Multiscale Phenomena in Bruggeman Composites
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Multiscale Phenomena in Bruggeman Composites Ralph Skomski, Jiangyu Li,* Jian Zhou, and David J. Sellmyer Department of Physics and Astronomy and Center for Materials Research and Analysis, *Department of Engineering Mechanics and Center for Materials Research and Analysis University of Nebraska, Lincoln, NE 68588
ABSTRACT Mechanical, magnetic, and transport properties of arbitrary inhomogeneous composites are investigated by a Bruggeman-type mean-field approach. The theory yields materials parameters as functions of the volume fractions, geometries, and materials constants of the phases. Each system is described by a single response parameter g, which is equal to the percolation threshold of the composite. For macroscopic systems, the approach yields very simple expressions, but nanoscale and multiferroic effects yield relatively complicated corrections to g. In the respective cases, the parameter g depends on the length scale of the composite and has the character of a combination of magnetic, electric, and mechanical degrees of freedom.
INTRODUCTION Composites combine the advantages of different single-phase materials and range from naturally occurring biological structures and traditional materials to artificial materials used in transport, space, microelectronic, and other high-tech applications [1-11]. For example, the composite structure of naturally occurring skeletal materials, such as bones and wood, ensures stiffness without brittleness, and the same principle is exploited in artificial mechanical materials, from concrete to reinforced polymers. The question arises how the properties of a composite depend on the properties of the constituents and on how the length scale and geometry of the structure. Bruggeman's early work on the effective-medium description of dielectric and other composites [1] has lead to the concept of an effective medium. The idea is to start from exact solutions for small volume fractions of a second phase in a main or matrix phase. Arbitrary volume fractions are treated by selfconsistently embedding the phases in an effective medium [1]. Figure 1 shows some geometries. The approach describes a variety of static and dynamic electromagnetic, mechanical, and diffuse phenomena. Physical phenomena include but are not restricted to electrical conduction (conducting composites, insulating inclusions in metallic matrix, metalsuperconductor composites), thermal conduction (heat insulation using composite construction materials), diffusion (hydrogen and nitrogen transport in intermetallic composites), magnetism (effective susceptibility), electrodynamics (static and dynamic dielectric response of inhomogeneous media, materials with negative index of refraction), rheology (viscosity of colloidal suspensions, such as blood, food, gels), mechanical composites (elasticity of reinforced construction materials, filled polymers, such as car tires).
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Figure 1. Considered geometries: (a-f) three-dimensional, (g-j) two-dimensional, and (k) onedimensional. The direction of the appl
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