摘要:

The history of this field is reviewed, with emphasis on the relationship to the development of molecular field concepts in dielectric theory, in the last century, and with emphasis on the relationship to the study of disordered structures, in recent decades. A few of the many methods for calculating effective conductivities will be presented and discussed. One of these is based on the direct macroscopic application of the Clausius‐Mossotti relationship. In that connection we emphasize the shortcomings of the commonly accepted Lorentz derivation for the internal field and restate a less well known existing alternative derivation. The symmetrical and unsymmetrical effective medium theories of Bruggeman are presented. Connection is made to transport in randomly chosen resistor networks, to percolation threshold problems, and to transport in magnetic fields in the presence of inhomogeneities. Two more specialized topics are also discussed. One of these is the variability in field effect transistor thresholds arising from the limited size of the samples in which threshold is determined by the onset of percolation. The other specialized topic: The occurrence of strong spatial inhomogeneities in fields and currents in metals, in the presence of lattice defects, even though the mean free path is large compared to the extent of the defect.

ISSN:0094-243X    

DOI:10.1063/1.31150

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The complex effective dielectric constant of a composite medium &egr;eis a function of the complex dielectric constants of the homogeneous components &egr;Pdi which depends also on the microscopic geometry. A characteristic geometric function is introduced to describe this dependence for the case of &egr;eand other, similar material constants, and its general analytical properties are derived and discussed. A useful representation is found for this function and we show how it may be used to derive rigorous bounds on &egr;ein various situations. The characteristic function is also used to discuss the behavior of &egr;ein a disordered conductor‐dielectric mixture near the percolation threshold of the conductor. It is found that Re &egr;ediverges as the threshold is approached from either side. At the threshold itself, both Re&egr;eand Im&egr;eare shown to acquire a peculiar frequency dependence.

ISSN:0094-243X    

DOI:10.1063/1.31177

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

We survey inhomogeneous materials, both microscopic and macroscopic. We elucidate the conditions under which the transport properties of a microscopically inhomogeneous material become local so that the problem of determining macroscopic properties becomes the same as for macroscopically inhomogeneous materials. We review percolation briefly, survey the basic theoretical tools for dealing with inhomogeneous materials, and describe a few typical theoretical results. Finally, we review the results of our studies of metal‐non‐metal transitions in microscopically inhomogeneous materials.

ISSN:0094-243X    

DOI:10.1063/1.31178

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The formal analogy existing between problems studied in the microscopic theory of disordered alloys and problems concerned with the effective (macroscopic) behavior of heterogeneous materials is discussed. Attention is focused on 1) analogous approximations (effective medium approximations) developed for the microscopic problems by scattering theory concepts and techniques, but for the macroscopic problems principally by intuitive means, 2) the link, provided by scattering theory, of the intuitively developed approximations to a well‐defined perturbative analysis, 3) the possible presence of conditionally convergent integrals in effective medium approximations.

ISSN:0094-243X    

DOI:10.1063/1.31179

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Computer‐generated pictures are presented of the connected component (’’infinite cluster’’) found at concentrations just above the threshold for 2D site percolation in large (400×400 site) lattices. For each case, we also show the ’’backbone’’ of the cluster, the smaller set of sites through which a current may flow. The simulations are contrasted with the model of conduction just above threshold due to Skal and Shklovskii and to de Gennes. That model is found to be inconsistent with the observed critical behavior of the conductivity in 2D and 3D models, but may apply to percolation in 4D and above. We show that a proper treatment of inhomogeneity on scales smaller than the coherence length is necessary to account for the observed conductivity and backbone volume just above threshold, and introduce a self‐similar model which accounts reasonably well for these properties.

ISSN:0094-243X    

DOI:10.1063/1.31180

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Near the conduction threshold, the electrical conductivity of a random network exhibits power law behavior. An exponent theory modelled on the scaling theory of critical phenomena will be described, which relates the power laws which describe the various ways to approach the threshold. The particular case of finite sample size will be given special attention. The resistor lattice exponents are also relevant to more general inhomogeneous conductors. The dimensionality dependence of the conduction exponents will be reviewed.

ISSN:0094-243X    

DOI:10.1063/1.31128

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

A general statistical mechanics is developed for the effects of randomly distributed inhomogeneities on the electronic properties of conducting and non‐conducting media. The theory, valid for all concentrations, sizes, and shapes of the inhomogeneities, is based on an expansion of the system energy in a powers of a complex vector order parameter &Dgr;?. The theory yields the conductivity and complex dielectric function for all frequencies, and in a trivial limit reduces to the results of the Effective Medium Approximation. The onset of metal‐nonmetal transitions is accurately predicted. As a simple example, renormalization group predictions for critical exponents are shown to be a special case of the theory.

ISSN:0094-243X    

DOI:10.1063/1.31129

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The coherence length &xgr; and penetration depth &lgr; set the characteristic length scales in superconductors, typically 100−5,000 A˚. A lattice of flux lines, each carrying a single quantum, can penetrate type II superconductors, i.e., those for which &kgr;≡&lgr;/&xgr;≳1/&sqrt;2. Inhomogeneities on the scale of the flux lattice spacing are required to pin the lattice to prevent dissipative flux motion. Recent work using voids as pinning centers has demonstrated this principle, but practical materials rely on cold‐work, inclusions of second phases, etc. to provide the inhomogeneity. For stability against thermal fluctuations, the superconductor should have the form of many filaments of diameter &angupr;10−100 &mgr;m imbedded in a highly conductive normal metal matrix. Such wire is made by drawing down billets of copper containing rods of the superconductor. An alternative approach is metallurgical one of Tsuei, which leads to thousands of superconducting filamentary segments in a copper matrix. The superconducting proximity effect causes the whole material to superconduct at low current densities. At high current densities, the range of the proximity effect is reduced so that the effective superconducting volume fraction falls below the percolation threshold, and a finite resistance arises from the copper matrix. But, because of the extremely elongated filaments, this resistance is orders of magnitude lower than that of the normal wire, and low enough to permit the possibility of technical applications.

ISSN:0094-243X    

DOI:10.1063/1.31130

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Based on the assumption of compositon homogeneity, a physical picture of hopping conduction in granular metals is develped which gives temperature and electric field dependences of the conductivity in excellent agreement with experiment. The same hopping conduction picture, when coupled with the assumption about spin‐dependent tunneling, is found to explain the striking temperature variation of magnetoresistance in granular Ni‐SiO2. Two material characterization parameters, C and ≳o, are identified which respectively define the temperature and the electric field scales of granular metal systems. The relationship between C and ≳o, and the composition dependence of C are discussed.

ISSN:0094-243X    

DOI:10.1063/1.31131

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Pure metals at a low temperature have an exceedingly anisotropic conductivity tensor in high magnetic fields, and one which is commonly strongly dependent on the orientation of the field relative to the crystal axes. A polycrystalline sample is therefore a mixture of very different species, and a general account of what is involved in calculating the bulk properties of polycrystalline copper serves to illustrate the characteristic features that recur in studies of magnetoresistance. It has probably been taken for granted too readily in the past that carefully prepared single‐crystal samples are homogeneous, and such puzzling observations as the material defects than from any intrinsic property. In such a case as this, defect size and free path may be comparable, generating a peculiarly difficult set of problems. The aim of the talk will be to set the scene for more specialized contributions rather than go into the details of any one aspect.

ISSN:0094-243X    

DOI:10.1063/1.31132

出版商:AIP    

年代:1978

数据来源: AIP