Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Structural,mechanical and thermal properties of some Holmium Pnictides under pressure: A theoretical approach

The high pressure structural, elastic and thermal properties of holmium pnictides HoX (X=N, P, As and Bi) were investigated theoretically by using an inter-ionic potential theory with modified ionic charge parameter. We have predicted a structural phase transition from NaCl (B₁) to CsCl (B₂)-type structure at pressure of 139 GPa for HoN, 52 GPa for HoP, 44 GPa for HoAs and 26 GPa for HoBi. Other properties, such as lattice constant, bulk modulus, cohesive energy, second and third-order elastic constants were calculated and compared with the available experimental and theoretical data. In order to gain further information the brittle behaviour of these compounds was observed. Some other properties like Shear modulus (G), Young's modulus (E), Poisson's ratio (ν), anisotropy factor (A), sound velocities, Debye temperature (θ_D) were calculated. The variation of elastic constants (C₁₁ and C₄₄) and Debye temperature (θ_D) with pressure was also presented.     

First-principles investigations on elastic, phonon and thermodynamic properties of SrB6 under pressure

The elastic, phonon and thermodynamic properties of the divalent alkaline-earth hexaboride SrB₆ are investigated by using plane-wave pseudopotential density functional theory method. The calculated structure parameters and bulk modulus are well consistent with the available experiment and theoretical data. The pressure dependences of elastic constants C_ij, bulk modulus B₀, shear modulus G, Young's modulus E and Poisson's ratio σ are also presented. With these elastic parameters, we investigate the mechanical stability and compressibility of SrB₆. For the thermodynamic properties, both phonon and quasi-harmonic Debye model methods are adopted. Through the comparison with experimental and other theoretical results, we found the method of quasi-harmonic Debye model is a little better. Moreover, the phonon dispersion relations are also obtained. It is found that there are two LO/TO splitting around 5 THz and 26 THz, respectively.     

The first principles study on the Boron antimony compound

We present the results of our calculations on Boron antimony (BSb) compound in zinc-blende (ZB) and rock-salt (RS) structures by performing ab initio calculations within the local density approximation (LDA). Some basic physical properties, such as lattice constant, bulk modulus, cohesive energy, phase transition pressure, second-order elastic constants (C_ij), phonon frequencies, and some band structural parameters are calculated and compared with those obtained with other recent theoretical works. In order to further understand the behaviour of BSb compound, we have also predicted, the pressure-dependent behaviours of the band gap, second-order elastic constants (C_ij), Young's modulus, poison ratios (ν), Anizotropy factor (A), sound velocities, and Debye temperature for this hypothetical compound.     

Single-crystal elastic constants of magnesium difluoride (MgF2) to 7.4 GPa

The six independent elastic constants (C₁₁, C₁₂, C₁₃, C₃₃, C₄₄, and C₆₆) of single-crystal MgF₂ in the rutile structure have been measured by Brillouin spectroscopy at room temperature from ambient conditions to 7.4 GPa. Measurements were performed on two monocrystals with perpendicular faces, (001) and (100). A quasi-linear fit from finite strain theory was applied to the experimental data revealing the pressure dependence of the six elastic constants of MgF₂. The shear modulus C_S=1/2(C₁₁−C₁₂), and the aggregate shear (Voigt–Reuss–Hill) modulus G show a softening with increasing pressure, indicating the approach of the rutile-to-CaCl₂-type structural phase transition at P~9 GPa. The adiabatic bulk modulus (Reuss average) and its pressure derivative have been determined: K_0S=105.1±0.3 GPa, (∂K_0S/∂P)_T=4.14±0.05. The pressure–volume equation of state of MgF₂ was computed self-consistently from the Brillouin data. Our results are in good agreement with X-ray diffraction data. As the phase transition is approached, MgF₂ becomes strongly anisotropic and develops partially auxetic behavior (a negative Poisson's ratio in certain directions).     

Elasticity of single-crystal phase D (a dense hydrous magnesium silicate) by Brillouin spectroscopy

Phase D (MgSi₂O₆H₂) is the only hydrous magnesium silicate, where all Si atoms are octahedrally coordinated. The single-crystal elastic constants of phase D have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₃₃, C₄₄, C₁₂, C₁₃ and C₁₄, based on a trigonal unit cell, are 284.4±3.0, 339.4±9.1, 120.7±1.9, 89.4±4.2, 126.6±3.1 and −4.7±1.4 GPa, respectively. The aggregate adiabatic bulk modulus, using the Voigt-Reuss-Hill (VRH) scheme, is 175.3±14.8 GPa and the shear modulus is 104.4±13.6 GPa. These data yield the compressional-wave velocity, V_p=9.70±0.51 km/s, and the shear-wave velocity, V_s=5.59±0.36 km/s, at ambient conditions. Thus, phase D is not only the most closely packed but the least compressible hydrous magnesium silicate known to date.     

Static and vibrational properties of equiatomic Na-based binary alloys

The computations of the static and vibrational properties of four equiatomic Na-based binary alloys viz. Na_0.5Li_0.5, Na_0.5K_0.5, Na_0.5Rb_0.5 and Na_0.5Cs_0.5, to second order in local model potential is discussed in terms of real-space sum of Born von Karman central force constants. The local field correlation functions due to Hartree (H), Ichimaru-Utsumi (IU) and Sarkar et al. (S) are used to investigate the influence of the screening effects on the aforesaid properties. Results for the lattice constants C₁₁, C₁₂, C₄₄, C₁₂-C₄₄, C₁₂/C₄₄ and bulk modulus B obtained using the H-local field correction function have higher values in comparison with the results obtained for the same properties using IU- and S-local field correction functions. The results for the Shear modulus (C′), deviation from Cauchy's relation, Poisson's ratio σ, Young modulus Y, propagation velocity of elastic waves, phonon dispersion curves and degree of anisotropy A are highly appreciable for the four equiatomic Na-based binary alloys.     

Theoretical studies of structural, elastic, electronic and lattice dynamic properties of AlxYyB1−x−yN quaternary alloys

A theoretical study on the structural, elastic, electronic and lattice dynamic properties of Al_xY_yB_1−x−yN quaternary alloys in zinc-blend phase has been carried out with first-principles methods. Information on the lattice parameter, the lattice matching to available substrates and energy band-gaps is a prerequisite for many practical applications. The dependence of the lattice parameter a, bulk modulus B, elastic constants C₁₁, C₁₂ and C₄₄, band-gaps, optical phonon frequencies (ω_TO and ω_LO), the static and high-frequency dielectric coefficients ε (0) and ε (∞) and the dynamic effective charge Z^? were analyzed for y=0, 0.121, 0.241, 0.362 and 0.483. A significant deviation of the bulk modulus from linear concentration dependence was observed. A set of isotropic elastic parameters and related properties, namely bulk and shear moduli, Young's modulus, Poisson's ratio are numerically estimated in the frame work of the Voigt-Reuss-Hill approximation. The resistance to changes in bond length and lateral expansion in Al_xY_yB_1−x−yN increase with increasing y concentration. We observe that at y concentration about 0.035 and 0.063, Al_xY_yB_1−x−yN changes from brittle to ductile and Γ-X indirect fundamental gap becomes Γ-Γ direct fundamental gap. There is good agreement between our results and the available experimental data for the binary compound AlN, which is a support for those of the quaternary alloys that we report for the first time.     

First-principles calculations of structural stability and mechanical properties of tungsten carbide under high pressure

The structural stability and mechanical properties of WC in WC-, MoC- and NaCl-type structures under high pressure are investigated systematically by first-principles calculations. The calculated equilibrium lattice constants at zero pressure agree well with available experimental and theoretical results. The formation enthalpy indicates that the most stable WC is in WC-type, then MoC-type finally NaCl-type. By the elastic stability criteria, it is predicted that the three structures are all mechanically stable. The elastic constants C_ij, bulk modulus B, shear modulus G, Young?s modulus E and Poisson?s ratio ν of the three structures are studied in the pressure range from 0 to 100 GPa. Furthermore, by analyzing the B/G ratio, the brittle/ductile behavior under high pressure is assessed. Moreover, the elastic anisotropy of the three structures up to 100 GPa is also discussed in detail.     

Elasticity and thermodynamic properties of RuB2 under pressure

First-principles calculations of the crystal structure and the elastic properties of RuB₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The elastic constants c_ij, the aggregate elastic moduli (B, G, E), Poisson's ratio, and the elastic anisotropy with pressure have been investigated. Through the quasi-harmonic Debye model considering the phonon effects, the isothermal bulk modulus, the thermal expansions, Grüneisen parameters, and Debye temperatures depending on the temperature and pressure are obtained in the whole pressure range from 0 to 60 GPa and temperature range from 0 to 1100 K as well as compared to available data.     

Anomalous thermoelastic behaviour of orientationally disordered (NH4I)x(KI)1−x mixed crystals

We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). This ETSM has been applied to reveal the second order elastic constants (C₁₁, C₁₂ and C₄₄) in the dilute regimes 0≤x≤0.50. Our theoretical results have reproduced well the observed variations of C₁₁ (x=0.14, 0.43) and C₁₂ (x=0.14, 0.43) with temperature. The anomalous elastic behaviour observed in C₄₄ below 150 K for x=0.43 has been predicted well by ETSM results in the orientationally disordered (NH₄I)_x(KI)_1−x mixed crystals. Our results for C₁₂ are in good agreement with the experimental data available for x=0.14 and 0.43. Besides, the third and fourth order elastic constants and the results on cohesive and thermophysical properties are also discussed.     

Electronic and high pressure elastic properties of RECd and REHg (RE=Sc,La and Yb) intermetallic compounds

Structural, electronic, elastic and mechanical properties of Cd and Hg based rare earth intermetallics (RECd and REHg; RE=Sc, La and Yb) have been investigated using the full-potential linearized augmented plane-wave (FP-LAPW) method within the density-functional theory (DFT). The ground state properties such as lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′) have been obtained using optimization method and are found in good agreement with the available experimental results. The calculated enthalpy of formation shows that LaHg has the strongest alloying ability and structural stability. The electronic band structures and density of states reveal the metallic character of these compounds. The structural stability mechanism is also explained through the electronic structures of these compounds. The chemical bonding between rare earth atoms and Cd, Hg is interpreted by the charge density plots along (1 1 0) direction. The elastic constants are predicted from which all the related mechanical properties like Poisson’s ratio (σ), Young’s modulus (E), shear modulus (G_H) and anisotropy factor (A) are calculated. The ductility/brittleness of these intermetallics is predicted. Chen’s method has been used to predict the Vicker’s hardness of RECd and REHg compounds. The pressure variation of the elastic constants is also reported in their B₂ phase.     

Ab initio calculations of elastic constants and thermodynamic properties of Li2O for high temperatures and pressures

The elastic constants and thermodynamic properties of Li₂O for high temperatures and pressures are calculated by the ab initio unrestricted Hartree-Fock (HF) linear combination of atomic orbital (LCAO) periodic approach. The lattice constant, elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. It is found that at zero pressure the elastic constants C₁₁, C₁₂ and C₄₄, bulk modulus B and Debye temperature Θ_D decrease monotonically over the wide range of temperatures from 0 to 1100 K. When the temperature , C₁₂ approaches zero, consistently with the transition temperature 1200 K. However, with increasing pressure, they all increase monotonically and the anisotropy will weaken.     

Elastic and electronic properties of YNi2B2C under pressure from first principles

The elastic and electronic structure properties of YNi₂B₂C under pressure are investigated by performing the generalized gradient approximation (GGA) and local density approximation (LDA) correction scheme in the frame of density functional theory (DFT). The pressure dependences of the normalized lattice parameters a/a₀ and c/c₀, the ratio c/a, and the normalized primitive volume V/V₀ of YNi₂B₂C are also obtained. The lattice constants and bulk modulus obtained are in agreement with the available experimental and other theoretical data. We have also studied the pressure dependences of elastic properties. It is found that, as pressure increases, the elastic constants C₁₁, C₃₃, C₆₆, C₁₂, and C₁₃ increase, the variation of elastic constant C₄₄ is not obvious. Moreover, our compressional and shear wave velocities V_L=6.99 km/s and V_S=3.67 km/s as well as the Debye temperature Θ=549.7 K at 0 GPa compare favorably with the available experimental data. The pressure dependences of band structures, energy gap and density of states are also investigated.     

Enhancement of surface mechanical properties by using TiN[BCN/BN]n/c-BN multilayer system

The aim of this work is to improve the mechanical properties of AISI 4140 steel substrates by using a TiN[BCN/BN]_n/c-BN multilayer system as a protective coating. TiN[BCN/BN]_n/c-BN multilayered coatings via reactive r.f. magnetron sputtering technique were grown, systematically varying the length period (Λ) and the number of bilayers (n) because one bilayer (n = 1) represents two different layers (t_BCN + t_BN), thus the total thickness of the coating and all other growth parameters were maintained constant. The coatings were characterized by Fourier transform infrared spectroscopy showing bands associated with h-BN bonds and c-BN stretching vibrations centered at 1400 cm⁻¹ and 1100 cm⁻¹, respectively. Coating composition and multilayer modulation were studied via secondary ion mass spectroscopy. Atomic force microscopy analysis revealed a reduction in grain size and roughness when the bilayer number (n) increased and the bilayer period decreased. Finally, enhancement of mechanical properties was determined via nanoindentation measurements. The best behavior was obtained when the bilayer period (Λ) was 80 nm (n = 25), yielding the relative highest hardness (∼30 GPa) and elastic modulus (230 GPa). The values for the hardness and elastic modulus are 1.5 and 1.7 times greater than the coating with n = 1, respectively. The enhancement effects in multilayered coatings could be attributed to different mechanisms for layer formation with nanometric thickness due to the Hall-Petch effect; because this effect, originally used to explain increased hardness with decreasing grain size in bulk polycrystalline metals, has also been used to explain hardness enhancements in multilayered coatings taking into account the thickness reduction at individual single layers that make up the multilayered system. The Hall-Petch model based on dislocation motion within layered and across layer interfaces has been successfully applied to multilayered coatings to explain this hardness enhancement.     

An examination of the structural,electronic, elastic,vibrational and thermodynamic properties of Ru2YGa (Y = Sc,Ti and V) Heusler alloys

The structural, electronic, elastic, vibrational and thermodynamic properties of the Ru₂YGa (Y = Sc, Ti and V) Heusler alloys in L2₁ type cubic structure have been analyzed systematically using first principles density functional theory (DFT) together with the Generalized Gradient Approximation (GGA) method. The values of calculated lattice constant (a₀), elastic constants (Cij), Bulk modulus (B), Shear modulus (G), ratios of B/G, Young's modulus (E) and Poisson ratio (ν) are in good agreement with the available theoretical and experimental results. The electronic band structures, corresponding total and partial density of states have also been obtained. The calculated band structures demonstrate that Ru2YGa (Y = Sc, Ti and V) alloys are metallic. The phonon dispersion curves, total and partial density of states of these alloys have been computed for the first time by adopting the direct method. It is considered that all alloys are dynamically stable in L2₁ structure.     

First-principles study of lattice dynamics of LiFePO4

Lattice dynamics of lithium iron orthophosphate (LiFePO₄) isostructural with olivine have been investigated using the first-principles calculations taking into account the on-site Coulomb interaction within the GGA + U scheme. Born effective charge tensors, phonon frequencies at the Brillouin zone center and phonon dispersion curves are calculated and analyzed. The Born effective charge tensors exhibit anisotropy, which gives a convincing evidence for the one-dimensional Li migration tunnel along the [010] direction in LiFePO₄, which has been proposed by other theoretical calculations and experimental observation. The calculated phonon frequencies at the Γ point of the Brillouin zone show good agreement with the available experimental observations.     

Full potential calculation of structural, elastic properties and high-pressure phase of binary noble metal carbide: ruthenium carbide

We present in this paper the results of an ab initio theoretical study within the local density approximation (LDA) to determine in rock-salt (B1), cesium chloride (B2), zinc-blende (B3), and tungsten carbide (WC) type structures, the structural, elastic constants, hardness properties and high-pressure phase of the noble metal carbide of ruthenium carbide (RuC).The ground state properties such as the equilibrium lattice constant, elastic constant, the bulk modulus, its pressure derivative, and the hardness in the four phases are determined and compared with available theoretical data. Only for the three phases B1, B3, and WC, is the RuC mechanically stable, while in the B2 phase it is unstable, but in B3 RuC is the most energetically favourable phase with the bulk modulus 263 GPa, and at sufficiently high pressure (P_t=19.2 GPa) the tungsten carbide (WC) structure would be favoured, where ReC-WC is meta-stable.The highest bulk modulus values in the B3, B2, and WC structures and the hardnesses of H(B3)=36.94 GPa, H(B1)=25.21 GPa, and H(WC)=25.30 GPa indicate that the RuC compound is a superhard material in B3, and is not superhard in B1 and WC structures compared with the H(diamond)=96 GPa.     

Elastic and thermal properties of Sr1−xYxCoO3

The elastic and thermal properties of Sr_1?xY_xCoO₃ (0 ≤ x ≤ 0.5) have been investigated, probably for the first time, by using modified rigid ion model. We present the elastic constants (C_11, C_12, C₄₄) and other elastic properties like bulk modulus (B), Young's modulus (Y), shear modulus (G), Poisson's ratio (σ), Lame's parameter (μ, λ), transverse, longitudinal and average wave velocity (υ_t, υ_l and υ_m) and anisotropy parameter (A). Besides, we have reported the thermodynamic properties molecular force constant (f), Reststrahlen frequency (υ), cohesive energy (φ), Debye temperature (θ_D) and Gruneisen parameter (γ). We have also computed the variation of specific heat (C) and volume thermal expansion coefficient (α). The computed results on the elastic and thermodynamic properties are the first report on them. This model is capable of explaining the Cauchy's discrepancy, elastic and thermal properties successfully.     

Thermoelectric power of potassium doped lanthanum manganites at low temperatures

The temperature-dependent resistivity and thermoelectric power of monovalent (K) doped La_1−xK_xMnO₃ polycrystalline pellets (x=0.05, 0.10 and 0.15) between 50 and 300 K are reported. K substitution enhances the conductivity of this system. Curie temperature (T_C) also increases from 260 to 309 K with increasing K content. In the paramagnetic region (T>T_C), the electrical resistivity is well represented by adiabatic polaron hopping, while in the ferromagnetic region (T<T_C), the resistivity data show a nearly perfect fit for all the samples to an expression containing, the residual resistivity, spin-wave and two-magnon scattering and the term associated with small-polaron metallic conduction, which involves a relaxation time due to a soft optical phonon mode. Small polaron hopping mechanism is found to fit well to the thermoelectric power (S) data for T>T_C whereas at low temperatures (T<T_C) in ferromagnetic region (S_FM), S_FM is well explained with the spin-wave fluctuation and electron–magnon scattering. Both, resistivity and thermopower data over the entire temperature range (50–300 K) are also examined in light of a two-phase model based on an effective medium approximation.