Calculated elastic properties of M2AlC (M=Ti, V, Cr, Nb and Ta)

M₂AlC phases, where M is a transition metal, are layered ternary compounds that possess unusual properties. In this paper, we have calculated the elastic properties of M₂AlC, with M=Ti, V, Cr, Nb and Ta, by means of ab initio total energy calculations using the projector augmented-wave method. We have derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂AlC aggregates. We have estimated the elastic modulus of Cr₂AlC with 357.7 GPa while the values of all other phases are in the range 309±10 GPa. We suggest that this can be understood based on the calculated bond energies for the M-C bonds. Furthermore, our results indicate a profound elastic anisotropy of M₂AlC even compared to materials with a well-established anisotropic character such as α-alumina. Finally, we have estimated the Debye temperatures of M₂AlC from the average sound velocity.     

Ab initio study of Nb2SC and Nb2S2C: Differences in coupling between the S and Nb-C layers

Using ab initio calculations, we have studied the structurally related compounds Nb₂SC and Nb₂S₂C. In Nb₂S₂C (space group , prototype Bi₂Te₃), S atoms are nearest neighbours, while in Nb₂SC (space group P6₃/mmc, prototype Cr₂AlC) this is not the case. The calculated equilibrium volume for these two phases deviates by 1.6-3.7% to previously-published experimental data and the bulk modulus-to-c₄₄ ratios obtained are 1.5 and 5.9, respectively. These results indicate a resemblance of Nb₂S₂C to hexagonal BN and graphite. Furthermore, we have demonstrated that the uniform compression method is adequate for estimating the elastic properties of Nb₂SC, a so-called MAX phase. It is our ambition that these calculations will stimulate further experimental research on these compounds.     

Electronic structure of Sc2AC (A=Al, Ga, In, Tl)

Using ab initio calculations, we have studied Sc₂AC with A=Al, Ga, In and Tl. We show that C 2p and Sc 3d as well as A p and Sc 3d states are hybridized, but the antibonding states in the vicinity of the Fermi level weaken the overall bonding. In terms of the chemical bonding, the influence of the size of the A element is minute. Furthermore, the bulk modulus of the corresponding binary transition metal carbide is not conserved in these phases. Therefore, Sc₂AC can be classified as weakly coupled MAX phases according to Sun and co-workers [Z. Sun, D. Music, R. Ahuja, S. Li, J.M. Schneider, Phys. Rev. B 70 (2004) 092102]. It is our ambition that these calculations will stimulate experimental research on these compounds.     

Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

Prediction study of structural and elastic properties under pressure effect of M2SnC (M=Ti, Zr, Nb, Hf)

Using first-principles calculations, we have studied the structural and elastic properties of M₂SnC, with M=Ti, Zr, Nb and Hf. Geometrical optimization of the unit cell is in good agreement with the available experimental data. The effect of high pressures, up to 20 GPa, on the lattice constants shows that the contractions along the a-axis were higher than those along the c-axis. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The elastic constants and their pressure dependence are calculated using the static finite strain technique. A linear dependence of the elastic stiffnesses on the pressure is found. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂SnC aggregates. We estimated the Debye temperature of M₂SnC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Ti₂SnC, Zr₂SnC, Nb₂SnC, and Hf₂SnC compounds.     

Acoustical and elastic properties of transition metal nitrides

Elastic moduli of transition metal nitrides, TiN, ZrN and HfN, have been evaluated using electrostatic and Born repulsive potentials. Acoustical dissipation due to phonon-phonon (p-p) interaction, thermoelastic mechanism and dislocation damping due to screw and edge dislocations has been evaluated in the temperature range 50-500 K along the three crystallographic directions of propagation, viz. [1 0 0], [1 1 0] and [1 1 1] for longitudinal and shear modes. Grüneisen numbers, acoustic coupling constants and their ratios have been evaluated for the longitudinal and shear waves. Results are in good agreement with available data.     

Local flattening of the Fermi surface and quantum oscillations in the magnetoacoustic response of a metal

In the present work, we theoretically analyze the effect of the Fermi surface local geometry on quantum oscillations in the velocity of an acoustic wave travelling in metal across a strong magnetic field. We show that local flattenings of the Fermi surface could cause significant amplification of quantum oscillations. This occurs due to enhancement of commensurability oscillations modulating the quantum oscillations in the electron density of states on the Fermi surface. The amplification in the quantum oscillations could be revealed at fitting directions of the magnetic field.     

Elastic properties of tantalum carbide (TaC)

Elastic properties of TaC have been investigated experimentally and by model calculations. The elastic stiffness coefficients c₁₁=597(11) GPa and c₄₄=153(2) GPa were determined on a (100)-oriented disc-shaped monocrystal at room temperature using a plane-wave ultrasound method. The corresponding theoretical values (c₁₁=621(3), c₄₄=166.8(3) GPa) agree within 4 and 8%, respectively. Therefore, we are confident that the predicted value for c₁₂ is equally accurate, and this allows the prediction of the Bulk and Young's moduli and the Poisson ratio. Data published earlier are critically reviewed and predictions concerning the possibility to synthesize extremely incompressible carbides are made.     

Superconducting NbB2: An ab initio study of elastic constants

The five different elastic constants of the superconducting NbB₂ are calculated for the first time by ab initio density functional method with both correlation and exchange potentials. In the absence of experimental data, the results are compared with those of other related diborides. The fully relaxed and isotropic bulk moduli are also estimated and the implication of their comparison is made.     

Measurement of the elastic properties of evaporated C60 films by surface acoustic waves

Surface Acoustic Wave (SAW) pulses were excited in C₆₀ films deposited on quartz and silicon substrates using pulses from excimer lasers with wavelengths of 248 nm and 308 nm for excitation. An optical beam-deflection technique and polymer electret transducers were utilized to detect the propagation of the SAW pulse with high spatial and temporal resolution, allowing an accuracy of better than 0.1% for SAW velocity measurements. With this technique the frequency dependence of the SAW velocity was determined for a number of fullerite films and density, as well as elastic bulk properties of the films were derived by a theoretical analysis of the dispersion effect.     

Indentation Load Effect on Young＇s Modulus and Hardness of Porous Sialon Ceramic by Depth Sensing Indentation Tests

Depth sensing indentation （DSI） tests at the range of 200-1800mN are performed on porous sialon ceramic to determine the indentation load on Young＇s modulus and hardness values. The Young modulus and hardness （Dynamic and Martens） values are deduced by analysing the unloading segments of the DSI test load-displacement curves using the Oliver-Pharr method. It is found that Young＇s modulus ET, the dynamic hardness HD and the Martens hardness HM exhibit significant indentation load dependences. The values of Young＇s modulus and hardness decrease with the increasing indentation load, as a result of indentation load effect. The experimental hf /hm ratios lower than the critical value 0.7, with hm being the maximum penetration depth during loading and hf the final unloading depth, indicate that our sample shows the work hardening behaviour.     

Martensitic transformation of TiNiPd high-temperature shape memory alloys: A first-principles study

Heat of formation, elastic property and electronic structure of TiNiPd high-temperature shape memory alloys have been investigated by first-principles calculations using the pseudopotentials plane-wave method. The results show that the heat of formation difference between austenite and martensite plays an important role in the martensitic transformation. The effect of Pd content on the martensitic transformation temperature and transformation type is clarified based on the elastic constants of the B2 phases. High martensitic transformation temperature can be attributed to a low shear resistance C′. Furthermore, the mechanism of the effect of Pd addition on elastic constants is explained on the basis of the electronic structure.     

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.     

Electronic structure,chemical bonding and elastic properties of the first thorium‐containing nitride perovskite TaThN3

The full‐potential linearized augmented plane wave method with the generalized gradient approximation for the exchange and correlation potential (LAPW‐GGA) is used to understand the electronic and elastic properties of the first thorium‐containing nitride perovskite TaThN₃. Total and partial density of states, charge distributions as well as the elastic constants, bulk modulus, compressibility, shear modulus, Young modulus and Poisson ratio are obtained for the first time and analyzed in comparison with cubic ThN. The chemical bonding in TaThN₃ is a combination of ionic Th–N and of mixed covalent–ionic Ta–N bonds. The cubic TaThN₃ is semiconducting with the direct gap at about 0.65 eV. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction study of elastic properties under pressure effect for filled tetrahedral semiconductors LiZnN, LiZnP and LiZnAs

First principle calculations of elastic properties under pressure of the filled tetrahedral semiconductors LiZnN, LiZnP and LiZnAs are presented, using the pseudo-potential plane-waves approach based on density functional theory, within the local density approximation. Elastic constants, bulk modulus, Young’s modulus and Poisson’s ratio are calculated at zero pressure. A linear dependence of the bulk modulus and elastic constants with applied pressure is found. As the experimental elastic constants are not available for LiZnX, we have also calculated the elastic constants of GaN, GaP and GaAs, the binary analogues of LiZnN, LiZnP and LiZnAs, respectively, for checking the reliability and accuracy of our predicted results for LiZnX. The obtained results agree well with the available experimental data.     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Multilayer model of interlayer spacing in graphite intercalation compounds

The elastic deformation of host layers is calculated by constructing a model where the host layers, regarded as continuous two-dimensional elastic sheets, are infinitely stacked and compressible intercalants, represented by harmonic springs, are intercalated into them. If we treat the intercalants as being rigid relative to the soft host layers in the stage-1 graphite intercalation compound, Li_xC₆ (0≤x≤1), the calculated average gallery spacing agrees well with the experiments, without using any adjustable parameter. Received: 14 April 2000 / Accepted: 17 April 2000 / Published online: 23 August 2000     

Electronic structure and shearing in nanolaminated ternary carbides

We have studied shearing in M₂AlC phases (M=Sc,Y,La,Ti,Zr,Hf,V,Nb,Ta,Cr,Mo,W) using ab initio calculations. We propose that these phases can be classified into two groups based on the valence electron concentration induced changes in C₄₄. One group comprises M=V B and VIB, where the C₄₄ values are approximately 170 GPa and independent of the corresponding MC. The other group includes M=IIIB and IVB, where the C₄₄ shows a linear dependency with the corresponding MC. This may be understood based on the electronic structure: shear resistant bands are filled in M₂AlC phases with M=V B and VIB, while they are not completely filled when M=IIIB and IVB. This notion is also consistent with our stress-strain analysis. These valence electron concentration induced changes in shear behaviour were compared to previously published valence electron concentration induced changes in compression behaviour [Z. Sun, D. Music, R. Ahuja, S. Li, J.M. Schneider, Phys. Rev. B 70 (2004) 092102]. These classification proposals exhibit identical critical valence electron concentration values for the group boundary. However, the physical mechanisms are not identical: the classification proposal for the bulk modulus is based on MC-A coupling, while shearing is based on MC-MC coupling.     

Crystal Structure and High Hardness Mechanism of Orthorhomic Si2N2O

A quasi-single-phase orthorombic Si2N20 compound is obtained by hot-pressing sintering using homogeneous precursors as raw materials under nitrogen atmosphere. The bulk hardness of orthorombie Si2N20 （o-Si2N2 O） is investigated by a nanoindenter experiment; the results show that o-Si2N20 with maximal value about 19 GPa has a high hardness covalent crystal besides β-Si3N4. It is discovered that the high hardness is mainly attributed to the unique crystal structure. The bridging O atoms in the o-Si2N20 are responsible for decreasing hardness. It is found that the Si-O bonds in the open tetrahedral crystal structure are more easily broken and tilted than other bonds.     

Theoretical investigations of structural, elastic and thermodynamic properties for PtN2 under high pressure

We have investigated structural and elastic properties of PtN₂ under high pressures using norm-conserving pseudopotentials within the local density approximation (LDA) in the frame of density-functional theory. Calculated results of PtN₂ are in agreement with experimental and available theoretical values. The a/a₀, V/V₀, ductility/brittleness, elastic constants C_ij, shear modulus C′, bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio σ and anisotropy factor A as a function of applied pressure are presented. Through the quasi-harmonic Debye model, we also study thermodynamic properties of PtN₂. The thermal expansion versus temperature and pressure, thermodynamic parameters X (X=Debye temperature or specific heat) with varying pressure P, and heat capacity of PtN₂ at various pressures and temperatures are estimated.