Influence of cluster mobility on Cu precipitation in a-Fe: A cluster dynamics modeling T. Jourdan * , F. Soisson, E. Clouet, A. Barbu CEA, DEN, Service de Recherches de Me ´tallurgie Physique, F-91191 Gif-sur-Yvette, France Received 23 November 2009; received in revised form 4 February 2010; accepted 8 February 2010 Available online 5 March 2010 Abstract A cluster dynamics model has been parametrized to quantitatively reproduce results obtained by atomistic kinetic Monte Carlo (AKMC) modeling on the precipitation of Cu in a-Fe under thermal aging. The cluster mobility, highlighted by AKMC, is shown to have a significant effect on the precipitation kinetics and can reconcile the experimentally observed fast kinetics with the relatively low diffusivity of Cu monomers. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Precipitation; Kinetics; Modeling; Monte Carlo techniques 1. Introduction The precipitation of copper in iron during thermal aging or under irradiation in reactor pressure vessel steels is known to lead to the hardening and embrittlement of these materials. Given that the solubility limit in a-Fe is lower than 2% even at high temperatures (850 °C) [1], such effects can be expected at low Cu concentrations. For supersatura- tions as low as 1.2%, the precipitation has been shown to be homogeneous until approximately 600 °C [2]. Under irradiation, this conclusion still holds and no significant induced segregation is observed [3,4]: the kinetics is acceler- ated because of the supersaturation in vacancies. Due to the small lattice mismatch, the precipitates are spherical and are coherent with the matrix for a radius lower than 2 nm [5,6]. This coherency at small sizes has turned Fe–Cu alloy into a model system to validate numerical methods such as the rigid lattice atomistic kinetic Monte Carlo [7–9] (AKMC) model. In addition, the spherical shape of the precipitates, the low concentration of Cu necessary for the precipitation and the almost pure Cu content of the precipitates [10,11] greatly simplify the use of mesoscopic simulation approaches such as cluster dynamics (CD) [12,3]. Using this latest method, Christien and Barbu obtained a good agreement with the experimental mean radius of clusters after around 1 h under thermal aging [13], using a capillary approximation for the binding energies and a Cu diffusivity of 7:7  10 15 cm 2 s 1 at 500 °C. Possible rea- sons for the discrepancy at short times were a finite reac- tion kinetics at the interface or heterogeneous nucleation on impurities [3]. Golubov et al. used a lower value for the diffusivity 2:26  10 16 cm 2 s 1 at 500 °C with different binding energies accounting for the structural transforma- tion body-centred cubic (bcc) ? 9R that the Cu clusters undergo at a radius of around 2 nm [14]. However, using these values the coarsening rate was lower than the exper- imental one. Similar results were obtained by Wagner and Kampmann [15], even by taking into account the increase of the coarsening rate through the overlapping of the diffu- sion fields. Recently, AKMC simulations [16], parametrized by ab initio calculations, have shown that due to the trapping of vacancies inside Cu clusters, these clusters can be consid- ered as mobile for sizes up to several hundreds of atoms for 1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.02.014 * Corresponding author. E-mail address: thomas.jourdan@cea.fr (T. Jourdan). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 58 (2010) 3400–3405