Opara Jarosław, Straumal Boris, Zięba Paweł
Łukasiewicz Research Network-Institute for Ferrous Metallurgy, K. Miarki Str. 12, 44-100 Gliwice, Poland.
Institute of Solid State Physics of the Russian Academy of Sciences, 142432 Chernogolovka, Russia.
Materials (Basel). 2021 Aug 31;14(17):4985. doi: 10.3390/ma14174985.
The fundamentals of discontinuous precipitation (DP) reaction modelling using a cellular automata (CA) method are presented. In the proposed CA model, cell states, internal variables, equations, and transition rules were defined to predict the manner of mass transport during DP reaction and to relate changes in the microstructure with corresponding changes in chemical composition. Furthermore, the concept of digital material representation (DMR) was introduced into the CA model, which allowed schematic images of the microstructure to be used as starting structures in the modelling of the DP reaction. The preliminary assumptions adopted in the proposed CA model for the DP reaction were verified by numerical simulations of the growth of discontinuous precipitates at a steady-state at the example of Al-22 at.% Zn alloy. The outcomes achieved from the CA simulations were presented in a different form than that most commonly used previously (single concentration profiles), namely as the 2D maps showing changes in Zn content accompanying the successive stages of growth of discontinuous precipitates. The model used for the description of the solute diffusion along of the reaction front (RF) allowed two-dimensional systems at the nano-scale to be treated within a reasonable simulation time. The obtained results indicate that the developed CA model was able to realistically simulate the DP reaction, which was confirmed by the visualisation of migrating RFs together with associated chemical composition changes in the microstructure.
介绍了使用元胞自动机（CA）方法进行不连续析出（DP）反应建模的基本原理。在所提出的CA模型中，定义了元胞状态、内部变量、方程和转变规则，以预测DP反应过程中的质量传输方式，并将微观结构的变化与化学成分的相应变化联系起来。此外，数字材料表征（DMR）的概念被引入到CA模型中，这使得微观结构的示意图能够用作DP反应建模的初始结构。以Al-22 at.% Zn合金为例，通过对稳态下不连续析出物生长的数值模拟，验证了所提出的DP反应CA模型所采用的初步假设。CA模拟得到的结果以一种与之前最常用的形式（单一浓度分布）不同的形式呈现，即作为二维图，显示了伴随不连续析出物连续生长阶段的Zn含量变化。用于描述溶质沿反应前沿（RF）扩散的模型使得在合理的模拟时间内能够处理纳米尺度的二维系统。所得结果表明，所开发的CA模型能够真实地模拟DP反应，这通过迁移RF的可视化以及微观结构中相关化学成分变化得到了证实。
