We have determined morphology diagrams in two and three dimensions for two different phase-field models [A.A Wheeler, B.T. Murray, R.J. Schaefer, Physica D 66 (1993) 243; A. Karma, W.-J. Rappel, Phys. Rev. E 57 (1998) 4323] for the parameters undercooling and anisotropy of surface tension. The comparison with analytical predictions show a qualitative correspondence, however, the predicted shape of the morphology boundary differs significantly from the shape found in our simulations. The two investigated models show the same quantitative behavior. Our simulations in 3D have shown that the shape of the morphology boundary is qualitatively similar to the one in 2D. However, we find that the border is shifted by an amount of 0.3% on the anisotropy axis. Our simulated 3D structures show a qualitative correspondence to the ones we have found in in situ experiments with xenon. (c) 2006 Elsevier B.V. All rights reserved.