Numerical study of the stability of double fingers with the phase-field model.

Doublon is one of the typical patterns found in crystal growth. It is a bound state of two fingerlike patterns. In this paper, we obtain a phase diagram for doublons with numerical simulations of the phase-field model. Numerical simulations are performed in a channel. Two small seeds of crystal with different sizes are set on the left side of the channel as an initial condition, in order to find whether the two fingers grow into a doublon or one finger overcomes the other owing to mutual competition. It is confirmed that a stable doublon is formed when the undercooling is large and the anisotropy is weak. Furthermore, we find a doublon with oscillating groove in a certain parameter range. We investigate more carefully the transition between the doublon and the dendrite by changing the anisotropy parameters stepwise, and show that the difference of the tip velocities of the doublon and the dendrite increases continuously from zero at a critical value of anisotropy.