Tuneability amplification factor and loss of high-contrast composites

Abstract

The problem of tuneability of nonlinear ferroelectric-dielectric composite materials is addressed. Attention is concentrated on the analysis of the tuneability amplification factor, K, of a composite material, which is introduced as the ratio of the effective tuneability of a composite material to the tuneability of its ferroelectric (tuneable) component. Previously, ferroelectric-dielectric composite materials have been designed with an effective tuneability amplification factor slightly greater than 1 (i.e. 1.1-1.4) [A.K. Tagantsev et al., J. Electroceramics 11 (2003) p.5; A.G. Kolpakov et al., J. Electroceramics 18 (2007) p.129].It is demonstrated that the tuneability amplification factor can take values significantly greater than 1. Numerical prototypes (structural designs integrated with finite element method tools) of microstructures are presented with K in the range 3 to 30. The effective tuneability of nonlinear composite materials strongly depends on the microgeometry and microtopology of the material and, in general, cannot be described in terms of volume fraction of components of composite material. In the designs presented, the increased tuneability is due to concentration of the high electric field in narrow regions with carefully selected geometry. The problem of loss in ferroelectric-dielectric composite materials is discussed. In the general case, the loss tangent stays between that of the components of the composite. For high-contrast ferroelectric-dielectric composite materials, the effective loss tangent is practically equal to the loss tangent of the ferroelectric.

Optimal Random Packing of Spheres and Extremal Effective Conductivity

“…This relates minimization Problem (1) to the discrete Laplacian on a graph, with the eigenvalues and other objects of graph theory developed in [17][18][19][20]. Functional (1) was applied to the many-bodies capacity problem to explain Tamm's screening effect [21,22].…”