A kinetic theory of nucleation in dilute solid solutions; Application to the precipitation of carbon and nitrogen in α-iron

Abstract

A kinetic theory of nucleation and growth of precipitate particles in solid solutions is derived. This theory, which is applicable at low solute concentration and rather low solute-solute binding energy, is obtained by application of equilibrium conditions to the reversible chemical rate equations of cluster formation. The equilibrium approximation permits sufficient cancellation of terms in the equations so that the remaining equations are integrable. Computer solutions for a variety of parameters of the kinetic equations were used to check the range of validity of the approximation necessary to obtain the analytic expression. The analytic expression describes the experimentally observed time dependence of the precipitation of carbon and nitrogen in α-iron. The analytic theory also predicts an average binding energy of precipitate atoms in a cluster which is in reasonable agreement with experimentally derived carbon-carbon and nitrogen-nitrogen binding energies in iron. The size of the fundamental precipitate nucleus, as well as the distribution of sizes of precipitate particles, is also predicted, but no experiments exist to check these predictions.