We present Monte Carlo simulations of the formation of a new phase (e. g., hydride in metal) during uptake of atoms by a nanoparticle. The corresponding kinetics exhibit a short initial stage, which is sensitive to the specification of the subsurface layers, and a more universal long stage with the time scale proportional to L-z, where L is the lattice size, and 2.3 <= z <= 3 is the exponent dependent on the diffusion dynamics. For realistic diffusion dynamics, the model also predicts the third late stage when the growth of a new phase becomes very slow compared to that observed during the former stages. (C) 2008 Elsevier B.V. All rights reserved.