Morphological stability of two-dimensional new phase precipitate located at the grain boundary

The diffusion growth of two-dimensional new phase precipitate located at the grain boundary of a finite thickness is considered taking into account diffusion fluxes of impurity atoms from the bulk of a grain depth to the grain boundary. The stability of the growing precipitate of a relatively small radius to small random perturbations of its shape is analyzed taking into account the surface kinetics of the impurity atoms on the grain boundary-precipitate interface. The threshold radii of the precipitate are found, above which the amplitude of the shape distortion and the amplitude of the relative shape deformation of the precipitate rise.