On the theory of the galvanomagnetic properties of composite materials: Lattice model
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DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
On the Theory of the Galvanomagnetic Properties of Composite Materials: Lattice Model B. Ya. Balagurov Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119334 Russia email: [email protected], [email protected] Received January 14, 2015
Abstract—The problem of the galvanomagnetic properties of composite materials is formulated for a lattice model. The effective galvanomagnetic characteristics of a weakly heterogeneous lattice are determined in the ˆ (r) from average value 〈 σ ˆ 〉. In the quadratic approximation in the deviation of local conductivity tensor σ ˆ e of a binary lattice case of a low concentration (c Ⰶ 1) of “defect” bonds, effective conductivity tensor σ model is calculated in the clinear approximation. Effective medium method equations are derived for the formulated lattice problem, and the results are compared with the results obtained in a continuous medium model. DOI: 10.1134/S1063776115060035
1. INTRODUCTION One of the main methods for the experimental investigation of the properties of metals and semicon ductors is to measure their galvanomagnetic charac teristics (Hall coefficient, magnetoresistance, etc.). Such macroscopic experiments make it possible to determine the carrier concentration and mobility and other microscopic characteristics of homogeneous conductors. The possibility of extraction of such infor mation from experimental data is provided by, e.g., the developed electron theory of metals [1]. However, the interpretation of similar experimental data for com posite materials encounters serious difficulties because of the absence of a general theory of galvanomagnetic phenomena for heterogeneous media. A theoretical study of the electrical conductivity of composite materials in magnetic field H encounters the same difficulties as in the case of H = 0, i.e., fun damental difficulties related to the disordering of such systems. Moreover, additional (as compared to a homogeneous medium at H = 0) parameters, namely, ohmic anisotropy and the antisymmetric Hall compo nent of a conductivity tensor, appear in the problem. Nevertheless, the problem of the galvanomagnetic properties of composite materials can be solved by analytical methods in some limiting cases [2–8]. ˆe For example, the effective conductivity tensor σ of a weakly heterogeneous medium at H ≠ 0 was calcu lated in [2–4]. This problem was solved in a linear concentration approximation for spherical inclusions [5] and for inclusions of an arbitrary shape [4]. The Hall coefficient in the case of a weak magnetic field was studied by analytical methods in [6, 7]. A consis tent theory of the galvanomagnetic properties of binary composite materials in a weak magnetic field is
presented in [8], where expressions for the Hall coef ficient and magnetoresistance were derived. However, this problem has not been resolved in the general case. Since it is difficult to study the galvanomagnetic properties of heterogeneous m
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