Efficient adaptive phase field simulation based on a finite volume method is carried out to study the morphological development during directional solidification of a nickel/copper alloy. The adaptive nature of the method allows the calculation to cover different length scales for the interface, solute diffusion, and heat conduction. With the frozen temperature approximation, our calculated results are in reasonable agreement with previous ones (J. Crystal Growth 200 (1999) 583). However, the use of a much larger domain allows us to perform simulation at low speed near the onset of constitutional supercooling, where both solutal boundary layer and cell wavelength are large. For the same domain size, the calculated results without using the frozen temperature approximation remain about the same, even though the release of latent heat lowers the steady interface position and the thermal gradient in the melt side. (C) 2003 Elsevier Science B.V. All rights reserved.