Rapid directional solidification under a constant thermal gradient was simu
lated by a new phase-field model. The banded structures in an Al-Cu alloy w
ere successfully reproduced. Only a few cells or dendrites survive in every
transition steps into the plane-front mode, which explains the large grain
size of banded structure observed in experiments. The noise level in conce
ntration plays a crucial role in the transition procedure of the cell/dendr
ite into the plane-front mode and so in the overall pattern formation of th
e banded structure. (C) 2001 Elsevier Science B.V. All rights reserved.