Investigation of the diffusion of atomic fission products in UC by density functional calculations Émile Bévillon ⇑ , Roland Ducher, Marc Barrachin, Roland Dubourg IRSN, SEMIC, DPAM, LETR, Centre de Cadarache, 13115 Saint Paul Lez Durance, France article info Article history: Received 23 July 2012 Accepted 17 November 2012 Available online 29 November 2012 abstract Activation energies of U and C atoms self-diffusion in UC, as well as activation energies of hetero-diffu- sion of fission products (FPs) are investigated by first-principles calculations. According to a previous study which showed a likely U site occupation was favoured for all the FPs, their diffusion is restricted to the uranium sublattice of UC in the present study. In this framework, long-range displacements are only possible through a concerted mechanism with a surrounding uranium vacancy. Using the apparent formation energies of the uranium vacancy defect calculated in our previous study and the classical approach used in UO 2 by Andersson et al., the activation energies of the main fission products in the var- ious stoichiometric domains have been calculated. The results are compared to those obtained with the five frequency model applied to two representative fission products, Xe and Zr. Interestingly, despite strong differences of formalism, both models provided similar activation energies. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction A more and more secure and efficient nuclear fuel is required for normal and off-normal reactor operations or current and future facilities. This implies a better knowledge of the fuel matrix behav- iour in all conditions which is significantly associated to bulk and point defects properties and to the behaviour of fission products (FPs). Many efforts based on first-principles calculations have been done or are currently in progress in order to characterize stabilities and transports of these FPs in the fuel matrix at the atomic scale. Most of these studies concerns UO 2 , which is currently used in nu- clear reactor. Many bulk and point defect calculations [1–8] and numerous FPs [9–21] were the subject of investigations. With the GENIV project, alternative potential nuclear fuels have regained some interest. It mainly concerns uranium nitride (UN) and carbide (UC), due to their high thermal conductivities [22–24] and high metal densities. These interesting properties are however counterbalanced by some drawbacks such as signifi- cant fuel swelling and fission gas release in real operating conditions [25]. This leads to the progressive loss of some of the interesting peculiarities of these potential nuclear fuels. As a consequence, the knowledge of FPs behaviour is even more crucial and could improve the design of the fuel. Concerning UN, bulk and point defects [26–32] as well as FPs [33] studies are also available. In the case of UC, previous studies focused on bulk, point defects [28,34–37] and stabilities of FPs [36,38]. The investigation of the FPs migration properties will be the subject of the present work. FP migration in the irradiated fuel is indeed one of the key factors determining FP speciation and formation of separate phases in association with pure thermody- namic considerations. In a previous study [38], the incorporation and solution energies of the most abundant FPs were calculated. The results showed that for almost all the FPs, the occupation of U sites is found the most stable. This occurs by the occupation of a single uranium vacancy or through the occupation of a Scho- ttky defect. Considering the Schottky defect location would have implied a loss of symmetry of the system, many non-equivalent sites and many non-equivalent diffusion paths. As a consequence, and due to calculation limitations, we only considered the occupa- tion of a single uranium vacancy, even when FPs were found more stable within a Schottky defect. The stabilization provided by the carbon vacancy of the Schottky defect is thus neglected in the present study. Diffusion through the uranium sublattice of UC inevitably im- plies a fission product located in a U site (FP U ) surrounded by a ura- nium vacancy (V U ) in its direct vicinity. Without this vacancy no displacement can occur, at least not for the present diffusion process. Long-range FP displacements are thus correlated to the presence and behaviour of this U vacancy and depend on the sta- bility of the cluster formed by the fission product and the vacancy (FP U aV U ). Diffusion also depends on various migration processes related to this cluster. It is a hetero-diffusion process and two methods are used to compute the activation energy which charac- terizes such diffusions: the classical approach of Andersson et al. [20] and the five frequency model [39]. 0022-3115/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnucmat.2012.11.030 ⇑ Corresponding author. E-mail address: emile.bevillon@yahoo.fr (É. Bévillon). Journal of Nuclear Materials 434 (2013) 240–247 Contents lists available at SciVerse ScienceDirect Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat