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

Abstract

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.

Influence of periodic pressure on dendritic morphology and sidebranching

“…The effect of periodic pressure on dendritic growth has been studied experimentally and numerically by using the phase field method [11][12][13][14][15] . Phase field method [16][17][18][19][20][21][22][23] is a powerful tool to study dendritic growth and sidebranching during pressurized solidification [14,15,[24][25][26] . Börzsönyi et al [14,15] studied the effect of pressure on melting point in phase field model, and found that oscillating pressure or heating can tune the frequency of dendritic sidebranching dramatically.…”

“…Börzsönyi et al [14,15] studied the effect of pressure on melting point in phase field model, and found that oscillating pressure or heating can tune the frequency of dendritic sidebranching dramatically. The underlying mechanism for dendritic sidebranching has been explored by applying periodic pressures at different frequencies using 3-D phase field modeling [25] . It is revealed that if the frequency of pressure is lower than the critical value, both the tip velocity and the sidebranching would be completely synchronized with the perturbation.…”

“…The 3-D phase field model has been described in detail in Ref. [25]. The 3-D controlling equations (anisotropic) for phase field and solute field [18,19,27] are as follows:…”

“…Other parameters in these equations, simulation parameters, and the crystal anisotropy were set the same as in Ref. [25]. Adaptive mesh refinement and parallel computing were adopted in this work to solve the governing equations [27] .…”

“…All the differences in sidebranching behavior can be attributed to the different modulation mechanisms in the two cases. Tip growth velocity changes synchronously with that of external pressure due to the classical Clausius-Clapeyron equation [25] . More exactly, the frequency of tip velocity is the same as that of periodic pressure in the two cases.…”