Classical Dielectric Theory Research Articles

Surface reactions and excitations

Observations are presented of the growth of oxide nuclei on Al and Cu which illustrate the power of clean surface and RHEED techniques when combined with electron microscopy. Inelastic scattering and image potential effects in the RHEED and glancing angle microscopy situation are estimated using classical dielectric excitation theory. Attention is drawn to resonance effects which may occur in the surface excitations on small particles. Possible Bloch wave transitions corresponding to novel inelastic scattering processes inside the crystal and which may be significant in the glancing angle case are described.

Theory of transient response for arbitrarily strong driving fields

A theory of the dynamical Kerr effect is developed for arbitrarily strong driving fields using a modification of the Mori equation of motion due to Grigolini et al. Using the multidimensional expansion of Grigolini and Ferrario the non-Markovian Mori equation may be written in Markov form. It is possible then to derive a macro–micro correlation theorem for the system by applying the method of Kivelson et al. In this way it is possible to bypass the linear response approximation of classical dielectric theory.

The study of interfacial tension at different solid-liquid interfaces as a function of electric field

A study of the solid/liquid interface of different systems was carried out by measuring the potential dependence of meniscus rise at partially immersed solid electrodes. The results with metal/ and semiconductor/electrolyte interfaces are discussed in the light of the already-established electrocapillary phenomenon on mercury and previously-published differential capacitance data on solid electrodes. With both systems the experimental results are consistent with a physical interpretation based on a straightforward relationship between the meniscus height and interfacial tension. In the case of metal/insulating liquid systems there exist strong discrepancies between the experimental results and theoretical predictions of classical dielectric theory. Such discrepancies as well as the possible contribution of the interfacial tension are discussed.

Phonons in Metal Films and Fast-Electron Energy Loss in the Phonon Spectral Range

The phonons in a metal film and their excitation by fast-charged particles normally transmitted through the film are studied within the framework of a classical dielectric theory. The bulk phonons are described by means of the jellium model which treats the ions as a continuum plasma and the conduction electrons in the Thomas-Fermi screening approximation. The dispersion relation of the surface modes is obtained from the matching boundary conditions which must be satisfied by the solutions of Maxwell's equations. We find two kinds of modes connected with surface effects, which are distinguished by the nature of the fields which they induce inside the film. Firstly, there is a true-surface-mode branch which exists only at short wave-lengths. Secondly, we find a family of modes which carry oscillatory fields in the direction perpendicular to the film and which are called surface-bulk modes because of their mixed character. The energy loss experienced by fast electrons through the excitation of phonons is divided as usual into a bulk energy loss and various surface energy losses, all of which are studied analytically in detail. The effective bulk-loss intensity in a film remains significantly larger than the surface losses, even for very thin films. This indicates that the bulk phonons interact almost as strongly with electrons in thin films as in thick films, which contrasts with the case of plasmons where the effective bulk energy loss vanishes for sufficiently thin films. The predicted bulk energy loss due to phonons should be observable in sufficiently thick metal films with available experimental techniques. On the other hand, since the surface losses would be much enhanced for specularly reflected electrons at grazing-angle incidence they might become observable under such conditions.

Reactivities of ions and ion-pairs in the base-catalyzed reaction of phenyl glycidyl ether and benzoic acid in various solvents

The conductance of pyridinium benzoate has been measured in various solvents such as nitrobenzene, benzonitrile, o-dichlorobenzene, monochlorobenzene, and toluene, and its dissociation constant, K, was determined, using the Kraus and Bray's equation with the Λ0 value estimated from Walden and Ulich's rule and Stokes's law. The logarithm of K was found to be linear with the reciprocal of the dielectric constant, ε, or with the Kirkwood–Laidler–Eyring function, (ε − 1)/(2ε + 1). Kinetic studies for pyridine-catalyzed reaction between phenyl glycidyl ether and benzoic acid were also made in these solvents. Both the free ions and ion-pairs including the molecular addition complex participate in the reaction. The apparent rate constants, k″, of the reaction were shown to be linear with 1(K/c)1/2, c being the concentration of pyridinium benzoate. The intercepts of such lines give the rate constant for formation of ion-pairs, ki and the slopes yield the rate constant for formation of free ion, kf. The free ion rate constant increases fairly rapidly as the dielectric constant decreases, while the ion-pair reaction constant drifts downward comparatively slowly. A plot of the logarithm of kf or kf(K/c)1/2 against 1/ε or (ε − 1)/(2ε + 1) is found to be linear, but the plots of log ki against the same function are curved. The tangent of the curve is steeper for polar solvents than for non-polar solvents. The results have been compared with those predicted from classical dielectric theory.

The relation between refractive index and density of minerals related to the Earth's mantle

It is known that the density of many minerals is related to the (average) index of refraction by a linear law called the Gladstone-Dale law. It is shown that this law is generally applicable only to minerals whose anion is oxygen and whose mean molecular weight is close to 21. Another relationship, called Drude's law, which is deduced from classical dielectric theory, fits the data just as well as the empirical linear law. The correlation between density and index includes the minerals arising from various combinations of SiO2, MgO, Al2O3, Na2O, and K2O. An implication is that density controls certain physical properties of oxides, independently of composition or crystal class. This is analogous to the rule found by Birch which relates sound velocity to density and holds for the same groups of minerals.

Theoretical and Experimental Effects of Spatial Dispersion on the Optical Properties of Crystals

The classical dielectric theory of optical properties is a local theory, and results in a dielectric constant dependent only on frequency. This dielectric behavior can be written as a sum over resonances, each resonance occurring at a particular frequency. The spatial dispersion (i.e., nonlocal dielectric behavior) effect considered here is the effect of the wave-vector dependence of the resonant frequencies on optical properties. The additional boundary condition needed for the application of such a theory is discussed for the case in which the resonance is due to an exciton band and the wave-vector dependence to the finite exciton mass. Experimental data presented on the reflection peaks due to excitons in CdS and ZnTe exhibit gross departures from the reflectivities expected from classical theory. Particularly striking are sharp subsidiary reflectivity spikes. The departures from classical results are all well represented by calculations based on the theory of spatial resonance dispersion and a simple approximation to the drived boundary condition.