We use the cellular automaton (CA) approach to model binary diffusion in solids. We define an asynchronous CA model and formally take its continuum limit and show it approaches a differential equation model derived in previous work (Ribera, Wetton, and Myers, 2019, arXiv:1911.07359 [cond-mat.stat-mech]) that exhibits the Kirkendall effect. The framework allows the exploration of other state change rules based on additional physical mechanisms.
Ribera, H., Wetton, B. T. R., & Myers, T. (2020). Cellular automaton model for substitutional binary diffusion in solids. Journal of Mathematical Modeling, 8(1), 91-104. doi: 10.22124/jmm.2020.13012.1255
MLA
Helena Ribera; Brian T. R. Wetton; Timothy Myers. "Cellular automaton model for substitutional binary diffusion in solids". Journal of Mathematical Modeling, 8, 1, 2020, 91-104. doi: 10.22124/jmm.2020.13012.1255
HARVARD
Ribera, H., Wetton, B. T. R., Myers, T. (2020). 'Cellular automaton model for substitutional binary diffusion in solids', Journal of Mathematical Modeling, 8(1), pp. 91-104. doi: 10.22124/jmm.2020.13012.1255
VANCOUVER
Ribera, H., Wetton, B. T. R., Myers, T. Cellular automaton model for substitutional binary diffusion in solids. Journal of Mathematical Modeling, 2020; 8(1): 91-104. doi: 10.22124/jmm.2020.13012.1255
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