Polycrystalline Elastic Moduli Research Articles

First Principles Study of Al-Li Intermetallic Compounds

The structural properties, heats of formation, elastic properties, and electronic structures of four compositions of binary Al-Li intermetallics, Al3Li, AlLi, Al2Li3, and Al4Li9, are analyzed in detail by using density functional theory. The calculated formation heats indicate a strong chemical interaction between Al and Li for all the Al-Li intermetallics. In particular, in the Li-rich Al-Li compounds, the thermodynamic stability of intermetallics linearly decreases with increasing concentration of Li. According to the computational single crystal elastic constants, all the four Al-Li intermetallic compounds considered here are mechanically stable. The polycrystalline elastic modulus and Poisson's ratio have been deduced by using Voigt, Reuss, and Hill approximations, and the calculated ratios of bulk modulus to shear modulus indicate that the four compositions of binary Al-Li intermetallics are brittle materials. With the increase of Li concentration, the bulk modulus of Al-Li intermetallics decreases in a linear manner.

First principles calculations of the structure and elastic constants of α, β and γ uranium

This study analyzes structural and elastic properties of five uranium crystal structures: the face centered orthorhombic A20 (α phase), the tetragonal D8b (β phase), body centered tetragonal (bct), body centered cubic (γ phase) and face centered cubic structures. Calculations are performed within the density functional theory framework employing the Projector Augmented Wave method and the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE–GGA) of the exchange correlation. The elastic constants are used to compute polycrystalline elastic moduli, Poisson’s ratio and the Debye temperature for all five structures. The α and γ phase properties are compared with theoretical and experimental results. The complex tetragonal 30atom beta phase is examined in detail. Representation of the β phase by a bct structure is examined; we find that the structure of the β phase is significantly different from the bct phase but exhibits similar elastic properties. This is the first comprehensive investigation into the elastic constants of uranium utilizing the PBE–GGA.

First principles study of the structural, elastic, electronic and optical properties of CaSrTt (Tt=Si, Ge, Sn and Pb)

We present an ab initio study of the structural, elastic, electronic and optical properties of CaSrTt (Tt=Si, Ge, Sn and Pb) compounds. To more-accurately describe the properties of these materials, the calculations were based on the DFT theory with the generalized gradient approximation (GGA). In particular, the calculated lattice constants are in good agreement with the experimental results, with a deviation less than 0.67%, 2.74% and 1.7% for a, b and c, respectively. For the equilibrium volume, the deviation does not exceed 4.7%. Single-crystal elastic stiffness (Cij) values were calculated and the polycrystalline elastic moduli (B and G) were estimated utilizing Voigt, Reuss and Hill’s approximations. The electronic band-structure calculations indicate that these compounds are semiconductors, in agreement with the literature data on their Ae2Tt analogues. The dielectric function, refractive index, extinction coefficient, reflectivity spectrum and electron energy loss are calculated over a spectral range from 0 to 45eV.Unfortunately, there is no available previous study for comparison.

Systematic study of the elastic properties of Mn3AC antiperovskite with A = Zn, Al, Ga, In, Tl, Ge and Sn

First principle calculations were made to investigate the elastic properties of Mn3AC antiperovskites, A=Zn, Al, Ga, In, Tl, Ge and Sn. The estimated equilibrium lattice parameters are in agreement with the experimental ones. From the single crystal elastic constants we have calculated the polycrystalline elastic moduli: the bulk modulus B, shear modulus G, tetragonal shear modulus G′, Young’s modulus Y, Cauchy’s pressure CP, Poisson’s ratio v, elastic anisotropy factor and Pugh’s criterion G/B. Using Debye’s approximation we have deduced the elastic wave velocities and Debye’s temperature.

Structural, electronic and elastic properties of the new ternary alkali metal chalcogenides KLiX (X = S, Se and Te)

The structural, electronic and elastic properties of the tetragonal alkali metal chalcogenides KLiX [X: S, Se and Te] have been investigated using the full-potential (linearized) augmented plane wave plus local orbitals method. The exchange–correlation potential is treated within the generalized gradient approximation of Wu and Cohen. Moreover, the alternative form of GGA proposed by Engel and Vosko is also used for the electronic properties. The calculated structural parameters are in excellent agreement with the experimental data. The elastic constants Cij are predicted using the total energy variation versus strain technique. The polycrystalline elastic moduli, namely; shear modulus, Young’s modulus, Poisson’s ratio, sound velocities and Debye temperature are derived from the obtained single-crystal elastic constants. Brittleness behavior of these compounds is interpreted via the calculated elastic constants Cij. Calculated band structures show that KLiS and KLiSe have an indirect energy band gap, whereas KLiTe has a direct energy band gap. The contribution of alkali metals and chalcogen atoms to the electronic band structure and electronic density of states has been analyzed. This is the first quantitative theoretical prediction of the elastic and electronic properties for these investigated compounds and still awaits experimental confirmations.

Structural, elastic, electronic and magnetic properties of Mn3ZnC and Mn3GeC

We report first-principles calculations, on the structural, elastic, electronic and magnetic properties of Mn3ZnC and Mn3GeC antiperovskite. Our calculations show that these compounds are more stable in the ferromagnetic states, the estimated equilibrium lattice parameters (a and V) are in agreement with the experimental ones. From the single crystal elastic constants; we have derived the polycrystalline elastic moduli, the calculated bulk modulus of Mn3ZnC and Mn3GeC which are respectively 191 and 221GPa. Mn3ZnC shows a weak resistance to shear deformation (54GPa) as compared to Mn3GeC (116GPa). Similarly to previous studies on carbides antiperovskite, these compounds are good electrical conductors. The investigation of the total and partial densities of states shows that the conductivity is assured by d electrons of the transition metal atoms. The ground state was found ferromagnetic and the magnetic moment in these compounds is mainly related to the spin polarisation of Mn d electrons. The average magnetic moment per unit formula decreases from 7.02μB to 3.18μB for Mn3ZnC and Mn3GeC respectively.

First principles study of structural, phonon, optical, elastic and electronic properties of Y3Al5O12

Structural, phonon, optical, elastic and electronic properties of Y3Al5O12 have been investigated by means of the first principles method with the Cambridge Serial Total Energy Package (CASTEP) code based on the density functional theory. The calculated lattice parameters, valence charge density, bond length and single crystal elastic properties at zero pressure are in good agreement with the available experimental data. The close agreement with the experimental values provides a good confirmation of the reliability of the calculations. Optical, elastic and phonon properties of Y3Al5O12 under pressures are performed. The results that are obtained show the changes of optical and elastic properties under the influence of applied pressure, and proving the dynamical stability of YAG are destructed when applied pressure up to 7GPa. Moreover, polycrystalline elastic moduli are deduced according to the Reuss assumption. Those elastic constants provide important parameters that describe reliability of both physical model and engineering application at the atomistic level. The result of the density of states explains the nature of the electronic band structure.

Fabrication and buckling behavior of polycrystalline palladium, cobalt, and rhodium nanostructures

Abstract Novel fabrication techniques were developed to manufacture polycrystalline palladium, cobalt, and rhodium nanopillars with diameters of approximately 130 nm. These nanostructures have length-to-radius ratios in the range of 4 and 20. Using uniaxial nano-compression techniques, the buckling behaviors of the produced nanopillars were characterized and critical buckling loads were extracted. The tangent moduli, which were extracted from plots of critical buckling load as a function of effective specimen cross-sectional area, of palladium, cobalt, and rhodium nanopillars are 90 ± 6 GPa, 175 ± 9 GPa, and 375 ± 23 GPa, respectively. As expected, these calculated values are slightly smaller than the bulk polycrystalline elastic moduli for all three materials. Post compression scanning electron microscope images revealed ductile behavior for palladium nanostructures, while cobalt and rhodium specimens failed by fracture.

First-principles studies of Ni–Ta intermetallic compounds

The structural properties, heats of formation, elastic properties, and electronic structures of Ni–Ta intermetallic compounds are investigated in detail based on density functional theory. Our results indicate that all Ni–Ta intermetallic compounds calculated here are mechanically stable except for P21/m-Ni3Ta and hc-NiTa2. Furthermore, we found that Pmmn-Ni3Ta is the ground state stable phase of Ni3Ta polymorphs. The polycrystalline elastic modulus has been deduced by using the Voigt–Reuss–Hill approximation. All Ni–Ta intermetallic compounds in our study, except for NiTa, are ductile materials by corresponding G/K values and poisson's ratio. The calculated heats of formation demonstrated that Ni2Ta are thermodynamically unstable. Our results also indicated that all Ni–Ta intermetallic compounds analyzed here are conductors. The density of state demonstrated the structure stability increases with the Ta concentration.

Theoretical investigation of the elastic, thermodynamic, electronic and magnetic properties of PrNi 2Si 2 and PrNi 2Ge 2

The structural, elastic, thermodynamic, electronic and magnetic properties of ferromagnetic tetragonal PrNi 2Si 2 and PrNi 2Ge 2 compounds have been calculated using the full-potential linear muffin-tin orbital (FP-LMTO) method. The exchange–correlation potential is treated within the local spin density approximation of Perdew and Wang (LSDA–PW). Moreover, we have added the Coulomb interaction U to improve the electronic band structure calculations and the magnetic properties. The calculated structural parameters are in good agreement with the experimental data. The elastic constants C ij are predicted using the total energy variation versus strain technique. The polycrystalline elastic moduli, namely; shear modulus, Young’s modulus, Poisson’s ratio, sound velocities and Debye temperature are derived from the obtained single-crystal elastic constants. Ductility behavior of these compounds is interpreted via the calculated elastic constants C ij . Electronic and bonding properties are discussed from the calculations of band structure and density of states. The thermodynamic properties are predicted through the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variation of the bulk modulus, lattice constant, heat capacities and Debye temperature with pressure and temperature are successfully obtained.

Alloying effects on the elastic parameters of ferromagnetic and paramagnetic Fe from first-principles theory

The elastic properties of paramagnetic face-centered-cubic (fcc) Fe1-xMx (M = Al, Si, V, Cr, Mn, Co, Ni, and Rh; 0 ≤ x ≤ 0.1) random alloys are investigated using the exact muffin-tin orbitals density functional method in combination with the coherent-potential approximation. We find that the theoretical lattice parameter of fcc Fe is strongly enlarged by Al, V, and Rh and slightly reduced by Si, Cr, and Co, while it remains nearly constant with Mn and Ni. Both positive and negative alloying effects appear for the elastic constants Cij(x) of fcc Fe. These findings are in contrast to those obtained for ferromagnetic body-centered-cubic (bcc) Fe alloys, where all alloying elements considered here are predicted to enlarge the lattice parameter and decrease the C11(x) and C12(x) elastic constants of bcc Fe. With some exceptions, alloying has much larger effects on ferromagnetic bcc alloys than on paramagnetic fcc ones. Based on the theoretical elastic parameters of the paramagnetic fcc and ferromagnetic bcc phases, simple parameterizations in terms of chemical composition of the equilibrium lattice constants, single-crystal elastic constants, and polycrystalline elastic moduli of Fe-based alloys are presented.

First-principles study on the crystal, electronic structure and mechanical properties of hexagonal Al 3RE (RE = La, Ce, Pr, Nd, Sm, Gd) intermetallic compounds

The structural properties, elastic properties and electronic structures of hexagonal Al 3RE intermetallic compounds are calculated by using first-principles calculations based on density functional theory. Since there exists strong on-site Coulomb repulsion between the highly localized 4f electrons of RE atoms, we present a combination of the GGA and the LSDA+ U approaches in order to obtain the appropriate results. The GGA calculated lattice constants for the hexagonal Al 3RE intermetallic compounds are in good agreement with available experimental values. The results of cohesive energy indicate that these compounds can be stable under absolute zero Kelvin and the stability of Al 3Gd is the strongest in all of the hexagonal Al 3RE compounds. The densities of states for GGA and LSDA+ U approaches are also obtained for the Al 3RE intermetallic compounds. The mechanical properties are calculated from the GGA method in this paper. According to the computed single crystal elastic constants, Al 3La, Al 3Sm and Al 3Gd are mechanically unstable, while Al 3Ce, Al 3Pr and Al 3Nd are stable. The polycrystalline elastic modulus and Poisson’s ratio have been deduced by using Voigt–Reuss–Hill (VRH) approximations, and the calculated ratio of bulk modulus to shear modulus indicates that Al 3La compound is ductile material, but Al 3Ce, Al 3Pr, Al 3Nd, Al 3Sm and Al 3Gd are brittle materials.

Ab initio study of the modification of elastic properties of α-iron by hydrostatic strain and by hydrogen interstitials

The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of α-iron is investigated using ab initio density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisotropic shear moduli. For the key slip planes in α-iron, [ 1 1 ¯ 0 ] and [ 1 1 2 ¯ ] , we find a shear modulus reduction of approximately 1.6% per at.% H.

First-principles calculations of the β′-Mg7Gd precipitate in Mg-Gd binary alloys

The metastable β′ phase is often the most effective hardening precipitate in Mg-Gd based alloys. In this paper, the structural, elastic and electronic properties of the recently identified β′-Mg7Gd precipitate in Mg-Gd binary alloys were investigated using first-principles calculations based on density functional theory. The lattice mismatches between the coherent β′-Mg7Gd precipitate and α-Mg matrix are discussed and used to rationalize the experimentally observed morphology of the precipitate. The mechanical properties were investigated through analysis of the single-crystal elastic constants and the polycrystalline elastic moduli. It is found that β′-Mg7Gd is brittle in nature. Strong covalent bonding in β′-Mg7Gd, as inferred from its electronic structure, further explains its mechanical properties. Our theoretical results show good agreement with experimental measurements.

First principles study of structural, elastic and electronic properties of ACY3 (A=Al, In and Tl)

Abstract Structural, elastic and electronic properties of ACY 3 (A = Al, In and Tl) were investigated by means of pseudopotential plane wave method (PP–PW). Our calculated lattice parameters and equilibrium volumes are in good agreement with the available experimental data. Predicted single crystal elastic constants show a weak dependence on the substitution of Al by In or Tl atoms. Also polycrystalline elastic moduli ( B , G , E , v and A ) were deduced and compared to those of related antiperovskite compounds. From the B / G ratio, we have observed that these compounds can be classified as brittle materials. The band structure shows a metallic character, the conductivity is mostly governed by the Y d states. Hybridization states along Y–C atoms and Y–A atoms show respectively a mixture of ionic-covalent and pure ionic bonding in the charge density maps.

First-principles studies of Al–Ni intermetallic compounds

The structural properties, heats of formation, elastic properties, and electronic structures of Al–Ni intermetallic compounds are analyzed here in detail by using density functional theory. Higher calculated absolute values of heats of formation indicate a very strong chemical interaction between Al and Ni for all Al–Ni intermetallic compounds. According to the computational single crystal elastic constants, all the Al–Ni intermetallic compounds considered here are mechanically stable. The polycrystalline elastic modulus and Poisson's ratio have been deduced by using Voigt, Reuss, and Hill (VRH) approximations, and the calculated ratio of shear modulus to bulk modulus indicated that AlNi, Al 3Ni, AlNi 3 and Al 3Ni 5 compounds are ductile materials, but Al 4Ni 3 and Al 3Ni 2 are brittle materials. With increasing Ni concentration, the bulk modulus of Al–Ni intermetallic compounds increases in a linear manner. The electronic energy band structures confirm that all Al–Ni intermetallic compounds are conductors.

A first-principles study on the structural, elastic and electronic properties of AlCSc 3 and AlNSc 3

We present an ab initio study of the structural, elastic and electronic properties of the antiperovskite compounds AlCSc 3 and AlNSc 3. The calculated lattice parameters and equilibrium volumes are in good agreement with the available experimental data. Single-crystal elastic constants were calculated and the polycrystalline elastic moduli were estimated according to Voigt, Reuss and Hill’s approximations. The band structure shows a metallic character of both compounds; strong hybridization between Sc d–C p (or N p) and Sc d–Al p states was observed from the partial density of states. A significant charge transfer from Al to C (or N) atoms was observed. Moreover, these compounds are bonded by a mixture of ionic–covalent bonding.

Structural and elastic properties of Cu6Sn5 and Cu3Snfrom first-principles calculations

We investigated the elastic properties of two tin-copper crystalline phases, the η′-Cu6Sn5 and ε-Cu3Sn, which are often encountered in microelectronic packaging applications. The full elastic stiffness of both phases is determined based on strain-energy relations using first-principles calculations. The computed results show the elastic anisotropy of both phases that cannot be resolved from experiments. Our results, suggesting both phases have the greatest stiffness along the c direction, particularly showed the unique in-plane elastic anisotropy associated with the lattice modulation of the Cu3Sn superstructure. The polycrystalline moduli obtained using the Voigt-Reuss scheme are 125.98 GPa for Cu6Sn5 and 134.16 GPa for Cu3Sn. Our data analysis indicates that the smaller elastic moduli of Cu6Sn5 are attributed to the direct Sn–Sn bond in Cu6Sn5. We reassert the elastic modulus and hardness of both phases using the nanoindentation experiment for our calculation benchmark. Interestingly, the computed polycrystalline elastic modulus of Cu6Sn5 seems to be overestimated, whereas that of Cu3Sn falls nicely in the range of reported data. Based on the observations, the elastic modulus of Cu6Sn5 obtained from nanoindentation tests admit the microstructure effect that is absent for Cu3Sn is concluded. Our analysis of electronic structure shows that the intrinsic hardness and elastic modulus of both phases are dominated by electronic structure and atomic lattice structure, respectively.

Ab initiocalculations of elastic properties of bcc Fe-Mg and Fe-Cr random alloys

Using the ab initio exact muffin-tin orbitals method in combination with the coherent-potential approximation, we have calculated the elastic parameters of ferromagnetic ${\text{Fe}}_{1\ensuremath{-}m}{\text{Mg}}_{m}$ $(0\ensuremath{\le}m\ensuremath{\le}0.1)$ and ${\text{Fe}}_{1\ensuremath{-}c}{\text{Cr}}_{c}$ $(0\ensuremath{\le}c\ensuremath{\le}0.2)$ random alloys in the body-centered cubic (bcc) crystallographic phase. Results obtained for ${\text{Fe}}_{1\ensuremath{-}c}{\text{Cr}}_{c}$ demonstrate that the employed theoretical approach accurately describes the experimentally observed composition dependence of the polycrystalline elastic moduli of Fe-rich alloys encompassing maximum $\ensuremath{\sim}10%$ Cr. The elastic parameters of Fe-Cr alloys are found to exhibit anomalous composition dependence around 5% Cr. The immiscibility between Fe and Mg at ambient conditions is well reproduced by the present theory. The calculated lattice parameter for the Fe-Mg regular solid solution increases by $\ensuremath{\sim}1.95%$ when 10% Mg is introduced in Fe, which corresponds approximately to 11% decrease in the average alloy density, in perfect agreement with the experimental finding. At the same time, we find that all of the elastic parameters of bcc Fe-Mg alloys decrease almost linearly with increasing Mg content. The present results show a much stronger alloying effect for Mg on the elastic properties of $\ensuremath{\alpha}\text{-Fe}$ than that for Cr. Our results call for further experimental studies on the mechanical properties of the Fe-Mg system.

Structural, Elastic, and Electronic Properties of Al-Cu Intermetallics from First-Principles Calculations

The structural, elastic, and electronic properties of Al-Cu intermetallics were investigated using first-principles calculations. The polycrystalline elastic modulus and Poisson’s ratio were deduced from calculated single-crystal elastic constants, and the calculated structural properties agreed well with previous experimental results. Meanwhile, the elastic anisotropy of Al-Cu intermetallics was analyzed based on the directional dependence of the Young’s modulus and its origin explained based on the electronic nature of the crystals.