastic constants of the lattices is, however, still not clear. In this work, we propose a mechanism based on the experimental and theoretical results of binary and rare-earth (RE) doped FeGa single-crystals. Doping traces of RE atoms effectively increase the density of nanoinclusions in the A2 matrix, due to the high selectivity of RE atoms they possess stronger bonding interaction with Fe atoms rather than Ga atoms. As a consequence, the elastic constant c12 significantly increases with the rising density of tetragonal nanoinclusions as opposed to the constant c11, resulting in a remarkable enhancement in magnetostriction due to the immediate relevance between magnetostriction (λ001) and c11−c12. A superior magnetostriction of 390 ppm is obtained in the RE-doped single-crystal due to lattice softening induced by the nanoinclusions. This uncovered mechanism sheds light onto the contribution of RE atoms on the magnetostriction in FeGa single-crystals, and establishes a foundation for developing new-generation dual-phase magnetostrictive materials with unprecedented levels of magnetostriction.

Volume-matched ferroelectric and piezoelectric ZnO/MgO superlattice

Wurtzite ZnO as a multifunctional material is attractive due to the ferroelectricity and piezoelectricity; Cubic MgO is also a very useful insulator oxide for applications in emerging electronics. Using the volume matching condition, we construct a stable 1 × 1 ZnMgO superlattice alternating along the crystallographic c-direction. We then calculate the electronic, ferroelectric and piezoelectric properties of the ZnMgO superlattice through density-functional theory. It is found that the epitaxial tensile strain can effectively reduce the polarization barrier without significantly reducing the polarization, increase the piezoelectric constant e33 and soften the elastic constant C33. In addition, the piezoelectric modulus d33 is enhanced by about 4 times, and the electromechanical coupling coefficient k33 is nearly doubled at 4% strain.

Three-dimensional overall stress analysis for double-coated structure with equal coating thickness

The three-dimensional solution is derived in this article for the double-coated structure of the transversely isotropic material. The displacements and stresses are given by explicit expression, which will help researchers and designers gain insight into the impact of the properties of different coating materials on the structural performance. Numerical results show increasing the coating thickness, adjusting the elastic constants c13 and c33 of the coating material I can significantly reduce the maximum shear stress of the interface. In addition, theoretically, not only can the three-dimensional method predict the critical load and the failure area under minimum shear failure, but it also preliminary inference the bonding performance between different materials. Compared with the single-coating structure, the double-coating structure can not only accurately simulate the bonding layer between the coating and the substrate, but also improve the problem of interface stratification caused by the great difference of material properties.

The elastic properties of disordered Fe–Ni alloys under high pressures from first-principles calculations

The elastic constants and the elastic anisotropy in hexagonal close-packed Fe–Ni alloys have been investigated at high pressures by plane-wave density functional calculations within the generalized gradient approximation and the Monte Carlo special quasi-random structure method. The comparisons with previous calculations and experiments are shown and discussed. We find that adding Ni to Fe has a certain influence on the structure and elasticity of hexagonal close-packed Fe–Ni alloys generally. In particular, the elastic constant C44 is seriously affected by the increasing Ni content. Furthermore, the elastic moduli and wave velocities yielded from disordered structures are slightly greater than those from the ordered structures in previous calculations at high pressures. Interestingly, the elastic anisotropies of the compressional wave are close to 1.1 and there are small changes with increasing pressure and Ni content, which indicates that the anisotropies are little affected by pressures and Ni content within disordered structure.

Energetic Validation of Various Crystal Structures in Zr2CoZ (Z = Al, Ga, In) Heusler Alloys

We energetically validate new Zr2CoZ (Z = Al, Ga, In) systems in the most common cubic crystal structures of Heusler alloys, that is, regular and inverse full-Heusler structures. The regular Heusler structure, namely, the L21 (Cu2MnAl-type), is energetically more favorable in Zr2CoZ than the inverse Heusler (Hg2CuTi-type), as confirmed by the density functional theory calculations and a semiempirical Miedema’s model. The values of the independent elastic constants (c11, c12, c44) obtained for the studied Zr2CoZ Heusler alloys in the L21 structure fulfill the conditions of Born stability for cubic crystals. Our results of electronic structure calculations show that Zr2CoZ in the L21 structure are metallic ferromagnets with a main contribution from the Co magnetic moment, whose value is within the range of 1.425–1.472 μB. By adapting the simplest deformation from a cubic to tetragonal structure (Bain transformation) as well as the orthorhombic distortion of an energetically favorable regular Heusler structure, we discuss the stability of the L21 structure and the possibility of structural transformation in Zr2CoZ series. The energy of the L21 phase in the Zr2CoIn compound increases leading to relative stabilization of the tetragonal phase of this compound with c/a = 1.37 for the volume 7% lower than the equilibrium value.

Ab initio predictions of structure and physical properties of the Zr2GaC and Hf2GaC MAX phases under pressure

The electronic structure, structural stability, mechanical, phonon, and optical properties of Zr2GaC and Hf2GaC MAX phases have been investigated under high pressure using first-principles calculations. Formation enthalpy of competing phases, elastic constants, and phonon calculations revealed that both compounds are thermodynamically, mechanically, and dynamically stable under pressure. The compressibility of Zr2GaC is higher than that of Hf2GaC along the c-axis, and pressure enhanced the resistance to deformation. The electronic structure calculations reveal that M2GaC is metallic in nature, and the metallicity of Zr2GaC increased more than that of Hf2GaC at higher pressure. The mechanical properties, including elastic constants, elastic moduli, Vickers hardness, Poisson’s ratio anisotropy index, and Debye temperature, are reported with fundamental insights. The elastic constants C11 and C33 increase rapidly compared with other elastic constants with an increase in pressure, and the elastic anisotropy of Hf2GaC is higher than that of the Zr2GaC. The optical properties revealed that Zr2GaC and Hf2GaC MAX phases are suitable for optoelectronic devices in the visible and UV regions and can also be used as a coating material for reducing solar heating at higher pressure up to 50 GPa.

Large Bandgap Topological Insulator in Oxide APoO3 (A = Be, Mg, Ca, Sr, Ba, and Ra) Perovskite: An Ab Initio Study

Under the density functional theory framework, we have calculated the electronic and elastic properties of APoO3 (A = Be, Mg, Ca, Sr, Ba, and Ra) cubic perovskites. We found that CaPoO3, SrPoO3, BaPoO3, and RaPoO3 are topological insulators (TIs) with very large bandgaps of 0.861, 0.871, 0.820, and 0.810 eV, respectively. The nontrivial band topology together with the Z2 topological number of APoO3 perovskite are investigated. We also theoretically determine the three independent elastic constants C11, C12, and C44 of the APoO3 perovskite. The bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, and anisotropy factor are also calculated from the obtained elastic constants. We found that the Debye temperature for the APoO3 perovskite is around 330-370 K. In the bulk APoO3 perovskite, if the center Po atom is shifted 0.09Å away from the center, the induced electric polarization is quite large, being around 0.02 C/m2. In the surface band calculation, we found that both AO and PoO2 surfaces give rise to contributions to the conduction channel. If the Po atom moves both in-plane and out-of-plane, we show that both electric polarization and topologically protect surface conduction states exist in APoO3 perovskite, indicating that these oxide APoO3 perovskites are ferroelectric TIs and might be useful for spintronic applications.

Упругие свойства нанокристаллических кубических сульфидов Ag-=SUB=-2-=/SUB=-S и ZnS

The structure of Ag2S/ZnS heteronanostructures is considered taking into account the anisotropy of the elastic properties of Ag2S and ZnS sulfides. It is shown that a large amount of cubic zinc sulfide stabilizes the cubic structure of beta-Ag2S argentite at 300 K during the deposition of Ag2S/ZnS heteronanostructures from colloidal solutions. The elastic stiffness constants c11, c12, and c44 of cubic argentite beta-Ag2S and sphalerite ZnS are estimated at a temperature of 300 K. Physically possible variants of the arrangement of silver atoms at fixed crystallographic positions of cubic argentite are determined. It is shown that the energetically most favorable is the formation of beta-Ag2S heterostructures, in which the interface is formed by the (hk0) plane of ZnS sphalerite and the (hk 0.5) plane of beta-Ag2S argentite. Calculation of the universal criterion for the anisotropy of the elastic properties of cubic argentite beta-Ag2S and sphalerite ZnS showed that the studied silver and zinc sulfides are elastically anisotropic.

Temperature Dependence of Normalized Sensitivity of Love Wave Sensor of Unidirectional Carbon Fiber Epoxy Composite on Mn-Doped 0.24PIN-0.46PMN-0.30PT Single Crystal Substrate

Love wave sensors have attracted significant interest due to their high sensitivity and low attenuation. Love mode acoustic dispersion relation, highest normalized mass sensitivity, optimum normalized waveguide layer thickness, and temperature coefficients of frequency (TCF) were theoretically studied for the carbon fiber epoxy composites (CFEC)/Mn:0.24PIN-0.46PMN-0.30PT structure sensor. The highest normalized mass sensitivity exhibits a decreasing trend as the temperature increases from 25 °C to 55 °C. TCF can be improved by increasing the normalized layer thickness (h/λ); however, the temperature dependence of normalized mass sensitivity decreases. For the carbon fibers (CFs) in the CFEC waveguide along the propagation direction of Love wave, the device has a relatively small TCF of −10.92 ppm/°C at h/λ = 0.4001, where the normalized mass sensitivity is approximately 1.5 times that of a typical fused quartz/ST-quartz configuration device. The theoretical results imply that good temperature stability and high measurement precision were obtained from the device in the system CFEC/Mn:0.24PIN-0.46PMN-0.30PT with the CFs in the CFEC along the propagation direction of Love wave (x-axis). The ideal waveguide material requires a small elastic constant c44; however, the ideal piezoelectric substrate requires large elastic constants c44E and c66E.