Using a vacancy diffusion mechanism for substitutional elements and an interstitial mechanism for carbon atoms, a Monte Carlo method was proposed for simulating the coherent precipitation of niobium carbide in α-iron. Iron, niobium, and carbon atoms were distributed on a rigid, simple cubic lattice which describes both the bcc ferrite structure and the fcc NaCl-type structure of NbC. The Monte Carlo parameters were fitted with good accuracy to the experimental diffusion and equilibrium data. A residence time algorithm was adapted in order to handle both the fast interstitial C diffusion and the slow substitutional Nb and Fe diffusion. Depending on the concentration and temperature, the simulations exhibited two kinds of kinetic paths: formation of transient iron carbides at high supersaturation, and nucleation of NbC precipitates at low supersaturation. Not only could the resulting kinetics of nucleation be compared with the classical theory but the simulations also provide information on cluster size, shape and density on the atomic scale which could then be directly compared with tomographic atom probe (TAP) results.

Monte Carlo Simulation of NbC Precipitation Kinetics in α-Fe. D.Gendt, P.Maugis, G.M.MartinNastar, F.Soisson: Defect and Diffusion Forum, 2001, 194-199[2], 1779-86