Interface/surface optical phonon in onion-like quantum dots

We calculate the interface/surface phonon in onion-like quantum dots by using dielectric continuum approach. The form of the phonon potential of the onion-like quantum dots and the electron-phonon interaction Hamiltonian are obtained. Core/shell quantum dots and quantum dot quantum well are studied in detail. The interface/surface phonon modes and corresponding frequencies as a function of the sizes of the structure are investigated. We observe that the asymptotic behavior is depended on the host medium. The sensitivity of the interface/surface phonon frequencies are decreasing with the increasing of the shell thickness. The contribution of different angular momentum quantum numbers to the electron-phonon interaction are given for the onion-like quantum dots. Numerical calculations are performed on the CdS/ZnS and CdS/ZnS/CdS heterostructure which is embedded in the polyethylene.     

Vibration analysis of multi-walled carbon nanotubes using a spring–mass based finite element model

We report a study of the vibrational characteristics of multi-walled carbon nanotubes modeled exclusively using springs and lumped masses. Based on the atomic microstructure of the nanotube, three-dimensional nanoscale spring elements are utilized to simulate the dynamic behavior of each layer of the multi-walled carbon nanotubes. Appropriate spring elements are also developed to model the interlayer interactions and describe the van der Waals potentials between carbon atoms on different layers. Direct application of the physical variables of molecular mechanics theory to the springs is used to simulate the relative translations and rotations between atoms as well as the masses of the carbon atoms. The stiffness and mass matrices of the problem are used to construct the dynamic equilibrium equation. The natural modes of vibration and the corresponding natural frequencies are derived by solving the eigenvalue problem for different support conditions. The present method suggests novel basic modes of vibration, beyond those reported in the literature pertaining to multi-walled carbon nanotubes. The effects on the basic modes and natural frequencies created by van der Waals interactions and geometric parameters such as number of layers and aspect ratio are investigated in the context of elastic support conditions. Comparisons with other theoretical studies reveal very good correlations in terms of fundamental modes and frequencies.     

Collective modes in Ca70Mg30 glass

The self-consistent phonon scheme given by Takeno and Goda, involving multiple scattering and phonon eigen frequencies which are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential in the solids, has been used to generate the collective modes in the Ca₇₀Mg₃₀ glass. A model potential is proposed to describe the effective interaction in the glass. Three different forms of the local field correction functions viz. Hartree, Taylor and Ichimaru and Utsumi are used to examine relative influence of exchange and correlation effects. The phonon frequencies of the longitudinal and transverse modes are computed employing the theoretical formulation of Hubbard and Beeby. The elastic property of the glassy system is then studied using the long wavelength limits of the phonon modes. The theoretical computations reproduce much better dispersion curves (both for the longitudinal and transverse phonons) compared to earlier reports and are found to be in good agreement with the available experimental results due to neutron scattering. Paper presented at the 5th IUMRS-ICA 98, October 1998, Bangalore.     

多层介质硬币形(Penny-Shaped)交界裂纹的弹性波散射

本文研究多层介质硬币形交界裂纹的弹性波散射.文中采用Hankel积分变换,得到了含有硬币形交界裂纹多层介质模型的散射波传递矩阵,并将散射问题为转化求解矩阵形式的对偶积分方程.作为特例,文中给出了单一弹性层与半空间的硬币形交界裂纹的弹性波散射远场模式,并计算了几组不同弹性常数组合情形下的远场模式的幅频特性曲线,其结果表明有共振峰存在.     

含界面裂纹圆形夹杂的十二次对称二维准晶热应力分析

针对点热源作用下,无限大十二次对称二维准晶基体和圆形弹性夹杂界面之间含多条裂纹的问题进行了研究。基于复变函数分区全纯理论、留数定理、广义 Liouville 定理、Riemann-Schwarz 解析延拓定理及复应力函数奇性主部分析方法,获得了集中热源作用于准晶基体内任意一点时,准晶基体和圆形弹性夹杂内外温度场、声子场热应力的一般复势解。由此获得了含一条界面裂纹和两条界面裂纹时温度场以及声子场热应力的封闭形式解答,将所得结果与已有结果进行了对比,验证了该方法的有效性。最后通过数值算例分析了夹杂半径、点热源强度及裂纹角度对热应力和裂纹尖端热应力强度因子的影响规律。结果表明：随着热源强度的增大,裂纹尖端的声子场热应力也逐渐增大;随着裂纹角度的增大,裂纹尖端的声子场热应力强度因子变大;随着半径的增大,热应力强度因子的变化趋势越来越明显,并且取得的峰值越高,即裂纹角度和夹杂半径的增加,促进了裂纹的扩展。这些结论为准晶材料的结构设计和使用提供了科学依据。     

Confocal micro-Raman observation of nanometer thick oxide layers on metal nanoparticles

It is shown for the first time that confocal micro-Raman spectroscopy can be used to detect metal oxide nanometer thick layers on metal nanoparticles. The measured frequencies of the observed oxide layers are shifted to lower frequencies and the line widths were asymmetrically broadened compared to Raman spectrum in bulk oxide of the metals. The effects are due to phonon confinement which occurs in materials of nanometer dimensions. Models of phonon confinement are used to estimate the thickness of the oxide layers.     

Thermomechanical analysis of residual stresses in brazed diamond metal joints using Raman spectroscopy and finite element simulation

Thermal residual stresses are one of the crucial parameters in engineered grinding tool (EGT) life and its consistency. Predicting failure of brazed diamond metal joints in EGTs is related to analyzing the thermal residual stresses during the cooling process. Thus thermal residual stresses have been simulated in a model with realistic materials properties, for instance isotropic hardening and a hyperbolic-sine creep law for SS316L and the silver–copper–titanium active filler alloy, named Cusil ABA™. Also, special modeling techniques such as tie constraint and sub-modeling have been used to model an intermetallic layer titanium-carbide (TiC) with dimensions in nanometers, where the rest of the model’s dimensions are in millimeters. To verify the simulated stress state of the diamond, Raman-active optical phonon modes at three different paths in the diamond were measured. As the experiments with Raman spectroscopy (RS) do not deliver stress components, the solution is to directly compute the peak shift of Raman spectrum. The splitting in phonon frequencies and the mixing of phonon modes contain information about the thermal residual stresses in the diamond. Finally the shift in the phonon frequencies was calculated from the different numerical residual elastic strain components and compared to the experimental results.     

Fast modal response method for structures

Regardless of their simplicity, all structures have an infinite number of degrees-of-freedom (d.o.f.) when subjected to dynamic loading. The usual finite element method reduces the infinite d.o.f. system to a model with a limited d.o.f. while capturing the significant physical behaviour. The modal analysis reduces the number of d.o.f. further to a limited number of modal co-ordinates. However, accurate results comparable to the original finite element model may not be possible unless higher modes are included. The present paper is to recommend a response analysis which makes use of both the natural modes and the mass and stiffness matrices of the system to improve the convergence with respect to the number of modes. While the effects of lower modes are analysed similar to the modal analysis, the effects of higher modes are included in the system matrices and the information for higher modes is not needed.     

Transmission of Phonons with Anomalous Dispersion through the Interface of Two Continuous Media

We solve the problem of phonon transmission through the interface between a quantum fluid with anomalous dispersion and a solid, for arbitrary angles of incidence. The Wiener–Hopf method is applied to solve the equations of the quantum fluid in the half-space, and in particular the solution is obtained for the dispersion relation of a Bose–Einstein condensate (BEC) and of superfluid helium at small wave vectors. It is shown that the solutions are running waves deformed near the border by specific surface standing waves. Boundary conditions are used to derive the transmission and reflection coefficients for the phonons, incident on either side of the interface, as a function of the incidence angles and the phonon frequencies. The deformation of wave packets passing through the interface is described both far from and near to the critical incidence angles.     

Revisit of an elliptic hole problem by using complex variable method

In this paper, the problem of an elliptic hole embedded in an infinite plate interacting with an arbitrary point load is revisited by using the complex variable method. Based on analytical continuation theorem, the continuity conditions across the interface are automatically satisfied in a straightforward manner. It is shown that the solution for an infinite domain with an elliptic hole can be obtained from the solution of the corresponding homogeneous problem merely by a simple algebraic expression. This relation is universal in the sense of being independent of the loading considered. The solution of the corresponding homogeneous problem is considered as the principal part of the complex potentials while the complementary part of the complex potentials can be obtained by using analytical continuation theorem. Different expressions of the complementary part of the complex potentials are presented in this paper which are all proved to be the same result.     

Transient infinite elements for contaminant transport problems

A time-dependent infinite element which can be used to simulate contaminant transport problems in infinite media is presented in this paper. Since this transient infinite element is constructed in a global co-ordinate system instead of a local one, a closed-form solution for the property matrices of the element has been derived from an advection–diffusion/dispersion problem in a homogeneous, anisotropic infinite medium. The numerical results from the present transient infinite element have excellent agreements with the corresponding analytical solutions. Compared with the previous infinite elements, the present infinite element has the following special characteristics: (1) both space and time variables were explicitly considered in the formulation; (2) its property matrices were expressed in a closed form; (3) it can be used to represent the far field of a mass/contaminant transport problem in a homogeneous, anisotropic infinite medium; (4) it was constructed in a global co-ordinate system. Therefore, it is highly recommended that the transient infinite element be used for the numerical simulation of contaminant transport problems in infinite media.     

Micromechanics of imperfect interfaces in heterogeneous materials

In the design of strong engineered materials-containing fibres or particulates to be used for impact and abrasive wear, one important problem is the magnitude of the stress concentration around these second-phase constituents. Analytical solutions for cylindrical and spherical inclusions embedded within infinite matrices are reviewed and assessed for their value in predicting the constitutive behaviour of heterogeneous materials. Solutions for two distinct interfacial behaviours are found in the literature: (1) radial displacement and stress continuity with zero shear stress across the interface (i.e. frictionless); and (2) an elastic interface (modelled as a very thin interfacial elastic layer) capable of supporting both normal and tangential displacements and stresses. However, both of these approaches incorporate constitutive behaviour that would be considered incompatible for real materials (e.g. interpenetration between reinforcement and matrix). In this study, finite element models are developed without these limitations and their results (stress concentration factors) are compared with analytically derived solutions. It is shown that for certain load cases analytical solutions inadequately model the idealized micromechanical behaviour of heterogeneous materials.     

First principles calculations of the electronic, dynamical, and thermodynamic properties of the rocksalt ScX (X = N, P, As, Sb)

We have investigated the electronic, dynamical, and thermodynamic properties of the rocksalt ScX (X = N, P, As, Sb) using a plane-wave pseudopotential method within the generalized gradient approximation in the frame of density functional perturbation theory. The calculated lattice constants are found to differ by less than 0.56% from the available experimental values. These materials have the indirect Γ–X band gaps and a wide and direct band gap at the X-point in band structure, which are closer to experimental results than the previous calculations. A linear-response approach is used to calculate the phonon frequencies, the phonon density of states and LO–TO splitting. The obtained phonon frequencies at the zone-center (Γ-point) for the Raman-active and infrared-active modes are analyzed. We also calculate the thermodynamic functions using the phonon density of states, and the calculated values are in nearly perfect agreement with experimental data.     

Monte Carlo Modeling of Phonons at Crystal Interfaces

One of the strategies in the effort to directly detect dark matter particles is to measure the phonon and charge signals produced in an incidental collision of a weakly interacting massive particle with a nucleon in a crystalline detector. Proper calibration of the detected phonon energy relies on detailed models of phonon propagation through the crystal to the instrumented surface. Previous Detector Monte Carlo incorporate probabalistic anharmonic decay and mass defect scattering but neglect the mode dependent scattering at crystal boundaries. We calculate mode specific reflection and transmission at detector interfaces with a simple acoustic mismatch model. We find that mode preserving transmission is the most probable outcome at germanium-aluminum detector interfaces, but the probability of reflection is not negligible. The average phonon reflection probability at near normal angles of incidence at a Ge/Al interface is near 20 %, but grows dramatically for oblique incidence. We develop a code using Geant4, which should allow modeling extensions to all phonon mediated dark matter detection schemes. Our models are adaptable to other crystal materials and are generally useful in any phonon interface problem.     

Recursive second order convergence method for natural frequencies and modes when using dynamic stiffness matrices

When exact dynamic stiffness matrices are used to compute natural frequencies and vibration modes for skeletal and certain other structures, a challenging transcendental eigenvalue problem results. The present paper presents a newly developed, mathematically elegant and computationally efficient method for accurate and reliable computation of both natural frequencies and vibration modes. The method can also be applied to buckling problems. The transcendental eigenvalue problem is first reduced to a generalized linear eigenvalue problem by using Newton's method in the vicinity of an exact natural frequency identified by the Wittrick–Williams algorithm. Then the generalized linear eigenvalue problem is effectively solved by using a standard inverse iteration or subspace iteration method. The recursive use of the Newton method employing the Wittrick–Williams algorithm to guide and guard each Newton correction gives secure second order convergence on both natural frequencies and mode vectors. The second order mode accuracy is a major advantage over earlier transcendental eigenvalue solution methods, which typically give modes of much lower accuracy than that of the natural frequencies. The excellent performance of the method is demonstrated by numerical examples, including some demanding problems, e.g. with coincident natural frequencies, with rigid body motions and large‐scale structures. Copyright © 2003 John Wiley & Sons, Ltd.     

Boundary integral equation method for two dissimilar elastic inclusions in an infinite plate

This paper provides a numerical solution for an infinite plate containing two dissimilar elastic inclusions, which is based on complex variable boundary integral equation (CVBIE). The original problem is decomposed into two problems. One is an interior boundary value problem (BVP) for two elastic inclusions, while other is an exterior BVP for the matrix with notches. After performing discretization for the coupled boundary integral equations (BIEs), a system of algebraic equations is formulated. The inverse matrix technique is suggested to solve the relevant algebraic equations, which can avoid using the assembling of some matrices. Several numerical examples are carried out to prove the efficiency of suggested method and the hoop stress along the interface boundary is evaluated.     

Water-wave propagation through an infinite array of floating structures

The frequency-domain problem of water-wave propagation through a periodically arranged infinite array of structures is solved using the method of matched asymptotic expansions for both shallow and deep water; the structures are assumed to be small relative to the wavelength and the array periodicity, and may be fixed or float freely. Explicit approximations to the frequencies of propagating modes are obtained, and used to illustrate how the frequencies are affected by geometrical and other parameters.     

Plasmon-phonon and plasmon-two different phonon interaction in Pb1−xMnxTe mixed crystals

Far-infrared reflection spectra in wide temperature range was used to investigate the vibrational properties of Pb_1−xMn_xTe (x = 0.0002, 0.002, 0.02 and 0.1) mixed crystals. To analyse the experimental results we use dielectric function that takes into account the existence of plasmon-phonon as well as the plasmon-two different phonon interaction. The best fit method revealed two frequencies of plasmon-phonon coupled modes and three frequencies of plasmon-two different phonon coupled modes. Further, the values for two different LO modes and plasma frequency (ω_P) are calculated. Results obtained from experimental spectra as the best fit, are in very good agreement with the theoretical prediction. The model of phonon behaviour based on Genzel's model was developed. It was found that the long wavelength optical phonon modes of these mixed crystals, exhibit an intermediate and two mode behaviour, coincidentally.     

Solution of three-dimensional, anisotropic, nonlinear problems of magnetostatics using two scalar potentials, finite and infinite multipolar elements and automatic mesh generation

The two-scalar potentials idea has been used with success for the computation of static magnetic fields in the presence of nonlinear isotropic magnetic materials by the finite element method. In this communication we formulate the two-scalar-potentials method for anisotropic materials and present a computer program and the solution of an example problem. The use of infinite multipolar elements is also discussed. Several advanced methods and ideas are employed by the program: scalar potentials, rather than vector potentials, giving only one unknown quantity; the finite element method, in which the solution is approximated by a continuous function; the Galerkin method to solve the differential equations; accurate infinite elements, which avoid the introduction of an artificial boundary for unbounded problems; automatic mesh generation, which means that the user can construct a large mesh and represent a complicated geometry with little effort; automatic elimination of nodes outside the iron, which restricts the iterations to the nonlinear anisotropic region with economy of computer time; use of sparse matrix technology, which represents a further economy in computer time when assembling the linear equations and solving them by either Gauss elimination or iterative techniques such as the conjugated gradient method, etc. The combination of these techniques is very convenient.     

FREQUENCY-INDEPENDENT INFINITE ELEMENTS FOR ANALYSING SEMI-INFINITE PROBLEMS

Two drawbacks exist with the infinite elements used for simulating the unbounded domains of semi-infinite problems. The first is the lack of an adequate measure for calculating the decay parameter. The second is the frequency-dependent characteristic of the finite/infinite element mesh used for deriving the impedance matrices. Based on the properties of wave propagation, a scheme is proposed in this paper for evaluating the decay parameter. In addition, it is shown that by the method of dynamic condensation, the far-field impedance matrices for waves of lower frequencies can be obtained repetitively from the one for waves of the highest frequency, using exactly the same finite/infinite element mesh. Such an approach ensures that accuracy of the same degree can be maintained for waves of all frequencies within the range of consideration. Effectiveness of the proposed method is demonstrated in the numerical examples through comparison with previous results.