Iterative Thermodynamic Augmentation of Spatially Resolved Analytic Microscopy for Fast-Diffusing Solutes

Abstract

The spatially resolved quantification of fast-diffusing solutes presents several challenges in analytic microscopy. Given the critical role of interstitially alloyed elements in physical metallurgy, we propose a computational framework that addresses this limitation by augmenting spatially resolved composition maps of substitutional elements with computationally derived interstitial distributions. The underlying methodology is an iterative thermodynamic model: exploiting the stark differences in solid-state diffusion kinetics, the model assumes a state of partial chemical equilibrium exclusively for the mobile interstitial species. An optimization scheme iteratively adjusts an uniform interstitial chemical potential across the mapped microstructure until the integrated local concentration converges with an independently measured bulk value. Ultimately, this approach extracts thermodynamically consistent interstitial concentration maps from robust, low-noise microscopy data, yielding quantitative spatial arrays that are otherwise time- and resource-intensive to obtain at best.