ELECTRIC FIELD EFFECTS ON THE ELASTIC CONSTANTS OF NENATICS II

The threshold potentials for different types of electric Freedericksz transitions are calculated from the free energy density expression for nematics in an external electric field derived by the present authors. It is found that the experimentally determined elastic constants should be replaced by the effective elastic constants. With the effective elastic constants some of the discrepancies between earlier theoretical calculations and experimental data can be expl ained qualitatively.     

DETERMINATION OF ELASTIC CONSTANTS OF ANISOTROPIC LAMINATED PLATES USING ELASTIC WAVES AND A PROGRESSIVE NEURAL NETWORK

In this paper, a procedure is suggested to inversely determine the elastic constants of anisotropic laminated plates using a progressive neural network (NN). The surface displacement responses are used as the inputs for the NN model. The outputs of the NN are the elastic constants of anisotropic laminated plates. The hybrid numerical method (HNM) is used to calculate the displacement responses of laminated plates to an incident wave for given elastic constants. The NN model is trained using the results from the HNM. A modified back-propagation learning algorithm with a dynamically adjusted learning rate and an additional jump factor is developed to tackle the possible saturation of the sigmoid function and to speed up the training process for the NN model. The concept of orthogonal array was adopted to generate the representative combinations of elastic constants, which reduces significantly the number of training data while maintaining its data completeness. Once trained, the NN model can be used for on-line determination of the elastic constants if the dynamic displacement responses on the surface of the laminated plate can be obtained. The determined elastic constants are then used in the HNM to calculate the displacement responses. The NN model would go through a progressive retraining process until the calculated displacement responses using the determined results are sufficiently close to the actual responses. This procedure is examined for an actual glass/epoxy laminated plate. It is found that the present procedure is very robust and efficient for determining the elastic constants of anisotropic laminated plates.     

The second and third order elastic constants of alkali metals

The second and third order elastic constants of the alkali metals have been calculated on the long wave method using the Heine-Abarenkov lacal model potential with different exchange-correlation corrections. It is found that the use of an exchange correlation correction which satisfies the compressibility sum rule leads to a good agreement between the calculated and measured second order elastic constants of the alkali metals Na, K, Rb and Cs. The shear elastic constants however come out correct even if the compressibility sum rule is violated by the exchange-correlation correction. The third order elastic constants and the pressure derivatives of the second order elastic constants and the pressure derivatives of the second order elastic constants calculated on the HA local potential are lower than the experimental values at room temperature. The discrepancy is pronounced for the heavier alkali metals. Similar calculations using the Wallace potential for Li, Na and K and the Schneider-Stoll potential for Rb give the pressure derivative in good agreement with experiment. In view of the important role by the exchange correlation correction, Suzuki's results calculated without taking this correction into account can only be accepted with some reservation.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

Anharmonic properties of rocksalt structure solids

An effort has been made for obtaining the anharmonic properties of rocksalt structure solids starting from primary physical parameters viz. nearest-neighbor distance and hardness parameter assuming long- and short-range potentials at elevated temperatures. The elastic energy density for a deformed crystal can be expanded as power series of strains for obtaining coefficients of quadratic, cubic and quartic terms which are known as the second-, third- and fourth-order elastic constants, respectively. When the values of the higher-order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. In this study, higher-order elastic constants are computed up to their melting temperature for rocksalt structure solids, which are alkali cyanides, sodium and potassium halides. The first order pressure derivatives of second- and third-order elastic constants, the second-order pressure derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures for these substances. The results thus obtained are compared with experimental data and found in well agreement with present values.     

Accurate calculations of the high-pressure elastic constants based on the first-principles

The energy term corresponding to the first order of the strain in Taylor series expansion of the energy with respect to strain is always ignored when high-pressure elastic constants are calculated. Whether the modus operandi would affect the results of the high-pressure elastic constants is still unsolved. To clarify this query, we calculate the high-pressure elastic constants of tantalum and rhenium when the energy term mentioned above is considered and neglected, respectively.Results show that the neglect of the energy term corresponding to the first order of the strain indeed would influence the veracity of the high-pressure elastic constants, and this influence becomes larger with pressure increasing. Therefore, the energy term corresponding to the first-order of the strain should be considered when the high-pressure elastic constants are calculated.     

Anharmonic properties of TmTe

Data on elastic constants and associated properties at high temperature for TmTe crystal are presented and discussed starting from primary physical parameters viz. nearest neighbour distance and hardness parameter assuming long- and short-range potentials. When the values of the higher order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. In this study, higher order elastic constants and related properties are computed upto 1000 K for TmTe. The first-order pressure derivatives of second- and third-order elastic constants, the second-order pressure derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures. The results thus obtained are compared with other available data and found in well agreement with present values.     

立方结构Fe基磁性材料弹性系数第一性原理计算

通过赝势平面波法(CASTEP)及全电势线性缀加平面波法(FLAPW)，以bcc-Fe为对象，研究第一性原理计算立方结构Fe基磁性材料弹性系数的方法，分析影响计算立方结构Fe基磁性材料弹性系数准确度的各项因素. 结果表明，在第一性原理弹性系数计算中，晶格常数是决定弹性系数计算准确度的关键因素；势函数的选择也会影响计算准确度. 使用全电势基矢的FLAPW法可以得到更为精准的弹性系数计算结果. 计算得到bcc-Fe的弹性系数C₁₁，C₁₂，C₄₄分别为246 GPa，121 GPa，113 GPa，与实验值基本一致. 利用本方法，计算了新型Fe-Ga磁致伸缩材料的弹性系数C₁₁，C₁₂，C₄₄分别为207 GPa，166 GPa及108 GPa. 关键词： 弹性系数 磁致伸缩材料 赝势平面波法 全电势线性缀加平面波法     

Elastic constants of a nematic liquid crystal: Quadrupole-quadrupole interaction in the ellipsoidal approximation

The elastic constants of a nematic liquid crystal are calculated by means of a pseudo-molecular method that considers the quadrupolar intermolecular interaction with a screening length governing the range of the forces. The bulk as well as the surface-like elastic constants are determined as functions of the eccentricity of the interaction volume of ellipsoidal shape. It is shown that the elastic constants become negative for some values of the eccentricity, and, therefore, that the screened quadrupolar interaction could be the source of instabilities in the nematic phase and should be taken into account to interpret threshold phenomena in these systems.     

Calculation of Elastic Constants of Ag/Pd Superlattice Thin Films by Molecular Dynamics with Many-Body Potentials

The calculation of elastic constants of Ag/Pd superlattice thin films by molecular dynamics simulations with many-body potentials is presented. It reveals that the elastic constants C11 and C55 increase with decreasing modulation wavelength A of the films, which is consistent with experiments. However, the change of C11 and C55 with A is found to be around the values determined by a rule of mixture using bulk elastic constants of metals. No supermodulus effect is observed and it is due to cancellation between enhanced and reduced contributions to elastic constants from Ag and Pd layers subjected to compressive and tensile strains, respectively.     

具有六方晶系结构的多晶体材料弹性常数——Y弹性常数

利用最近提出的新的物理参量——Ｙ弹性常数,将其应用于具有六方晶系结构的多晶体材料.推导了六方晶系结构的多晶体材料之Ｙ弹性常数,通过算例与具有六方晶系结构的多晶体材料之X射线弹性常数进行了比较.运用这个Ｙ弹性常数进一步推导出的多晶体材料整体之机械弹性常数的表达式与Kneer的研究结果中的表达式虽然形式不同,但针对具体材料所计算的结果却完全符合. 关键词： Y弹性常数 六方晶系 多晶体材料     

Third-order elastic constants of the alloy Fe72Pt28

The complete sets of second- and third-order elastic constants of the cubic Fe₇₂Pt₂₈ have been obtained using the strain energy density derived from interactions up to three nearest neighbours of each atom in the unit cell. The finite strain elasticity theory has been used to get the strain energy density of Fe₇₂Pt₂₈. The strain energy density is compared with the strain-dependent lattice energy density obtained from the continuum model approximation and the expressions for the second- and third-order elastic constants of Fe₇₂Pt₂₈ are given. The second-order potential parameter is deduced from the measured second-order elastic constants of Fe₇₂Pt₂₈ and the third-order potential parameter is estimated from the Lennard-Jones inter-atomic potential for Fe₇₂Pt₂₈. The inter-lattice displacements; the three independent second-order elastic constants and the six independent third-order elastic constants of Fe₇₂Pt₂₈ are also determined. The second-order elastic constants are compared with the experimental elastic constants of Fe₇₂Pt₂₈. We also study the effect of pressure on the second-order elastic constants of Fe₇₂Pt₂₈.     

Elastic constants for NaCl and KCl solids at high temperatures

In the present study we derive new relationships to predict the temperature dependence of elastic constants. Proposed relationships are applied to study elastic constants of NaCl and KCl. A linear relationship between thermal expansivity and elastic constants at high temperatures is found to exhibit for solids. The extrapolated data on elastic constants in very high temperature region obtained in the present study are useful to understand the thermoelastic properties of NaCl and KCl. A close agreement between theory and experiment reveals the validity of the formulations used.     

Modal resonant ultrasound spectroscopy for ferroelastics

Recent experimental and theoretical improvements of resonant ultrasound spectroscopy (RUS) are summarized to investigate elastic constants of phases in shape memory alloys. The proposed inversion procedure, described in this work, is particularly suitable to reliable evaluation of the temperature dependence of elastic constants of low-symmetry ferroelastic materials which may be strongly elastically anisotropic and tend to exist in twinned forms. The method is applicable even for the evaluation of single-crystal elastic constants from RUS measurements on microtwinned crystals, since it involves a homogenization algorithm based on the macroscopic deformation response of the layered structure. This potentially allows performing meaningful acoustic studies on samples with a general submicron-size layered structure.     

关于岩石三阶弹性常数的超声测量方法

油气储层岩石的三阶弹性常数反映了该岩石的速度应力敏感性,是利用声波测井或地震资料进行原位地应力反演的基本参数。本文阐述了利用声弹性理论在实验室测量岩石三阶弹性常数的原理与方法,并给出了部分实验结果。这些参数将为研究声波在预应力声场中传播规律的提供基础数据,同时也为定量分析利用交叉偶极声波测井评价地应力的精度提供了依据。不同岩石的三阶弹性常数较大差异表明,通过速度各向异性进行应力反演时必须考虑岩石本身非线性的差异。     

Elastic constants of nonionic anharmonic crystals

Taking into account the entire anharmonicity of the crystal an exact relation between the long-wavelength limit of the static self-energy and the isothermal elastic constants is established. The result can be reformulated as a sum rule for the displacement correlation function. The diagram technique is also employed to discuss the equation for the elastic constants in the pseudoharmonic approximation as well as to derive the integral equations for the quasiparticle parameters.     

Temperature dependent ultrasonic properties of aluminium nitride

Hexagonal wurtzite structured aluminium nitride has been characterized by the theoretical calculation of ultrasonic attenuation, ultrasonic velocity, higher order elastic constants, thermal relaxation time, acoustic coupling constants and other related parameters in temperature range 200-800 K for wave propagation along the unique axis of the crystal. Higher order elastic constants of AlN at different temperatures are calculated using Lennard-Jones potential for the determination of ultrasonic attenuation. A decrease in ultrasonic velocity with temperature has been predicted, which is caused by reduction in higher order elastic constants with temperature. The temperature dependent ultrasonic properties have been discussed in correlation with higher order elastic constants, thermal relaxation time, thermal conductivity, acoustic coupling constants and thermal energy density. Anomalous behaviour of the attenuation is found at 400 K. On the basis of attenuation, the ductility and performance of AlN have been studied.     

Third order elastic constants of V3Si and V3Ge

General expressions have been derived for the second order elastic constants and third order elastic constants of the A-15 structure compounds with the nearest neighbour central interaction. The second order elastic constants, the third order elastic constants and the pressure derivatives of the second order elastic constants of V₃Si and V₃Ge are reported and compared with the available experimental measurements.     

Theories of surface elasticity for nanoscale objects

The emergence of nanotechnology has driven recent interest in systems having surface atoms as a significant fraction of all atoms present, in particular nano-sheets (ultra-thin slabs), nano-wires, and nano-particles. In these systems, the bulk (i.e. non-surface region or interior) is typically strained in response to the stress of the surface. This elastic strain of the bulk in turn changes the surface lattice constants. Since the bulk and the surface are coupled, the problem must be solved self-consistently. Solving this problem requires a quantitative model of the surface elastic properties which are different from the bulk. In this paper we consider various models that have been proposed for surface elasticity. Our goal is to elucidate the relationship between two contrasting approaches: (1) the Shuttleworth equation which defines a surface stress based on the strain derivative of the surface energy and (2) the Gurtin-Murdoch (GM) theory which considers the surface layer as a membrane with residual strain and with elastic constants different from the bulk. The GM theory is analogous to the 2-D Frenkel-Kontorova (FK) model and can be used to obtain quantitative parameters for the FK model. We present an embedded atom method calculation of the surface elastic constants of Cu(1 1 1) using the GM theory with the surface represented by a membrane one atomic layer thick. This quantitative approach describes the elastic properties of surfaces in a physically appealing way. Just as the bulk elastic constants provide direct information regarding the stress/strain relationship in a bulk material, the surface elastic constants provide similar information for a surface monolayer. This theory will allow elasticity analysis and atomistic calculations of properties of nano-scale objects.     

Mechanical elastic constants and diffraction stress factors of macroscopically elastically anisotropic polycrystals: the effect of grain-shape (morphological) texture

The effect of the grain-shape (‘morphological’) texture of a polycrystal on the mechanical elastic constants and diffraction (X-ray) stress factors is investigated. To this end, the Eshelby–Kröner grain interaction model originally devised for polycrystals consisting of spherical grains is extended to ellipsoidal grain morphology. Results obtained for the mechanical elastic constants show that a polycrystal consisting of ellipsoidal grains with their principal axes aligned along common directions (i.e. when an ideal grain-shape texture occurs) is macroscopically elastically anisotropic. Also the diffraction (X-ray) stress factors are affected by the grain-shape texture; they reflect the macroscopic elastic anisotropy by resulting in nonlinear so-called sin²?ψ plots. In general, a grain-shape texture can have a moderate effect on the mechanical elastic constants and a pronounced effect on the diffraction elastic constants, depending on the crystal symmetry and single-crystal elastic anisotropy.