Phase Field Simulation on Directional Solidification of Succinonitrile (SCN)–Acetone Organic Model Alloy

Abstract

Phase field simulation on directional solidification of succinonitrile (SCN)-acetone organic model alloy was performed. The development of concentration and phase field profile was calculated in order to clarify the dependences of growth velocity V and temperature gradient G on the morphology of growing crystal.Concerning the primary dendrite arm spacing, 1 , the relationship between 1 4 G 2 V=kÁT 0 and V was examined, where k and ÁT 0 are partition coefficient and temperature difference between liquid and solid phases, respectively. The calculated values of 1 4 G 2 V=kÁT 0 did not show a universal relationship but the trends of the present calculation can be understood by extrapolation from experimental data. The power law index of V for the 1 4 G 2 V=kÁT 0 -V plot took similar values between the experiments and the present calculation for some cases. The 1 -V relationship did not show dependences on temperature of the low temperature side and nor acetone concentration. For the curvature radius R, the R-V relationship can be fitted by a simple function regardless the value of G. In addition, the calculated values of R and the power low indexes of V for R were compared to the dendrite growth theory and good accordance was confirmed.

Global theory of steady deep-cellular growth in directional solidification

“…It has been also a center of research activities on pattern formation and transition in the broad areas of nonlinear science as well as applied mathematics (Refs. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]) for decades.…”

Global stabilities, selection of steady cellular growth, and origin of side branches in directional solidification

“…The subject has also been studied by many researchers numerically with the phase field model in recent years (see, for instance, Refs. [28][29][30]). The numerical simulations may reproduce the cellular patterns resembling those observed in the experiments.…”

Steady deep-cellular growth in solidification

“…Accordingly, these works cannot determine the global interface shape of cell, the location of cell's tip and bottom, the total length of cell, the concentration of the impurity at cell's tip and bottom, and, in particular, the mathematical relationships between all these important quantities and the operating conditions. There are also many numerical works in the literature in recent years [10,11]. The numerical works may show the global patterns of cellular array, they, however, cannot explore the properties of singularity of the system at the bottom of root, nor provide the profound mechanisms behind the phenomenon.…”