Simplified Kinetic Model of Flux-Driven Phase Transitions and Patterns Competition in Open 2D System

The regular solution approximation has a successful history of applications in the thermodynamics and kinetics of decomposition in alloys, treated as closed systems. It provides a qualitatively proper description of all stages of spinodal and nucleation-mediated decomposition for alloys under homogeneous external conditions without external fluxes. In this article, the kinetic mean-field model for open (flux-driven) systems is extended by incorporating the divergence of in- and out-fluxes into the master equations for occupation probabilities. The closest experimental analog of this model is the pattern formation during the co-deposition of a binary alloy under frozen bulk diffusion, but with reasonable surface diffusion, where the deposition rate V serves as the main external parameter. However, some peculiarities of the model may also be useful for describing eutectic and off-eutectic crystallizations. Rate-dependent phase T − C diagrams are determined for the steady the states of such an open system. The ratedependent instability region is subdivided into three distinct steady-state morphologies: spots (“gepard”-like), layers (“zebra”-like) – labyrinth or lamellae, and mixed patterns (a combination of “gepard” and “zebra”). This morphology map depends on the initial conditions, revealing memory effects and hysteresis. This implies that, unlike the equilibrium state of a closed system, which acts as an attractor for the evolution paths, the steady states of flux-driven systems may not be attractors. Variations of the model, including Monte Carlo simulations, are also discussed.