Papers by Author: Philippe Maugis

Abstract: Experiments of niobium diffusion at infinite dilution and Nb reaction-diffusion in pure iron and in ferrites with different amounts of carbon were performed, for comparison, in order to understand the influence of carbon on the diffusion process in the Nb-Fe system. A proportional decrease of the diffusion coefficient with the increasing amount of carbon was found. This effect seems to be stronger than in the self-diffusion analyzing the literature; moreover SIMS measurements in niobium- implanted samples show a redistribution of carbon during the first steps of the diffusion process. For those reasons, a stronger effect of carbon-niobium interaction over the carbon-vacancy interaction seems to be responsible for the decrease in the diffusion coefficient.

Abstract: High Resolution Transmission Electron Microscope and Electron Energy Loss Spectroscopy and have been used to characterize the structure and chemical composition of niobium carbonitrides in the ferrite of a Fe-Nb-C-N model alloy at different precipitation stages. Experiments seem to indicate the coexistence of two types of precipitates: pure niobium nitrides and mixed sub-stoichiometric niobium carbonitrides. In order to predict the chemical composition of these precipitates, a thermodynamical formalism has been developed to evaluate (i) the nucleation and growth rates (classical nucleation theory) and (ii) the chemical composition of nuclei and existing precipitates. A model based on the numerical resolution of former equations, is used to compute precipitates size distribution evolution at a given temperature. The predicted compositions are in very good agreement with experimental results.

Abstract: This paper presents a physically based precipitation model which aims at describing precipitation kinetics when it occurs exclusively on dislocations. We present specific nucleation, growth and coarsening equations, which are integrated in a set of differential equations. This model is successfully applied to the case of precipitation of NbC in a ferritic steel, whose kinetics has been determined by small-angle neutron scattering.

Abstract: The precipitation of niobium carbides in industrial steels is commonly used to control the recrystallization process or the amount of interstitial atoms in solid solution. It is then important to understand the precipitation kinetics and especially the competition between homogeneous and heterogeneous precipitation, since both of them have been observed experimentally, depending on the alloy composition, microstructure and thermal treatments. We propose Monte Carlo simulations of NbC precipitation in α-iron, based on a simple atomic description of the main parameters which control the kinetic pathway : - realistic diffusion properties, with a rapid diffusion of C atoms by interstitial jumps and a slower diffusion of Fe and Nb atoms by vacancy jumps - a simple model of grain boundaries which reproduces the equilibrium segregation properties of Nb and C - a point defect source which drives the vacancy concentration towards its equilibrium value. Depending on the precipitation conditions, MC simulations predict different kinetic behaviours, including homogeneous and heterogeneous NbC precipitation, early segregation of C atoms and its importance as a first stage for NbC precipitation, wetting phenomena on grain boundaries and transient precipitation of metastable carbides.

Abstract: We test the main approximations of the classical laws for nucleation, growth and coarsening by comparison with atomistic simulations of the kinetics of precipitation. We investigate the kinetics of phase separation in dilute A-B solid solutions by precipitation of B atoms in the Arich matrix. Classically, the kinetics is represented by the time evolution of the total number of particles and their mean radius. In this work, the kinetics is predicted by three types of models: (a) an Atomic-scale Kinetic Monte Carlo (AKMC) model based on a vacancy diffusion mechanism, (b) a Cluster Dynamics model, and (c) the MultiPreci model, based on the coupling of the classical laws of nucleation, growth and coarsening. Cluster Dynamics and the Multipreci model have been parameterized such that the thermodynamic and kinetic parameters (solubility, diffusion coefficient, interface energy) be identical to that of the AKMC. Under these conditions we find that the classical laws are in good agreement with the atomistic simulations as long as the thermodynamics of the solid solution remains strictly regular. As expected, Cluster Dynamics compares better with the atomistic simulations, especially if a precise description of the energetics of the smallest clusters is applied.