Abstract
A cellular automata (CA) approach to modeling both Ostwald ripening and Rayleigh instability was developed. Curvature-driven phase interface migration was implemented to CA model, and novel CA rules were introduced to ensure the conservation of phase volume fraction of nearly equilibrium two-phase system. For transient Ostwald ripening, it is shown that the temporal growth exponent m is evolving with time and non-integer temporal exponents between 2 and 3 are predicted. The varying temporal growth exponent m is related to the particle size distributions (PSDs) evolution. With an initial wide PSD, it becomes narrowed toward steady state. With an initial narrow PSD, it becomes widened at first and then narrowed toward steady state. For Rayleigh instability, two cases (one with sinusoidal perturbation on the surface of the long cylinder, and the other with grain boundaries in the interior of the long cylinder) were simulated, and the breakup of the long cylinder was shown for both cases. In the end, a system containing long cylinders with interior grain boundaries was simulated, which demonstrated the integration of Rayleigh instability and Ostwald ripening relating to the spheroidization of the lamellar structure.
Highlights
Ostwald ripening and Rayleigh instability are two distinct processes, but with the same driving force coming from the reduction in the interface/surface area
We present a novel cellular automata approach to modeling both Ostwald ripening and Rayleigh instability based on the curvature-driven mechanism
To investigate the ability of the current cellular automata (CA) model in simulating Ostwald ripening for different volume fractions (f v ) of second phase particles, systems with 10%, 50% and 90% volume fractions volume fractions of second phase particles, systems with 10%, 50% and 90% volume fractions were simulated, and the microstructure evolution, time dependence of the average grain size, and were simulated, and the microstructure evolution, time dependence of the average grain size, and the fitted temporal exponent of the three systems are shown in Figures 2–4, respectively
Summary
Ostwald ripening and Rayleigh instability are two distinct processes, but with the same driving force coming from the reduction in the interface/surface area The former is an observed phenomenon for a system with second-phase particles of various sizes dispersed in a matrix, in which larger particles grow at the expense of the smaller ones. The second phase particles disperse in the matrix and still undergo transformation which leads to the growth of large particles and shrinkage of small particles In this way, the microstructures of materials can be tailored as well as the properties. CA models have been successfully applied to simulate grain growth based on the curvature-driven mechanism [37,38,39,40,41,42,43,44,45], and it is much promising to extend the CA method to model Ostwald ripening and Rayleigh instability, which are curvature-driven phenomena. The successive occurrence of Rayleigh instability and Ostwald ripening in a system with long cylinders was captured by the model
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