Electrochemomechanics with flexoelectricity and modelling of electrochemical strain microscopy in mixed ionic-electronic conductors

Abstract

Recently, a new scanning probe microscopy approach, referred to as electrochemical strain microscopy (ESM), for probing local ionic flows and electrochemical reactions in solids based on the bias-strain coupling was proposed by Morozovska et al. Then, a series of theoretical papers for analyzing the image formation and spectroscopic mechanism of ESM were published within the framework of Fermi-Dirac statistics, the Vegard law, the direct flexoelectric coupling effect, the electrostriction effect, and so on. However, most of the models in these papers are limited to the partial coupling or particular process, and numerically solved by using decoupling approximation. In this paper, to model the ESM measurement with the coupling electrical-chemical-mechanical process, the chemical Gibbs function variational principle for the thermal electrical chemical mechanical fully coupling problem is proposed. The fully coupling governing equations are derived from the variational principle. When the tip concentrates the electric field within a small volume of the material, the inhomogeneous electric field is induced. So, both direct and inverse flexoelectric effects should be taken into account. Here, the bulk defect electrochemical reactions are also taken into account, which are usually omitted in the existing works. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, and piezoelectric and non-piezoelectric dielectrics. As an application of this work, a developed initial-boundary value problem is solved numerically in a mixed ion-electronic conductor. Numerical results show that it is meaningful and necessary to consider the bulk defect chemical reaction. Besides, the chemical reaction and the flexoelectric effect have an interactive influence on each other. This work can provide theoretical basis for the ESM as well as investigating the bulk chemical reaction process in solids.