Semi-infinite Solids Research Articles

The measurement of thermal diffusivities for semi-infinite solids using the photothermal displacement method

This paper develops a more accurate method of measurement for thermal diffusivity using photothermal displacement spectroscopy. In previous studies, thermal diffusivities for materials with a finite thickness have been determined by the angle of deformation and the phase difference, with regard to the relative positions of the pump and probe beams. In this study, a complete theoretical treatment and experimental measurement, through the photothermal displacement technique, have been conducted for semi-infinite solid materials. To verify the method developed, the measurement has been carried out for an alloy of pure copper and nickel with both finite and semi-infinite thicknesses. In the results of the study, the measured values for semi-infinite materials differed from those reported in the literature by at most 1% of the standard deviation, while the corresponding differences for finite materials were at most 3% of the standard deviation. Consequently, the model for semi-infinite solids is proposed as a highly accurate method for measuring thermal diffusivity.

Backscattering coefficients for low energy positrons and electrons impinging on bulk solidtargets

The backscattering coefficients (BSCs) for semi-infinite solids of normally incident 1–4 keVelectrons and positrons are stochastically modeled and calculated by the MonteCarlo method. This paper aims at discussing the differences observed between theproperties of electrons and positrons impinging on solid targets based on theuse of the differential elastic scattering cross-section which has been obtainedusing the Bentabet and Bouarissa approximation (2006 Phys. Lett. A 355 390).A new mathematical equation was developed for the adjustable parameterβ of the Bentabet et al approximation and seems to be valid for other elements. Both electronand positron BSC simulated results show good agreement with the experimental orcomputed data reported by other authors.

Excitation of excitons in semi-infinite solids with a nonrelativistic electron beam

The instability of an infinite thin electron beam propagating in vacuum over the surface of an isotropic nongyrotropic crystal is investigated. The possibilities of exciting additional longitudinal waves and polarization waves are analyzed. The dispersion laws of exciton-beam coupled waves are obtained. It is demonstrated that the interaction of the beam with the additional bulk longitudinal wave and the surface polarization wave leads to the appearance of the absolute instability.

Implementation of Green's function molecular dynamics: An extension to LAMMPS

The Green's function molecular dynamics method, which enables one to study the elastic response of a three-dimensional solid to an external stress field by taking into consideration only the surface atoms, was implemented as an extension to an open source classical molecular dynamics simulation code LAMMPS. This was done in the style of fixes. The first fix, FixGFC, measures the elastic stiffness coefficients for a (small) solid block of a given material by making use of the fluctuation–dissipation theorem. With the help of the second fix, FixGFMD, the coefficients obtained from FixGFC can then be used to compute the elastic forces for a (large) block of the same material. Both fixes are designed to be run in parallel and to exploit the functions provided by LAMMPS. Program summary Program title: FixGFC/FixGFMD Catalogue identifier: AECW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: yes No. of lines in distributed program, including test data, etc.: 33 469 No. of bytes in distributed program, including test data, etc.: 1 383 631 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Linux Has the code been vectorized or parallelized?: Parallelized via MPI RAM: Depends on the problem Classification: 7.7 External routines: MPI, FFTW 2.1.5 ( http://www.fftw.org/), LAMMPS version May 21, 2008 ( http://lammps.sandia.gov/) Nature of problem: Using molecular dynamics to study elastically deforming solids imposes very high computational costs because portions of the solid far away from the interface or contact points need to be included in the simulation to reproduce the effects of long-range elastic deformations. Green's function molecular dynamics (GFMD) incorporates the full elastic response of semi-infinite solids so that only surface atoms have to be considered in molecular dynamics simulations, thus reducing the problem from three dimensions to two dimensions without compromising the physical essence of the problem. Solution method: See “Nature of problem”. Restrictions: The mean equilibrium positions of the GFMD surface atoms must be in a plane and be periodic in the plane, so that the Born–von Karman boundary condition can be used. In addition, only deformation within the harmonic regime is expected in the surface layer during Green's function molecular dynamics. Running time: FixGFC varies from minutes to days, depending on the system size, the numbers of processors used, and the complexity of the force field. FixGFMD varies from seconds to days depending on the system size and numbers of processors used.

Longitudinal wave response of a chiral slab interposed between micropolar solid half-spaces

A plane longitudinal displacement wave is made incident upon a chiral slab of uniform thickness, interposed between two different semi-infinite micropolar elastic solids. The amplitude ratios of various reflected and refracted waves are obtained using the two possible sets of boundary conditions. The variations of various amplitude ratios with the angle of incidence as well as with the frequency are depicted graphically, for a specific problem. The effect of chirality parameter and the thickness of the chiral slab on these amplitude ratios have been noticed. Results of some earlier researchers have also been reduced as special cases of present formulation.

SH surface wave in multicracked solids

We focus on the dispersion spectra of surface coherent waves in damaged semi-infinite elastic solids. The damage region is located within the surface layer containing depth-depending concentration of parallel closed cracks. The dispersion equation is similar to that for the Love waves in a coated substrate, except that the layer's effective elastic properties, being deduced from multiple scattering theory, are frequency-dependent and complex. For healthy elastic solids, the grazing SH wave is nondispersive. The dispersion under study is induced by the presence of cracks. The effect of both the magnitude of crack-concentration and its profile into the depth is investigated. The reliability of the semianalytical predictions is also discussed through a comparison with the numerical results obtained by using a finite-difference code.

Evaluation of the thermal comfort of ceramic floor tiles

In places where people are bare feet, the thermal sensation of cold or hot depends on the environmental conditions and material properties including its microstructure and crustiness surface. The uncomforting can be characterized by heated floor surfaces in external environments which are exposed to sun radiation (swimming polls areas) or by cold floor surfaces in internal environments (bed rooms, path rooms). The property named thermal effusivity which defines the interface temperature when two semi-infinite solids are putted in perfect contact. The introduction of the crustiness surface on the ceramic tiles interferes in the contact temperature and also it can be a strategy to obtain ceramic tiles more comfortable. Materials with low conductivities and densities can be obtained by porous inclusion are due particularly to the processing conditions usually employed. However, the presence of pores generally involves low mechanical strength. This work has the objective to evaluate the thermal comfort of ceramics floor obtained by incorporation of refractory raw materials (residue of the polishing of the porcelanato) in industrial atomized ceramic powder, through the thermal and mechanical properties. The theoretical and experimental results show that the porosity and crustiness surface increases; there is sensitive improvement in the comfort by contact.

EVALUATION OF THE THERMAL COMFORT IN CONTACT WITH CERAMIC TILES

In places where people are bare feet, the thermal sensation of cold or hot depends on the environmental conditions and material properties including its microstructure and crustiness surface. The uncomforting can be characterized by heated floor surfaces in external environments which are exposed to sun radiation (swimming polls areas) or by cold floor surfaces in internal environments (bed rooms, path rooms). The property named thermal effusivity which defines the interface temperature when two semiinfinite solids are putted in perfect contact. The introduction of the crustiness surface on the ceramic tiles interferes in the contact temperature and also it can be a strategy to obtain ceramic tiles more comfortable. Materials with low conductivities and densities can be obtained by porous inclusion are due particularly to the processing conditions usually employed. However, the presence of pores generally involves low mechanical strength. This work has the objective to evaluate the thermal comfort of ceramics floor obtained by incorporation of refractory raw materials (residue of the polishing of the porcelanato) in industrial atomized ceramic powder, through the thermal and mechanical properties. The theoretical and experimental results show that the porosity and crustiness surface increases; there is sensitive improvement in the comfort by contact.

Quantum field theory of van der Waals friction

van der Waals friction between two semi-infinite solids, and between a small neutral particle and semi-infinite solid is studied using thermal quantum field theory in the Matsubara formulation. We show that the friction to linear order in the sliding velocity can be obtained from the equilibrium Green functions and that our treatment can be extended for bodies with complex geometry. The calculated friction agrees with the friction obtained using a dynamical modification of the Lifshitz theory, which is based on the fluctuation-dissipation theorem. We show that it should be possible to measure the van der Waals friction in noncontact friction experiment using state-of-the-art equipment.

Theory of images in plane-layered axisymmetric elastostatics

A fundamental theorem which automatically transforms the solution due to the presence of an arbitrary axisymmetric singularity in an unbounded homogeneous isotropic elastic solid into the corresponding solution for two perfectly bonded isotropic semi-infinite elastic solids is systematically applied in a stepwise fashion to obtain the complete image system when an arbitrary axisymmetric singularity is operative in or near a thick elastic layer which separates two other dissimilar isotropic semi-infinite elastic solids. The solution is closed and well structured. As an illustration, the distant effect in the interface layer produced by an influencing normal point force is luminously revealed to be two-dimensional, consisting of a combination at the origin of a bending hot spot and an infinite line of centres of dilatation. We conclude the paper with a complete theory of images for a free elastic layer under the influence of both axisymmetric and asymmetric singularities. We find that if the influencing displacement field is the gradient of a harmonic function, then the calculation of the induced elastic field reduces to the operation of differentiation only.

Electroelastic field concentrations and polarization switching induced by circular electrode at the interface of piezoelectric disk composites

The electromechanical field concentrations due to circular electrode at the interface of piezoelectric disk composites have been discussed. This paper consists of two parts. In the first part, the problem of an internal electrode embedded at the interface of two dissimilar semi-infinite piezoelectric solids was formulated by means of Hankel transforms, and the solution was solved exactly. In the second part, finite element analysis was carried out to study electromechanical response in piezoelectric disk composites containing a circular electrode at the interface by introducing a model for polarization switching in local areas of field concentrations. A nonlinear behavior induced by localized polarization switching was observed between the strain and the voltage applied to the electrode.

Practical Green’s function approach to the simulation of elastic semi-infinite solids

This paper is concerned with the principles of Green's function-based molecular dynamics (GFMD) simulations of semi-infinite elastic solids and their application to various contact mechanical problems. A methodology to compute the (renormalized) elastic interactions of surface atoms is presented first. It is based on the fluctuation-dissipation theorem, with the help of which thermal fluctuations of atomic displacements can be related to the elastic Green's functions and thus to the effective coupling between surface atoms. We suggest a sparse representation of these renormalized spring constants and present numerical results for some simple two- and three-dimensional lattices. The renormalized elastic interactions can be obtained for relatively small systems and then be extrapolated to large systems. They incorporate the full elastic response of semi-infinite solids in a way that only surface atoms have to be considered in molecular dynamics simulations. The usefulness of GFMD is demonstrated by applying it to various idealized contact models, such as nonadhesive Hertzian contacts as well as nonadhesive contacts between flat, semi-infinite elastic solids and a self-affine, rigid substrate. In all cases, a zero probability density $P(p)$ for infinitesimally small contact pressures $p$ is found, as predicted theoretically. If the self-affine, nonadhesive surfaces are under such high loads that the contact is complete, the pressure histogram can be represented by a Gaussian also in accordance with theoretical predictions. However, if the topography of the substrate resembles that of industrial steel surfaces and the loads are moderate, $P(p)$ decays exponentially for medium and large $p$ in contradiction to theoretical predictions for randomly rough surfaces.

Two-dimensional analysis of the effect of an electrode layer on surface acoustic waves in a finite anisotropic plate

The effect of a metal layer over an elastic substrate on surface acoustic wave propagating in the structure can be evaluated precisely for semi-infinite solids and infinite plates, but there is no accurate analytical solution if the finite size of the plate has to be considered. By expanding displacements with eigensolutions of surface acoustic waves in a semi-inifite solid, a set of two-dimensional equations similar to the Mindlin plate theory are obtained. Then for a thin electrode layer, the effect is considered through the approximation of displacements in the metal layer with the ones in the substrate, and an integration over the thickness incorporated the properties of the metal layer into equations through the modification of material properties with the decaying indices of surface acoustic waves and the thickness of the metal layer. Using AT-cut quartz crystal as the substrate, we present the effect of silver electrode layers of finite thickness on the phase velocity of propagating surface acoustic waves.

A two-dimensional theory for the analysis of surface acoustic waves in finite elastic solids

The analysis of surface acoustic waves in elastic solids started from a semi-infinite isotropic elastic body with solutions and techniques dated back to Lord Rayleigh. These solutions have explained the surface acoustic wave phenomena and guided its engineering applications in many fields. Research work followed have been using the same semi-infinite model with solution techniques for approximate and exact results in both analytical and numerical manners for many application problems involving finite elastic solids. On the other hand, we have noticed that various two-dimensional theories, notably plate theory by Mindlin, have been derived to study the bulk wave propagation in finite elastic solids like plates and bars with satisfactory results. The lack of such a two-dimensional theory has made the analysis of surface acoustic wave propagation in various waveguides primitive and difficult because the precise solutions cannot be obtained through any analytical effort and numerical solutions are also difficult to obtain because of the complicated nature of problems. To meet the need of a simplified analytical method for surface acoustic waves in finite elastic solids, we start the derivation from the well-known three-dimensional solutions of semi-infinite elastic solids. Using exact solutions as the basis for the two-dimensional expansion, we found that the usual procedure of dimension reduction works perfectly in this case because the unknown wavenumber is eventually removed in the expansion process, and the depth of the solid is considered through integration constants that are exponentially decaying functions of the wavenumber, which is to be specified. In addition, we also found the two-dimensional equations give the exact phase velocity without corrections of any kind in the limiting case in which the solid is semi-infinite. With these equations, two-dimensional solutions of mechanical displacements and phase velocity can be obtained analytically from four coupled differential equations that are similar to Mindlin plate equations. We demonstrated the applications of the two-dimensional theory with the analysis of surface waves in isotropic elastic rectangular strips. The velocity and displacement results offer a chance to understand surface acoustic waves in finite solids and the presence of overtone modes and transition zones.

Improved analytical solution for inverse heat conduction problems on thermally thick and semi-infinite solids

Analytical solutions to inverse heat conduction problems with a far-field boundary condition are derived for one- and two-dimensional problems using a Laplace transform technique. Accuracy of the predictions is improved by superposition of successive corrections to the function used to approximate the measured data. Long-term history of high frequency modes in both time and space is neglected noting that these components do not penetrate deeply into the solid. The two-dimensional solution is a relatively simple extension of the one-dimensional formulation. The present results are most useful for determining surface temperature and heat flux based on measured data from a row of sensors at a single depth below the surface and a known or measured boundary condition far from the surface.

Meshless analysis of unsteady-state heat transfer in semi-infinite solid with temperature-dependent thermal conductivity

In this paper, meshless element-free Galerkin (EFG) method has been extended to obtain the numerical solution of linear and non-linear heat transfer in semi-infinite solids. A model problem has been solved using constant and temperature-dependent thermal conductivities of the material. For the linearization of nonlinear equations, quasilinearization scheme is adopted to avoid iterations and for time integration, backward difference method has been used. The meshless formulation has been presented for a non-linear heat transfer in semi-infinite solids. The EFG results have been obtained for a model problem using cubic spline weight function. The results obtained by the EFG method are compared with those obtained by finite element and analytical methods.

A Two-dimensional Theory for Surface Acoustic Wave Propagation in Finite Piezoelectric Solids

Surface acoustic waves (Rayleigh waves) are analyzed for semi-infinite anisotropic solids only for essential propagation characteristics like the velocity and decaying parameters, which are important in engineering applications. The limitations of these results are obvious because devices are usually built on a finite piezoelectric substrate with propagation properties different from the analytical model with which the parameters are derived. For an accurate analysis of the dominant mode of surface acoustic wave propagation in plate-like finite piezoelectric solids, a two-dimensional theory has been developed based on the exponential expansion of displacements and electrical potential in the thickness direction, effectively creating a theory similar to popular plate theories of Mindlin, Lee, and others.

Adsorbate vibrational mode enhancement of radiative heat transfer and van der Waals friction

We study the dependence of the heat transfer and the van der Waals friction between two semi-infinite solids on the dielectric properties of the bodies. We show that the heat transfer and van der Waals friction at short separation between the solids may increase by many orders of magnitude when the surfaces are covered by adsorbates, or can support low-frequency surface plasmons. In this case the heat transfer and van der Waals friction are determined by resonant photon tunneling between adsorbate vibrational modes, or surface plasmon modes. The enhancement of the van der Waals friction is especially large when in the adsorbed layer there is an acoustic branch for the vibrations parallel to the surface like in the case of Cs adsorption on Cu(1 0 0) surface. In this case we show that even for separation d = 10 nm, the van der Waals friction induced by adsorbates can be so large that it can be measured with the present state-of-the-art equipment. The van der Waals friction is characterized by a strong distance dependence (∼1/ d 6), and at small distances it can be much larger than the electrostatic friction observed in [B.C. Stipe, H.J. Mamin, T.D. Stowe, T.W. Kenny, D. Rugar, Phys. Rev. Lett. 87 (2001) 096801].

Instability in flow through elastic conduits and volcanic tremor

The stability of fluid flow through a narrow conduit with elastic walls is explored, treating the fluid as incompressible and viscous, and the walls as semi-infinite linear Hookean solids. Instabilities analogous to roll waves occur in this system; we map out the physical regime in which they are excited. For elastic wave speeds much higher than the fluid speed, a critical Reynolds number is required for instability. However, that critical value depends linearly on wavenumber, and so can be made arbitrarily small for long waves. For smaller elastic wave speeds, the critical Reynolds number is reduced still further, and Rayleigh waves can be destabilized by the fluid even at zero Reynolds number. A brief discussion is given of the nonlinear dynamics of the instabilities for large elastic wave speed, and the significance of the results to the phenomenon of volcanic tremor is presented. Although magma itself seems unlikely to generate flow-induced vibrations, the rapid flow through fractured rock of low-viscosity fluids exsolved from magma appears to be a viable mechanism for volcanic tremor.

Influence of octupole photoionization transitions on the angular distribution of photoelectrons from solids with account for elastic scattering

Using the transport theory approach, equations are derived for the angular dependence of XPS intensities from semi-infinite solids taking into account elastic scattering of photoelectrons and non-dipolar transitions up the second-order corrections. The unpolarized excitation source is considered. The elastic scattering is the main term smearing the non-dipolar contribution in complete analogy with smearing of dipole contribution. Some additional terms are shown to be negligible in comparison with the main term for complete sets of emission and azimuth angles, three representative single scattering albedo values and several representative sets of the second-order non-dipolar parameters. The photoelectron angular distributions are calculated for Al 2s and Ag 3d lines using transport theory and Monte-Carlo simulation. The Monte-Carlo calculations are in agreement with transport theory approach.