Lattice constants and anisotropic microstrain at low temperature in 242Pu–Ga alloys

We attempted to characterize by neutron powder diffraction the monoclinic α′ phase that is known to form at low temperatures in dilute Pu–Ga alloys. This attempt was unsuccessful, as we did not detect any transformation to the α′ phase, but instead observed a line-broadening effect in the fcc?δ?phase. This effect is large enough to be visible in the raw diffraction data and is highly anisotropic in crystal space. The onset temperature of the line broadening (150?K) coincides with previous observations of the δ–α′ transformation. Bulk α′ was not observed. We believe that the development of α′ nuclei creates a spatially inhomogeneous stress distribution in the?δ?matrix, which in turn exhibits an anisotropic response, governed by its elastic anisotropy. We have analysed this observation of anisotropic microstrains in terms of the fictive microstresses required to produce them by elastic deformation. During the course of this work, we found a pseudo-isotope effect in the room temperature lattice constants of Pu–Ga alloys. The alloys made from nominal ²⁴²Pu isotope show systematically higher lattice constants than the corresponding ²³⁹Pu alloys, and the size of the effect is proportional to the Ga concentration. We believe that this effect is associated with the higher levels of radiation damage from isotopic impurities in the ²⁴²Pu alloys.     

Effective dielectric and piezoelectric constants of thin polycrystalline ferroelectric films

The averaged dielectric, piezoelectric, and elastic constants of thin polycrystalline barium titanate and lead titanate films are calculated within a modified effective-medium approximation, which takes fully into account piezoelectric interactions between crystallites. Films with c-or a-type crystal texture resulting from mechanical interaction with the substrate are considered when the film becomes ferroelectric under cooling of the heterostructure. The dependences of the effective material constants of textured films on the residual macroscopic polarization of a film are described. An analysis is made of the effect of two-dimensional clamping of a film on a thick substrate on measurements of dielectric and piezoelectric constants. Fiz. Tverd. Tela (St. Petersburg) 40, 2206–2212 (December 1998)     

BaTiO3晶体结构及弹性的分子动力学模拟

有效的势函数是分子动力学模拟的关键. 引入了一种势函数,该势函数的特点是运用参数r_eff计算原子间的静电作用. 通过分子动力学方法模拟得到了BaTiO₃晶体立方相、四方相结构的对关联函数和X射线衍射谱,计算得出了它们的晶格常数及弹性常数. 模拟结果与实验结果符合较好.该势函数可以有效地模拟BaTiO₃晶体的热学和力学性能. 关键词： 分子动力学模拟 势函数 3铁电晶体')" href="#">BaTiO₃铁电晶体     

The determination of stresses in thin films; modelling elastic grain interaction

X-ray diffraction is frequently employed for the analysis of mechanical stresses in polycrystalline specimens. To this end, suitable so-called diffraction elastic constants are needed for determining the components of the mechanical stress tensor from measured lattice strains. These diffraction elastic constants depend on the single-crystal elastic constants of the material considered and the so-called grain interaction, describing the distribution of stresses and strains over the crystallographically differently oriented crystallites composing the specimen. Well-known grain interaction models, as due to Voigt, to Reuss, to Neerfeld and Hill and to Eshelby and Kröner, may be applied to bulk specimens, but they are generally not suitable for thin films. In this paper, an average 'effective' grain interaction model is proposed that consists of a linear combination of basic extreme models including new models specially suited to thin films. Experimental verification has been achieved by X-ray diffraction strain measurements performed on a sputter-deposited copper film. This is the first time that anisotropic grain interaction has been analysed quantitatively.     

First-principles study of elastic and vibrational properties of Ni<Subscript>2</Subscript>MnIn magnetic shape memory alloys

We present the results of ab initio calculations of lattice dynamics and the second order elastic stiffness constants of nickel-based magnetic shape memory alloy Ni₂MnIn in stoichiometric composition. The plane wave basis sets and pseudopotential method within spin-polarized generalized gradient approximation (σ-GGA) scheme of the density functional theory (DFT) is applied. Elastic constants are calculated by tetragonal and monoclinic isochoric strains on cubic L2₁ structure. The calculated elastic constants agree very well with the recent ultrasonic experimental data. Phonon dispersion spectra are investigated within linear response technique of the density functional perturbation theory (DFPT). A vibrational anomaly is observed in phonon spectra at the transverse acoustic mode (TA₂) in [ζ ζ0] direction at wavevector ζ = 0.3 as an indication of the structural instability of the system to shear deformation. This anomaly is also verified by the low shear modulus and large elastic anisotropy ratio. Phonon dispersion curves are in excellent agreement with the results of recent neutron diffraction experiments.     

Direction-dependent elastic grain-interaction models – a comparative study

Mechanical and diffraction (X-ray) elastic constants (diffraction (X-ray) stress factors for macroscopically elastically anisotropic specimens) can be calculated for polycrystalline specimens from single-crystal elastic data by employing elastic grain-interaction models. Traditionally, only so-called isotropic grain-interaction models are considered: all directions in the polycrystal are taken equivalent with respect to the grain interaction. Only recently, so-called direction-dependent, i.e. anisotropic grain-interaction models, have been proposed. These models can express the effects of the reduced dimensionality of thin films, of the surface anisotropy of bulk polycrystals and of a grain-shape (morphological) texture on the elastic properties of polycrystals. In this work, the available, recently proposed direction-dependent grain-interaction models will be compared, in particular on the basis of numerical calculations of diffraction and mechanical elastic constants, of variances of certain orientation-dependent stress and strain tensor components and of the distributions of strains in the Euler (orientation) space. It will be demonstrated that the so-called Vook–Witt and inverse Vook–Witt models become (but only approximate) equivalent to the Eshelby–Kröner model for certain grain-shape textures.     

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.     

Taking account of grain interaction in calculating the elastic properties of textured materials

A method of calculating the modulus of elasticity of polycrystalline, textured, macroscopically orthotropic material from the properties of the structural elements is proposed; the method is based on the calculation of corrections to the statistical means of the crystallite elastic constants. The results of Young's-modulus calculations for samples of the alloys VT1-0 and OT4-1 are compared with values obtained in the approximations of Voigt, Roiss, and Hill.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 61–65, March, 1982.     

尺寸相关的弹性常数对应变硅纳米线电学性质的影响

从Keating模型出发,基于离散化思想建立了计算单晶硅纳米线弹性常数和杨氏模量的半连续原子晶格力学模型. 从微扰理论和形变势理论出发,采用有限差分方法建立了计算不同晶向应变硅纳米线价带结构的数值模型. 结合上述的两个计算模型,进而应用经典弹道传输模型研究了轴向应力和弹性常数对p型硅纳米线弹道晶体管电学特性的影响. 研究结果表明,硅纳米线的弹性常数和杨氏模量呈现尺寸效应,该结果与分子动力学的模拟结果具有很好的一致性. 同时发现尺寸相关的弹性常数对硅纳米线晶体管输运电流的影响强烈依赖于单轴应力对输运电流的影 关键词： 应变硅纳米线 弹性常数 弹道电流 价带结构模型     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

Structural and elastic properties of TiN under high pressure

We have investigated the structural and elastic properties of TiN at high pressures by the first-principles plane wave pseudopotential density functional theory method at applied pressures up to 45.4 GPa. The obtained normalized volume dependence of the resulting pressure is in excellent agreement with the experimental data investigated using synchrotron radial x-ray diffraction (RXRD) under nonhydrostatic compression up to 45.4 GPa in a diamond-anvil cell. Three independent elastic constants at zero pressure and high pressure are calculated. From the obtained elastic constants, the bulk modulus, Young's modulus, shear modulus, acoustic velocity and Debye temperature as a function of the applied pressure are also successfully obtained.     

On the structural phase transition in rare earth elpasolites

The structural phase transition in two representatives of the rare earth elpasolite fluorides, Rb₂NaHoF₆ and Rb₂NaTmF₆, are studied in detail. The symmetry of the soft mode is determined from Raman spectra, X-ray and neutron powder diffraction data to be ₄ ⁺ . From the temperature dependence of the elastic constants of both compounds, estimates of various phase transition parameters are given, e.g. strain soft mode coupling constant and soft mode frequency. The softening of the elastic constants forT>T _c is explained by the strain coupling to the fluctuations of the soft mode coordinates. The energy of the soft phonon at the zone boundary is estimated from the data and compared with that of K₂ReCl₆. The phase transition mechanisms in rare earth elpasolites and hexahalometallates are discussed.     

Elasticity of BaFCl single crystal under hydrostatic pressure

The sound velocities for longitudinal and transverse waves have been measured in single crystalline BaFCl at room temperature using ultrasonic pulse echo and Brillouin scattering techniques. The complete set of elastic constants is deduced and lead to the bulk moduli values of BaFCl at ambiant conditions (, , ) which are compared with those obtained by a shell model. Moreover, using the ultrasonic technique under pressure, the pressure derivatives of the second order elastic constants at 298 K have been determined up to 0.3 GPa. All moduli increase linearly with pressure in this pressure range, allowing to determine directly and separately the first derivative of the bulk modulus B'₀ = 5.8. These data are used to calculate a Murnaghan equation of state. A detailed comparison is given between our results with those recently obtained by X-ray diffraction on powder or calculated using the local density approximation method. Finally, the anisotropy of BaFCl under pressure is discussed. Received: 19 March 1998 / Revised: 15 May 1998 / Accepted: 19 May 1998     

Concentration dependences of the elastic constants of the two-dimensional graphene-silicene system

The concentration dependences of the elastic constants of the two-dimensional Si _x C_{1 − x} system have been investigated with the use of the Harrison bonding-orbital method and the Keating model. The central and non-central force constants and the Grüneisen parameter have been considered by means of the bonding-orbital method. All quantities under consideration have been shown to exhibit a nonlinear behavior during the transition from graphene to silicene. A nontrivial role of the short-range repulsion has been discussed. The second-order and third-order elastic constants, the pressure dependences of the second-order elastic constants, as well as the Poisson’s ratio and Young’s modulus have been investigated in the Keating model. It has been found that the elastic constants and Young’s modulus change almost linearly upon the transition from graphene to silicene, whereas the other quantities under consideration exhibit nonlinearity.     

High‐pressure Brillouin study of the elastic properties of rare‐gas solid xenon at pressures up to 45 GPa

The pressure dependences of three adiabatic elastic constants, adiabatic bulk modulus, refractive index, and elastic anisotropy, as well as Cauchy deviation of fcc solid Xe have been determined up to 10 GPa at 296 K by high‐pressure Brillouin scattering spectroscopy. The characteristics of elastic properties at high pressure of rare‐gas solid Xe are investigated by comparison with the previous studies on Ne, Ar, and Kr. Above 10 GPa, the occurrence of splitting in the Brillouin signals and the direction dependence of acoustic velocities for solid Xe clearly show partial phase transformation to the hcp structure reported by the previous X‐ray diffraction and Raman scattering studies. The shear elastic modulus in the hcp phase of solid Xe has also been estimated at pressures up to 45 GPa by using the pressure dependence of the Raman wavenumber shift for the E_2g mode. Copyright © 2008 John Wiley & Sons, Ltd.     

Elestic constants in the interfacial layer at the nematic-liquid-crystal-vapour interface

Summary Close to the interface between a nematic liquid crystal (NLC) and another medium, the elastic constants become functions of distancez from the interface and of angle θ between the directorn and the unit vectork orthogonal to the interface. Furthermore, due to the breaking of the translation symmetry at the interface, a lot of new subsurface elastic contributions can appear. In a previous paper we investigated these subsurface anomalies by using a simple molecular model based on induced-dipole-induced-dipole interactions and by making numerical calculations in the special case of a planar director distortion. In this way, only the numerical values of some effective subsurface elastic constants that characterise planar director distortions could be obtained. In this paper we make a more complete analytical calculation of all the subsurface elastic constants by using a microscopic model and a more general theoretical procedure. The microscopic interaction energy is written in a general form that allows us to investigate different kinds of intermolecular interactions (induced diple-induced dipole, quadrupole-quadrupole and so on). Both thez-dependence and the θ-dependence of the subsurface elastic constants are obtained in a closed analytical form. In the special case of induced-dipole-induced-dipole interactions and for planar director distortions, our analytical results are shown to agree with the previous numerical results. The important macroscopic effect of these elastic subsurface anomalies is discussed.     

Extension of the Vook–Witt and inverse Vook–Witt elastic grain-interaction models to general loading states

The recently developed Vook–Witt and inverse Vook–Witt elastic grain-interaction models have been employed for the calculation of mechanical elastic constants and diffraction (X-ray) stress factors of, in particular, thin films. However, their applicability is limited to a planar, rotationally symmetric state of macroscopic, mechanical stress. For such a loading state (and an, at least, transversely, elastically isotropic specimen), only two mechanical elastic constants are necessary to describe mechanical elastic behaviour and only the sum of two diffraction (X-ray) stress factors is needed to relate lattice strains to the one independent component of the mechanical stress tensor. The restriction to a planar, rotationally symmetric state of mechanical stress will be removed in this work. Calculation of the full stiffness tensor and all six diffraction (X-ray) stress factors then becomes possible. It was found previously that the Vook–Witt and inverse Vook–Witt models become (but only approximately) equivalent to the Eshelby–Kröner model for certain ideal grain-shape textures. For this reason, results of numerical calculations of mechanical elastic constants and diffraction (X-ray) stress factors, based on the Vook–Witt and inverse Vook–Witt models, will be presented and compared to corresponding results obtained from the Eshelby--Kröner grain-interaction model considering ideal grain-shape (‘morphological’) textures.     

An ab initio study of the structural,elastic, electronic and optical properties of the newly synthesized nitridoaluminate LiCaAlN2

The structural parameters, elastic constants, electronic structure and optical properties of the recently reported monoclinic quaternary nitridoaluminate LiCaAlN₂ are investigated in detail using the ab initio plane-wave pseudopotential method within the generalized gradient approximation. The calculated equilibrium structural parameters are in excellent agreement with the experimental data, which validate the reliability of the applied theoretical method. The chemical and structural stabilities of LiCaAlN₂ are confirmed by calculating the cohesion energy and enthalpy of formation. Chemical band stiffness is calculated to explain the pressure dependence of the lattice parameters. Through the band structure calculation, LiCaAlN₂ is predicted to be an indirect band gap of 2.725 eV. The charge-carrier effective masses are estimated from the band structure dispersions. The frequency-dependent dielectric function, absorption coefficient, refractive index, extinction coefficient, reflectivity coefficient and electron energy loss function spectra are calculated for polarized incident light in a wide energy range. Optical spectra exhibit a noticeable anisotropy. Single-crystal and polycrystalline elastic constants and related properties, including isotropic sound velocities and Debye temperatures, are numerically estimated. The calculated elastic constants and elastic compliances are used to analyse and visualize the elastic anisotropy of LiCaAlN₂. The calculated elastic constants demonstrate the mechanical stability and brittle behaviour of the considered material.     

第一性原理计算α-ScDx(D=H,He)的弹性常数

本文采用第一性原理方法研究了α相钪氢化合物(α-ScH _x )和α相钪氦化合物(α-ScHe _x )的弹性常数,其中x=0,1/4,1/8,1/32表示H原子和He原子在α-ScD_x(D=H,He)中的浓度.研究结果表明,对于钪,氢和氦对晶体的弹性性质的影响截然不同.钪氢化合物晶体的弹性常数基本上随着晶体中氢的浓度增加而增加,这跟实验测量得出的结论一致;然而,钪氦化合物体系的弹性常数几乎随着氦浓度的 关键词： 第一性原理 弹性常数 x')" href="#">α-ScH _x x')" href="#">α-ScHe _x     

α-Ti2Zr高压物性的第一性原理计算研究

基于密度泛函理论的第一性原理计算获得了α-Ti₂Zr的晶体结构、弹性常数、德拜温度和电子分布情况, 研究了它们与压力的关系. 计算得到的晶体结构参数与实验值一致. 运用有限应变方法计算得到了α-Ti₂Zr的体积模量B、剪切模量G、杨氏模量E和泊松比σ. B和E的零压值分别为101.2和35.6 GPa. G/B的值较小, 并且随着压力的增加而减小, 表明α-Ti₂Zr具有优异的延展性. 基于弹性常数得到平均声速, 从而获得了德拜温度Θ=321.7 K. 通过解Christoffel方程获得的压缩波和剪切波数据揭示α-Ti₂Zr具有较强的各向异性. 此外, 压力诱导电子从s轨道到d轨道的转移说明在一定压力下α-Ti₂Zr将转变为β相. 关键词： 第一性原理 α-Ti₂Zr')" href="#">α-Ti₂Zr 物性 高压