Slab Of Finite Thickness Research Articles

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes ( approximately hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given.

Ab initiotheory of perpendicular magnetotransport in metallic multilayers

The current-perpendicular-to-plane ~CPP! magnetotransport of a metallic sample sandwiched by two ideal leads is described at an ab initio level. The so-called ‘‘active’’ part of the system is either a trilayer consisting of two magnetic slabs of finite thickness separated by a nonmagnetic spacer or a multilayer formed by alternating magnetic and nonmagnetic layers. We use a transmission matrix formulation of the conductance based on surface Green’s functions as formulated by means of the tight-binding linear muffin-tin orbital method. The formalism is extended to the case of lateral supercells with random arrangements of atoms of two types, which in turn allows to deal with specular and diffusive scattering on equal footing, and which is applicable also to the case of noncollinear alignments of the magnetization in the layers. Applications refer to fcc-based Co/Cu/Co~001! trilayers and multilayers, considering in detail the effect of substitutional alloying in the spacer and in the magnetic layers, as well as interdiffusion at the interfaces.

Electron energy-loss spectroscopy in systems of polarizable spheres

We start with a brief presentation of the dielectric formalism used to calculate the energy loss of high-energy electrons (100 keV) passing through a random system of polarizable spheres embedded in a homogeneous matrix. The formalism is then extended to the case of electrons traveling parallel to a homogeneous slab of finite thickness in which either ordered or disordered collections of polarizable spheres are embedded. For an ordered system in which the spheres are in a cubic array, the calculated energy-loss spectra are compared with those of an alternative theory. For a slab with disordered collections of spheres we find the energy-loss spectra using the recursive Green's function method and compare our results with the available experimental data as well as with an extension of the semiclassical-infinite-barrier (SCIB) model. Finally, we discuss the relevance of our work as well as trends for future research.

A discussion on an apparent MO theory paradox

A discussion on an apparent MO theory paradox, concerning the probability of positioning a particle within a nodal plane, is carried out in terms of particle confinement probability within finite thickness slabs encompassing the plane in question. It is also discussed how using extended wave functions, the joint position plus kinetic resultant probability distribution, just fulfilling the uncertainty principle, produces a compensating effect on the particle probability of sharing position or momentum within the two half‐spaces delimited by the considered nodal plane.

Casimir effect for two lossy dispersive dielectric slabs

The electromagnetic field is quantized using the Green's-function method for the geometry of a Fabry-Perot cavity, made up of two identical lossy dispersive slabs of finite thickness. The dielectric functions of the slabs are assumed to be an arbitrary complex function of frequency obeying causality requirements. The attractive Casimir force between the two slabs is calculated by the help of the latter field operators, via evaluating the difference between the vacuum pressures on both sides of each slab. Special attention is paid to the limiting case of the Casimir effect for two conducting plates. The Lorentz model of the dielectric function is used to demonstrate the variation of the force in terms of plasma frequency. The Casimir force expression is also related to the imaginary part of the response function. The latter expression is used to introduce the repulsive Casimir force between two conducting plates located inside a Fabry-Perot cavity.

The Time Delay for a Perceptible Thermal Disturbance in a Slab

If a thermal disturbance such as a step change in temperature is applied at each surface of a homogeneous slab of thickness 2L, the effect of cooling at x = +L at first has no effect at x = −L but is clearly evident after a time described by a Fourier number F0 = λt/ρcpL2 of around 0.2. To establish the time of a perceptible change the minimum value of φi − (φ1 + (φ2) is sought, where φ1 is the flux into a semi-infinite solid and φ1 and φ2 are the first and second eigenfunction contributions to the solution for a slab of finite thickness. Cooling throughout the slab is determined virtually by the first eigenfunction alone after F0 = 0.22. For a fluid-cooled slab these values are larger.

C5H5 on a Pt(111) Surface: Electronic Structure and Bonding

The chemisorption of cyclopentadienyl (c-C5H5) on Pt(111) has been studied using qualitative band-structure calculations in the framework of the tight-binding implementation of the extended Huckel method. We modeled the metal surface by a two-dimensional slab of finite thickness, with an overlayer of c-C5H5, one c-C5H5 per nine surface Pt atoms. The c-C5H5 molecule is attached to the surface with its five C atoms bonding mainly with three Pt atoms. The Pt−Pt bonds in the underlying surface and the C−C bonds of c-C5H5 are weakened upon chemisorption. Forward-donation from the adsorbate to the substrate is significant, and there is also substantial back-donation, as reported in the literature for benzene on Pt and Ni surfaces. We found that the band of Pt 5dz2 orbitals plays an important role in the bonding between c-C5H5 and the surface, as do the Pt 6s and 6pz bands.

Magnetic breakdown in a normal-metal–superconductor proximity sandwich

We study the magnetic response of a clean normal-metal slab of finite thickness in proximity with a bulk superconductor. We determine its free energy and identify two (meta-)stable states, a diamagnetic one where the applied field is effectively screened, and a second state, where the field penetrates the normal-metal layer. We present a complete characterization of the first order transition between the two states which occurs at the breakdown field, including its spinodals, the jump in the magnetization, and the latent heat. The bistable regime terminates at a critical temperature above which the sharp transition is replaced by a continuous cross-over. We compare the theory with experiments on normal-superconducting cylinders.

Multiply scattered light correlations in an expanded temporal range

The multiple scattering of light from a Brownian particle suspension is considered for backscattering as well as transmission through a finite-thickness slab. A method for calculation of the radiative transfer propagator is developed permitting to extend significantly a range of time wherein the temporal correlation function can be found. Using the elaborated approach, numerical results are obtained in good agreement with experiment. A deviation of a correlation function initial slope from linear is shown to arise from a contribution of a finite number of scattering orders. The correlation functions for polarized and depolarized scattered light components are calculated inside and outside the backscattering cone. The transmittion correlation function is found for time intervals far exceeding a characteristic time of Brownian diffusion. A double-scattering term of the temporal correlation function is obtained that is valid for any time interval.

Effect of electrostatic boundary conditions and system size on the interfacial properties of water and aqueous solutions

The consequences of the choice of electrostatic boundary conditions on the interfacial properties of water and on the free energy of ion adsorption from aqueous solution have been investigated. The Ewald summation method for lattices, which are periodic in two dimensions, is considered to be the most adequate method in slabs of finite thickness in one dimension. In agreement with the physics of the problem a field-free region in the bulk phases is observed. The use of spherical truncation methods like the shifted-force method leads to unphysical results. The electrostatic potential depends on the size of the system. Ewald summation methods for three-dimensional lattices lead to results in qualitative agreement with the corresponding two-dimensional lattice sum. The computed value of the electrostatic potential depends on an additional parameter, namely the lattice constant c in the direction perpendicular to the interface. The results for Ewald summation in three dimensions converge to the results for Ewald summation in two dimensions for large c, the shifted-force results converge to the same limit, when the surface area of the simulation cell becomes very large and the cut-off distance increases accordingly.

Laser through-cutting and drilling models for ablating/decomposing materials

A previously-developed three-dimensional conduction model for scribing of a thick solid has been extended to predict the transient temperature distribution inside a finite thickness slab that is irradiated by a moving laser source, and the cutting rate and profile carved by evaporation of material. The laser may operate in CW or in pulsed mode (with arbitrary temporal intensity distribution) and may have an arbitrary spatial intensity profile. The governing equations are solved using a finite-difference method on a boundary-fitted co-ordinate system. Results for cutting rates and profiles are presented for materials that ablate or decompose upon laser irradiation (without significant formation of liquid), for different material thicknesses, traverse speeds, and pulsing conditions. For drilling (zero traverse speed), a numerically much more efficient two-dimensional axisymmetric version of the model has also been implemented, and similar results for drilling behavior are also presented.

Investigation of heat transfer in a polymeric phase change material for low level heat storage

A new material for low level heat storage has been elaborated. It is a stable mixture of water with a water soluble polymerised and cross-linked monomer such as polyacrylamid. Quantitative results regarding the thermophysical properties of the material are presented. These parameters are used in a theoretical approach describing the progression of a phase change front in a slab of finite thickness, and the computed results are found to be in good agreement with the experimental data for the considered duration of freezing and thawing in samples.

Variationally improved Fermi beam solutions

The time-independent, transmission problem for a purely scattering, homogeneous slab of finite thickness is considered. This problem corresponds to a planar beam of radiation impinging perpendicularly upon one surface of a source-free slab. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that radiation backscattering is negligibly small. Generally, this problem is approximated by the classic Fermi solution. By using the recently reported solution for an obliquely incident pencil beam, we show that the Fermi solution (or any other approximate solution) can be improved via a variational formalism.

Heating a slab of finite thickness with a pulsed laser in view of the theory of linear systems

The problem of heating a slab of finite thickness induced by surface absorption of a pulsed laser is solved using the two-dimensional Laplace integral transform technique. In the solution procedure the cases of constant and temperature-dependent absorption coefficient of the front surface considering different cooling conditions at the front and rear surfaces are taken into account. Mathematical expressions for the temperature distribution within the slab, and the temperature of its front and rear surfaces as a function of the time are obtained for all cases considered. The time required to initiate melting is found only for the case of temperature-dependent surface absorption and negligible cooling at both surfaces. The linear system theoretical treatment showed that the slab behaves like a linear system only for the case of temperature-independent absorption coefficient, where it is found to be invariant and its transfer function is defined. To illustrate the physical validity of the results obtained, computations are carried out on Al and Au slabs during and after irradiation with a measured time-dependent laser pulse profile.

The Fermi beam solution generalized to oblique incidence

We consider the time-independent, monoenergetic searchlight problem for a purely scattering, homogeneous slab of finite thickness. This problem corresponds to a pencil beam of radiation impinging upon one surface of a source-free slab at an arbitrary oblique angle of incidence. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that radiation backscattering is negligibly small. Under these assumptions, we obtain the full three-dimensional solution for the angular flux of radiation. This solution is a generalization of the classic Fermi solution, obtained in the special case of perpendicular beam incidence.

Pressure effects in the planar solidification of a finite slab: convective cooling and prescribed heat flux boundary conditions

The classical Stefan problem assumes a fixed melting temperature. However, when the solid phase is the one with lower density (e.g., water) the solidification of the system causes an overall volume increase that is often contrasted by the container walls. In that case the growing pressure determines a continuous lowering of the freezing point, and the temperature field as well as the interface motion are strongly affected. This paper is concerned with these aspects of the problem; the planar solidification of a slab of finite thickness, contrasted by an opposing elastic force, is numerically simulated. The effects of two different boundary conditions are analysed. When the solidification is driven by convective cooling, the continuous advancement of the melting front is replaced by an asymptotic behaviour, until thermal equilibrium is attained. When the boundary condition is specified in terms of a prescribed heat flow, the melting front velocity is slowed down by a growing adverse temperature gradient. The influence of various parameters on the process is presented and discussed.

Antenna design with the use of photonic band-gap materials as all-dielectric planar reflectors

A finite thickness slab of two-dimensional photonic band-gap (PBG) material is analyzed to determine the plane-wave reflection and transmission coefficients as functions of the angle of incidence. It is shown that within the band-gap, where there is total reflection, the reflection is equivalent to that from a plane surface located within the PBG material (the reflection plane concept). The two-dimensional PBG material is used as an all-dielectric reflector for an electric dipole antenna. Field patterns computed with the use of the reflection plane concept are compared with measurements made on an experimental model and are found to be in good agreement. A three-dimensional PBG material with a BCC lattice is also used as a reflector for an electric dipole antenna. Field patterns calculated for this structure using the finite-difference-time-domain (FDTD) method are also in good agreement with measurements. © 1996 John Wiley & Sons, Inc.

Nonlocal density functional calculations of the jellium metal surface

AbstractThe Becke exchange functional is used for calculation of properties of the jellium model using the slab geometry inside a box with the infinite potential barriers at the boundaries. We simplify semianalytical representation of matrix elements. We calculate the surface energies and work functions with self‐consistent electron densities. For all densities (here, we give results in erg/cm2 for rs = 2.07 bohr, in comparison with the LSD approximation (−602)) and the uncorrected Pw GGA‐II (−730), the Becke‐II exchange only (−1212), and the Becke‐II exchange with Perdew86 correlation (−830) [always close to Pw GGA‐I (−814)] give smaller surface energies. The most important factor determining values of surface energies from different GGAS seems to be a form of a correlation potential. We also calculate the effect of finite slab thickness and the vacuum region thickness on the surface energy at the LSD level and indicate its importance in various jellium model calculations. © 1995 John Wiley & Sons, Inc.

The effect of surfaces on the tunneling density of states of an anisotropically paired superconductor

We present calculations of the tunneling density of states in an anisotropically paired superconductor for two different sample geometries: a semi-infinite system with a single specular wall, and a slab of finite thickness and infinite lateral extent. In both cases we are interested in the effects of surface pair breaking on the tunneling spectrum. We take the stable bulk phase to be of $d_{x^2-y^2}$ symmetry. Our calculations are performed within two different band structure environments: an isotropic cylindrical Fermi surface with a bulk order parameter of the form $\Delta\sim k_x^2-k_y^2$, and a nontrivial tight-binding Fermi surface with the order parameter structure coming from an anti-ferromagnetic spin-fluctuation model. In each case we find additional structures in the energy spectrum coming from the surface layer. These structures are sensitive to the orientation of the surface with respect to the crystal lattice, and have their origins in the detailed form of the momentum and spatial dependence of the order parameter. By means of tunneling spectroscopy, one can obtain information on both the anisotropy of the energy gap, $|\Delta(\p)|$, as well as on the phase of the order parameter, $\Delta(\p) = |\Delta(\p)|e^{i\varphi(\p)}$.

Planar solidification of a finite slab: effects of the pressure dependence of the freezing point

Planar solidification in a slab of finite thickness is numerically simulated. The solid density is assumed to be lower than the liquid density and the phase change material expands while freezing (e.g. water). The effects of an opposing elastic force, due to the interaction with the container, are analysed. The increasing pressure determines a continuous lowering of the melting temperature; as a result the interface motion and the temperature field are strongly affected. The time square-root dependence of the melting front position fails down and is replaced by an asymptotic behaviour.