Nucleation energy in the solid state

In this paper we discuss the thermodynamics of incoherent homogeneous nucleation. It is assumed that volume mismatch between a precipitate and a matrix decreases with the growth of the precipitate. Under this assumption an energetically favored nucleation may occur for any cluster size. It is found that the relative volume difference between the unstressed precipitate and unstressed matrix is of an oscillating character and might have low values, e.g., $\ensuremath{\sim}{10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}3}%$ for a precipitate containing $\ensuremath{\sim}{10}^{3}$ Co atoms in Au matrix.