B.V. Paranjape

Non-radiative surface plasma-polariton modes of inhomogeneous metal circular cylinders

The theory is given of the non-radiative surface plasmon-polariton modes of metal cylinders, modelled by a spatially dispersive free electron gas within a Bloch hydrodynamic formulation. Dispersion equations for homogeneous and inhomogeneous cylinders are derived for nth cylindrical harmonic, and the dispersion properties are investigated as a function of n, cylindrical radius and surface structure. The position, and splitting with n, of the surface modes is found to be considerably different from those based on a model that neglects spatial dispersion. This is particularly true for very small cylinder radii.

The surface plasmon modes of spherical voids in irradiated metals

Abstract The surface plasmon modes of spherical voids in metals modeled by a free-electron gas are calculated within a hydrodynamic formulation. Spatial dispersion, retardation, and surface electron density variation are included. A sharp-surface model is considered first and it is shown that the modes are non-radiative. A novel matrix method is used to discuss the sensitivity of the results to the use of different surface density profiles. It is shown that the interplay between surface inhomogeneity and spatial dispersion always results in a mode in the near neighbourhood of the sharp-surface mode. There are, however, other structure-induced modes which are well-separated from the sharp-surface results. The l = 0 breathing mode is affected by retardation and surface structure but is unaffected by spatial dispersion.

Surface plasmon in a parallel magnetic field

Abstract Using a hydrodynamic model the dispersion relation for the surface plasmon is calculated in an external magnetic field parallel to the surface when the wave propagates perpendicular to the magnetic field. In the limit of zero wave vector, the results reduce to those of Chiu and Quinn who have used the dielectric constant in the local theory.

Interaction between rare gas atoms outside metal surfaces: Role of plasma excitations

Abstract After a short discussion of the effective van der Waals interaction between a pair of rare gas atoms at an arbitrary orientation and well outside a planar metal surface, the lateral interaction between two such atoms is studied in the presence of surface plasmon excitations. Some suggestions are made as to which atoms and which metal surfaces should be favourable for observing interaction effects depending on these collective excitations. Thermal desorption experiments as a function of coverage should then contain information relating to surface plasmons.

Mean free path effects in the dielectric function of a liquid metal

Abstract Mean free path effects are introduced into the frequency and wavenumber dependent dielectric function e(q, ω) of a simple liquid metal such as Na. It is pointed out that, at least in principle, e(q, 0) can be brought into contact with experiment through (a) electrical resistivity and (b) effective ion-ion interactions. The frequency dependence of e(q, ω) is then considered, using the Lindhard expression as a starting point. This is shown to link the real parts of the dielectric function e(q, ω) and the conductivity [sgrave](q, ω) via a function dependent on Fermi surface blurring. The frequency dependence of this function is determined in the long wavelength limit, and contact with the Drude-Zener theory is established. Finally, the long wavelength form of e(q, ω) is related to plasmon properties of liquid metals and to the ion-ion dynamical structure factor.

Unified treatment of motion of an extended defect and a crack via Legendre's equation

Abstract The motion of a straight screw dislocation in the lattice snapping model of Celli and Flytzanis (V. Celli, N. Flytzanis, Journal of Applied Physics 41 (1970) 4443) is first treated in the almost continuum limit and shown to lead to a differential equation for the displacement which is Legendres equation, but with pure imaginary argument. The intimate relation between this problem and the continuum limit of the brittle–elastic bond model of Slepyan is then demonstrated. Again, a related, though different, form of Legendres equation emerges in the continuum limit. Different boundary conditions from the dislocation propagation require another solution of Legendres equation, again for pure imaginary argument. Finally the displacements of the crack problem and the screw dislocation in these breaking-bond models are shown to be precisely related by an integral equation, which is formulated here.

Ionic and electronic transport in liquid metals: Relation between longitudinal and transverse effects

Abstract Utilizing relations due to Moreau and to Bridgman, plus the Wiedemann-Franz law, it is first demonstrated that a longitudinal effect, the Thomson thermoelectric coefficient, σ T is given by LP R , where L is the Lorenz number while P and R characterize transverse effects, represented by Ettingshausen and Hall coefficients, respectively. Corresponding effects are then defined for ionic transport, motivated by the observed Haeffrer effect for isotopes but written initially for an isotopically pure liquid metal. In this way, we have related a longitudinal ionic density gradient to a similar transverse gradient in the Hall configuration in a transverse magnetic field. The latter gradient is shown to be precisely determined by the ratio eE H k B T , where E H is the Hall electric field. Generalizing to a binary mixture of isotopes, the Haeffner effect follows directly by momentum transfer arguments.

THE DEFORMATION OF BUBBLES AND DROPS IN IMMISCIBLE FLUIDS

Abstract We consider the uniform motion of a drop of one fluid moving in another immiscible, unbounded, fluid. We examine the condition of normal stress balance across the interface. Consistent application of this condition to linear order in the velocity requires the introduction of a new parameter, Δ, which takes into account deformations of the drop from a spherical shape. Imposing a condition for the critical size of these deformations allows us to predict the maximum size of the drop for a given terminal velocity. For the case of raindrops this gives a maximum size of approximately 2 millimeters.

Reflection and transmission of phonons at a planar interface between two dissimilar solids

Abstract Two semi-infinite dissimilar crystals with, however, the same crystal structure and lattice parameter are in contact at a planar interface. Using a simple force constant model, restricted to near-neighbour interaction reflection and transmission coefficients for sound waves propagating along one solid are calculated. At low frequencies the reflection and transmission coefficients are determined solely by the force constants and the atomic masses in the two media. At high frequencies the transmission coefficient becomes small if the force constant at the interface between the two media is weak. Information of the local force constant in the interface region can be gained at least in principle, by measuring the reflection and transmission coefficients at high frequencies.

Nernst, ettingshausen and righi-leduc phenomena in relation to the quantum hall effect in two-dimensional electron assemblies

Abstract In three-dimensional metallic conductors, it is well established from the early work of Moreau and Bridgman that the Nernst and Ettingshausen effects have magnitudes closely linked with the Hall constant R . The purpose of the present note is to provide theoretical motivation for experimental study of the Nernst, Ettingshausen and Righi-Leduc phenomena in the two-dimensional electron assembly present in GaAs/AlGaAs heterojunction.