Subdiffusion kinetics of nanoprecipitate growth and destruction in solid solutions
This paper is a study of fractional differential generalizations of the Ham and Aaron-Kotler precipitation models used for the kinetics of subdiffusion-limited growth and dissolution of new-phase precipitates. Diffusion models that are based on the concept of normal impurity diffusion were successfully used to describe many phenomena. However, there are many examples that anomalous diffusion (predominantly subdiffusion) is also a very important model of many practical applications. Classical diffusion \((\alpha = 1)\) is based on Gaussian statistics and the second Fick law and leads to the dependence \(\Delta(t)=\sqrt{\langle x^2(t)\rangle}\propto^{1/2}\), but there are also available cases where \(\alpha\neq 1\) leads to sub- or super-diffusions with anomalous self-similarity diffusion. Existing diffusion models of precipitation reflect rather incompletely the properties of transport phenomena occurring in actual materials, thus the authors study the subdiffusion-limited kinetics of the growth and decomposition of new-phase precipitates using fractional differential generalizations of classical models of precipitate growth and dissolution in solid solutions. The whole paper is divided into six sections. After the introduction, we have a presentation of the mathematical basis of random walks with impurity localization in Section 2, then a generalization of the Ham model (Section 3) with Monte Carlo simulations in the framework of the Ham approach (Section 4). In Section 5, there is a proposal of subdiffusion generalization of the Aaron-Kotler model in terms of fractional derivatives. A summary of the paper is provided in Section 6.
scientific article; zbMATH DE number 6487445
scientific article