Elastic Constants C11 Research Articles

Elastic properties of solid-solution refractory metal carbides with vacancy from virtual crystal approximation and supercell method

The virtual crystal approximation (VCA), as an efficient approach, has been used to study the alloys composed of refractory metals. In this work, we estimate the VCA in the application of solid-solution refractory metal carbides with point defects within the framework of ab initio calculations. Results indicate the VCA predicted Cij are different from those from supercell method with the same stress-stain approach. The elastic constants C44 from VCA are close to the average values derived from the refractory metal carbides. For the solid-solution refractory metal carbides with the severe lattice distortion, Cij are very sensitive to the atomic displacement and their moduli are softened. The carbon vacancies have a large effect on the elastic constants, whereas product a small effect on the anisotropy and hardness of solid-solution refractory metal carbides.

Mechano-Chemical Properties of Electron Beam Irradiated Polyetheretherketone.

In this study, the mechano-chemical properties of aromatic polymer polyetheretherketone (PEEK) samples, irradiated by high energy electrons at 200 and 400 kGy doses, were investigated by Nanoindentation, Brillouin light scattering spectroscopy and Fourier-transform infrared spectroscopy (FTIR). Irradiating electrons penetrated down to a 5 mm depth inside the polymer, as shown numerically by the monte CArlo SImulation of electroN trajectory in sOlids (CASINO) method. The irradiation of PEEK samples at 200 kGy caused the enhancement of surface roughness by almost threefold. However, an increase in the irradiation dose to 400 kGy led to a decrease in the surface roughness of the sample. Most likely, this was due to the processes of erosion and melting of the sample surface induced by high dosage irradiation. It was found that electron irradiation led to a decrease of the elastic constant C11, as well as a slight decrease in the sample’s hardness, while the Young’s elastic modulus decrease was more noticeable. An intrinsic bulk property of PEEK is less radiation resistance than at its surface. The proportionality constant of Young’s modulus to indentation hardness for the pristine and irradiated samples were 0.039 and 0.038, respectively. In addition, a quasi-linear relationship between hardness and Young’s modulus was observed. The degradation of the polymer’s mechanical properties was attributed to electron irradiation-induced processes involving scission of macromolecular chains.

Prediction the structural, electronic, elastic and dynamical properties of LiAlGe and LiInGe half-Heusler crystals by density functional theory

In the present study, structural, electronic, elastic and vibrational properties of LiInGe and LiAlGe half-Heusler compounds are investigated using density functional theory implemented in ABINIT and Quantum ESPRESSO programs. Generalized gradient approximation as an exchange correlation functional is used in Kohn-Sham equations to find lattice parameters, energy band gaps and three elastic constants C11, C12 and C44 for LiInGe and LiAlGe crystals. Density functional perturbation theory has been adopted in the study of lattice dynamics. As a result of the calculations, it is concluded that the phonon dispersion curves have positive frequency values throughout the entire Brillouin region and the dynamic stability of both crystals is strong. It is estimated as a result of calculations that this stabilization is impaired at a pressure value of approximately 492.65 kbar for LiInGe crystal and approximately 962.16 kbar for LiAlGe crystal.

Effect of pressure on structural, elastic and mechanical properties of cubic perovskites XCoO3 (X = Nd, Pr) from first-principles investigations

In this current research article, the structural elasto-mechanical and thermal properties of cubic perovskites XCoO3 (X = Nd, Pr) have been studied theoretically under different pressures. The structure is optimized and calculated optimized data is in well agreement of available literature. All these calculations are performed by considering Perdew Burke Ernzerhof Generalized Gradient Approximation type exchange and correlation functional within Wien2k-code. The second order cubic independent elastic constants C11, C12 and C44 are computed by using this optimized data. The dynamical stability criteria is checked by computed constants and used to find the elastic moduli; shear, Young's and Bulk modulus. The other mechanical properties like Poisson's ratio, anisotropic factor, Pugh's ratio, shear constant, Cauchy pressure, Lame's constants, Kleinmann parameter are quantified and discussed. The results portray the ductility of XCoO3 (X = Nd, Pr) perovskites and utility in high temperature devices.

Elastic deformation and elastic wave velocity of iron and its binary interstitial alloys: Temperature, pressure and interstitial atom concentration dependences

Based on the BCC binary interstitial alloy model with the condition that the interstitial atom concentration is very small compared to the main metal atom concentration and the elastic deformation theory of this alloy obtained on the basis of statistical moment method, we perform numerical calculations for elastic deformation quantities such as the elastic moduli E, K, G, the elastic constants C11, C12, C44, the longitudinal wave velocity Vd and the transverse wave velocity Vn of metal Fe and alloys FeSi, FeC, FeH. Numerical results for Fe are in good agreement with experiments and other calculations. The temperature and pressure dependence of the elastic deformation quantities for FeSi, FeC, FeH are similar to those for Fe. The elastic deformation quantities of FeSi, FeC, FeH in the range from 0 to 1000 K, from 0 to 10 GPa and from 0 to 5% of silicon (carbon, hydrogen) atom concentrations predict experimental results.

Brillouin Light Scattering Characterisation of Gray Tone 3D Printed Isotropic Materials.

Three-dimensional direct laser writing technology enables one to print polymer microstructures whose size varies from a few hundred nanometers to a few millimeters. It has been shown that, by tuning the laser power during writing, one can adjust continuously the optical and elastic properties with the same base material. This process is referred to as gray-tone lithography. In this paper, we characterize by Brillouin light scattering the complex elastic constant of different reticulated isotropic polymers, at longitudinal phonon frequencies of the order of 16 GHz. We estimate the real part of the constant to vary from 7 to 11 GPa as a function of laser power, whereas its imaginary part varies between 0.25 and 0.6 GPa. The linear elastic properties are further measured at a fixed laser power as a function of temperature, from C to C. Overall, we show that our 3D printed samples have a good elastic quality with high Q factors only ten times smaller than fused silica at hypersonic frequencies.

A molecular dynamics study of the mechanical properties of kaolinite under uniaxial and isothermal compression at various temperatures

AbstractUniaxial and isothermal compression tests of kaolinite were carried out using molecular dynamics simulations. Five different temperatures (300, 400, 500, 600 and 700 K) and pressures ranging from 0.0001 to 50 GPa were selected to study the temperature and pressure effects on the mechanical properties of kaolinite. As kaolinite may undergo a phase transition at ~1572 K, a highest temperature of 700 K was chosen to avoid such structural change. The Young's modulus, strength and elastic constants of kaolinite under various temperatures were calculated, and the relative change of the elastic constant C33 with temperature was found to be almost 12 times greater than the relative change of the interlayer constant C11. The microstructures under various compressive strains were tracked and they exhibited various failure modes in three directions. The temperature and pressure effects on the mechanical properties of three crystal directions were analysed. The results showed that the Young's modulus of the z-direction is the most affected by temperature; however, the influence of temperature on the strengths of the three crystal directions was the same. In addition, the structure of the z-direction was the most sensitive to temperature under the same hydrostatic pressure due to the weak interactions between layers.

Investigation on the structural, electronic, elastic and mechanical properties of Ti2Al(C1-xOx) solid solutions: First-principles calculations

In the present work, the structural, electronic, elastic and mechanical properties of Ti2AlC and Ti2Al(C1-xOx) solid solutions were investigated using first-principles calculations for varied O content incorporation (x = 0, 0.125, 0.25, 0.375, 0.5). According to the calculation results, all Ti2Al(C1-xOx) solid solutions with various x values are stable, and the bonding strength of the Ti–Al bond increases with the doping of O element. In addition, the shear modulus G and C44 elastic constant of Ti2Al(C1-xOx) solid solutions are both lower than the bulk modulus B, indicating that the phase has good damage tolerance. Not only that, compared with Ti2AlC, the plasticity and toughness of Ti2Al(C1-xOx) solid solutions are improved with the increase of O atom doping and doping ratio. Simultaneously, the doping of O atom is also beneficial to reduce the generalized stacking fault energy of Ti2AlC, making the Ti2Al(C1-xOx) solid solutions more prone to shear deformation, thereby further enhancing plasticity.

Acoustic Anomalies and the Critical Slowing-Down Behavior of MAPbCl3 Single Crystals Studied by Brillouin Light Scattering

Inelastic light scattering spectra of organic–inorganic halide perovskite MAPbCl3 single crystals were investigated by using Brillouin spectroscopy. Sound velocities and acoustic absorption coefficients of longitudinal and transverse acoustic modes propagating along the cubic [100] direction were determined in a wide temperature range. The sound velocities exhibited softening upon cooling in the cubic phase, which was accompanied by the increasing acoustic damping. The obtained relaxation time showed a critical slowing-down behavior, revealing the order–disorder nature of the phase transition, which is consistent with the growth of strong central peaks upon cooling toward the phase transition point. The temperature dependences of the two elastic constants C11 and C44 were obtained in the cubic phase for the first time. The comparison of C11 and C44 with those of other halide perovskites showed that C11 of MAPbCl3 is larger and C44 is slightly smaller compared to the values of MAPbBr3 and MAPbI3. It suggests that MAPbCl3 has a more compact structure (smaller lattice constant) along with stronger binding forces, causing larger C11 and bulk modulus in this compound, and that the shear rigidity is exceedingly small similar to other halide perovskites. The reported elastic constants in this study may serve as a testbed for theoretical and calculational approaches for MAPbCl3.

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.

Structural, electronic and magnetic properties of inverse spinel NiFe2O4: DFT + U investigation

We have used ab initio density functional theory (DFT) to explore the structural, mechanical, electronic and magnetic properties of inverse spinel NiFe2O4. The ultra-soft pseudopotential method parametrized under generalized gradient approximation (GGA) for the exchange-correlation functional with Hubbard correction (GGA + U) was applied. The equilibrium lattice parameter was estimated to be 8.4620 Å and the 3 independent elastic constants C11, C12 and C44 were found to be 304.12 GPa, 144.45 GPa and 57.46 GPa, respectively. GGA + U formalism could successfully explain the semiconducting and ferrimagnetic behaviour of NiFe2O4. The spin-polarized electronic density of states reveals that the p−d hybridization between O and Fe atoms is responsible for the semiconducting nature of NiFe2O4. The ferrimagnetic behaviour of inverse spinel NiFe2O4 can be explained through the anti-parallel spin configuration of tetrahedrally and octahedrally occupied Fe atoms. The resultant magnetic moment is thus solely contributed by the octahedrally occupied Ni atoms. Spin-polarized band structure calculations reveal indirect band gap of 1.6 eV for spin-up channel and direct band gap of 2.2 eV for spin-down channel.

High-throughput prediction of intrinsic properties of L12-(Nix1,Crx2,Cox3)3(Aly1,Tiy2) precipitates

The structural and mechanical properties, e.g., lattice constants, elastic constants, elastic moduli, Poisson’s ratios, and Vickers hardness, of L12-(Nix1,Crx2,Cox3)3(Aly1,Tiy2) precipitates are predicted by high-throughput first-principles calculations combined with exact muffin-tin orbitals and coherent potential approximation methods. It turned out that the elastic constants C11 and C44, shear modulus, Young’s modulus, Vickers hardness, and yield strength raise with increasing Ni, Cr, Co, or Al content as a whole, the elastic constant C12, Poisson’s ratios, and Pugh’s ratio decrease gradually, reflecting that the content change of Ni, Cr, Co elements on the left has basically similar effects on the physical properties of L12 precipitates, while the influences of Al and Ti on the right are opposite. Moreover, increasing Ni and Al, Cr and Al, or Co and Al contents at the same time is more conducive to improve the deformation resistance of alloys, but rapidly decrease the plastic properties. Meanwhile, the crystal structures of L12 precipitates may be mechanically unstable due to negative C11−C12 values when Ni, Cr, or Co concentration is less than 30 at%, and the ductile-brittle transition will occur for the L12 particles with high Cr and Al contents or Co and Al contents due to B/G<1.75. By comparison, Co3Al and Cr3Al precipitates exhibit excellent deformation resistance, (Cr,Co)3Ti and (Ni,Co)3Ti particles demonstrate outstanding plastic properties in the [001] and [111] directions, respectively. This work provides valuable insights for the intrinsic properties of L12-(Nix1,Crx2,Cox3)3(Aly1,Tiy2) precipitates.

First-principles calculations on mechanical properties of Rh2MnZn Heusler alloy

Heusler alloys are a huge family of binary, ternary and quaternary compounds and contain a wide range of unique properties, which made Heusler compounds to be the efficient materials for diverse applications. When it comes to the commercial applications mechanical properties are worth of check on and turn out to be the significant factor in the processing and final use of the materials. These properties make the study proficient by examine the nature of material under external pressure. In this study, we estimated mechanical properties of Rh2MnZn full-Heusler alloy using the full-potential linearized augmented plane wave method (FP-LAPW) method within the density functional theory (DFT). We have obtained C11, C12 and C44 elastic constants due to cubic symmetry using Charpin method implemented in Wien2k code. Further, using these elastic constants mechanical properties such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, anisotropic factor and Cauchy’s pressure are calculated. These moduli depicted hardness, ductility and elastic anisotropy of the alloy.

First-principles calculations to investigate elasto-mechanical and opto-electronic properties of pyrochlore oxides X2Zr2O7 (X=La, Nd)

This paper contains the comparative study of elasto-mechanical, electronic and optical properties of pyrochlores. These structures are first optimized and second order-independent cubic elastic constants C11, C12 and C44 are computed using the optimized data. These computed cubic elastic constants are further used to check the mechanical stability, Poisson's ratio, Pugh's ratio and Cauchy pressure which depicts the flexible and ductile nature of both materials. Kleinman ratio is more significant for La2Zr2O7, so it has excellent bond stretching minimization phenomena. Young's modulus and lame's constants describe that Nd2Zr2O7 is stiffer and difficult to compress than La2Zr2O7. Debye temperature and sound velocities are also calculated for both oxides. Due to the high melting temperature, Nd2Zr2O7 is suitable for high-temperature environments and is used in aerospace and construction industries. Band structures reveal that these oxides are metallic as there appears no gap in electronic dispersion relations. Analysis of the density of states reveals the magnetic nature of these oxides as the density of states is not the perfect image of each other in both spin channels. The imaginary part of the dielectric function also shows the optically metallic nature and suitability for sensors and opto-electronic devices.

Ab initio systematic description of thermodynamic and mechanical properties of binary bcc Ti-based alloys

The effects of the dissolution of 3d, 4d and 5d metals and Al, Ga, Ge, In and Sn in the bcc Ti lattice (β-phase) were studied within the framework of first-principles calculations. Lattice parameters, mixing enthalpies, single-crystal elastic constants C11, C12, C44 and C′, polycrystalline elastic moduli E, G, and plasticity characteristics of bcc Ti-based solid solutions in a wide concentration range up to 50 at% were investigated using the EMTO-CPA method. The PAW-SQS method was used to study the effects of alloying and local atomic relaxations on the indicated properties of Ti-X bcc alloys, where X is a series of 4d elements Nb, Mo, Tc, Ru, Rh, and 5d elements Ta, W, Re, Os, Ir for the set of concentrations: 6.25, 25 and 50 at%. The effect of concentration and periodic dependences on the properties of alloys and the dependence of elastic properties on the electronic structure were analyzed. It is shown that the calculated elastic constant C′ is a convenient and useful parameter for ranking chemical elements according to the relative strength of the stabilizing effect on the β-phase, in addition, the concentration dependences of C′ demonstrate softening with concentration increasing in the case of late transition metals, thereby reflecting the tendency of these metals to form intermetallic compounds with titanium, while early transition metals show a linear grow in stability with increasing concentration.

Ferroelectricity and Piezoelectric Response of (Sc,Y)N/(Al,Ga,In)N Monolayer Alternating Stacked Structures by First‐Principles Calculations

Group III‐nitrides with doping recently attract great interest because of their outstanding ferroelectric and piezoelectric properties. Herein, the spontaneous polarization and piezoelectricity of the wurtzite III‐nitrides (AN, A = Al, Ga, In) with the rare earth element (R = Sc, Y) doping (w‐R0.5A0.5N) are investigated by first‐principles calculations. The polar w‐R0.5A0.5N and nonpolar h‐R0.5A0.5N are stable, which is proved by the elastic constants and phonon band structures. The w‐Sc0.5In0.5N and w‐Y0.5In0.5N can be applied to the ferroelectric field owing to their very small ferroelectric switching barriers (0.149 eV for w‐Sc0.5In0.5N and 0.042 eV for w‐Y0.5In0.5N) with large ferroelectric polarization (1.088 C m−2 for w‐Sc0.5In0.5N and 0.937 C m−2 for w‐Y0.5In0.5N). Furthermore, the w‐Y0.5In0.5N has a large piezoelectric strain constant d33 (14.018 pC N−1) based on the elastic constant C33 softening and the increase of the piezoelectric constant e33, which is three times larger than that of w‐InN (4.191 pC N−1). It is found that the biaxial tensile strain of 2% along in‐place significantly enhances the d33 and e33, which increase to 35.572 pC N−1 and 2.669 C m−2 from 14.018 pC N−1 and 1.700 C m−2 of free w‐Y0.5In0.5N, respectively.

Effect of Cr and Al on Elastic Constants of FeCrAl Alloys Investigated by Molecular Dynamics Method

The FeCrAl alloy system is recognized as one of the candidate materials for accident-tolerant fuel (ATF) cladding in the nuclear power industry due to its high oxidation resistance under irradiation and high-temperature environments. The concentrations of Cr and Al have a significant effect on elastic properties of the FeCrAl alloy. In this work, elastic constants C11, C12, C44, bulk modulus and shear modulus of FeCrAl alloy were calculated with molecular dynamics methods. We explored compositions with 1–15 wt.% Cr and 1–5 wt.% Al at temperatures from 0 K to 750 K. The results show that the concentrations of Al and Cr have different effects on the elastic constants. When the concentration of Al was fixed, a decrease in bulk modulus and shear modulus with increasing Cr content was observed, consistent with previous experimental results. The dependence of elastic constants on temperature was also the same as in the experiments. Investigations into elastic properties of defect-containing alloys have shown that vacancies, voids, interstitials and Cr-rich precipitations have different effects on elastic properties of FeCrAl alloys. Investigations of elastic properties of defect-containing alloys have shown that vacancies, void, interstitials and Cr-rich precipitations have different effects on elastic properties of FeCrAl alloys. Therefore, the present results indicate that both the Cr and Al concentrations and radiation defects should be considered to develop and apply the FeCrAl alloy in ATF design.

Anomalous elasticity of talc at high pressures: Implications for subduction systems

Talc is a layered hydrous silicate mineral that plays a vital role in transporting water into Earth’s interior and is crucial for explaining geophysical observations in subduction zone settings. In this study, we explored the structure, equation of state, and elasticity of both triclinic and monoclinic talc under high pressures up to 18 GPa using first principles simulations based on density functional theory corrected for dispersive forces. Our results indicate that principal components of the full elastic constant tensor C11 and C22, shear components C66, and several off-diagonal components show anomalous pressure dependence. This non-monotonic pressure dependence of elastic constant components is likely related to the structural changes and is often manifested in a polytypic transition from a low-pressure polytype talc-I to a high-pressure polytype talc-II. The polytypic transition of talc occurs at pressures within its thermodynamic stability. However, the bulk and shear elastic moduli show no anomalous softening. Our study also shows that talc has low velocity, extremely high anisotropy, and anomalously high VP/VS ratio, thus making it a potential candidate mineral phase that could readily explain unusually high VP/VS ratio and large shear wave splitting delays as observed from seismological studies in many subduction systems.

BIẾN DẠNG ĐÀN HỒI VÀ VẬN TỐC SÓNG ĐÀN HỒI CỦA CÁC HỢP KIM TAM NGUYÊN FeCrSi VÀ AuCuSi

The paper uses the model of cubic ternary substitutional and interstitial alloy and conditions in which the interstitial atom concentration is very small compared to the substitutional atom concentration, the substitutional atom concentration is very small compared to the main metal atom concentration. On that basis together with the elastic wave and the elastic deformation theory of this alloy obtained by the statistical moment method, we perform numerical calculations for temperature, pressure, the concentration of substitutional atoms, and concentration of interstitial atoms dependences of the elastic moduli E, K, G, the elastic constants C11, C12, C44, the longitudinal wave velocity Vd and the transverse wave velocity Vn of alloys FeCrSi and AuCuSi. Numerical results for FeCrSi and AuCuSi are compared with that of Fe, FeCr, FeSi, Au, AuCu, AuSi, and other calculations, and experiments. Numerical results for ternary alloys predict experimental results in the future.

Unusual crystal phases of noble metals Ir, Os, and hardness of Ir-Os systems from high throughput density functional calculations

The platinum-group elements (PGMs) owing their high chemical stability, and unique properties, have recently attracted great research interest in various promising applications. Herein using state-of-the-art first-principles evolutionary algorithms, we explore the thermodynamic and mechanical properties of Ir, Os, and their alloys. Hitherto unknown polytype-phases of Ir (6H, 4H, 2H) and Os (6H, 4H) have been predicted, two of these (4H-Ir, and 4H-Os) were recently observed experimentally. Os and, to more extent, Ir polytypes divulge weak thermodynamic instabilities. Phonon dispersion and elastic constants calculations were carried out to demonstrate the dynamical and mechanical stabilities of these phases. For the Ir-Os alloys, four ordered structures (Pm-3 m (IrOs3, Ir3Os), P-6 m2 (IrOs), P-3 m1 (IrOs2)) have been predicted, which are found mechanically and dynamically stables and manifest insignificantly thermodynamic instabilities. Furthermore, our obtained results show that Ir-Os systems evince outstanding mechanical properties, IrOs3 has high bulk modulus (∼421GPa), large shear modulus (∼266GPa), and Young’s modulus (659 GPa); whereas IrOs2 possesses a remarkable large elastic constants C11 (779GPa) and C33 (814GPa). The anisotropic calculations show that IrOs3 exhibits that greatest anisotropy in the universal elastic anisotropy index AU, shear modulus (AG) and Young’s modulus (AE); while IrOs2 has the smallest elastic anisotropy. Moreover, IrOs3 reveals distinguished hardness of 27.6GPa, which is 3% weaker than 2H-Os (28.6GPa), and is so far one of the hardest materials among the PGMs binary alloys.