On the scatter ranges for the elastic moduli of random aggregates of general anisotropic crystals

A randomly inhomogeneous material may have macroscopic properties (elasticity, conductivity) scattered over some uncertainty intervals, despite the idealistic uniqueness assumption of homogenization theory. Based on minimum energy principles and certain statistical isotropy-symmetry hypotheses, our partly third-order bounds on the effective properties of random polycrystals are expected to estimate those scatter ranges. Explicit expressions are given and calculated for the elastic moduli of the random aggregates of some known monoclinic and triclinic crystals, which yield results in agreement with those calculated for higher-symmetry crystals: the moduli are determinable within an accuracy of two or three significant digits in most cases. It is shown, however, that with some real-world exotic crystals the bounds may fall far apart, and further theoretical and experimental studies on them deserve attention.     

Bounds on the reflectivity of two-component composite

Bounds on the effective permittivity circumscribe 2D area in the complex plane representing possible values of permittivity. It is shown that the corresponding possible values of reflectivity occur within the interval determined by the lowest and the highest reflectivity value, which represent minimum and maximum values of reflectivity found at the permittivity bounds.     

Asymptotic properties of multistate random walks. II. Applications to inhomogeneous periodic and random lattices

The previously developed formalism for the calculation of asymptotic properties of multistate random walks is used to study random walks on several inhomogeneous periodic lattices, where the periodically repeated unit cell contains a number of inequivalent sites, as well as on lattices with a random distribution of inequivalent sites. We concentrate on the question whether the random walk properties depend on the spatial arrangement of the sites in the unit cell, or only on the number density of the different types of sites. Specifically we consider lattices with periodic and random arrangements of columns and lattices with periodic and random arrangements of anisotropic scatterers.     

Effect of surface elasticity on scattering of elastic P-waves from a nanofiber including an inhomogeneous interphase

Scattering of elastic P-waves from a nanofiber in a matrix is studied analytically throughout this paper. An inhomogeneous interphase region is considered between the nanofiber and the matrix. Dividing the interphase into homogeneous sublayers, surface elasticity effects are studied in the layers adjacent to matrix and nanofiber. Wave function expansion method is used to solve the corresponding equations in all three phases including fiber, interphase, and matrix. Dynamic stress concentration factors around the nanofiber are calculated and utilizing a parametric study, effects of different parameters, such as nanoscale interface, interphase thickness, and interphase rigidity are investigated. The results indicate that considering the effects of surface elasticity in wave scattering problems from inhomogeneous interphases show a major impact on the results. The dimensionless equations presented in this paper provide the possibility of further numerical studies.     

New frontiers in metamaterials research: Novel electronic materials and inhomogeneous metasurfaces

In reviewing some recent work in metamaterials, we highlight two exciting new frontiers just emerging in this field — metamaterials made by new electronic materials (particularly graphene) and inhomogeneous metasurfaces to control light wave-fronts.     

Bounds for effective parameters of multicomponent media by analytic continuation

Recently D. Bergman introduced a method for obtaining bounds for the effective dielectric constant (or conductivity) of a two-component medium. This method does not rely on a variational principle but instead exploits the properties of the effective parameter as an analytic function of the ratio of the component parameters. We extend the method to multicomponent media using techniques of several complex variables.     

La3Ga5SiO14晶体的介电性质、弹性与压电性质

研究了La3Ga5SiO14晶体的介电性质、弹性和压电性质，其中弹性和压电性质是利用高频振动模式通过谐振法测定的. 关键词： 介电性质 弹性 压电性质     

The influence of 3d-metal alloy additions on the elastic and thermodynamic properties of CuPd3

Embedded-atom method （EAM） potentials are used to investigate the effects of alloying （e.g. 3d-metals） on the trends of elastic and thermodynamic properties for CuPd3 alloy. Our calculated lattice parameter, cohesive energy, and elastic constants of CuPd3 are consistent with the available experimental and theoretical data. The results of elastic constants indicate that all these alloys are mechanically stable. Further mechanical behavior analysis shows that the additions of Cr, Fe, Co, and Ni could improve the hardness of CuPd3 while V could well increase its ductility. Moreover, in order to evaluate the thermodynamic contribution of 3d-metals, the Debye temperature, phonon density of states, and vibrational entropy for CuMPd6 alloy are also investigated.     

非均匀背景中任意柱状热斗篷的研究与设计

在变换热力学的基础上,通过坐标变换的方法严格推导出在层状背景和渐变背景下二维任意形状热斗篷导热系数的通解表达式,并在此基础上设计出非均匀背景下二维非共形热斗篷.全波仿真结果表明:在不同背景下,热流均能绕过保护区域流出,保护区域的温度保持不变,而且热斗篷外的温度场并没有破坏,具有很好的热保护和热隐身的效果.这一方法考虑到背景的复杂性,更加贴近工程实际应用,为未来灵活控制热流传递提供了一种可行的方法,对目标热隐身和热保护具有重要借鉴意义.     

Bounds and exact theories for the transport properties of inhomogeneous media

We investigate the bounds of Milton on the transport coefficient of a two-component composite, in their application to the square and hexagonal arrays of cylinders, and the three cubic lattices of spheres. We show that, in all five cases, as more information is supplied about the geometry of the composite, the bounds converge to the precise point obtained from an exact theory specific to the geometry in question. We illustrate the use of the bounds in determining whether a set of known values of the transport coefficient adequately specifies the general behaviour of that quantity. We determine the values of two structure-dependent parameters for cell materials with spheroidal cells and the value of one parameter for hexagonal and square arrays of cylinders with missing array elements. These parameters determine bounds both on the transport and on the elastic properties of the respective materials.     

Interchangeability and bounds on the effective conductivity of the square lattice

The effective conductivity ^* of an infinitely interchangeable two-component random medium is considered. This class of media includes cell materials in the continuum and the bond lattice on ^d , where the cells or bonds are randomly assigned the conductivities ₁ and ₂ ( ₁, ₂ne0) with probabilitiesp ₁ andp ₂=1–p ₁. A rigorous basis for the very old and widely used low volume fraction expansion of ^* is established, by proving that ^* is an analytic function ofp ₂ in a suitable domain containing [0, 1]. In the case of the bond lattice ind=2, rigorous fourth-order upper and lower bounds on ^* valid for allp ₂, ₁, and ₂ are derived. The four perturbation coefficients entering into the bounds are obtained from the first-order volume fraction coefficient using the method of infinite interchangeability.     

高斯型非均匀应力对铁磁薄膜磁化性质的影响

采用Monte-Carlo方法研究了高斯型非均匀应力对的铁磁薄膜磁化性质的影响.结果表明: 与易轴平行的拉应力和与易轴垂直的压应力能够增大系统的矫顽场, 而与易轴平行的压应力和与易轴垂直的拉应力则会减小系统的矫顽场.在矫顽场增大(减小)的同时, 系统还伴随着剩磁及其矩形度的增大(减小).更有意义的是, 在与易轴平行的压应力或与易轴垂直的拉应力作用下, 在应力的集中区域会出现“易轴旋转”的现象. 这种产生“易轴旋转”的应力集中区域的范围强烈地依赖于应力的强度和分布宽度. 关键词： 铁磁薄膜 非均匀应力 Monte-Carlo方法 磁滞回线     

Prediction of effective stagnant thermal conductivities of porous materials at high temperature by the generalized self-consistent method

The generalized self-consistent method is developed to deal with porous materials at high temperature, accounting for thermal radiation. An exact closed form formula of the local effective thermal conductivity is obtained by solving Laplace's equation, and a good approximate formula with uncoupled conductive and radiative effects is given. A comparison with available experimental data and theoretical predictions demonstrates the accuracy and efficiency of the present formula. Numerical examples provide a better understanding of interesting interaction phenomena of pores in heat transfer. It is found that the local effective thermal conductivity divides into two parts. One, attributed to conduction, is independent of pore radius for a fixed porosity and, furthermore, is independent of temperature (actually, it is approximately independent of the temperature) if it is non-dimensionalized by the thermal conductivity of the matrix. The other is due to thermal radiation in pores and strongly depends on the temperature and pore radius. The radiation effect can not be neglected at high temperature and in the case of relatively large pores.     

Characterization of the variation of the material properties in a freestanding inhomogeneous thin film

This Letter presents a new technique for measuring the variation of the material properties along the thickness in a freestanding inhomogeneous thin film. The analytical results reveal a simple relation between the material properties and the set of cut-off frequencies of Lamb waves. The influence of the graded properties on the variation of cut-off frequencies in three different kinds of models, including artificial FGM model, sub-surface damage model, and nano-porous thin film model, is discussed. These results provide theoretical guidance for characterizing the material property variations of MEMS/NEMS.     

基底微缺陷对介质薄膜光学性能影响的理论研究

基于非均匀膜理论提出一种存在微缺陷的介质基底的折射率分层模型，将基底依次分为表面层、亚表面层和体材料层，其中表面层和亚面层分别等效为折射率服从统计分布的非均匀膜，将它们分别再次细分为N₁和N₂个子层，每一子层均视为均匀介质 膜.应用光学薄膜特征矩阵法对其进行理论分析，并对单层介质膜的光学性能进行数值计算. 研究结果表明：基底的表面和亚表面微缺陷改变了薄膜和基底的等效折射率，导致了准Brew ster角和组合反射率与理想情形的偏离.同时这些微缺陷也改变了光在薄膜和基底中的传播 特性，因此反射相移和相位差均偏离理想情形.在研究基底的微缺陷对多层介质膜光学性能 影响的分析和计算时，该模型同样适用. 关键词： 微缺陷 介质薄膜 非均匀膜 光学性能     

Influence of elastic strains on the adsorption process in porous materials. Thermodynamics and experiment

If we disregard the shape of the boundary hysteresis loop, H1 for SBA-15, MCM-41 and KIT-6, H2 for p⁺-type porous silicon and porous glass, the hysteretic features inside the loop are qualitatively the same for all these systems and show that none of them are composed of independent pores whether the pores are interconnected or not. We hence believe that the physical parameter which couples the pores is not the interconnectivity but the elastic deformation of the porous matrix. The thermodynamic approach we develop includes the elastic energy of the solid. We show that the variation of the surface free energy, which is proportional to the deformation of the porous matrix, is an important component of the total free energy. With porous silicon, we experimentally show that a stress external to the porous matrix exerted by the substrate on which it is supported significantly increases the total free energy and the adsorbed amount and decreases the condensation pressure compared to that of the same porous matrix detached from its substrate which is the relaxed state of the supported layer. This stress can be partly relaxed by making thicker porous layers due to the breaking of Si-Si bonds. This results in the shift of the isotherms towards that of the membrane. We propose a new interaction mechanism occurring through the pore wall elastic deformation in which the external mechanical stress is imposed on a given pore by its neighbours.     

Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity

We present a two-dimensional mathematical model of a composite material with conducting inclusions (fibers) embedded in a matrix. Our main objective is to study how polydispersity (two different sizes of particles) affects the overall conductivity of the composite. If the conductivity of inclusions is higher than the conductivity of the matrix, then previous studies suggest an increase of the effective conductivity due to polydispersity. We show that for high volume fraction when inclusions are not well-separated and percolation effects play a significant role, polydispersity may result in either an increase or decrease of the effective conductivity. Our proof is based on the method of functional equations and it provides sufficient conditions for both the increase and the decrease of the effective conductivity.     

Effects of compression on the sound absorption of porous materials with an elastic frame

The absorption characteristics of a porous material are well known to vary during compression. The transfer matrix method is applied with an elastic frame to explore the effect of compression on absorption properties. In this work, the materials are treated as elastic rather than being made of rigid models. The absorption coefficients of the uncompressed and compressed porous material are initially calculated and verified from the experimental measurements. Then, numerical predictions of absorption coefficient are made for the compressed porous material.     

Si-Li合金相嵌锂性能和弹性性能的第一性原理计算

采用基于密度泛函理论的第一性原理平面波赝势方法,计算了锂离子电池硅负极材料在嵌Li过程中形成LixSi合金相(0≤x≤4.4)的形成能、嵌Li电位、晶体结构、电子结构和弹性性能。计算结果表明,随着嵌Li量的增加,LixSi合金体系总量能逐渐降低,LixSi合金相的形成能均为负值,表明硅负极材料的嵌Li反应在热力学可以自发进行;随着嵌Li量的增加,LixSi合金相的平均嵌Li电位逐渐降低,体积膨胀率逐渐增大,这与实验测得的结果具有良好的一致性。LixSi合金相在费米能级附近的电子主要由Si原子的p电子和Li原子的s电子共同贡献,LixSi合金相的费米能态密度随着嵌Li量的增加在整体上呈现增大趋势,电子导电性增强。随着嵌Li量的增加,LixSi合金相的体积模量(B)、剪切模量(G)和杨氏模量(E)逐渐降低,G/B值表明LixSi合金相均呈脆性,导致硅在嵌Li过程容易发生脆性结构破坏。