Calculation Of Elastic Constants Research Articles

Exploring novel phases of Cd–O system at ambient pressure

First-principles evolutionary searches are used to explore stable Cd–O compounds at ambient pressure. Besides the well-known rock-salt CdO, a new cubic thermodynamically stable phase CdO2 with space group Pa3 and two metastable compounds: zinc-blende and wurtzite phases of CdO have been discovered at ambient pressure. Among these, CdO2 was successfully synthesized with perfect structural agreement to our theoretical predictions. The global stability of the well known rock-salt phase of CdO, our calculations of elastic constants and phonon dispersion curves demonstrate that the Pa3, zinc-blende and wurtzite structures are mechanically and dynamically stable. Finally, the state-of-the-art LDA-1/2 methods reveal that at ambient conditions, zinc-blende and wurtzite phases are semiconducting with a direct band gap (Γ–Γ) of 0.89 eV and 0.97 eV respectively; whereas the semiconducting cubic-Pa3 structure shows direct band gap (Γ–Γ) of ∼2.93 eV and an indirect band gap of ∼2.58 eV agreeing well with the experimental value of ∼2.4 eV.

Structural, electronic, sodium diffusion and elastic properties of Na–P alloy anode for Na-ion batteries: Insight from first-principles calculations

Sodium-ion batteries (NIBs) as an alternative to lithium-ion batteries (LIBs) have recently received great attentions because of the relatively high abundance of sodium. Searching for suitable anode materials has always been a hot topic in the field of NIB study. Recent reports show that phosphorus-based materials are potential as the anode materials for NIBs. Using first-principles calculations, herein, we study the atomic and electronic structures, diffusion dynamics and intrinsic elastic properties of various Na–P alloy compounds (NaP5, Na3P[Formula: see text], NaP and Na3P) as the intermediate phases during Na extraction/insertion in phosphorus-based anode materials. It is found that all the crystalline phases of Na–P alloy phases considered in our study are semiconductors with band gaps larger than that of black phosphorus (BP). The calculations of Na diffusion dynamics indicate a relatively fast Na diffusion in these materials, which is important for good rate performance. In addition, the diffusion channels of sodium ions are one-dimensional in NaP5 phase and three-dimensional in other three phases (Na3P[Formula: see text], NaP and Na3P). Elastic constant calculations indicate that all four phases are mechanically stable. Among them, however, NaP5, Na3P[Formula: see text] and NaP alloy phases are ductile, while the fully sodiated phase Na3P is brittle. In order to improve the electrochemical performance of Na–P alloy anodes for NIBs, thus, promoting ductility of Na–P phase with high sodium concentration may be an effective way.

Derivation of enhanced potentials for cerium brannerite and the calculation of lattice and intrinsic defect properties

A new potential has been derived for ceria and used to calculate its lattice and defect properties. The Ce4+⋯O2- potential is obtained via a combination of empirical fitting to crystal structural data and parametric fitting to additional physical properties, while the O2-⋯O2- potential is transferred from earlier publications on UO2 and PuO2. The overall potential is subsequently verified and validated by calculation of elastic and dielectric constants, whose values agree favourably with those measured experimentally. The potential is then employed to calculate intrinsic defect formation energies and predict the most favourable type of intrinsic disorder.

Cubic C₃N: A New Superhard Phase of Carbon-Rich Nitride.

Using the particle swarm optimization technique, we proposed a cubic superhard phase of C3N (c-C3N) with an estimated Vicker’s hardness of 65 GPa, which is more energetically favorable than the recently proposed o-C3N. The c-C3N is the most stable phase in a pressure range of 6.5–15.4 GPa. Above 15.4 GPa, the most energetic favorable high pressure phase R3m-C3N is uncovered. Phonon dispersion and elastic constant calculations confirm the dynamical and mechanical stability of c-C3N and R3m-C3N at ambient pressure. The electronic structure calculations indicate that both c-C3N and R3m-C3N are indirect semiconductor.

First-principle study on the structural, elastic and electronic properties of CrB4 hard material under different pressures

The crystal structures, elastic, mechanical and electronic properties of Pnnm-CrB4 crystal are explored using the first-principles calculation. The lattice constant, elastic constants, bulk modulus are calculated under different pressures. Phonon dispersion and elastic constant calculations show that Pnnm-CrB4 is thermodynamically and mechanically stable at standard pressure. The structural analysis shows that the pressure has different effect for the three axes, and c-axis is the most compressible and b-axis is the least compressible, which is consistent with the analysis of the bulk moduli along a-, b-, and c-axis. In addition, CrB4 behaves in a brittle manner within the given pressure range and the analysis of the Poisson's ratios indicates that CrB4 is a covalent material. Band structure, electron local function and density of states are also calculated. And the results show that no band gap exists in the band structure and CrB4 has the metallic character, which is consistent with the result of density of state.

Theoretical study of high-pressure phase stability of NaZr2(PO4)3 via elastic constants and equation of state

Phase stability of \(\mathrm {NaZr_2(PO_4)_3}\) has been studied through density functional theory calculations of elastic constants, equation of state and enthalpies. The changes in elastic constants as a function of pressure show that the ambient rhombohedral (R\(\bar{3}c\)) \(\mathrm {NaZr_2(PO_4)_3}\) becomes unstable above 8 GPa and this instability is driven by a softening of C\(_{44}\) elastic constant through one of the Born stability criteria. High-pressure equation-of-state and enthalpy calculations further show that the ambient rhombohedral (\(R\bar{3}c\)) structure transforms first into another rhombohedral (R3) phase and subsequently to LiZr\(_2\)(PO\(_4\))\(_3\)-type orthorhombic phase at pressures above 6 and 8 GPa respectively which are in agreement with a recent x-ray diffraction study. Analysis of interatomic distances show that LiZr\(_2\)(PO\(_4\))\(_3\)-type orthorhombic structure allows for shorter Na–O and Zr–P bonds at high pressures which appears to enable strong bonding and stability. Calculated formation enthalpy and bulk modulus of the ambient phase of \(\mathrm {NaZr_2(PO_4)_3}\) are found to be in reasonable agreement with the respective experimental values.

First-principles study of the double perovskites Sr2XOsO6 (X = Li, Na, Ca) for spintronics applications

We investigated double perovskite compounds of the form Sr 2 XOsO 6 (X = Li, Na, Ca) using the full-potential linearized augmented plane wave (FP-LAPW) method. For the exchange-correlation energy, Wu and Cohen generalized gradient approximation (WC-GGA), Perdew, Burke and Ernzerhof GGA (PBE-GGA), Engel and Vosko GGA (EV-GGA), and GGA plus Hubbard U-parameter (GGA + U) were used. The calculated structural parameters are in good agreement with the existing experimental results. Calculation of different elastic constants and elastic moduli reveals that these compounds are elastically stable and possess ductile nature. The GGA + U approach yields quite accurate results of the bandgap as compared with the simple GGA schemes. The density of states plot shows that Sr-4d, Os-5d and O-2p states predominantly contribute to the conduction and valence bands. Further, our results regarding to the magnetic properties of these compounds reveal their ferromagnetic nature. In addition, these compounds seem to possess half-metallic properties, making them useful candidates for applications in spintronics devices.

Higher-order elastic constants and megabar pressure effects of bcc tungsten:Ab initiocalculations

The general method for the calculation of $n\mathrm{th}$ ($n\ensuremath{\ge}2$) order elastic constants of the loaded crystal is given in the framework of the nonlinear elasticity theory. For the crystals of cubic symmetry under hydrostatic compression, the two schemes of calculation of the elastic constants of second, third, and fourth order from energy--finite strain relations and stress--finite strain relations are implemented. Both techniques are applied for the calculation of elastic constants of orders from second to fourth to the bcc phase of tungsten at a 0--600 GPa pressure range. The energy and stress at the various pressures and deformations are obtained ab initio in the framework of projector augmented wave+generalized gradient approximation (PAW+GGA) method, as implemented in Vienna Ab initio Simulation Package (VASP) code. Using the obtained results, we found the pressure dependence of Gr\uneisen parameters for long-wave acoustic modes in this interval. The Lam\'e constants of second and third order were estimated for polycrystalline tungsten. The proposed method is applicable for crystals with arbitrary symmetry.

Nonlinear elastic response and anharmonic properties of MgO single crystal: First-principles investigation

Knowledge of the nonlinear elastic response and anharmonic properties of MgO single crystal is important for interpreting the seismically observed velocity variations in the Earth’s mantle and constructing reliable mineralogical modes of the Earth’s interior. However, investigations on these properties of it have not been performed sufficiently to date. So the nonlinear elastic response of the MgO is first studied by calculating the second-, third-, and fourth-order elastic constants. Results show that our predications on the high-order elastic constants exhibit excellent agreement with the available experimental ones and other theoretical values, which indicates that the present computational approach is suitable for the calculations of the high-order elastic constants and it can be expanded into other complex systems. Then on the basis of the elastic constants, the related anharmonic properties such as the first-order pressure derivatives of the second- and third-order elastic constants, Grüneisen constants of the long-wavelength acoustic modes, and ultrasonic nonlinear parameters are also investigated. The predications on the anharmonic properties first given in the present work are hoped to serve as a valuable guidance or reference for further related investigations.

Ground state of the U2Mo compound: Physical properties of the Ω-phase

Using ab initio calculations, unexpected structural instability was recently found in the ground state of the U2 Mo compound. Instead of the unstable I4/mmm and the Pmmn structures, in this work the P6/mmm (#191) space group, usually called Ω-phase, is proposed as the fundamental state. Total energy calculations using Wien2k code slightly favoured the last structure. Electronic and elastic properties are studied in this work in order to characterize the physical properties of this new phase. The stability of the Ω-phase is studied by means of its elastic constants calculation and phonon dispersion spectrum. Analysis of isotropic indices shows that the new phase is a ductile material with a minimal degree of anisotropy, suggesting that U2 Mo in the P6/mmm structure is an elastic isotropic material. Analysis of charge density, density of electronic states (DOS) and the character of the bands revealed a high level of hybridization between d-molybdenum electronic states and d- and f-uranium ones.

First principles calculations of formation energies and elastic constants of inclusions α-Al2O3, MgO and AlN in aluminum alloy

In this paper, the formation energies and elastic constants of [Formula: see text]-Al2O3, MgO and AlN in both rock salt (cubic) and wurtzite (hexagonal) structures were investigated by first principles calculations. The results show that the formation energy being −17.8, −6.3, −3.06 and −3.46 eV/formula unit for [Formula: see text]-Al2O3, MgO, AlN (rock salt) and AlN (wurtzite). It suggests that in the ground state, [Formula: see text]-Al2O3 is relatively more stable than MgO and AlN. The elastic properties for a polycrystalline in the ground state were calculated with the obtained elastic constants, the elastic properties reveal the rock salt structure AlN is the hardest particles among all the inclusions, and all of these inclusions are classified as brittle materials, which is detrimental to the ductile nature of aluminum matrix. The calculated anisotropy index shows that the AlN (wurtzite) and [Formula: see text]-Al2O3 have a lower degree of anisotropy compared with MgO and AlN (rock salt). The calculated results are in good agreement with the values of experimental and other works.

Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond

Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g., diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elastic constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than themore » TOECs reported in previous theoretical studies. Lastly, our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.« less

Evidence of the stability of Mo2TiAlC2 from first principles calculations and its thermodynamical and optical properties

The elastic, thermodynamic, and optical properties of Mo2TiAlC2 are investigated by first-principles calculations. Our results indicate that the a axis is stiffer than c axis within 0–100GPa. Elastic constants calculations predict the large stability range of Mo2TiAlC2 under pressure. Several important thermodynamic properties are discussed detailedly, including the Debye temperature, thermal expansion coefficient, and heat capacity. The bonding properties are studied from the elastic quantities and electronic properties. The electronic properties are investigated, including the energy band structure, and density of states. The evidence of the instability of Mo3AlC2 and stability of Mo2TiAlC2 are successfully obtained.

The Stable or Metastable Phases in Compressed Zn-O Systems**Supported by the National Natural Science Foundation of China under Grant No 11347007, the Qing Lan Project, the Colleges and Universities in Jiangsu Province Natural Science Research Project under Grant No 14KJB460013, and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Variable-composition evolutionary structure searches are used to explore stable stoichiometries for the Zn-O system below 300 GPa. Our results confirm the previous structural phase transition sequence of pressurised ZnO. ZnO is thermodynamically stable up to 300 GPa and zinc peroxide (ZnO2, space group Pa3̄) is metastable under lower pressure. Insulating I4/mcm-ZnO2 is thermodynamically stable between 128.3–300 GPa. Insulated metastable P3121-ZnO2, controlling the pressure range of 51.5–128.3 GPa, has a wide band gap compared to the Pa3̄-ZnO2 and I4/mcm-ZnO2. Phonon and elastic constant calculations conclude the dynamical and mechanical stability for the explored thermodynamically stable or metastable structures.

The calculation of radial and tangential force constants for nickel using an experimental phonon spectrum

The possibility of calculating radial and tangential force constants, as well as elastic constants of face-centered cubic (FCC) metals, has been demonstrated for the case study of nickel on the basis of the experimentally measured phonon spectrum, which is theoretically described by the DeLaunay model in terms of the dynamic matrix D(q). The proposed calculation procedure is an alternative to the Born–von Karman model, which is widely applied for the description of the phonon spectrum in terms of force constants for interatomic interactions and in calculations of elastic constants using the phonon spectrum. The reliability of the obtained force constants for phonon spectrum was verified by comparison between the experimental and calculated data for the phonon spectrum and elastic constants for nickel. The obtained values of force constants for nickel have been compared with the theoretically calculated values using the pseudopotential method.

Prediction of a Superhard Carbon-Rich C–N Compound Comparable to Diamond

Until now, it has been a challenge both in experiment and in theory to design new superhard materials with high hardness values that are comparable to that of diamond. Here, by using first-principles calculations, we have introduced two new phases for a carbon-rich C–N compound with stoichiometry C3N, which is predicted to be energetically stable or metastable with respect to graphite and solid N2 at ambient pressure. It is found that C3N has a layered structure containing graphitic layers sandwiched with freely rotated N2 molecules. The layer-structured C3N is calculated to transform into a three-dimensional C2221 structure at 9 GPa with sp3-hybridized C atoms and sp2-hybridized N atoms. Phonon dispersion and elastic constant calculations reveal the dynamical and mechanical stability of the C2221 phase of C3N at ambient pressure. Significantly, first-principles ideal strength calculations indicate that the C2221 phase of C3N is a superhard material with an estimated Vickers hardness (∼76 GPa) comparable ...

Calculation of Elastic Bond Constants in Atomistic Strain Analysis.

Strain analysis has significance both for tailoring material properties and designing nanoscale devices. In particular, strain plays a vital role in engineering the growth thermodynamics and kinetics and is applicable for designing optoelectronic devices. In this paper, we present a methodology for establishing the relationship between elastic bond constants and measurable parameters, i.e., Poisson’s ratio ν and systematic elastic constant K. At the atomistic level, this approach is within the framework of linear elastic theory and encompasses the neighbor interactions when an atom is introduced to stress. Departing from the force equilibrium equations, the relationships between ν, K, and spring constants are successfully established. Both the two-dimensional (2D) square lattice and common three-dimensional (3D) structures are taken into account in the procedure for facilitating, bridging the gap between structural complexity and numerical experiments. A new direction for understanding the physical phenomena in strain engineering is established.

Theoretical prediction of the structural, electronic, mechanical and thermodynamic properties of the binary α-As2Te3 and β-As2Te3

The structural, electronic, mechanical and thermodynamic properties of α- and β-As2Te3 are investigated by using the first-principles. The optimized lattice constants of α- and β-As2Te3 are in a good agreement with the available experimental data. The electronic structures suggest that both of α and β phases are semiconductor. Further calculations of elastic constants confirm that both of them are mechanically stable and the β phase is stiffer than α phase. Furthermore, the ratio values of B/G and hardness are also calculated. The results reveal that α phase is ductile while β phase is brittle, and the hardness value is 3.56 GPa and 7.44 GPa for α and β phase, respectively. In addition, the 3D directional dependences of the reciprocal of Young's modulus and bulk modulus for α and β phase are also obtained. The results show that α phase exhibits remarkable anisotropy. Finally, the Debye temperature and minimum thermal conductivity are obtained.

New crystal structure and physical properties of TcB from first-principles calculations**Project supported by the Science Foundation of Baoji University of Arts and Sciences of China (Grant No. ZK11061) and the Natural Science Foundation of the Education Committee of Shaanxi Province, China (Grant Nos. 2013JK0637, 2013JK0638, and 2014JK1044).

By combining first-principles calculations with the particle swarm optimization algorithm, we predicted a hexagonal structure for TcB, which is energetically more favorable than the previously reported WC-type and Cmcm structures. The new phase is mechanically and dynamically stable, as confirmed by its phonon and elastic constants calculations. The calculated mechanical properties show that it is an ultra-incompressible and hard material. Meanwhile, the elastic anisotropy is investigated by the shear anisotropic factors and ratio of the directional bulk modulus. Density of states analysis reveals that the strong covalent bonding between Tc and B atoms plays a leading role in forming a hard material. Additionally, the compressibility, bulk modulus, Debye temperature, Grüneisen parameter, specific heat, and thermal expansion coefficient of TcB are also successfully obtained by using the quasi-harmonic Debye model.

Ab initio calculations of polarization, piezoelectric constants, and elastic constants of InAs and InP in the wurtzite phase

We report first-principle density functional calculations of the spontaneous polarization, piezoelectric stress constants, and elastic constants for the III–V wurtzite structure semiconductors InAs and InP. Using the density functional theory implemented in the VASP code, we obtain polarization values–0.011 and–0.013 C/m2, and piezoelectric constants e33 (e31) equal to 0.091 (–0.026) and 0.012 (–0.081) C/m2 for structurally relaxed InP and InAs respectively. These values are consistently smaller than those of nitrides. Therefore, we predict a smaller built-in electric field in such structures.