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.

在过去的十年中，电化学应变显微镜（ESM）已经成为研究纳米级电化学过程的有力工具，但其定量分析却颇具挑战性，涉及在高度集中的机电领域中进行复杂的机电耦合。在这项工作中，我们建立了电化学活性固体中移动离子的热力学和动力学的理论框架，其中通过浓度依赖的Vegard应变和应力依赖的扩散率来考虑完全的电化学-机械耦合。该理论被用于对带电扫描探针尖端下方的电化学过程进行建模，并通过快速傅里叶变换和有限差分分析相结合，以数值方式解决了高度不均匀的电化学机械场。仿真表明，ESM振幅与离子浓度和扩散率线性相关，而弛豫时间常数仅取决于扩散率，这使得这两个材料参数解耦成为可能。为了验证我们的模型分析，在固态电解质二氧化铈上进行了ESM映射和逐点松弛研究，实验数据与模型预测非常吻合。因此，该分析提供了一种强大的技术来分析ESM实验，并深入了解了尖端的纳米电化学过程。在固态电解质二氧化铈上进行了ESM映射和逐点松弛研究，实验数据与模型预测吻合良好。因此，该分析提供了一种强大的技术来分析ESM实验，并深入了解了尖端的纳米电化学过程。在固态电解质二氧化铈上进行了ESM映射和逐点松弛研究，实验数据与模型预测吻合良好。因此，该分析提供了一种强大的技术来分析ESM实验，并深入了解了尖端的纳米电化学过程。