Symmetries and modelling functions for diffusion processes

TL;DR

This paper introduces a symmetry-based constructive method for modeling diffusion processes using ERFEX, enabling high-accuracy analytical descriptions and extraction of diffusivity from experimental data, demonstrated on lithium diffusion on molybdenum surfaces.

Contribution

It presents a novel algorithm for constructing modeling functions based on ERFEX, integrating symmetry analysis with experimental data for diffusion modeling.

Findings

High-accuracy ERFEX approximation of concentration profiles

Extraction of diffusivity dependence from experimental data

Successful application to lithium diffusion on molybdenum surfaces

Abstract

A constructive approach to theory of diffusion processes is proposed, which is based on application of both the symmetry analysis and method of modelling functions. An algorithm for construction of the modelling functions is suggested. This algorithm is based on the error functions expansion (ERFEX) of experimental concentration profiles. The high-accuracy analytical description of the profiles provided by ERFEX approximation allows a convenient extraction of the concentration dependence of diffusivity from experimental data and prediction of the diffusion process. Our analysis is exemplified by its employment to experimental results obtained for surface diffusion of lithium on the molybdenum (112) surface pre-covered with dysprosium. The ERFEX approximation can be directly extended to many other diffusion systems.