Laser-induced surface acoustic waves for evaluation of elastic stiffness of plasma sprayed materials

The elastic properties of plasma sprayed deposits have been evaluated using a laser-excited surface acoustic wave (SAW) technique and an inversion processing analysis. The SAWs including Lamb and Rayleigh waves were generated in plasma sprayed NiCoCrAlY and ZrO₂, respectively, and their group velocity dispersions were used to determine the elastic properties (i.e.Young's modulus, Poison's ratio and density) of the deposits. Estimated elastic moduli from the velocity dispersions of A₀-mode Lamb waves are in the range of 40–140 GPa for the deposits, which are much lower than the values 220–240 GPa of the comparable dense materials. The dramatic reductions in modulus and density of ZrO₂ deposit have been attributed to the presence of high porosity and particularly microcracks. Moreover, this study has emphasized on exploiting the applicability of each kind of the SAWs for the elastic property evaluation of different sprayed materials. Both Lamb and Rayleigh wave dispersions are useful for the estimation of APS and VPS-deposited NiCrAlY, but S₀-Lamb and Rayleigh waves are exceptional for that of sprayed ZrO₂, because of its characterization of high acoustic attenuation and inconsequent displacement across the weak bonded interface of ZrO₂ and substrate.     

Pressure effects on elastic and thermodynamic properties of ZrB2

A theoretical formalism to calculate the single crystal elastic constants for hexagonal crystals from first principle calculations is described. The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. The calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young’s modulus, and Poisson’s ratio for ideal polycrystalline ZrB₂ are also calculated and compared with corresponding experimental values. The shear anisotropic factors and anisotropy in the linear bulk modulus are obtained from the single crystal elastic constants. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal. The calculated elastic properties are found to be in good agreement with experimental values when the generalized gradient approximation is used for the exchange and correlation potential. It is found that the elastic constants and the Debye temperature of ZrB₂ increase monotonically and the anisotropies weaken with pressure. The thermal properties including the equation of state, linear compressibility, ductility, and the heat capacity at various pressures and temperatures are estimated.     

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.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of hexagonal boron nitride

The second and third order elastic constants and pressure derivatives of second order elastic constants of hexagonal boron nitride have been obtained using the deformation theory. The strain energy derived using the deformation theory is compared with the strain dependent lattice energy obtained from elastic continuum model approximation to get the expressions for second and third order elastic constants. Higher order elastic constants are a measure of anharmonicity of crystal lattice. The six second-order elastic constants and the ten non-vanishing third order elastic constants and six pressure derivatives of hexagonal boron nitride are obtained in the present work and are compared with available experimental values. The second order elastic constant C ₁₁ which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C ₃₃. Since C ₃₃ being the stiffness tensor component along the c-axis of the crystal, this result is expected from a layer-like material like boron nitride (BN). The third order elastic constants of hexagonal BN are generally one order of magnitude greater than the second-order of elastic constants as expected of a crystalline solid. The pressure derivative dC ₃₃/dp obtained in the present study is greater than dC ₁₁/dp which indicates that the compressibility along c-axis is higher than that along ab-plane of hexagonal BN.     

Third-order elastic constants and the low-temperature limit of the Grüneisen parameter of Mg2Pb on axe's shell model

The third-order elastic constants and the pressure derivatives of the second-order elastic constants of Mg₂Pb are calculated. The Grüneisen parameters of the acoustic modes in six symmetry directions are then computed. It is significant that most of the transverse elastic modes have negative Grüneisen parameters. The low-temperature limit of the Grüneisen parameter is then evaluated. Its relevance to the low-temperature thermal expansion of Mg₂Pb is discussed.     

Nonlinear Elastic Properties of Superconducting Antiperovskites MNNi3 (M =Zn,Cd, Mg,Al, Ga,and In) from First Principles

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi ₃ (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs.     

A method for calibrating the line-focus-beam acoustic microscopy system

Absolute accuracy of the line-focus-beam (LFB) acoustic microscopy system is investigated for measurements of the leaky surface acoustic wave (LSAW) velocity and attenuation, and a method of system calibration is proposed. In order to discuss the accuracy, it is necessary to introduce a standard specimen whose bulk acoustic properties, (e.g., the independent elastic constants and density) are measured with high accuracy. Single crystal substrates of gadolinium gallium garnet (GGG) are taken as standard specimens. The LSAW propagation characteristics are measured and compared with the calculated results using the measured bulk acoustic properties. Calibration is demonstrated for the system using two LFB acoustic lens devices with a cylindrical concave surface of 1-mm radius in the frequency range 100 to 300 MHz.     

Elastic and electronic properties of the alkali pnictide compounds Li3Sb,Li3Bi,Li2NaSb and Li2NaBi

First principles calculations, by means of the full potential linearized augmented plane wave method within the density functional theory, were carried out for the electronic and elastic properties of the alkali pnictide compounds Li₃Sb, Li₃Bi, Li₂NaSb and Li₂NaBi. The exchange and correlation effects have been treated using the local density and the generalized gradient approximations. The calculated lattice parameters and bulk moduli are in good agreement with the available data. The ternaries are softer than the binaries. The calculated elastic constants show that the studied compounds satisfy the stability criteria and the binary compounds are more anisotropic than the ternaries. The elastic moduli and the Debye temperature of polycrystalline samples are also calculated, and the predicted Debye temperatures for the antimonide compounds are higher than those for the bismuthide ones. The calculated bandgaps are indirect with the top of the valence band at Γ, and they decrease in this order Li₃Sb–Li₂NaSb–Li₃Bi– Li₂NaBi.     

Surface Wave Utility in Composite Material Characterization

Abstract

A surface wave velocity measurement technique is used to supply supporting measurements in the computation of elastic constants for practical nondestructive evaluation of composite materials. Theoretical modeling work is carried out to illustrate the surface wave velocity changes as a function of angle with respect to the axes along the fibers of a unidirectional graphite epoxy composite material for a variety of different problems, including porosity (PC) changes, fiber volume fraction (FF) changes, and delamination. Experiments are conducted on two unidirectional reinforced composites and a (0–90)_s cross ply graphite epoxy laminate to illustrate the surface wave velocity measurements and the inverse computation procedure for evaluation of the stiffness coefficients. Variations of the feature values in the stiffness matrix are also discussed for inhomogeneities, delaminations through cracking, and large defects.     

The elastic properties of ion-implanted silicon

The elastic properties of silicon implanted with As⁺ and Si⁺ in the dose range 10¹⁴ to 10¹⁵ ion cm^–2 has been investigated. Reflection scanning acoustic microscopy techniques have been used to determine changes in the velocity of surface elastic waves (Rayleigh waves) on ion-implanted silicon. With the aid of theoretical models for this mode of wave propagation, the experimental velocity changes have been interpreted in terms of changes in the elastic constants of the implanted layer. These changes have been found to be dependent upon the level of radiation damage produced by the implantation process. Decreases of 30% in the bulk and shear elastic constants have been deduced for damage levels present at the onset of implantation-induced amorphization.     

Stress dependency on ultrasonic wave propagation velocity

The velocity of an ultrasonic wave propagating in the uniformly deformed isotropic solid was analysed by the Eulerian viewpoint. The pseudo elastic coefficient (PEC) was used to solve the equation of motion of the elastic wave under finite deformation. The infinitesimal displacement gradients are connected to the stress increments by thePEC. Using thePEC and the partial differential equation of motion, the velocity of ultrasonic wave was quantitatively related to applied stress, moreover, the stress dependence on longitudinal and transverse wave velocities propagating in the direction parallel or perpendicular to the uniaxial tensile direction could be cleared. Consequently, the Murnaghan's third order elastic constants can be calculated by precisely measuring the uniaxial tensile stress and ultrasonic wave velocity.     

Elastic constants of MoSi2 and WSi2 single crystals

Single crystals of MoSi₂ and WSi₂ with a body-centred-tetragonal C 1 1_b structure were fabricated using a floating-zone method. The elastic wave velocity was measured for samples with various orientations using a simple pulse echo method at room temperature, and six elastic stiffness constantsc _ij were calculated. The stiffness constants were a little higher for WSi₂ than for MoSi₂.c ₁₁ andc ₃₃ of these compounds were approximately equal toc ₁₁ of tungsten and molybdenum, respectively, althoughc _ij (i j) was a little higher for these compounds than for molybdenum and tungsten. Young's modulus 1/s ₁₁ was the highest in the <0 0 1> direction, and the lowest in the <1 0 0> direction. The shear modulus 1/s ₆₆ was high on the {0 0 1} plane and independent of shear direction. It was generally low on the close-packed {1 1 0} plane and largely dependent on shear direction. The elastic constants for the polycrystalline materials were estimated fromc _ij ands _ij . Poisson's ratiov was 0.15 for MoSi₂ and for WSi₂, and these values were much lower than for ordinary metals and alloys. The Debye temperature _D was estimated using the elastic-wave velocity of the polycrystalline materials via the elastic constants such as Young's modulus and shear modulus: it was 759 K for MoSi₂ and 625 K for WSi₂.     

LiNbO3和LiTaO3晶体电子结构、平面声波和光折射特性

本研究基于密度泛函理论的第一性原理超软赝势平面方法计算了LiNbO₃和LiTaO₃的晶格参数、电子结构和弹性常数, 并利用Christoffel方程研究了二者平面声波特征。结果表明: 两者的理论计算晶格参数和弹性常数与实验值接近, 禁带宽度分别为3.78和3.98 eV, 导带底和价带顶主要由O-2p和Nb-4d(Ta-5d)态电子贡献。化学键理论揭示Li和Nb(Ta)与O原子之间有两种成键类型。 电荷布局分析结果显示有两种相应的重叠布居数, Nb(Ta)-O键呈现强共价键作用, 并且Nb-O(Ta-O)键长小于Li-O键长。LiNbO₃和LiTaO₃晶体平面声波有两支横波和一支纵波, 纵波速度大于横波速度, 在xy平面呈现六重对称性, 在xz和yz平面各向异性程度强于xy平面, 沿[001]、晶向上两支横波振动速度相等。最后利用模守恒赝势(Norm-conserving)计算了介电常数和静态折射率, 计算表明LiNbO₃晶体的折射性能和非寻常光(e光)离散程度均强于LiTaO₃晶体。     

Ultrasonic dispersion and attenuation near the liquid-gas critical point of4He

We describe sound velocity and acoustic attenuation measurements at several frequencies between 0.5 and 5 MHz along the critical isochore of ⁴ He immediately above the critical pointT _c. The dispersion is obtained with respect to the velocity measurements by Barmatz taken at 1.8 kHz along the critical isochore. The dispersion and attenuation results are analyzed following the theory of Kawasaki and using the more recent modifications resulting from the Fixman-Mistura approach as described by Garland and co-workers. We have determined the critical exponent for the correlation length divergence to be v=0.66±0.04 and found good internal consistency between certain constants appearing in the theoretical expressions for both sound dispersion and attenuation. These experimentally determined constants are compared with those calculated from other experiments. Deviations in the observed acoustic properties from the predicted ones are discussed. They are similar to those found in acoustic experiments and in light scattering experiments near the critical point of Xe.     

On the electronic nature of silicon and germanium based oxynitrides and their related mechanical,optical and vibrational properties as obtained from DFT and DFPT

Electronic structure, bonding and optical properties of the orthorhombic oxynitrides Si₂N₂O and Ge₂N₂O are studied using the density function theory as implemented in pseudo-potential plane wave and full-potential (linearized) augmented plane wave plus local orbitals methods. Generalized gradient approximation is employed in order to determine the band gap energy. Indeed, the Si₂N₂O exhibits a large direct gap whereas Ge₂N₂O have an indirect one. Bonding is analyzed via the charge densities and Mulliken population, where the role of oxygen is investigated. The analysis of the elastic constants show the mechanical stability of both oxynitrides. Their bulk and shear modulus are slightly smaller than those reported on nitrides semiconductors due to the oxygen presence. The optical properties, namely the dielectric function, optical reflectivity, refractive index and electron energy loss, are reported for radiation up to 30 eV. The phonon dispersion relation, zone-center optical mode frequency, density of phonon states are calculated using the density functional perturbed theory. Thermodynamic properties of Si₂N₂O and Ge₂N₂O, such as heat capacity and Debye temperature, are given for reference. Our study suggests that Si₂N₂O and Ge₂N₂O could be a promising potential materials for applications in the microelectronics and optoelectronics areas of research.     

Non-destructive Evaluations of Gallium Nitride Nanowires

We have calculated the second and third order elastic constants of GaN nanowires at room temperature validating the interaction potential model. The ultrasonic attenuation and velocity in the nanowires are determined using the non-linear elastic constants for different diameters (97 nm -160 nm) of the wires at the nanoscale. Where possible, the results are compared with the experiments. Finally we established the correlation between the size dependent thermal conductivity and the ultrasonic attenuation of the nanowires.     

Mechanical and Thermophysical Properties of Cerium Monopnictides

The ultrasonic attenuation due to phonon–phonon interaction, thermoelastic relaxation and dislocation damping mechanisms has been investigated in cerium monopnictides CeX (X: N, P, As, Sb and Bi) for longitudinal and shear waves along \({\langle }100{\rangle }\), \({\langle }110{\rangle }\) and \({\langle }111{\rangle }\) directions. The second- and third-order elastic constants of CeX have also been computed in the temperature range 0 K to 500 K using Coulomb and Born–Mayer potential upto second nearest neighbours. The computed values of these elastic constants have been applied to find out Young’s moduli, bulk moduli, Breazeale’s non-linearity parameters, Zener anisotropy, ultrasonic velocity, ultrasonic Grüneisen parameter, thermal relaxation time, acoustic coupling constants and ultrasonic attenuation. The fracture/toughness ratio is less than 1.75, which shows that the chosen materials are brittle in nature as found for other monopnictides. The drag coefficient acting on the motion of screw and edge dislocations due to shear and compressional phonon viscosities of the lattice have also been evaluated for both the longitudinal and shear waves. The thermoelastic loss and dislocation damping loss are negligible in comparison to loss due to Akhieser damping (phonon–phonon interaction). The obtained results for CeX are in qualitative agreement with other semi-metallic monopnictides.     

Elastic Property Measurement Using Rayleigh-Lamb Waves

Abstract

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/μs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

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.     

Prediction study of the structural, elastic and electronic properties of ANSr3 (A = As, Sb and Bi)

Based on first-principles total energy calculations, we predict the elastic and electronic properties of the anti-perovskites AsNSr₃, SbNSr₃ and BiNSr₃ compounds. The calculated lattice constants are in good agreement with the available results. The independent elastic constants (C₁₁, C₁₂ and C₄₄) and their pressure dependence are calculated using the static finite strain technique. The isotropic elastic moduli, namely, bulk modulus (B), shear modulus (G), Young’s modulus (E), Poisson’s ratio (σ) and Lame’s constants (λ and μ) are calculated in framework of the Voigt–Reuss–Hill approximation for ideal polycrystalline ANSr₃ aggregates. By analysing the ratio between the bulk and shear moduli, we conclude that ANSr₃ compounds are brittle in nature. We estimated the Debye temperature of ANSr₃ from the average sound velocity. The band structures show that all studied materials are semiconductors. The analysis of the site and momentum projected densities, charge transfer and charge densities show that bonding is of covalent–ionic nature. This is the first quantitative theoretical prediction of the elastic and electronic properties of AsNSr₃, SbNSr₃ and BiNSr₃ compounds that requires experimental confirmation.