Morphological instability is an important subject in alloy directional solidification, and the development of cell allay is important to alloy properties In nature, as a result of cell arrangement, this problem is often three-dimensional (3D), even for thin-film, and Its Simulation is rather difficult. We have developed a 3D adaptive phase field model to simulate efficiently the directional solidification of a binary alloy. The morphological transition from 2D to 3D approximations are illustrated. and compared with available analytical and simulated results. The effect of anisotropy on the cell arrangement is discussed as well. (C) 2009 Elsevier Ltd. All rights reserved.