Influence of La doping on elastic and thermodynamic properties of SrMoO3

The elastic and thermodynamic properties for Sr_1−xLa_xMoO₃ (x = 0.0, 0.05, 0.1, 0.15, and 0.2) with temperature have been investigated, probably for the first time, by using modified rigid ion model (MRIM). The computed results on the elastic constants (C₁₁, C₁₂, and C₄₄) are the first report on them. Using these elastic constants we have computed other elastic properties such as B, β, G′, G, E, σ, B/G ratio, Cauchy pressure (C₁₂ − C₄₄) and Lame's parameters (μ, λ). We have also reported the thermodynamic properties such as ?, f, θ_D, θ_D1, υ₀, υ₁, γ, and α. The values of Young's modulus, shear modulus and compressibility for SrMoO₃ are in good agreement with the available experimental data. The concentration (x) dependence of θ_D in Sr_1−xLa_xMoO₃ suggests that increased La doping drives the system effectively away from the strong electron-phonon coupling regime. Specific heat is reported in the wide temperature range and compared with the respective experimental data available in the literature. The thermal expansion coefficient of SrMoO₃ is in good agreement with the other theoretical data.     

Structural,electronic, elastic,mechanical and thermal behavior of RESn3(RE = Y,La and Ce) compounds: A first principles study

The structural, electronic, elastic, mechanical and thermal properties of the isostructural and isoelectronic nonmagnetic RESn₃ (RE = Y, La and Ce) compounds, which crystallize in AuCu₃-type structure, are studied using first principles density functional theory based on full potential linearized augmented plane wave (FP-LAPW) method. The calculations are carried out within PBE-GGA, WC-GGA and PBE-sol GGA for the exchange correlation potential. Our calculated ground state properties such as lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′) are in good agreement with the experimental and other available theoretical results. We first time predict the elastic constants for these compounds using different approximations of GGA. All these RESn₃ compounds are found to be ductile in nature in accordance with Pugh's criteria. The computed electronic band structures and density of states show metallic character of these compounds. The elastic properties including Poisson's ratio (σ), Young's modulus (E), shear modulus (G_H) and anisotropy factor (A) are also determined using the Voigt–Reuss–Hill (VRH) averaging scheme. The average sound velocities (v_m), density (ρ) and Debye temperature (θ_D) of these RESn₃ compounds are also estimated from the elastic constants. We first time report the variation of elastic constants, elastic moduli, Cauchy's pressure, sound velocities and Debye temperatures of these compounds as a function of pressure.     

Electronic structure,phase stability and elastic properties of ruthenium based four intermetallic compounds: Ab-initio study

The structural, electronic and elastic properties of four RuX (X = Sc, Ti, V and Zr) intermetallic compounds have been investigated by using density functional theory within full potential linearized augmented plane wave method and using generalized gradient approximations in the scheme of Perdew, Burke and Ernzrhof (PBE), Wu and Cohen (WC) and Perdew et al. (PBEsol) for the exchange correlation potential. The relative phase stability in terms of volume-energy and enthalpy-pressure for these compounds is presented for the first time in three different (B₁, B₂ and B₃) structures. The total energy is computed as a function of volume and fitted to Birch equation of states to find the ground state properties such as lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′). It is found that the lattice parameters in B₂-phase agree well with the existing experimental and previous theoretical results. The second order elastic constants (SOECs) are also predicted for the above compounds. All the four compounds show ductile behavior. The ductility of these compounds has been analyzed using Pugh's rule. From the plots of electronic density of states (DOS), it can be concluded that these intermetallic compounds are metallic in nature.     

Structural,half-metallic and elastic properties of the half-Heusler compounds NiMnM (M = Sb,As and Si) and IrMnAs from first-principles calculations

The structural, half-metallic and elastic properties of the half-Heusler compounds NiMnM (M = Sb, As and Si) and IrMnAs were investigated using first-principles calculations within the generalized gradient approximation (GGA) based on density function theory (DFT). The most stable lattice configurations about site occupancy are (Ni)_4a(Mn)_4c(Sb)_4d, (Ni)_4a(Mn)_4c(As)_4d, (Ni)_4a(Mn)_4c(Si)_4d and (Ir)_4a(Mn)_4c(As)_4d, respectively, and the exchange of elements in Wyckoff position 4c and 4d results in an identical (symmetry-related) phase. The half-Heusler compounds show half-metallic ferromagnetism with a half-metallic gap of 0.168 eV, 0.298 eV, 0.302 eV and 0.109 eV, respectively, and the total magnetic moments (M_tot) are 4.00 μ_B, 4.00 μ_B, 3.00 μ_B and 3.00 μ_B per formula unit, respectively, which agree well with the Slater–Pauling rule based on the relationship of valence electrons. The compound (Ir)_4a(Mn)_4c(As)_4d with half-metallic ferromagnetic character was reported for the first time. The individual elastic constants, shear modulus, Young's moduli, ratio B/G and Poisson's ratio were also calculated. The compounds are ductile based on the ratio B/G. The Debye temperatures derived from the average sound velocity (ν_m) are 327 K, 332 K, 434 K and 255 K, respectively. The predicted Debye temperature for NiMnSb agrees well with the available experimental value, and the Debye temperatures for the rest three compounds were reported for the first time.     

Theoretical prediction of the structural,elastic, electronic and thermal properties of the MAX phases X2SiC (X = Ti and Cr)

The structural, elastic, electronic and thermal properties of the MAX phases Ti₂SiC and Cr₂SiC are studied by means of the pseudo-potential plane wave method within GGA and LDA. The effect of pressure on the normalized lattice constants a/a₀ and c/c₀ and the internal parameter z is investigated. Our results of elastic constants, sound velocities and Debye temperature are predictions. The Ti₂SiC and Cr₂SiC compounds behave as ductile material and show a stronger anisotropy. The analysis of the band structure and density of states show that these compounds are electrical conductors, having a strong directional bonding between Ti and C and Cr and C atoms assured by the hybridization of Ti–d and Cr–d atom states with C–p atom states. The thermal effect on the primitive cell volume, bulk modulus, heat capacities C_V and C_P were predicted using the quasi-harmonic Debye model.     

Mechanical and phonon properties of the superhard LuB2, LuB4, and LuB12 compounds

We have studied structural, elastic, and lattice dynamical properties of the LuB_2, LuB_4, and LuB₁₂ compounds by using the plane-wave pseudopotential approach to the density-functional theory within the generalized gradient approximation. We have considered three different crystal structures of LuB_x: LuB₂ (P6/mmm), LuB₄ (P4/mbm), and LuB₁₂ (Fm-3m). The most stable structure is found to be tetragonal (P4/mbm) structure. The comparative results on the basic physical parameters such as lattice constants, bulk modulus, bond distances, elastic constants, shear modulus, Young's modulus, and Poison's ratio are reported. Also, we have predicted that LuB₄ and LuB₁₂ compounds are potential superhard materials. Furthermore, the phonon dispersion curves and corresponding phonon density of states (DOS) are computed for considered phases. Our structural and some other results are in agreement with the available experimental and other theoretical data.     

First-principle calculations of structural,elastic and thermodynamic properties of Fe–B compounds

The structural, elastic and thermodynamic properties of FeB, Fe₂B, orthorhombic and tetrahedral Fe₃B, FeB₂ and FeB₄ iron borides are investigated by first-principle calculations. The elastic constants and polycrystalline elastic moduli of Fe–B compounds are usually large especially for FeB₂ and FeB₄, whose maximum elastic constant exceeds 700 GPa. All of the six compounds are mechanically stable. The Vickers hardness of FeB₂ is estimated to be 31.4 GPa. Fe₂B and FeB₂ are almost isotropic, while the other four compounds have certain degree of anisotropy. Thermodynamic properties of Fe–B compounds can be accurately predicted through quasi-harmonic approximation by taking the vibrational and electronic contributions into account. Orthorhombic Fe₃B is more stable than tetrahedral one and the phase transition pressure is estimated to be 8.3 GPa.     

Theoretical prediction of the electronic structure,bonding behavior and elastic moduli of scandium intermetallics

We report the structural, electronic, bonding, elastic and mechanical properties of nine scandium intermetallic compounds, ScTM (TM = Co, Rh, Ir, Ni, Pd, Pt, Zn, Cd and Hg), using ab initio density functional theory with the generalized gradient approximation for exchange and correlation potentials. The calculated structural parameters, such as the lattice constant (a₀), bulk modulus (B) and its pressure derivative (B₀) and elastic constants, are calculated using the CsCl-(B₂ phase) structure. The electronic and bonding properties of the ScX compounds are quantitatively analyzed using band structures, DOS, Fermi surfaces and contour plots. The mechanical properties and ductile behaviors of these compounds are also predicted based on the calculated elastic constants.     

Theoretical investigation of typical fcc precipitates in Mg-based alloys

First-principles calculations were performed to study structural, elastic and electronic properties of typical face-centered cubic (fcc) precipitates of Mg-based alloys (Mg₃Gd, Mg₃Gd_0.5Y_0.5 and Mg₃Zn₃Y₂) within the generalized gradient approximation. The calculated results show that the substitution of part of the Gd with Y in Mg₃Gd leads to a slight decrease in the cell volume (0.35%), and the lattice parameters obtained after full relaxation of crystalline cells are in good agreement with the experimental data. The calculated negative formation enthalpies and the cohesive energies show that these typical fcc precipitates of Mg-based alloys have good alloying ability and structural stability. According to the calculated density of states of these phases, it is found that the highest structural stability of Mg₃Zn₃Y₂ is attributed to an increase in the bonding electron numbers below the Fermi level. In addition, the elastic constants C_ij of these phases were also calculated, and the bulk modulus B, shear modulus G, Young^’s modulus E, Poisson^’s ratio ν and anisotropy value A of polycrystalline materials were derived from the elastic constants. The mechanical properties are further discussed.     

Electronic,optical and thermoelectric properties of Ce3PdIn11 and Ce5Pd2In19: An ab initio study

Density functional calculations with Engel and Vosko generalized gradient approximation are applied to investigate the electronic, optical and thermoelectric properties of Ce₃PdIn₁₁ and Ce₅Pd₂In₁₉ compounds. Analysis of the calculated band structure of Ce₃PdIn₁₁ and Ce₅Pd₂In₁₉ demonstrates their metallic character. The calculated densities of states N(E_F) of Ce₃PdIn₁₁ and Ce₅Pd₂In₁₉ at the Fermi level are 19.60 states/eV and 33.50 states/eV, respectively. The bonding nature in these compounds is discussed via the calculated contour map of the charge density in (1 1 0) crystallographic plane. Imaginary parts of the complex dielectric function show considerable isotropy between 3 and 14 eV Ce₃PdIn₁₁ have large dielectric constant. Thermoelectric properties results reveal that both compounds possess high Seebeck coefficient and electrical conductivity at high temperature. This is the first quantitative theoretical prediction of the theremoelectric properties for these investigated compounds and still awaits experimental confirmations.     

Density functional study of the structural,electronic, elastic and thermodynamic properties of ACRu3 (A = V,Nb and Ta) compounds

Using a density functional scheme, we have investigated for the first time the structural, electronic, elastic and thermal properties of the ideal cubic antiperovskite carbides ACRu₃ (A = V, Nb, Ta). The computed equilibrium lattice constants are in excellent agreement with the experimental data. The electronic band structures and densities of states profiles show that the studied compounds are conductors. Analysis of atomic site projected local density of states reveals that the bonding character may be described as a mixture of covalent–ionic and, due to the d states in the vicinity of the Fermi level, metallic. Pressure dependence up to 50 GPa of the single crystal and polycrystalline elastic constants has been investigated in details. Analysis of the B/G ratios shows that VCRu₃ is slightly brittle while NbCRu₃ and TaCRu₃ are slightly ductile. We have estimated the sound velocities in the principal directions. Through the quasi-harmonic Debye model, in which the phononic effects are taken into account, the temperature and pressure effects on the lattice constant, bulk modulus, heat capacity and Debye temperature are performed.     

First principle calculations of elastic and thermodynamic properties of Ir3Nb and Ir3V with L12 structure under high pressure

The structural and elastic properties of the L1₂ structure Ir₃Nb and Ir₃V under pressure have been investigated by means of the first principles calculations based on the density functional theory within the generalized gradient approximation. The lattice parameters of Ir₃Nb and Ir₃V obtained by minimization of the total energy are consistent with the available experimental and other theoretical results. In addition, the elastic constants (C₁₁, C₁₂, C₄₄) of Ir₃Nb and Ir₃V show that they are mechanical stable structures under pressure. The values of B/G exhibit an upward trend with increasing pressure, which means its ductility increased. When the pressure reaches 45 GPa, the Cauchy pressures and B/G values reveal that Ir₃Nb and Ir₃V change from brittle to ductile. Finally, through quasi-harmonic Debye model, the temperature and pressure dependences of thermodynamic properties are predicted in a wide pressure (0–50 GPa) and temperature (0–1200 K) ranges.     

Elastic constants of binary Mg compounds from first-principles calculations

Elastic constants (C_ij's) of 25 compounds in the Mg–X (X = As, Ba, Ca, Cd, Cu, Ga, Ge, La, Ni, P, Si, Sn, and Y) systems have been predicted by first-principles calculations with the generalized gradient approximation and compared with the available experimental data. Ductility and the type of bonding in these compounds are further analyzed based on their bulk modulus/shear modulus ratios (B/G), Cauchy pressures (C₁₂–C₄₄), and electronic structure calculations. It is found that MgNi₂ and MgCu₂ have very high elastic moduli. Mg compounds containing Si, Ge, Pb, Sn, and Y, based on their B/G ratios, are inferred as being brittle. A metallic bonding in MgCu₂ and a mixture of covalent/ionic bond character in Mg₂Si, as inferred from their electronic structures, further explain the corresponding mechanical properties of these compounds.     

The first-principles calculations for the elastic properties of Zr2Al under compression

The first-principles calculations were applied to investigate the structural, elastic constants of Zr₂Al alloy with increasing pressure. These properties are based on the plane wave pseudopotential density functional theory (DFT) method within the generalized gradient approximation (GGA) for exchange and correlation. The result of the heat of formation of Zr₂Al crystal investigated is in excellent consistent with results from other study. The anisotropy, the shear modulus, and Young's modulus for the ideal polycrystalline Zr₂Al are also studied. It is found that (higher) pressure can significantly improve the ductility of Zr₂Al. Moreover, the elastic constants of Zr₂Al increase monotonically and the anisotropies decrease with the increasing pressure. Finally, it is observed that Zr d electrons are mainly contributed to the density of states at the Fermi level.     

Influence of Deformation on the Energy Spectrum and the Optical Properties of Fullerene C<Subscript>20</Subscript> within the Hubbard Model

The anticommutative Green’s functions and energy spectra of fullerene C₂₀ with symmetry groups I_h, D_5d, and D_3d have been obtained in analytical form within the Hubbard model in the mean-field approximation. The methods of group theory have been used to classify energy states and identify allowed transitions in the energy spectra of C₂₀.     

Phase stability,bonding mechanism,and elastic constants of Mo5Si3 by first-principles calculation

We present results of first-principles local-density-functional calculations of the structural and elastic properties of Mo₅Si₃. Among the three different structures (D8_m, D8₈, and D8_l), the D8_m structure (referred to as the T1 phase) has the greatest binding with a high heat of formation of −3.8 eV/formula unit. The bonding in Mo₅Si₃ is found to have pronounced covalent components, characterized by the planar Mo–Si–Mo triangular bonding units on the (001) plane and by the unusually short Mo–Mo bonds directly along the c-axis. The calculated six elastic constants of the D8_m structure are in excellent agreement with the experimental values. While the bonding in the (001) basal plane is stronger than the bonding along the [001] direction (i.e. C₁₁+C₁₂>C₃₃ and C₆₆>C₄₄), the crystal anharmonicity is found to be higher along the [001] direction. The implication of our results on the anisotropy of thermal expansion coefficients is briefly discussed.     

Ab initio lattice dynamics of Ni2MnX (X = Sn, Sb) magnetic shape memory alloys

In this study, we present the results of first principles calculations of elastic constants and phonon properties of nickel-manganese based magnetic shape memory compounds Ni₂MnSn and Ni₂MnSb in stoichiometric composition. The plane wave basis sets and pseudopotential method within spin-polarized generalized gradient approximation (σ-GGA) scheme of the density functional theory is applied. In investigation of the phonon dispersion spectra, linear response technique of the Density Functional Perturbation Theory is used. Phonon softening is observed in dispersion spectra at the transverse acoustic mode (TA₂) in [ζ ζ 0] direction as an indication of the structural instability of these systems to shear deformation. The vibrational instability of Ni₂MnSb system is larger than that of Ni₂MnSn yielding negative phonon frequencies. This vibrational anomaly is also verified by the low shear modulus and large elastic anisotropy ratio. The minority spin Fermi surfaces of both systems exhibit strong nesting features.     

Stability and elastic properties of L12-(Al,Cu)3(Ti,Zr) phases: Ab initio calculations and experiments

The total energies and equilibrium cohesive properties of L1₂, DO₂₂ and DO₂₃ structures along Al₃Ti–Al₃Zr and Al₃X–Cu₃X (X = Ti, Zr) sections are calculated from first principles employing electronic density-functional theory (DFT), ultrasoft pseudopotentials and the generalized gradient approximation. Calculated heats of formation are consistent with a narrow field of stability of the L1₂ structure at 12.5 at.% Cu for ternary (Al,Cu)_0.75Zr_0.25 and (Al,Cu)_0.75Ti_0.25 intermetallics at low temperatures. Experimentally, samples homogenized at 1000 °C establish a more extensive stability field for the L1₂ phase in quaternary alloys with Cu concentrations ranging from 6.7 to 12.6 at.% Cu. Two L1₂ phases were observed in as-cast alloys with near equal amounts of Ti and Zr, as well as alloys homogenized at 1000 °C. Good agreement is obtained between calculated and measured values of lattice parameters and elastic moduli. These results demonstrate high accuracy of ab initio calculations for phase stability, lattice parameters and elastic constants in multicomponent trialumide intermetallics.     

Stability,elastic and electronic properties of the Rh–Zr compounds from first-principles calculations

A systematic investigation on structural, elastic and electronic properties of Rh–Zr intermetallic compounds is conducted using first-principles electronic structure total energy calculations. The equilibrium lattice parameters, enthalpies of formation (E_for), cohesive energies (E_coh) and elastic constants are presented. Of the eleven considered candidate structures, Rh₄Zr₃ is most stable with the lowest E_for. The two orthogonal-type, relative to the CsCl-type, are the competing ground-state structures of RhZr. The result is in agreement with the experimental reports in the literature. The analysis of E_for and mechanical stability excludes the presence of Rh₂Zr and RhZr₄ at low temperature mentioned by .Curtarolo et al. [Calphad 29, 163 (2005)]. It is found that the bulk modulus B increases monotonously with Rh concentration, whereas all other quantities (shear modulus G, Young's modulus E, Poisson's ratio σ and ductility measured by B/G) show nonmonotonic variation. RhZr₂ exhibits the smallest shear/Young's modulus, the largest Poisson's ratio and ductility. Our results also indicate that all the Rh–Zr compounds considered are ductile. Furthermore, the detailed electronic structure analysis is implemented to understand the essence of stability.     

First-Principles Phase Stability Calculations of Pseudobinary Alloys of (Al,Zn)3Ti with L 12, D 022, and D 023 Structures

The thermodynamic and mechanical stability of intermetallic phases in the Al₃Ti-Zn₃Ti pseudobinary alloy system is investigated from first-principles total energy calculations through electronic density-functional theory within the generalized gradient approximation. Both supercell calculations and sublattice-cluster-expansion methods are used to demonstrate that the addition of Zn to the Al sublattice of Al₃Ti stabilizes the cubic L1₂ structure relative to the tetragonal D0₂₂ and D0₂₃ structures. This trend can be understood in terms of a simple rigid-band picture in which the addition of Zn modifies the effective number of valence electrons that populate bonding and anti-bonding states. The calculated zero-temperature elastic constants show that the binary end members are mechanically stable in all three ordered phases. These results point to a promising way to cost effectively achieve the stabilization of L1₂ precipitates in order to favor the formation of a microstructure associated with desirable mechanical properties. This article was presented at the Multi-Component Alloy Thermodynamics Symposium sponsored by The Alloy Phase Committee of the joint EMPMD/SMD of The Minerals, Metals, and Materials Society (TMS), held in San Antonio, TX, March 12-16, 2006, to honor the 2006 William Hume-Rothery Award recipient, Professor W. Alan Oates of the University of Salford, UK. The symposium was organized by Y. Austin Chang of the University of Wisconsin, Madison, WI, Patrice Turchi of the Lawrence Livermore National Laboratory, Livermore, CA, and Rainer Schmid-Fetzer of the Technische Universitat Clausthal, Clauthal-Zellerfeld, Germany.