Diffusionless growth of crystals results in a microsegregation-free microstructure with the initial (nominal) chemical composition of binary systems. Normally, a transition from chemically partitioned growth to diffusionless solidification is accompanied by a morphological transition of the crystal shape. Therefore, first, the morphological transitions in rapidly solidifying crystal microstructures are discussed. Particularly, considering the transition from the solute diffusion-limited growth to purely thermally controlled growth of dendritic crystals, a presented model of rapid solidification predicts the abrupt change of growth kinetics with break points in the "dendrite tip velocity-undercooling" and "dendrite tip radius-undercooling" relationships. And second, it is shown that the abrupt change of growth kinetics occurs at the ending of the transition to purely thermally controlled growth and the onset of diffusionless solidification.