Electronic Structure and Thermodynamic Properties of the Cubic Antiperovskite Compound InNCe_{3} via First-Principles Calculations

Elastic, thermodynamic, electronic, and magnetic properties in the cubic antiperovskite InNCe $_{3}$ 3 compound are derived from the full-potential linear muffin-tin orbital method. From the computed elastic constants, theoretical values of Young’s modulus, the shear modulus, Poisson’s ratio, Lamé’s coefficients, sound velocities, and the Debye temperature are evaluated. Analysis of the ratio between the bulk modulus and the shear modulus shows that InNCe $_{3}$ 3 is brittle in nature. The variations of elastic constants with pressure indicate that this compound possesses higher mechanical stability in the pressure range from 0 to 40 GPa. The electronic and magnetic properties of this compound are calculated by adding the Coulomb interaction $U$ U to improve the results.     

Elastic, optoelectronic, and thermal properties of cubic CSi2N4: an ab initio study

The mechanical, optoelectronic, and thermodynamic properties of carbon silicon nitride spinel compound have been investigated using density functional theory. The exchange–correlation potential was treated with the local density approximation (LDA) and the generalized gradient approximation of Perdew–Burke and Ernzerhof (PBE-GGA). In addition, the Engel–Vosko generalized gradient approximation (EV-GGA) and the modified Becke–Johnson potential (TB-mBJ) were also applied to improve the electronic band structure calculations. The ground state properties, including lattice constants and bulk modulus, are in fairly good agreement with the available theoretical data. The elastic constants, Young’s modulus, shear modulus, and Poisson’s ratio have been determined by using the variation of the total energy with strain. From the elastic parameters, it is inferred that this compound is brittle in nature. The results of the electronic band structure show that CSi₂N₄ has a direct energy band gap (Γ–Γ). The TB-mBJ approximation yields larger fundamental band gaps compared to those of LDA, PBE-GGA, and EV-GGA. In addition, we have calculated the optical properties, namely, the real and the imaginary parts of the dielectric function, refractive index, extinction coefficient, reflectivity, and energy loss function for radiation up to 40.0 eV. Using the quasi-harmonic Debye model which considers the phononic effects, the effect of pressure P and temperature T on the lattice parameter, bulk modulus, thermal expansion coefficient, Debye temperature, and the heat capacity for this compound were investigated for the first time.     

Prediction Study of the Mechanical and Thermodynamic Properties of the \hbox {RBRh}_{3} (R = Sm, Eu, Gd, and Tb) Compounds

The structural, elastic, and thermodynamic properties of the cubic anti-perovskite $\hbox {RBRh}_{3}$ (R = Sm, Eu, Gd, and Tb) compounds have been investigated using first principles full-potential augmented-plane wave plus local orbitals (FP-APW+lo) method with the generalized gradient approximation. The ground-state quantities such as the lattice parameter, bulk modulus, and its pressure derivative, as well as elastic constants are estimated. Computed equilibrium lattice constants agree well with the available experimental data. The full set of first-order elastic constants and their pressure dependence, which have not been calculated or measured yet, have been determined. The elastic moduli increase linearly with increasing pressure and satisfy the generalized elastic stability criteria for cubic crystals under hydrostatic pressure. The shear modulus, Young’s modulus, and Poisson’s ratio are calculated for ideal polycrystalline $\hbox {RBRh}_{3}$ aggregates. The Debye temperature is estimated from the average sound velocity. From the elastic parameter behavior, it is inferred that cubic anti-perovskites $\hbox {RBRh}_{3}$ are ductile in nature and that the bonding is predominantly of an ionic nature. Following the quasi-harmonic Debye model, the temperature effect on the lattice constant, bulk modulus, heat capacity, and Debye temperature is calculated reflecting the anharmonic phonon effects.     

First-Principles Investigations on Structural,Phonon, and Thermodynamic Properties of Cubic \text {CeO}_{2}

The structural, phonon, and thermodynamic properties of the cubic \(\hbox {CeO}_{2}\) are investigated from first-principles calculations. The calculated lattice parameters, bulk modulus, and phonon dispersion curves are in agreement with available experimental data and other calculations. It is shown that the local density approximation (LDA)+ \(U\) method is more suitable for describing the properties of \(\hbox {CeO}_{2}\) compared with the LDA method. The pressure and temperature dependences of the specific heat, Debye temperature, and the thermal expansion coefficient are successfully obtained from the Debye–Grüneisen model by combining with the phonon density of states.     

Elastic Properties of Monoclinic \hbox {ZrO}_{2} at Finite Temperatures Via First Principles

The structural and elastic properties of orthorhombic $\hbox {ZrO}_{2}\,(m\hbox {-ZrO}_{2})$ as a function of temperature are investigated by the generalized gradient approximation (GGA) correction scheme in the framework of density functional theory (DFT) and the quasi-harmonic Debye model. The thirteen independent elastic constants of $m\hbox {-ZrO}_{2}$ at temperatures to 3200 K are theoretically investigated for the first time. It is found that with increasing temperature, all elastic constants change, especially $C_{35}\hbox { and }C_{25}$ change rapidly in the temperature range of 1400 K to 1600 K and 2200 K to 2600 K, respectively. We also obtain the bulk modulus $B$ , shear modulus $G$ , Young’s moduli $E$ , as well as Poisson’s ratio $\sigma $ of $m\hbox {-ZrO}_{2}$ at high temperatures. Our work suggests that it is very important to predict the melting properties of materials via the elastic constants at temperatures.     

Structural and lattice dynamical properties of Zintl NaIn and NaTl compounds

The first-principles calculations based on the density-functional theory have been performed using both the generalized–gradient approximation (GGA) and the local-density approximation (LDA) to investigate many physical properties of NaIn and NaTl compounds. Specifically, the structural (lattice constant, bulk modulus, pressure derivative of bulk modulus, phase transition pressure (P_t)), mechanical (second-order elastic constants (C_ij), Young’s modulus, isotropic shear modulus, Zener anisotropy factor, Poisson’s ratio, sound velocities), thermo dynamical (cohesive energy, formation enthalpy, Debye temperature), and the vibrational properties (phonon dispersion curves and one-phonon density of states) are calculated and compared with the available experimental and other theoretical data. Also, we have presented the temperature variations of various thermo dynamical properties such as free energy, internal energy, entropy and heat capacity for the same compounds.     

Electronic Structure,Phase Stability,and Elastic Properties of Inverse Heusler Compound Mn<Subscript>2</Subscript>RuSi at High Pressure

The structural, magnetic, electronic, and elastic properties of the new Mn-based Heusler alloy Mn₂RuSi at high pressure have been investigated using the first-principles calculations within density functional theory. Present calculations predict that Mn₂RuSi in stable \(F\bar {4}3m\) configuration is a ferrimagnet with an optimized lattice parameter 5.76 Å. The total spin magnetic moment is 2.01 μ _B per formula unit and the partial spin moments of Mn (A) and Mn (B) which mainly contribute to the total magnetic moment are 2.48 and ?0.66 μ _B, respectively. Mn₂RuSi exhibits half metallicity with an energy gap in the spin-down channels. The study of phase stability indicates that the elastic stiffness coefficients of Mn₂RuSi with \(F\bar {4}3m\) structure satisfy the traditional mechanical stability restrictions until up to 100 GPa. In addition, various mechanical properties including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio along with elastic wave velocitieshave also been obtained and discussed in details in the pressure range of 0–100 GPa based on the three principle elastic tensor elements C ₁₁, C ₁₂, and C ₄₄ for the first time.     

GGA and GGA+U Description of Structural, Magnetic, and Elastic Properties of Rh2MnZ (Z=Ge, Sn, and Pb)

Structural, magnetic, electronic, and elastic properties of Rh₂MnGe, Rh₂MnSn, and Rh₂MnPb Heusler compounds have been calculated using full potential linearized augmented-plane wave plus local orbitals (FP-L/APW+lo) method based on the spin density functional theory, within the generalized gradient approximation (GGA) and (GGA+U) (U is the Hubbard correction). Results are given for the lattice parameters, bulk moduli, spin magnetic moments and elastic constants. We have derived the bulk and the shear moduli, Young’s and Poisson’s ratio for Rh₂MnZ (Z=Ge, Sn, and Pb). The elastic modulus of Rh₂MnGe is predicted to be the highest. Also, we have estimated the Debye temperatures from the average sound velocity. We discuss the electronic structures, total and partial densities of states and local moments and we investigate the pressure effect on the elastic properties by calculating the elastic constants at various volumes.     

Structural,electronic, elastic and thermodynamic properties of AlSi2RE (RE = La,Ce, Pr and Nd) from first-principle calculations

It is of academic interest to study the ternary intermetallic compounds of the Al–Si–RE system for the development of both structural and functional materials. In this work, the structural, electronic, elastic and thermodynamic properties of the AlSi₂RE (RE = La, Ce, Pr and Nd) compounds was investigated using first-principle calculations based on density functional theory. The calculated structural parameters of AlSi₂RE compounds are consistent with the experimental data. Due to the fact that there is strong Coulomb correlation among the partially filled 4f electron for RE atoms, we present a combination of the GGA and the LSDA + U approaches to investigate the electronic structures of Al₃RE compounds in order to obtain the appropriate results. The elastic constants were determined from a linear fit of the calculated stress–strain function according to Hooke’s law. The bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio ν of polycrystalline AlSi₂RE compounds were determined using the Voigt–Reuss–Hill (VRH) averaging scheme. The Debye temperature of AlSi₂RE compounds can be obtained from elastic constants. The temperature dependence of the internal energy, free energy, entropy and heat capacity for AlSi₂RE compounds were also calculated by using the quasi-harmonic approximation.     

The effect of the phase transition on the elasticity of cubic platinum carbide

A study of the high-pressure elastic properties of ideal stoichiometric platinum carbide (PtC) in the rock-salt (RS) and zinc-blende (ZB) structures was conducted using first-principles calculations based on density functional theory, in which we employ the generalized gradient approximation of the Perdew–Burke–Eruzerhof form together with plane-wave basis sets for expanding the crystal orbitals and periodic electron density. Our calculation shows that the recently synthesized compound PtC possess a high-bulk modulus value in the RS phase and the ZB phase is more stable. The investigation of the elastic stability under pressure indicated that the transition pressure from ZB to RS structure of PtC is about 30 GPa and the high-pressure RS phase is stable up to 100 GPa. Our conclusions are consistent with the other theoretical predictions but are reversed with the diamond anvil cell experimental results. Therefore, the experimental observation of the RS structure in PtC remains a puzzle and our study indicates that more experimental and theoretical works need to be performed to ascertain the true nature of the newly discovered PtC material. In addition, the pressure dependence of the bulk modulus K, the shear modulus G, the Young’s modulus E, the Poisson’s ratio υ, the Debye temperature Θ _D, the compressional wave velocity V _p, the shear wave velocity V _s, and the elastic anisotropy factor A for the ZB and RS structures of PtC are all successfully obtained. Moreover, the pressure dependence of the longitudinal and the shear wave velocities in three directions [100], [110], and [111] for cubic PtC are also predicted for the first time.     

Electronic,elastic and optical properties on the Zn<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Mg<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se mixed alloys

The structural, elastic, electronic and optical properties of Zn_1−x Mg _x Se ternary mixed crystals are investigated by utilizing the first-principles plane-wave pseudopotential method within the LDA approximations. Some basic physical properties, such as lattice constant, bulk modulus, second-order elastic constants (C _ij ), Shear modulus, Young’s modulus, Poison’s ratio, Lamé constants and the electronic band structures, are calculated. We have, also, predicted the optical properties such as dielectric functions, refractive index and energy loss function of these ternary mixed crystals. Our results agree well with the available data in the literature.     

First principles investigation on the structural, mechanical and electronic properties of OsC2

The structural, mechanical and electronic properties of OsC₂ were investigated by use of the density functional theory. Seven structures were considered, i.e., orthorhombic Cmca (No. 12, OsSi₂), Pmmn (No. 59, OsB₂) and Pnnm (No. 58, OsN₂); tetragonal P4₂/mnm (No. 136, OsO₂) and I4/mmm (No. 139, CaC₂); cubic Fm–3m (No. 225, CaF₂) and Pa-3 (No. 205, PtN₂). The results indicate that Cmca in OsSi₂ type structure is energetically the most stable phase among the considered structures. It is also stable mechanically. OsC₂ in Pmmn phase has the largest bulk modulus 319 GPa and shear modulus 194 GPa. The elastic anisotropy is discussed.     

First-principles calculations of the structural and elastic properties of OsSi2 at high pressure

We investigated the pressure dependence of the structural and elastic properties of OsSi₂ in the range 0–60 GPa using first-principles calculations based on density functional theory. Calculations were performed within the local density approximation as well as the generalized gradient approximation to the exchange correlation potential. The calculated lattice constants and atomic fractional coordinates are in good agreement with previous experimental results. The pressure dependence of nine independent elastic constants, c₁₁, c₂₂, c₃₃, c₄₄, c₅₅, c₆₆, c₁₂, c₁₃, and c₂₃, of orthorhombic OsSi₂ has been evaluated. The isotropic bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, elastic anisotropy, and Debye temperature of polycrystalline OsSi₂ under pressure are also presented.     

First-principles study of structural,elastic, electronic and optical properties of orthorhombic NaAlF4

We have performed the ab initio total energy calculations using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT) to study the structural parameters, elastic, electronic, chemical bonding and optical properties of orthorhombic NaAlF₄. The calculated lattice parameters are in good agreement with experimental work. The bulk, shear and Young’s modulus, Poisson’s coefficient, compressibility and Lamé’s constants are firstly obtained using Voigt–Reuss–Hill method and the Debye temperature is estimated using Debye-Grüneisen model. Band structure shows a direct band gap at Γ point. Density of states and charge density have been studied, which show the bonding between Na and F is mainly ionic as well as that between Al and F. In order to clarify the mechanism of optical transitions of orthorhombic NaAlF₄, the complex dielectric function, refractive index, extinction coefficient, reflectivity, absorption efficient, loss function and complex conductivity function are calculated. The optical properties and origins of the structure have been analysed.     

Structural,elastic, and lattice dynamical properties of YB2 compound

In this work, density functional theory calculations on the structural, mechanical, lattice dynamical, and thermodynamical properties of YB₂ in AlB₂-type and monoclinic (C2/m) structures are reported. The local density approximation has been used for modeling exchange–correlation effects. We have predicted the lattice constants, bulk modulus, elastic constants, shear modulus, Young’s modulus, Poison’s ratio, Debye temperature, and sound velocities. Furthermore, the phonon dispersion curves, corresponding phonon density of states, some thermodynamical quantities such as internal energy, entropy, heat capacity, and their temperature-dependent behaviors are presented. Our structural and some other results are in agreement with the available experimental and theoretical data.     

The electronic, elastic and structural properties of Pd-Zr intermetallic

A first-principles plane-wave pseudopotential method based on the density functional theory was used to investigate the energetic, electronic structures and elastic properties of intermetallic compounds of Pd-Zr system. The Enthalpies of formation, the cohesive energies and elastic constants of these compounds were estimated from the electronic structure calculations and their structural stability was also analyzed. The results show that the PdZr₂ compound is stable, relative to other compounds, and as the concentration of Pd increases, the enthalpy of formation gradually increased except Pd₄Zr_3.The calculated elastic constants are then used to estimate mechanical properties of Pd-Zr intermetallics compounds. The brittle/ductile behavior is assessed by analyzing the phenomenological formula G/B of shear modulus (G) over bulk modulus (B). The new knowledge from this study could be used for future development of Pd-Zr system.     

FP-LAPW Calculation of Elastic, Thermal Properties and Chemical Bonding of Heavy REN (RE = Tb–Lu)

The full-potential linearised augmented plane wave (FP-LAPW) method has been used to study the elastic, thermal and bonding properties of heavy rare earth nitrides REN (RE = Tb–Lu). In the present work, band structure and density of states of TbN–LuN are studied. We have calculated the Young’s modulus E, shear modulus G, bulk modulus B, Poisson’s ratio υ, shear anisotropy factor A, and Lame’s coefficients μ & λ for all these compounds. Thermal property such as Debye temperature and average sound velocity have been estimated for all these compounds and their relation to elastic properties is discussed. To understand the bonding nature of these compounds, the electronic charge density has been calculated for all these compounds and the relation of this bonding with the mechanical properties has been studied. From the calculated ratio of bulk to shear modulus B/G, these compounds are found to be brittle in nature. The value of Poisson’s ratio suggests that these compounds are ionic and this is in agreement with the charge density plots which show the ionic bonding nature of these compounds. The G values show that these compounds are easier to shear on the plane [110] rather than on plane [100] for all the compounds except YbN.     

First-principles calculations of elastic moduli of Ti–Mo–Nb alloys using a cluster-plus-glue-atom model for stable solid solutions

Using the first-principles calculations, a cluster-plus-glue-atom model was employed to investigate the elastic and electronic properties of Ti–Mo–Nb alloys with cluster formula of [MoTi₁₄] (glue atom) _x (glue atom = Ti, Mo, Nb, x = 1 or 3) for a theoretical guidance in composition design of β titanium alloys. The bulk modulus, shear modulus, Young’s modulus, and Poisson ratio were evaluated from the calculated elastic constants using Voigt–Reuss–Hill average scheme on the periodic supercell model of cluster packing. The electronic properties of the Ti–Mo–Nb alloys were discussed by analyzing the electron density of state and Mulliken population. Meanwhile, we designed two series of Ti–Mo–Nb alloys, i.e., [MoTi₁₄]X₁ (X = Ti, Mo, Nb) and [YTi₁₄]Nb₃ (Y = Ti, Mo), and experimentally measured their mechanical properties. Our theoretical results (including mass density, Young’s modulus, ductility) based on our cluster packing model agreed well with the experimental data, especially for [TiMo₁₄]X₁ (X = Ti, Mo, Nb) alloy series. On the contrary, the random solid solution structures were mechanically unstable and the calculated values significantly deviated from the experiments. Based on the cluster-plus-glue-atom model, an Ashby map of E/ρ versus B/G was constructed and indicated the inverse correlation between stiffness and ductility, for which the random solid solution model was unable to reflect. The Mo/Ti = 1/14 rule derived from the cluster model may serve as an important guideline for composition design of Ti–Mo based systems to achieve low elastic modulus alloys with stable β phase.     

First-principles studies of typical long-period superstructures Al5Ti3, h-Al2Ti and r-Al2Ti in Al-rich TiAl alloys

First-principles calculations are performed to study the structural stabilities, electronic and elastic properties of typical long-period superstructures Al₅Ti₃, h-Al₂Ti and r-Al₂Ti in Al-rich TiAl alloys together with γ-TiAl. The obtained lattice parameters by relaxation of crystalline cells are in good agreement with the experimental data. The calculated formation enthalpies show that r-Al₂Ti has the highest structure stability from energetic point of view, and then followed by h-Al₂Ti, Al₅Ti₃ and γ-TiAl. The electronic density of states and charge density distribution indicate that due to strong hybridization between Al-2p and Ti-3d, there is a strong directional bonding between Ti and Al atoms. The elastic constants are calculated, suggesting that these structures are mechanically stable. Bulk modulus B, shear modulus G, Young’s modulus E and Poison’s ratio ν of polycrystalline materials are derived from the elastic constants. By several criteria, elastic anisotropies are analyzed, showing that these structures possess different degree of anisotropies.