The theoretical description of growth morphology diagram (morphodrome) of a two-dimensional crystal growing with impurities that shows possibility of habit change is presented. By taking into account the diffusion of adatoms along the edge of a step and contamination of kink sites with impurity atoms, we analyze the structures and growth rates of steps bounding a two-dimensional island on a (001) surface of a Kossel crystal. The first and second nearest-neighbor interactions as well as heights of activation barriers for different elementary processes on the crystal structure are taken into consideration. The change in growth habit from the square-like shape to the diamond-like one is predicted as an effect of strong interplay between edge diffusion and kink contamination. In the absence of edge diffusion, addition of impurities into kinks does not cause habit change. When the edge diffusion dominates the kinetics, the habit change is caused by edge diffusion, while kink contamination lowers the threshold supersaturation, at which habit change occurs. In case of moderate edge diffusion that is not strong enough to result in habit change, contamination of kinks with impurity atoms can cause habit change. The constructed morphodrome shows the dependence of the habit change threshold supersaturation on the concentration of impurities that is qualitatively similar to the experimental data. (c) 2004 Elsevier B.V. All rights reserved.