  By critically examining the traditional theory of homogeneous nucleation of
precipitates in solid solutions, it is revealed that the theory's assertion
regarding an increase in the nucleation free energy due to elastic strain
associated with the difference in atomic volumes between the two phases is
applicable to coherent precipitates, but becomes incorrect when applied to
incoherent precipitates. This conclusion is obtained by accounting for thermal
point defects in the matrix, which can be absorbed at the interface between an
incoherent particle and the matrix during nucleation, thereby relieving elastic
stresses. Accordingly, a new kinetic model based on the Reiss theory for binary
nucleation is proposed for predicting the nucleation rate of incoherent
precipitates by agglomeration of solute atoms and point defects, with a further
extension to account for excess vacancies formed under non-equilibrium
conditions of quenching experiments.
