Coherency stresses in multilayers

The determination of the elastic state of coherently matched layers is important in a wide range of domains, including epitaxial films on a substrate with different crystal structures, deformation of a lamella welded on a substrate and lamellar crystals. It is shown that the elastic state of coherently matched multilayers depends on two coupled field quantities: the stress (or equivalently the elastic strain) and the curvature. A general method is derived to determine these fields and the contribution of curvature on stress relaxation is emphasized. Detailed applications are given for the case of stress-free dilatation and pure shear.     

Influence of elastic strain on the density of phonon states and characteristics of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure

Appreciable elastic strain may considerably change the physical properties of crystals. This effect underlies the elastic stress technology, which has been intensively developed in recent years. The influence of elastic strain on the density of phonon states and on the properties of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure and a considerable difference between the anion and cation masses is studied using the molecular dynamics method. A number of crystal straining modes are considered. It is shown that the shear components of the strain tensor may significantly change the density of phonon states but slightly influence the frequencies of discrete breathers. Compression (tensile) strains raise (lower) the frequency of discrete breathers with a respective polarization.     

Special interaction between quasiperiodic grain boundaries and lattice dislocations in crystalline solids

A theoretical model is suggested which describes phason imperfections (specific excitations) in a quasiperiodic grain boundary in a polycrystalline solid as dilatation flexes. In the framework of the model, an elastic stress field of the quasiperiodic grain boundary is calculated as a stress field created by an ensemble of dilatation flexes (phason imperfections) located in the boundary. It is shown that there is a special elastic interaction between crystal lattice defects and quasiperiodic grain boundaries comprising phason imperfections. The strengthening effect in plastically deformed polycrystalline solids is quantitatively described which is related to the special elastic interaction between lattice dislocations and quasiperiodic grain boundaries. Received: 29 October 1996 / Revised: 22 August 1997 / Accepted: 13 November 1997     

Mechanism of formation of the equilibrium domain structure in crystals undergoing thermoelastic phase transitions

The mechanism of formation of the equilibrium domain structure during a thermoelastic phase transition is proposed. This mechanism is related to long-range elastic strain fields created by “elastic charges” at the free crystal surface. It is assumed that, during a phase transition, there appears not only the nonzero primary (antiferromagnetic, martensitic) order parameter in the crystal but also an internal (quasi-plastic) stress rigidly related to the order parameter. The orientation of this stress with respect to the crystallographic axes can be changed by external fields. Elastic charges arise due to those components of the internal stress tensor whose flux across the crystal surface is nonzero. The nonlocal destressing energy is found. It is shown that, for a certain shape of a sample, an inhomogeneous distribution of the primary order parameter (a domain structure) is energetically more favorable. The characteristic field at which a sample becomes a single domain is shown to be dependent on the shape of the crystal.     

Ductile titanium alloy with low Poisson's ratio

We report a ductile beta-type titanium alloy with body-centered cubic (bcc) crystal structure having a low Poisson's ratio of 0.14. The almost identical ultralow bulk and shear moduli of approximately 24 GPa combined with an ultrahigh strength of approximately 0.9 GPa contribute to easy crystal distortion due to much-weakened chemical bonding of atoms in the crystal, leading to significant elastic softening in tension and elastic hardening in compression. The peculiar elastic and plastic deformation behaviors of the alloy are interpreted as a result of approaching the elastic limit of the bcc crystal under applied stress.     

Observation of topological valley transport of elastic waves in bilayer phononic crystal slabs

In this Letter, we propose a unique bilayer design of phononic crystal slabs that are constructed by two layers of snowflake phononic crystal plates connected by a honeycomb array of cylinders. By tuning orientations of snowflake-shaped holes in both layers, we achieve two kinds of valley-projected topological elastic insulators distinguished by conventional and layer-polarized topological valley Hall phases. Then, between different conventional and layer-polarized topological valley Hall phases, two kinds of edge modes, layer-mixed and layer-polarized edge modes, are obtained and explored. In finite-size samples, the interesting topological transport properties, which the elastic wave can propagate alternatively between both layers and only in a single layer, are realized by exciting layer-mixed and layer-polarized edge states. In addition, we design an interlayer converter to realize conversion of the elastic wave propagation between both layers. Our research promotes the development of topological elastic insulators and provides a route for various practical applications.     

Thermodynamics of elastic strength of the metal surface layer

This paper presents a physicochemical model that establishes a connection between the elastic strength of the surface layer (SL) of metal and its surface Gibbs energy. The elastic limit of SL along the low-index face of the metal single crystal under stress during the transition from elastic to plastic deformation was calculated. Calculation shows that the elastic limit of metal SL with fcc and bcc structures is approximately three orders of magnitude higher than the yield strength of these metals in bulk and close to nanohardness of the metals, in particular; for Cu(111) и Al(111), it is 5.3 and 2.8?GPa, respectively. In the light of the proposed model, the effect of lowering the elastic strength of metal SL due to adsorption of surfactant is formulated.     

动态压缩下马氏体相变力学性质的微观研究

使用分子动力学方法,模拟了活塞以恒定加速运动从一端压缩单晶铁（沿［001］晶向）发生马氏体相变的微观过程.根据模拟结果将上述压缩过程分为弹性压缩、晶格软化、相变（bcc至hcp）、超应力松弛和高压相弹性压缩五个阶段,对各阶段的原子滑移规律和应力变化特征做了详细分析.分析得出应力超过约10 GPa时,开始出现弹性常数软化行为;层错结构（fcc）和孪晶界为新相形核的两种缺陷,前者更为稳定;相变后粒子首先进入超应力松弛状态（即沿加载方向的偏应力呈现负值）,在应力超过约36 GPa粒子转变为高压相弹性压缩状态. 关键词： 分子动力学 单晶铁 相变 动态压缩     

Unifying the criteria of elastic stability of solids

The elastic stability criterion formulated by Born is based on the convexity requirement of the equilibrium free energy F of a stress-free crystal under small strain fluctuation, that demands the elastic constant tensor C to be positive definite, |C| > 0. For a crystal subject to an external stress, Hill specifies that for the crystal to be stable, the difference between its internal energy change δE and the work done to the system δW must be positive, i.e. δE - δW > 0. Polanyi, Frenkel, and Orowan proposed a different stability criterion based on stress increment for a loaded system, τ(ε + Δε) - τ(ε) > 0 until the limit is reached at dτ/dε = 0. Although known empirically, the formal connection between the different criteria has not been established rigorously. Using finite deformation theory, we show quite simply that the different formulations of the stability criteria originate from the same necessary condition for the convexity of the free energy of the system subject to external loading, f = F - W. However, in practice caution must be taken in implementation of the different criteria; they may lead to quite different results, especially when stability bifurcation occurs.     

Deviatoric stress: a nuisance or a gold mine?

Both synchrotron radiation and deviatoric stress were once considered to be nuisances. Now synchrotron radiation is one of the most important tools available to scientists of all disciplines and deviatoric stress is one of the most useful aspects of x-ray diffraction at extreme conditions. Samples in high-pressure devices are under true hydrostatic pressure only when surrounded by a fluid, thus limiting true hydrostatic pressure studies at ambient temperatures to pressures below about 11?GPa. Elevated temperature is able to extend this limit but has rarely been used for this purpose. Instead, noble gases have been used as pressure media as their solids are especially soft. Deviatoric stress and resultant anisotropic elastic strain in solid samples and solid media have led to many subtle errors in determinations of elastic properties and crystal structures, especially in the days before it was realized that they could be measured and were potentially a valuable source of information. In recent years, measuring anisotropic elastic strain by x-ray diffraction has provided new insights into materials strength, elastic properties, crystal structures, mechanisms of phase transitions, slip systems, lattice preferred orientation, and, of course, ways to make corrections when deviatoric stress is indeed a nuisance.     

Theories of elastic properties and elastic waves of equal phase velocities in crystals

A survey is made of pairs of heteronormal planar elastic waves, which can propagate in an unlimited crystal medium and have equal theoretical values of the phase velocity, using Voigt elastic moduli. Such pairs are chosen for which it is possible that the theoretical equality of velocities will be disturbed when using another theory of the elastic properties of crystals with generally different tensors of material constants (for example Kuvshinskij J. V., Aero E. L.: Fiz. tv. tela5 (1963), 2591). In such a case, a comparison of the measured velocities of a suitable pair of waves can help to decide between the two theories. Pairs of waves are found for 12 non-piezoelectric crystal classes. Among such pairs it is easy to find pairs of waves of the same properties for piezoelectric crystal classes.     

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     

Elastic constitutive laws for incompatible crystalline media: the contributions of dislocations,disclinations and G-disclinations

Linear higher-grade higher-order elastic constitutive laws for compatible (defect-free) and incompatible (containing crystal line defects) media are presented. In the proposed model, the free energy density of a body subjected to elastic deformation under the action of surface tractions, moments or hyper-traction tensors (second-order tensors whose anti-symmetric part corresponds to moments) has contributions coming from the first two gradients of displacements. Thermodynamic considerations reveal that only the symmetric component of the gradient of elastic displacement, i.e., compatible elastic strain tensor, and the anti-symmetric component of the second gradient of elastic displacement, i.e., compatible third-order elastic curvature tensor, contribute to the free energy density during compatible deformation of the body. The line crystal defect contributions are accounted for by incorporating the incompatible components of elastic strains, curvatures and symmetric 2-distortions as state variables of the free energy density. In particular, the presence of generalized disclinations (G-disclinations) is acknowledged when the medium is subjected to surface hyper-traction tensors having a non-zero symmetric component along with surface-tractions on its boundary. Mechanical dissipation analysis provides for the coupling between the Cauchy stresses and third-order symmetric hyper-stresses. The free energy density and elastic laws for a defect-free and line crystal defected medium are proposed in a linear setting. In the special case of isotropy, the cross terms between elastic strains and curvatures contribute to the free energy density through a single elastic constant. More interestingly, the Cauchy and couple stresses are found to have contributions coming from both, elastic strains and curvatures.     

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.     

Ultrasonic characterization of Cu-Al-Ni single crystals lattice stability in the vicinity of the phase transition

Measurements of elastic constants of the austenite phase when approaching the phase transformation either upon cooling or stressing is of the crucial interest for the shape memory alloy field. Acoustic properties (wave velocity and also attenuation changes) of the Cu-Al-Ni single crystal were investigated in situ during stress-induced martensitic transformation at constant (room) temperature. The parent austenite cubic lattice of the Cu-Al-Ni exhibits very high elastic anisotropy (anisotropy factor A approximately 12). The measurements were made using nine combinations of (i) applied uniaxial compression in a given crystal direction, (ii) the wave propagation and (iii) polarization vectors. The chosen configurations are sufficient for evaluation of all independent third order elastic constants (TOEC). The longitudinal modes were also measured by the immersion technique, using the transducer pair in a water tank installed on the testing machine. The device works as "a ultrasonic extensometer" measuring a transverse strain of the specimen. The dependencies of both natural and initial wave velocities on the applied stress may be evaluated. Three elastic constants of the stress-induced martensite were determined. The elastic properties were found to vary with the increasing stress above the Ms transformation temperature, which is interpreted as a precursor for the martensitic transformation. The onset of the transformation was additionally identified from the acoustic emission measurement.     

Imaging of internal stress around a mineral inclusion in a sapphire crystal: application of micro‐Raman and photoluminescence spectroscopy

We developed a micro‐Raman and photoluminescence imaging technique for visualizing the internal stress fields in a sapphire crystal. The technique was applied to an Australian sapphire gemstone with a zircon inclusion. Considering piezospectroscopic effects on Raman and photoluminescence spectra, the Raman shifts of sapphire around the zircon inclusion were converted to hydrostatic pressure and deviatoric components of stress tensor. The internal stress was highly concentrated at the tips of the zircon crystal, where the deviatoric stress and the hydrostatic pressure component reached 700 and 470 MPa, respectively. Generation of compressive stress on the crystal surface of zircon can be explained by the difference in thermal expansion coefficients and elastic constants between sapphire and zircon. In general, internal stress fields induced by mineral inclusions reflect the pressure and temperature conditions at which the host sapphire gemstones were crystallized. Thus, the present technique can be utilized to identify the origin of gemstones. Copyright © 2012 John Wiley & Sons, Ltd.     

First-principles investigation on ideal strength of B2 NiAl and NiTi alloys

For B2 NiAl and NiTi intermetallic compounds, the ideal stress–strain image is lack from the perspective of elastic constants. We use first-principles calculation to investigate the ideal strength and elastic behavior under the tensile and shear loads. The relation between the ideal strength and elastic constants is found. The uniaxial tension of NiAl and NiTi along <001> crystal direction leads to the change from tetragonal path to orthogonal path, which is driven by the vanishing of the shear constant C(66). The shear failure under {110}{111} shear deformation occurring in process of tension may result in a small ideal tensile strength(~ 2 GPa) for NiTi. The unlikeness in the ideal strength of Ni Al and Ni Ti alloys is discussed based on the charge density difference.     

The origin of lattice instability in bcc tungsten under triaxial loading

Abstract

Stability of ideal bcc tungsten crystal under triaxial tensile loading was explored from first principles using an analysis of both elastic and dynamic stability. The triaxial stress state was considered as a superposition of axial and biaxial transverse stresses. The region of attainable stresses which was delimited using the computed tensile stress maxima was marginally reduced by occurrence of soft phonons in the crystal lattice. While, under purely hydrostatic tension, the crystal was predicted stable up to 48 GPa, greater magnitude of a differential stress reduced the value of a mean (hydrostatic) stress associated with first phonon instabilities to about 35 GPa. This value is rather close to that recently determined in experiment. Computed phonon spectra were successfully verified with the help of atomistic models of microscopic lattice deformation.     

基于微观结构计算晶体宏观弹性应变场

基于晶体的微观结构提出了一种计算晶体宏观弹性应变场的方法,将该方法应用于金属晶体Fe,得到的应变场与连续介质理论预测结果吻合地很好,从而证明了该方法的准确性.以该方法为基础,进一步考虑无限小应变与有限应变的差值,发现应变差值在晶体剧烈变形区域内较强,对金属晶体Cu位错应变场的计算表明这种应变差异可以用来描述位错的运动状态和芯域结构.该方法可为评估晶体缺陷附近应变状态提供依据.     

基于微观结构计算晶体宏观弹性应变场

基于晶体的微观结构提出了一种计算晶体宏观弹性应变场的方法,将该方法应用于金属晶体Fe,得到的应变场与连续介质理论预测结果吻合地很好,从而证明了该方法的准确性.以该方法为基础,进一步考虑无限小应变与有限应变的差值,发现应变差值在晶体剧烈变形区域内较强,对金属晶体Cu位错应变场的计算表明这种应变差异可以用来描述位错的运动状态和芯域结构.该方法可为评估晶体缺陷附近应变状态提供依据.