D. Stroud

Physical Properties of Macroscopically Inhomogeneous Media

Publisher Summary This chapter discusses several composites or granular or porous materials that display inhomogeneity on a macroscopic scale. In such materials, there are small, yet much larger than atomic, regions exhibiting macroscopic homogeneity. Different regions may display quite different properties. The chapter discusses the dc and ac electrical properties of composite media including the basic theory and results for dc electrical properties. It also presents a discussion of the effective-medium approximation, electrostatic resonances, exact bounds, and analytical properties and describes a number of static physical properties of composites. These properties include electrical conductivity and dielectric behavior near a percolation threshold, magnetotransport, thermoelectricity, superconductivity, and duality in two-dimensional composites. Finally, the chapter discusses the nonlinear properties and flicker noise in composites.

Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation

We calculate the surface plasmon dispersion relations for a periodic chain of spherical metallic nanoparticles in an isotropic host, including all multipole modes in a generalized tight-binding approach. For sufficiently small particles (kd ≪ 1, where k is the wave vector and d is the interparticle separation), the calculation is exact. The lowest bands differ only slightly from previous point-dipole calculations provided the particle radius a < d/3, but differ substantially at smaller separation. We also calculate the dispersion relations for many higher bands, and estimate the group velocity vg and the exponential decay length ξD for energy propagation for the lowest two bands due to singlegrain damping. For a/d = 0.33, the result for ξD is in qualitative agreement with experiments on gold nanoparticle chains, while for larger a/d, such as a/d = 0.45, vg and ξD are expected to be strongly k-dependent because of the multipole corrections. When a/d ∼ 1/2, we predict novel percolation effects in the spectrum, and find surprising symmetry in the plasmon band structure. Finally, we reformulate the band structure equations for a Drude metal in the time domain, and suggest how to include localized driving electric fields in the equations of motion.

Theory of the Thermodynamics of Simple Liquid Metals

Publisher Summary The chapter presents a discussion on the thermodynamic properties of conducting liquids. The chapter discusses calculating measurable quantities as the compressibility, specific heat, and melting curves of metals from knowledge of the fundamental interactions among the electrons and ions. To understand this problem, it is necessary to consider both the electronic structure and the “bonding” structure or ionic arrangement. These are closely interrelated. For example, any description of the ionic arrangement must take into account the presence of the conduction electrons. Conversely, the electronic structure must in turn be strongly affected by the physical arrangement of the ions. The interplay between these dual aspects of liquid metals is quite complex, which is discussed in this chapter. Liquid metals may be further divided into roughly nonoverlapping classes according to their electronic structure, the chapter defines these classes under normal condition. A central question regarding liquid metals is, of course, why they form simple liquids, or equivalently, why, structurally, they have two body-central forces. The answer, in the case of free-electron metals, lies in the predictions of perturbation theory as applied to an interacting electron gas. The perturbation arises from the metallic ions which carry with them, in an adiabatic way, the fundamental interaction between the electrons and ions—the pseudopotential. The response of the electrons to this perturbation is discussed in the chapter. Once the nature of the interatomic forces is known, the thermodynamics of the liquid metal can be determined by the methods of classical statistical mechanics. Some of the methods for so doing are discussed in this chapter.

Decoupling approximation for the nonlinear-optical response of composite media

A nonlinear decoupling approximation (NDA) is described for calculating the nonlinear-optical response of composite materials. The NDA is used in conjunction with the effective-medium approximation for the linear response to calculate the effective third-order susceptibility, χe, of model metal–insulator and semiconductor–insulator composites as a function of frequency and composition. It is found that the ratio χe can be strongly enhanced relative to χ1, the corresponding third-order nonlinear susceptibility of a pure constituent in bulk. The enhancement is found to be sensitive to composite topology as well as to composition. The nonlinear susceptibility of randomly oriented nonlinear ellipsoidal particles in a linear host is calculated in the dilute limit. The susceptibilities of the model composites are also shown to be strongly influenced by particle shape.

Numerical study of transport properties in continuum percolation

The authors present numerical simulations of AC conductance for a random resistor-capacitor network. The conductance obeys a probability density function p(g) varies as g- alpha (0( alpha (1). They use a highly efficient propagation algorithm to calculate the effective conductance of a long strip of a lattice. At low frequencies, they find that for the concentration p of conducting bonds less than the percolation threshold pc, the imaginary part of conductance is proportional to frequency Im(geff) approximately= omega and the real part of conductance shows an anomalous frequency dependence Re(geff) approximately= omega 2- alpha . The results of simulations in such a continuum system are in agreement with the predictions of the effective medium and the Maxwell-Garnett approximation. They also calculate the non-universal DC conductivity exponents in continuum percolation; the results are consistent with earlier theoretical predictions and numerical calculations.

Theory of Faraday rotation in granular magnetic materials

We present a formalism to treat Faraday rotation (FR) in composite media. The method is not limited to low concentrations of magnetically active inhomogeneities and is thus useful for understanding the magneto‐optical properties of such inhomogeneous media over the whole range of concentrations. It involves the calculation of an effective magnetic‐field‐dependent dielectric tensor ee using a tensor effective‐medium approximation. To illustrate the technique, we present the results of several model calculations involving both paramagnetic and ferromagnetic metals. We find that such materials have strongly enhanced FR over a wide range of frequencies. The effects of particle shapes on FR are discussed.

Thermal conductivity of graded composites: Numerical simulations and an effective medium approximation

We describe two methods for modeling the thermal conductivity and temperature profile in a graded composite film. The film consists of a random binary composite, whose concentration varies in the direction perpendicular to the film surface, and a fixed temperature difference is applied across the film. In the first method, the temperature profile is modeled directly, using a finite element technique in which the film is represented as a discrete network of thermal conductances, randomly distributed according to the assumed composition profile. The temperature at each node, and the effective thermal conductance, is then obtained by a transfer matrix technique. In the second approach, the film is treated by an effective-medium approximation, suitably generalized to account for the composition gradient. The methods are in rough agreement with each other, and suggest that thermophysical properties of the film can be treated reasonably well by approaches generalized from those which succeed in conventional composites.

Surface-enhanced plasmon splitting in a liquid-crystal-coated gold nanoparticle

We show that, when a gold nanoparticle is coated by a thin layer of nematic liquid crystal, the nanoparticle surface has a strong effect on the director orientation, but, surprisingly, this deformation can enhance the surface plasmon splitting. We consider three plausible liquid crystal director configurations in zero electric field: boojum pair (north-south pole configuration), baseball (tetrahedral), and homogeneous. From the discrete dipole approximation, we find that the surface plasmon splitting is largest for the boojum pair, and this result is in good agreement with experiment.

Theory of Faraday rotation by dilute suspensions of small particles

We consider Faraday rotation by a dilute suspension of small particles embedded in a host. Using the Maxwell‐Garnett approximation, we obtain an expression for the complex effective dielectric tensor of the composite in the low concentration limit. The Faraday coefficient becomes anomalously large near the surface plasmon frequency of the small particles. Numerical examples are given for the frequency‐dependent off‐diagonal part of the dielectric tensor and for the angle of rotation.

Phase stability in binary alloys

The hypothesis that Hume-Rotherys rules for phase stability in binary alloys are a consequence of the divergent slope of the wave-number-dependent dielectric function at 2kF is investigated. The relative energies of the fcc, bcc, and hcp structures of the alloy systems CuAl, LiMg, and CuZn are calculated with a realistic local pseudopotential model. Striking evidence of the screening anomaly is obtained in all cases. The calculations suggest alloy phase boundaries in the three systems studied which are for the most part in excellent agreement with experiment. The only exceptions are pure Cu and pure Zn, for which an incorrect structure is predicted, the former by a remarkably small 3 × 10-5 ryd per electron. It is suggested that both discrepancies might be rectified if the forces between d electrons on neighbouring sites were properly accounted for. In particular, it is argued that the attractive forces arising from the overlap of neighbouring d electrons and from their Van der Waals interactions provide a substantial impetus for a distorted structure in Zn. A thermodynamic instability arising from the divergent slope of the dielectric function is considered. Rough calculations are presented which indicate that when higher order terms in the electron-ion interaction are properly considered this instability will disappear, without, however, the phase boundaries being significantly altered. The principal conclusion, which is consistent with previous suggestions, is therefore that the Hume-Rothery rule arise not so much from the screening divergence itself as from the rapid variation of the dielectric function in the immediate vicinity of 2kF.