Cellular automaton model for substitutional binary diffusion in solids

TL;DR

This paper introduces a cellular automaton model for simulating one-dimensional binary diffusion in solids, providing a simple and effective alternative to traditional continuum models.

Contribution

It presents a novel cellular automaton approach that approximates the continuum equations of binary diffusion, bridging discrete and continuous modeling methods.

Findings

CA model approaches continuum limit as cells increase

Model offers a simple method for studying binary diffusion

Validates CA approach against existing continuum models

Abstract

In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing equations of the problem. We show that in the limit where the number of cells tends to infinity the CA model approaches a continuous model derived in previous work. Thus, showing that the CA approach provides a new, simple method to study and model binary diffusion.