Permittivity and permeability have been studied at microwave frequencies (1 to 20 GHz) on artificial dielectrics of metal particles randomly loaded in a polymer up to 40 vol%. Ni-Cr alloy powder (∼1 to 37 μm) in various size fractions was prepared by gas-water atomization, providing an oxide coating for interparticle isolation. The alloy is ferromagnetic below 165 K, enabling a magnetic measure of volume loading. The complex permeability results are in very good agreement with calculations of induced magnetic dipole effects as functions of frequency and particle diameter. Permittivity results are independent of particle size and essentially constant with frequency. When compared with a highly successful effective spherical cluster model and a well-founded empirical curve, the present alloy powder exhibits a residual upward deviation attributed to nonspherical morphology. In sum, the microwave electromagnetic behavior of such non-percolating composites is rather well understood.

Microwave spectroscopy revealed a non-metallic effective dielectric function of non- supported nanocrystal networks. This new result is in agreement with the size-induced metal-insulator transition (SIMIT) observed in isolated sub-μm conductors. Separating the particle contribution ε = ε1 + iε2 from the measured effective dielectric response leads to the conclusion that percolating networks of SIMIT particles are characterized by an enormous positive value of El and a conductivity σ ∼ ε2 much smaller than expected for metallic networks. Another non-metallic feature of the networks is the weak thermal influence on ε1 and ε2. All properties change sensitively with the filling factor f of the network. Their unusual dielectric properties make low- density nanocrystal networks candidates for applications e.g. as high permittivity capacitor materials or temperature-independent resistors.

In the early 1970's, Abeles et al developed a widely accepted model for electrical conduction in granular metal films based upon an assumed correlation between metal particle size and inter-particle tunneling gap width. The paper critically examines this assumption and other aspects of the theory. No observation of any such correlation has been reported, nor should it be expected, particularly in discontinuous films. The latter point requires separate considerations of the very different structures of discontinuous metal films, granular metals and cermets, using the “granular” term here in a more limited sense than usual.

Other aspects of the theory considered include its implied percolation topology and the field effect. Experimental data are also re-evaluated in terms of other common models. The paper concludes with a brief review of recent work in discontinuous metal films with suggestions for future theoretical and experimental work.

Electrical conduction in granular metals is simulated by mapping the hopping conductance between pairs of metal grains onto a simple cubic lattice with bonds between neighbors. By considering a log-normal distribution of grain sizes and the effect of disorder potential, the numerically calculated network conductance exhibit clear deviation from simple activation. Plotting -log a vs. T-½, where σ denotes conductivity and T the temperature, gives good straight line behavior with slopes comparable to those measured experimentally. Our results are noted to differ from those of Adkins et al.

Dimensional cross-over behavior of Anderson localization is presented. By delineating the physical basis of localization, it is shown that the localization phenomenon is sensitive to the spatial dimension of the randomness. Analytic and numerical results demonstrate that in an anisotropically random medium there is a critical amount of anisotropy which separates the system behavior into a ID-like regime and a 3D-like regime. Dimensional crossover is proposed as a viable experimental approach to observe the mobility edge.

A General Effective Media (GEM) equation is used to quantitatively describe the resistivity of the W - Al203 and Ni - Si02 cermet systems as a function of the relative volume fractions. The two percolation morphology parameters (øc and t) characterise the microstructure. A constant resistivity pl is assumed for the metal (W or Ni) while, in some cases, it is necessary that the resistivity of the insulator be modeled as the tunneling of electrons, through an oxide barrier, from a thermally excited charged grain to a neutral grain.

An explicit expression for the bulk effective thermoelectric coefficient αe of a two component composite is derived. This coefficient is found to depend only on the bulk effective electric conductivity σe and thermal conductivity γe, as well as on the moduli of the pure components. Using this expression and making standard scaling assumptions about the forms of σe and γe, the scaling behavior of αe, and of the effective figure of merit Ze are investigated. This behavior depends strongly on the thermal and electric conductivities ratios in the pure components. Upper and lower bounds for αe are calculated from its analytical properties.

Copper films of coverage coefficients ranging between 0.2 and 1 were evaporated onto glass substrates under vacuum conditions (p ≃ 10−8 Torr). For these films, the temperature dependences of resistance were measured in vacuo in situ. Making use of the obtained data TCR values, as a function of coverage coefficient and the activation energy for the films with different coverage coefficients were established. The resistance of films was found to change, and TCR values approaching zero for coverage coefficients between 0.63 and 0.75. This interval (∆qc) can be regarded as the percolation interval for discontinuous Cu films.

Different ways of pulsed current use for compaction of conducting materials have been studied during recent years, mainly in connection with technological problems of powder metallurgy. As a rule, the current is driven through a blank placed in a mould under external pressure [1-6]. Pulsed current action on a blank may lead to either partial or complete melting of granules [1,2], to the heating of granules and their plasticity increase [3], to the destruction of oxide films and granules surface activation [4,5] and to the break-down and sintering of chains forming channels in the direction of current [6].

We describe experiments in which the energetics of electrical conduction in discontinuous metal films are probed by inducing carriers electrostatically into the films. Both conductivity and thermopower show field effects that are generally of the expected form but they are very much smaller than the classic model for conduction in these systems would predict. Furthermore, in some cases at least, they can be shown to result from dielectric relaxation processes rather than from direct modification of basic transport energetics.

We discuss possible explanations, including that large potential disorder is present and that transport is controlled by energy structure that moves with the chemical potential, as would be the case i correlation energies determined carrier mobility. Experiments that measure the charging energies of the metal particles directly suggest that correlation is important, and we argue that progress in understanding conduction in granular metals depends on development of a model in which correlation energies play a critical role in controlling transport.

The nature of the percolation process in granular metals is examined for the first time by a computer simulation of a system of metallic grains embedded in an insulating matrix. Assuming that the intergrain conduction is due to quantum mechanical tunneling it is found that a percolation-like critical behavior of the conductivity is obtained, but that a percolation universal behavior will be found only in a very special case. In contrast, the behavior of the electrical noise does not deviate substantially from the universal one. Comparison of these results with recent experimental observations suggests that in the metallic range, both transport properties are controlled by the continuous metallic network rather than by intergrain tunnelin.. We propose that the metallic network resembles the previously studied system of ‘inverted random voids’.

A new way of obtaining binary composite materials having some properties of the critical percolation system is presented..These materials can be obtained by high-density current action on an initially well conducting mixture.This action destroys part of contacts between adjacent conducting granules bringing the system to the quasi-critical state.It is shown that quasi-critical s stems may have high values of dielectric constant ε′ ∼ 102-106 101 in the frequency range 0<f<1010Hz.Formation and dielectric properties of the systems are studied both by computer simulation and experi mentally.

While not telling the whole story, the representation of a composite medium by a homogeneous effective medium is often an excellent approximation for describing its macroscopic physical properties. Modern methods for calculating the effective medium properties are reviewed with special emphasis on understanding both successes and limitations. Outstanding problems that can and should be tackled are identified. The successes include calculations of the electrical conductivity, dielectric coefficient, and elastic stiffness moduli of composites with a periodic microstructure, and the simulation of those properties for disordered composites near a percolation threshold by means of discrete models such as a random-resistor-network. For composites where the microstructure is either unknown or very complicated, a whole class of exact bounds have been found for these properties based on various types of limited information. Recently, advances have been made in calculating the weak field magneto-transport and the thermoelectric behavior of two-component composites, and also some types of nonlinear properties. An important challenge remains the calculation of magneto-transport at high magnetic fields. Another is the theoretical treatment of multicomponent composites. A third is to find relations between different effective properties of a composite that can enable us to learn about property A by measuring a different property B. This is especially important when the measurement of A would destroy the sample, as when A is the yield stress, whereas the measurement of B is nondestructive, as when B is a small, nonlinear correction to the usual elastic stiffness moduli.

For two-component ceramic metal composites we address the inverse problem of estimating the volume fraction occupied by each component from measurements of the transmission and absorption coefficients at various frequencies of the applied radiation. We devise the algorithms, each based on representation formulas and bounds for the complex dielectric constant that were developed by Bergman and Milton. One inversion algorithm works remarkably well when the measurements are exact but fails completely when small errors are present. The second random throw algorithm works well when the measurement errors are large but is computationally intensive and is limited to small data sets. The third method based on single and two-point inversion, while not so accurate, is simple and efficient. The last two algorithms are implemented with experimental data and good agreement is obtained with the experimentally measured true volume fraction.

We consider the behavior of the dielectric constant of percolation composite systems. An example of such systems is a composite material consisting of a disordered mixture of metallic and insulating particles. A reduction in concentration P of the metallic (conducting) component reduces the static conductivity of the composite, so that it vanishes at some critical concentration PC known as the percolation threshold.

A formalism of extended irreversible thermodynamics (EIT) is used to study the physical aspects of heat, momentum and mass transport through porous media.

The thermodynamic space is enlarged with respect to that of classical linear irreversible thermodynamics (LIT) to include the mass, heat and momentum fluxes as independent variables. The time evolution equations for such variables are derived self-consistently and reduce to the usual constitutive equations of LIT when the appropriate limits are taken. Equations that involve effects characterized by terms of second order in the gradients of conserved variables (such as the Darcy-Brinkman law) may also be derived within the same formalism. Finally, EIT provides the natural framework beyond LIT to introduce non-isothermal effects in the study of transport phenomena in porous media.

There is a growing interest in composites in which conductive component has the elongated shape (sticks) because these systems can be used to describe various physical objects [1]. The main tool to investigate the systems is MC simulation. For example in papers [2-4] the percolation threshold in such systems has been explored and it was obtained that pcα r/L, where r is the radius of stick and L is it's length. In this work, we are suggest the calculation of dielectric constant and conductivity method based on effective medium approximation.

The complex permittivities of solid and pulverized samples of two plastics, Rexolite 1422 and Kynar, were measured at frequencies of 2.45, 11.5, and 22.0 GHz at 25°C by the short-circuited waveguide technique. Several dielectric mixture equations and extrapolation of functions of the real and imaginary parts of the permittivity that are linear with bulk density were then used to estimate the permittivities at solid-material densities from measurements on the pulverized samples. For these materials, the best estimates of the permittivities were provided by extrapolations that are consistent with the Complex Refractive Index and Landau and Lifshitz, Looyenga mixture equations. The Bottcher mixture equation often gave values very close to the Landau and Lifshitz, Looyenga equation, and the Bruggeman-Hanai, Rayleigh, and Lichtenecker mixture equations gave increasingly larger permittivity estimates in that order.

As Bednorz and Muller noted in their original publication reporting on the discovery of high temperature superconductivity, their oxides present many of the features of granular superconductors. This behavior was first primarily ascribed to poor connectivity of the grains in the bulk ceramic samples. but later studies have pointed out to more fundamental reasons for these similarities. We will discuss them after first reviewing the well established properties of low Tc granular superconductors.

A substantial part of my scientific career has been devoted to using the methods of electron paramagnetic (EPR) and electron spin resonance (ESR) in solids. The former describe investigations of microwave transitions between Zeeman levels of paramagnetic ions, whereas the latter indicate transitions between nearly free, but stationary spins in radicals and semiconductors as well as itinerant carriers in semimetals and metals. As early as 1962 an ESR study in intercalated graphites was undertaken in the latter. ESR was observed in C8K, C24K and C28Rb, but not in C8Rb, C8Cs and C24Cs [1]. From the observed linewidths, which are larger for heavier alkali intercalates with larger spin-orbit coupling, it was concluded that the carrier wave function was composed not only of carbon π but also of alkali-metal s orbitals, as theories later corroborated.