Mechanics of electrochemical strain microscopy: Computational simulations and experimental validations

Abstract

In the last decade, electrochemical strain microscopy (ESM) has emerged as a powerful tool to study electrochemical processes at the nanoscale, yet its quantitative analysis is quite challenging, involving complex electrochemo-mechanical coupling under highly concentrated electromechanical fields. In this work, we develop a theoretical framework of thermodynamics and kinetics for mobile ions in electrochemically-active solids, wherein full electrochemo-mechanical coupling is considered via concentration-dependent Vegard strain and stress-dependent diffusivity. The theory is applied to model electrochemical processes underneath a charged scanning probe tip, and implemented numerically to solve for the highly inhomogeneous electrochemo-mechanical field via combined fast Fourier transform and finite difference analysis. The simulations reveal that the ESM amplitude correlates linearly with both ionic concentration and diffusivity, while relaxation time constant depends only on diffusivity, making it possible to decouple these two material parameters. In order to validate our model analysis, ESM mapping and point-wise relaxation studies are carried out on solid state electrolyte ceria, and the experimental data agree with model predictions well. The analysis thus provides a powerful technique to analyze ESM experiments, and sheds deep insight into the nanoscale electrochemical process under a tip.