Nonlinear alternating current responses of graded materials

TL;DR

This paper investigates how gradation in dielectric properties of particles affects their nonlinear AC electrical responses, using a nonlinear differential effective dipole approximation and perturbation methods.

Contribution

It introduces a nonlinear differential effective dipole approximation and perturbation expansion to analyze the impact of gradation on AC responses in composite materials.

Findings

Fundamental and third-harmonic responses are sensitive to gradation profiles.

AC responses can be used for real-time monitoring of fabrication processes.

The methods agree well with first-principles calculations.

Abstract

When a composite of nonlinear particles suspended in a host medium is subjected to a sinusoidal electric field, the electrical response in the composite will generally consist of alternating current (AC) fields at frequencies of higher-order harmonics. The situation becomes more interesting when the suspended particles are graded, with a spatial variation in the dielectric properties. The local electric field inside the graded particles can be calculated by the differential effective dipole approximation, which agrees very well with a first-principles approach. In this work, a nonlinear differential effective dipole approximation and a perturbation expansion method have been employed to investigate the effect of gradation on the nonlinear AC responses of these composites. The results showed that the fundamental and third-harmonic AC responses are sensitive to the dielectric-constant and/or nonlinear-susceptibility gradation profiles within the particles. Thus, by measuring the AC responses of the graded composites, it is possible to perform a real-time monitoring of the fabrication process of the gradation profiles within the graded particles.