Abstract
Ordering and self-organization are critical in determining the dynamics of reaction-diffusion systems. Here we show a unique pattern formation mechanism, dictated by the coupling of thermodynamic instability and kinetic anisotropy. Intrinsically different from the physical origin of Turing instability and patterning, the ordered patterns we obtained are caused by the interplay of the instability from uphill diffusion, the symmetry breaking from anisotropic diffusion, and the reactions. To understand the formation of the void/gas bubble superlattices in crystals under irradiation, we establish a general theoretical framework to predict the symmetry selection of superlattice structures associated with anisotropic diffusion. Through analytical study and phase field simulations, we found that the symmetry of a superlattice is determined by the coupling of diffusion anisotropy and the reaction rate, which indicates a new type of bifurcation phenomenon. Our discovery suggests a means for designing target experiments to tailor different microstructural patterns.
Highlights
The dynamics of reaction-diffusion systems is dictated by the coupling of reaction and diffusion
We investigate the ordering and self-organization in a reaction-diffusion system with thermodynamic instability and kinetic anisotropy, through a combination of analytical study and phase field simulations
We establish a general theoretical framework to predict the symmetry of superlattices associated with anisotropic diffusion
Summary
Ordering and self-organization are critical in determining the dynamics of reaction-diffusion systems. The self-organizations induced by thermodynamic instability and the breaking of point symmetry are widely observed in systems without reactions, e.g., multi-domain patterning in second-order ferroelectric and ferromagnetic phase transitions, which is dominated by long-range electric/magnetic interactions[13,14,15,16] In those cases, long-range interactions play a critical role in pattern formation. We report a unique self-organization mechanism to understand the formation of void/gas bubble superlattices in crystals, which originates from the interplay of thermodynamic instability, diffusion anisotropy and reaction kinetics. We consider two ways to modify the diffusion terms, by adopting Cahn-Hilliard type diffusion[31] and anisotropic diffusion The former could introduce thermodynamic instability and up-hill diffusion, while the latter suggests a breaking of point symmetry. Information, which are consistent with previous theoretical studies[32,33]
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