Theory of He trapping, diffusion, and clustering in UO 2 Younsuk Yun * , Olle Eriksson, Peter M. Oppeneer Department of Physics and Materials Science, Uppsala University, Box 530, S-751 21 Uppsala, Sweden article info Article history: Received 19 November 2008 Accepted 15 December 2008 PACS: 66.30.Jt 61.72.y 61.72.Ji abstract We have performed ab initio total energy calculations to investigate the behavior of helium and its diffu- sion properties in uranium dioxide (UO 2 ). Our investigations are based on the density functional theory within the generalized gradient approximation (GGA). The trapping behavior of He in UO 2 has been modeled with a supercell containing 96-atoms as well as uranium and oxygen vacancy trapping sites. The calculated incorporation energies show that for He a uranium vacancy is more stable than an oxygen vacancy or an octahedral interstitial site (OIS). Interstitial site hopping is found to be the rate-determin- ing mechanism of the He diffusion process and the corresponding migration energy is computed as 2.79 eV at 0 K (with the spin-orbit coupling (SOC) included), and as 2.09 eV by using the thermally expanded lattice parameter of UO 2 at 1200 K, which is relatively close to the experimental value of 2.0 eV. The lattice expansion coefficient of He-induced swelling of UO 2 is calculated as 9  10 2 . For two He atoms, we have found that they form a dumbbell configuration if they are close enough to each other, and that the lattice expansion induced by a dumbbell is larger than by two distant interstitial He atoms. The clustering tendency of He has been studied for small clusters of up to six He atoms. We find that He strongly tends to cluster in the vicinity of an OIS, and that the collective action of the He atoms is sufficient to spontaneously create additional point defects around the He cluster in the UO 2 lattice. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Many fission products (Xe, Kr, I, etc.) as well as a-particles (He) are produced during and after the irradiation of fuel in nuclear reactors. The presence of the fission products and He atoms can lead to the formation of bubbles and to a possible swelling of the fuel material, mostly UO 2 or mixed oxides, because of their low sol- ubility in the fuel lattice [1–3]. Especially, a large concentration of He is created during the long-term storage of spent fuel which af- fects the mechanical properties of the burned-up fuel material with possible consequences for the long-term storage process [4]. For those reasons, the behavior of He has been experimentally investigated to improve the performance and stability of the nucle- ar fuel [5]. Several experimental studies have been carried out to determine the most favorable location as well as diffusion coeffi- cient of He in UO 2 [6–8]. The formation of He bubbles has been investigated as a function of temperature and implantation condi- tions in UO 2 [9]. Theoretical studies have contributed also to understanding the behavior of He trapped at various defects and the variation of the lattice parameter of UO 2 induced by He [10–13]. Despite the amount of work already done, some open questions do remain. For instance, the stability of He trapped at a vacancy or an interstitial site has been debated so far. Petit et al. [11] and Crocombette [12] suggested that the most stable trap site for He is a uranium vacancy (V U ) while two other theoretical groups predicted that the occupancy of interstitial sites would be more probable [10,13]. In addition, theoretical investigations of the migration behavior of He are lacking and little is known about diffusion properties of He in UO 2 . Most of all, a precise investiga- tion of He bubble nucleation has not been performed for the UO 2 fuel matrix by an ab initio approach so far. The purpose of this study is to investigate in detail the diffusion properties of He and its site stability in UO 2 by carrying out ener- getic calculations based on the density functional theory (DFT). First, we have determined the most stable location of He from the calculated incorporation energy, using generalized gradient approximation (GGA) [14] calculations. We have performed nudged elastic band (NEB) [15,16] calculations, to clarify the site stability from the energy path of He between two trap sites. In or- der to understand the diffusion mechanism of He, the migration energy has been calculated by taking into account spin-polariza- tion (SP), spin-orbit coupling (SOC), and finite temperature effects. Next, we have calculated the lattice expansion coefficient of UO 2 due to interstitial He. We have also investigated the structure and behavior of two He atoms in the UO 2 matrix calculating the to- tal energy of possible configurations of two He atoms and the lat- tice expansion induced by them. Lastly, the clustering behavior of He has been investigated more precisely, by increasing the number of He atoms in the supercell and letting all atomic positions relax 0022-3115/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2008.12.311 * Corresponding author. Tel.: +46 18 471 7308; fax: +46 18 471 3524. E-mail address: younsuk.yun@fysik.uu.se (Y. Yun). Journal of Nuclear Materials 385 (2009) 510–516 Contents lists available at ScienceDirect Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat