Extrinsic contributions in a nonuniform ferroic sample: Dielectric, piezoelectric and elastic

TL;DR

This paper develops a theoretical model to quantify extrinsic contributions to permittivity, piezoelectricity, and elasticity in nonuniform ferroic samples, considering domain wall motions and surface layer effects.

Contribution

It introduces a model linking domain wall motions and surface layers to extrinsic properties, enabling calculation of their magnitudes in ferroic materials.

Findings

Extrinsic contributions are proportional across permittivity, piezoelectricity, and elasticity.

The model explains how surface layers influence domain wall restoring forces.

Applicability to single crystals and ceramics is discussed.

Abstract

The contribution Delta_epsilon of extremely small motions of domain walls to small-signal permittivity of a multidomain ferroelectric sample has been a research issue for many years. In ferroelastic ferroelectrics such motions contribute also to their piezoelectric (by Delta_d) and elastic (by Delta_s) properties. Data about their simultaneous existence are scarce but those available point to mutual proportionality of Delta_epsilon, Delta_d and Delta_s, as expected. To understand the magnitude of extrinsic contributions, the origin of the restoring force acting on domain walls must be understood. In the present contribution the theory has been developed based on the model of a plate-like sample in which the ferroelectric- ferroelastic bulk is provided with a nonferroic surface layer. Motion of domain walls in the bulk results in a change of electric and elastic energy both in the bulk and in the layer, which provides the source of restoring force. This makes it possible to determine all mentioned extrinsic contributions. We discuss the applicability of the model to available data for single crystals and also for ceramic grains.