On the kinetics of dendritic sidebranching: A three dimensional phase field study

The underlying mechanism for dendritic sidebranching was studied using 3-D phase field modeling. Results showed that in 3-D the requirement of applying the random thermal noise to induce dendritic sidebranching (i.e., normally the case for 2-D phase field simulations) was fully relaxed. The stretching of the secondary or higher order arms occurred spontaneously and symmetrically as the growth of the dendrite. With periodic external perturbation and if the stimulating frequency was lower than a critical value, both tip velocity and sidebranching would get completely synchronized with the perturbation. Whereas if the perturbation frequency was higher than the critical value, rather than increasing, the sidebranching frequency would become stable and maintain at the same magnitude as that of the natural sidebranching, i.e., when no external perturbation was applied. It was shown that the underlying mechanism for sidebranching was deterministic rather than stochastic, and anisotropy tendency and curvature effect were shown to be the most important influence factors. Moreover, the difference of the anisotropy tendency would lead to an uneven distribution of curvature on the solid/liquid interface, i.e., formation of concave and convex geometries. The growth of these geometries would subsequently break the initial spherical structure of solid seed and lead to further sidebranching.