Kinetics of heterogeneous grain boundary precipitation of NbC in a-iron: A Monte Carlo study C. Hin a,c, * , Y. Bre ´chet b , P. Maugis c,d , F. Soisson a a Service de Recherches de Me ´tallurgie Physique, DMN-SRMP, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France b SIMAP, Domaine Universitaire, 1130 rue de la Piscine, BP 75, 38 402 Saint Martin d’He `res Cedex, France c Arcelor Research, Voie Romaine-BP 30320, 57283 Maizie `res-les-Metz, France d ENSCIACET-INPT, 118 Route de Narbonne, 31077 Toulouse Cedex 4, France Received 12 November 2007; received in revised form 29 June 2008; accepted 25 July 2008 Available online 12 September 2008 Abstract We propose Monte Carlo simulations of the NbC grain boundary (GB) precipitation kinetics in a-iron, based on an atomic descrip- tion of the main mechanisms that control the kinetic pathway. The simulation involves realistic diffusion mechanisms, with a rapid dif- fusion of C atoms by interstitial jumps and a slower diffusion of Fe and Nb atoms by vacancy jumps; a simple model of the GB which reproduces the equilibrium segregation properties of Nb and C; and a point defect source which drives the vacancy concentration towards its equilibrium value. Depending on the precipitation conditions, Monte Carlo simulations predict different kinetic behaviours, including early segregation of C atoms at the grain boundaries, transient precipitation of metastable carbides, and homogeneous and heterogeneous NbC precipitation. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Steels; Heterogeneous nucleation of phase; MC simulations; Precipitation; Grain boundary 1. Introduction The precipitation of carbides in steels is frequently observed at high temperatures in the austenitic phase and at low temperatures in the ferritic phase. Low-carbon steels commonly contain chemical elements which can enhance carbide precipitation (e.g. Nb, V and Ti): this effect is used, for example, for the hardening of high- strength low-alloy (HSLA) steels. One can also take advantage of carbide precipitation to control the recrys- tallization process and the number of interstitial atoms in solid solution. It is therefore important to predict the precipitation kinetics both in order to be able to choose the compositions and thermal treatments to obtain a given microstructure, and to predict its subsequent evolution. We focus here on the precipitation of niobium carbides in a-iron, which have been recently extensively studied both experimentally [1–11] and by modelling [2,12,13]. The NbC precipitates have a NaCl-like structure, with – for precipi- tates larger than typically 1 nm in thickness – Ba ¨ker–Nut- ting orientation relationships with the body-centred cubic (bcc) iron matrix: {001} NbC //{0 0 1} a and h100i NbC // h110i a [1–3,12]. The coherency between precipitates and the matrix has been debated [1,3]: because of the large dif- ference between the lattice parameter of NbC (4.47 A ˚ ) and that of ferrite (2.87 A ˚ ), one can expect a rapid loss of coherency during the precipitation, at least in the direction h001i NbC //h001i a where the difference reaches almost 40%. However, during the first stages of precipitation, small and flat precipitates could maintain a partial coherency [1]. Experimental studies have been also devoted to the evolution of the shape and size of precipitates 1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.07.045 * Corresponding author. Address: Service de Recherches de Me ´tallurgie Physique, DMN-SRMP, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France. E-mail address: celine_hin@yahoo.fr (C. Hin). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 56 (2008) 5653–5667