Second-moment interatomic potential for aluminum derived from total-energy calculations and molecular dynamics application

We have obtained an interatomic potential for Al within the second-moment approximation of the tight-binding theory by fitting to the volume dependence of the total energy of the metal, computed by first-principles APW calculations. This scheme was applied to calculate the bulk modulus, elastic constants, vacancy formation and surface energies of Al. The predicted values are in good agreement with the measurements. We also have used this potential to perform molecular-dynamic simulations and determine the temperature dependence of the lattice constant and atomic mean-square displacements (MSDs), as well as the phonon spectra and surface related thermodynamic properties. A satisfactory accuracy has been obtained, denoting the success of the method.     

Determination of Temperature-Dependent Elasto-Plastic Properties of Thin-Film by MD Nanoindentation Simulations and an Inverse GA/FEM Computational Scheme

This study presents a novel numerical method for extracting the tempe -rature-dependent mechanical properties of the gold and aluminum thin-films. In the proposed approach, molecular dynamics (MD) simulations are performed to establish the load-displacement response of the thin substrate nanoindented at temperatures ranging from 300-900 K. A simple but effective procedure involving genetic algorithm (GA) and finite element method (FEM) is implemented to extract the material constants of the gold and aluminum substrates. The material constants are then used to construct the corresponding stress-strain curve, from which the elastic modulus, yield stress and the tangent modulus of the thin film are subsequently derived. Results from high-temperature (900 K) nanoindentation MD simulation show that the value of elastic modulus of the gold and aluminum thin-films could decrease by 63.9% and 73.1%, respectively, as compared with the room temperature values. The resulting temperature-dependent stress-strain curves presented in this paper provide the crucial requirement for quantitative computer simulation of nanofabrication process.     

Characterization of all the elastic,dielectric, and piezoelectric constants of uniaxially oriented poled PVDF films

Polyvinylidene fluoride (PVDF), a piezoelectric material, has many useful applications, for example, as sensors, transducers, and surface acoustic wave (SAW) devices. Models of performance of these devices would be useful engineering tools. However, the benefit of the model is only as accurate as the material properties used in the model. The purpose of this investigation is to measure the elastic, dielectric and piezoelectric properties over a frequency range, including the imaginary part (loss) of these properties. Measurements are difficult because poled material is available as thin films, and not all quantities can be measured in that form. All components of the elastic stiffness, dielectric tensor, and electromechanical coupling tensor are needed in the models. The material studied here is uniaxially oriented poled PVDF that has orthorhombic mm2 symmetry. Presented are the frequency dependence of all nine complex elastic constants, three complex dielectric constants, and five complex piezoelectric constants. The PVDF was produced at Raytheon Research Division, Lexington, MA. Measurements were made on thin films and on stacked, cubical samples. The elastic constants c₄₄^D and c₅₅^D, the dielectric constants e₁₁^T and e₂₂^T , as well as the piezoelectric constants g₁₅ and g₂₄ reported here have not been published before. The values were determined by ultrasonic measurements using an impedance analyzer and a least square data-fitting technique     

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.     

Elastic Constants of Synthetic Single Crystal Corundum at Room Temperature

The six elastic constants (and six elastic compliances) of corundum were determined in the kilocycle per second frequency range by an accurate resonance method. The results were checked in the megacycle per second range with a less accurate, pulse velocity method. The elastic moduli for polycrystalline alumina calculated from the single crystal compliances determined by the resonance method are in good agreement with experimental values obtained on high density polycrystalline alumina. The variation of Young’s modulus and of the shear modulus with orientation was calculated from the compliances and the results are shown graphically. The results of the present work do not agree well with previous work on single crystal sapphire. The specification of orientation and the theory used to calculate the elastic constants are given in detail to support the contention that the results of the present work are correct.     

Selected mechanical properties of gold,silver, aluminium and germanium coatings

Selected mechanical properties such as tensile properties, internal friction, internal stress, adhesion and crack formation of metallic coatings were investigated in the as-deposited and annealed conditions. In addition, the density, elastic constants and thermal expansion coefficient of the metallic coatings were measured on self-supported coatings and they agree well with tabulated values. The experimental procedures are presented and those characteristics peculiar to coatings are discussed.     

Higher order elastic constants of rare earth metals: gadolinium,dysprosium and erbium

The expressions for the second and third order elastic constants of the rare earth metals, gadolinium dysprosium and erbium have been worked out and their values have been determined. The present theoretical values are compared with the experimentally observed results. It is also suggested that the third order elastic constants of these metals may be measured using ultrasonic technique under high pressures.     

Determination of elastic constants of titanium diboride (TiB2) from first principles using FLAPW implementation of the density functional theory

First principles computational calculations of anisotropic elastic constants of titanium diboride, TiB₂, were performed using the implementations of the Hartree–Fock (HF) method and the density functional theory (DFT). TiB₂ has hexagonal crystal structure, thus five independent elastic constants are needed to completely determine its elastic properties including polycrystalline elastic modulus, Poisson’s ratio and the elastic anisotropy of the crystal. The HF method employed molecular orbitals constructed from the linear combination of atomic orbitals (LCAO). The DFT calculations were based on the full potential linearized augmented plane wave (FLAPW) method with the generalized gradient approximation (GGA). Five independent elastic distortions of the unit cell were employed to determine the anisotropic elastic constants under the unrelaxed and relaxed configurations of Ti and B atoms in the unit cell. The calculation methods as well as the internal atomic relaxations of the elastic cell distortions were found to have a significant effect on the numerical values of elastic constants. Estimations of polycrystalline elastic constants and their comparison with the experimentally determined values were also performed. The agreement of the DFT (FLAPW) calculations including internal atomic relaxations, with the experimental data is very good. The HF calculations overestimated the elastic constants upto around 20%. Elastic anisotropy, the nature of chemical bonding and the electronic charge transfer between constituent atoms in TiB₂ have also been explored to assess the origins of high elastic stiffness of this compound.     

Predictions of elastic property on 2.5D C/SiC composites based on numerical modeling and semi-analytical method

In this paper, the predictions of elastic constants of 2.5D (three-dimension angle-interlock woven) continue carbon fiber reinforced silicon carbide (C/SiC) composites are studied by means of theoretical model and numerical simulation. A semi-analytical method expressing elastic constants in terms of microstructure geometrical parameters and constitute properties has been proposed. First, both the geometrical model of the 2.5D composite and the representative volume element (RVE) in both micro- and meso-scale are proposed. Second, the effective elastic properties of the RVE in 2.5D C/SiC composites are obtained using finite element method (FEM) simulation based on energy equivalent principle. Finally, the remedied spatial stiffness average (RSSA) method is proposed to obtain more accurate elastic constants using nine correction factor functions determined by FEM simulations, also the effects of geometrical variables on mechanical properties in 2.5D C/SiC composites are analyzed. These results will play an important role in designing advanced C/SiC composites.     

Second moment approximation of tight-binding potential for γFe applicable up to 1700 K

The atomic potential of γFe has been constructed on the basis of the second-moment approximation of the tight-binding scheme potential. To apply this potential to molecular dynamics simulations at high temperatures up to about 1700 K, the cut-off distance has been set to the sixth neighbours and other parameters have been determined from fitting to physical properties of γFe such as the cohesive energy, vacancy formation energy, lattice constant, elastic constants and bulk modulus. This potential can also describe the temperature dependencies of the lattice constant and the specific heat at constant pressure and can simulate hypothetical melting of γFe.     

Elastic properties of proton exchanged lithium niobate

A method is demonstrated for determination of elastic constants of anisotropic layers on arbitrarily anisotropic and piezoelectric substrates only using the easily measured velocity of surface acoustic waves. By means of a detailed theoretical analysis it is shown that by use of the presented method, the elastic stiffness constants and propagation properties of any nonpiezoelectric isotropic, cubic, or even trigonal layer can be determined. The method is applied to proton-exchanged lithium niobate (PE:LiNbO(3)). Complete measurements of dispersion characteristics of Rayleigh waves on Y -cut PE:LiNbO(3) and calculated values of all elastic stiffness constants of the proton-exchanged film are reported.     

Structural, elastic and thermophysical properties of divalent metal oxides with NaCl structure

In the present paper, we have investigated the high-pressure structural phase transition of divalent metal oxides using the three-body potential modified by incorporating the covalency effects. Phase transition pressures are associated with a sudden collapse in volume. The phase transition pressures and associated volume collapses obtained from present potential model show a generally better agreement with available experimental data than others. The elastic constants and their pressure derivatives are also reported. It is found that the present model has a promise to predict the phase transition pressure and, the elastic constants and their pressure derivatives of other chalcogenides as well. Moreover the thermophysical properties have also been obtained successfully.     

Elastic constants of metal/ceramic composites with lamellar microstructures: Finite element modelling and ultrasonic experiments

The elastic properties of single domains of lamellar AlSi12/Al₂O₃ composites produced by metal infiltration of freeze cast preforms have been examined. The anisotropic elastic constants determined from ultrasonic phase spectroscopy (UPS) experiments have been compared to microstructure based FE-models created with the program OOF2, micromechanical models (Mori–Tanaka and inverse Mori–Tanaka) and an analytical model for an ideal laminate. The influences of lamellae orientations and ceramic contents on the elastic constants have been investigated. Along the lamellae directions the microstructure based FE model and the inverse Mori–Tanaka model are in good agreement with experimental results. Perpendicular to the lamellae the experiment shows a stiffer than expected elastic behaviour.     

First-principles elastic constants and electronic structure of beryllium chalcogenides BeS, BeSe and BeTe

A theoretical study of structural, elastic and electronic properties of BeS, BeSe and BeTe is presented using the full-potential augmented plane-waves plus local orbitals (APW + lo) within density-functional theory (DFT). Results are obtained using both the local-density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation potentials. The ground-state properties, like lattice constant, bulk modulus and its first derivative obtained from our calculations agree very well with experimental and other theoretical calculations. Band structures, and total valence charge densities including spin–orbit interaction are analyzed in great detail. The calculated values of the energy gaps, bandwidths, and spin–orbit splittings and the correct band degeneracies are compared to experimental and/or ab initio results. The calculated energy gap for the series of beryllium chalcogenides BeS, BeSe and BeTe is found to be indirect (Γ–X) and underestimated by about 40% for both LDA and PBE-GGA compared to experiment. We have also reported the elastic constants of these materials; the elastic constants have been derived by the stress–strain relation.     

Complete determination of elastic moduli of interpenetrating metal/ceramic composites using ultrasonic techniques and micromechanical modelling

The complete stiffness matrices of several metal/ceramic composites were analysed using the complementary ultrasonic spectroscopic techniques ultrasound phase spectroscopy (UPS) and resonant ultrasound spectroscopy (RUS). Three different aluminum/alumina composites having complex interpenetrating architectures were studied: a composite based on freeze-cast ceramic preform, a composite based on open porous ceramic preform obtained by pyrolysis of cellulose fibres, and a composite based on discontinuous fibre preform. Six of the nine independent elastic constants describing orthotropic elastic anisotropy were pre-determined by ultrasound phase spectroscopy and used as initial guess input for resonant ultrasound spectroscopy analysis, making the final results of all nine elastic constants more reliable. In all cases, consistent and reproducible results are obtained. Finally the experimental results were compared with effective elastic constants calculated using micromechanical modelling and a good correspondence between both is obtained.     

The Young's modulus and Poisson's ratio of arsenic,antimony and bismuth

The orientational dependences of the Young's modulus and Poisson's ratio of the A7 structure elements arsenic, antimony, and bismuth are investigated, using available experimental data of the six elastic compliance constants. The behaviour of these technical elastic constants in antimony and bismuth is shown to differ not only in degree but also in kind from that of arsenic, which exhibits the characteristics expected of a layer-like crystal; arsenic is elastically a very anisotropic material, its Young's modulus varies by a factor as large as 11.3: the largest anisotropy ratio reported for a metallic element.     

Linear combinations of the third-order elastic and piezoelectric constants of quartz

The DC-field-induced change in the resonant frequency of the extentional mode of quartz rods is related to the third-order elastic and the third-order piezoelectric constants. Five linear combinations of these constants are determined by least-squares fit to data obtained from 50 different rods. The results are notable for their small standard errors of about two percent on average. They also agree very well with the values obtained independently by the transit-time method.     

The stress distribution around a crack perpendicular to an interface between materials

The plane strain problem of a crack terminating perpendicular to a planar interface between two isotropic half spaces with different elastic constants is solved to obtain the distribution of stress in the vicinity of the crack tip. The relative elastic constants are shown to strongly affect the relative magnitudes of the various stress components as well as their radial drop off with distance from the crack tip. The implications of the results with regard to failure modes in composite materials are discussed.     

First-principles studies of the electronic and elastic properties of metal nitrides XN (X = Sc, Ti, V, Cr, Zr, Nb)

Electronic and elastic properties of a series of the transition metal ion mononitrides (ScN, TiN, VN, CrN, ZrN, NbN) have been modeled in the framework of ab initio plane wave spin-polarized calculations using the generalized gradient and local density approximations. The calculated band structures are typical for metallic compounds, except for ScN, whose band structure is that one of the gapless semiconductor. Strongly delocalized d states of transition metal ions are spread over a wide region of about 10-12 eV and are strongly hybridized with the nitrogen 2p states. Among the considered nitrides, only CrN exhibits a clear difference between the spin-up and spin-down states, which would manifest itself in magnetic properties. The overall appearance of the calculated cross-sections of the electron density difference changes drastically when going from Sc to Nb in the considered series of compounds. For the first time the calculated tensors of the elastic constants and elastic compliance constants were used for the analysis and visualization of the directional dependence of the Young’s moduli. It was shown that ScN and VN can be characterized as more or less elastically isotropic materials, whereas in TiN, CrN, ZrN, and NbN the Young’s moduli vary significantly in different directions. The maximal values of the Young’s moduli are along the crystallographic axes, the minimal values are along the bisector direction in the coordinate planes; the difference between them in the case of CrN exceeds one order of magnitude. In addition, pressure dependence of the “metal - nitrogen” distance was modeled.