The morphological stability of spherical and cylindrical crystals and an infinite plane growing from a supersaturated solution is studied using the principle of maximum entropy production in the Mullins and Sekerka approximation. In contrast to the first two geometries, the computational results for a plane agree completely with the results obtained on the basis of the classical linear perturbation theory. The concept of the binodal of a morphological transition is introduced in order to interpret the results for the sphere and cylinder. The boundaries of the metastable region are investigated. Morphological phase diagrams of stable-unstable growth are presented in terms of the variables surface energy and supersaturation as well as the variables crystal size and supersaturation. The physical nature of the appearance of metastability in this system is discussed.