Stability of helium bubbles in alpha-iron: A molecular dynamics study G. Lucas * , R. Schäublin Ecole Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherche en Physique des Plasmas, Association Euratom-Confédération Suisse, CH 5332 Villigen PSI, Switzerland article info PACS: 61.80.Az 61.72.Ày 61.72.Qq abstract Molecular dynamics simulations were performed to estimate the dissociation energies of helium intersti- tials, vacancies and self-interstitial atoms from small helium–vacancy clusters. Several sets of empirical potentials have been tested and compared with available ab initio calculations in order to provide the best combination of potentials to study the stability of small helium bubbles. The behavior of the cluster seems to be better described using Ackland potential for the Fe–Fe interactions and Juslin potential for the Fe–He interactions. From the calculations, it appears that the dissociation energies mainly depend on the helium-to-vacancy ratio rather than the cluster size. The helium/vacancy crossover slightly varies with increasing number of vacancies, but the crossover defining the loop-punching regime decreases strongly with increasing cluster sizes. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Ferritic steels are possible structural materials for future fusion reactors. During the operation of these reactors, materials are sub- jected to 14 MeV neutron irradiation, generating helium by trans- mutation reactions and simultaneously energetic displacement damage. High helium concentrations are known to induce the for- mation of He bubbles and consequently enhance void swelling. He- lium may also lead to the modification of microstructural and mechanical properties such as high temperature embrittlement, surface roughening and blistering [1]. These deteriorations may re- sult from the insolubility of He, which therefore tends to precipi- tate into vacancies, voids or grain boundaries. Small He n V m clusters may play an important role in the nucle- ation of He bubbles. However the atomistic properties of He in metal are difficult to identify experimentally. Thus atomistic simulations such as molecular dynamics provide useful tools to study the formation and the stability of these clusters and their im- pact on moving dislocations, vector of plasticity [2]. Here we present the results of an empirical molecular dynamics study on the formation of small helium–vacancy clusters in bcc iron, which will provide insight into the growth of the bubble in materials. 2. Computational method The modified molecular dynamics code MOLDY [3] has been used to study the formation of small helium–vacancy clusters. The calculations were carried out on a cluster of Apple Mac OS X computers with dual G5 2.0 or 2.5 Ghz processors. The formation energies of the helium–vacancy clusters He n V m are evaluated using different empirical potentials. To describe Fe–Fe interactions, the potentials developed by Ackland et al. [4] or Dudarev et al. [5] are employed. The He–He interactions are de- scribed using the Beck potential [6]. And finally two different potentials have been used the Fe–He interaction, namely the Wil- son–Johnson potential [7] and the newly developed Juslin potential [8]. The latter potential is a purely repulsive pair potential, which has been specifically designed to reproduced formation and migra- tion energies of small helium–vacancy clusters in iron obtained by ab initio calculations. Here, the formation energies are defined as the difference in total energy between a crystal containing a defect and a perfect crystal of the same number of iron atoms with the corresponding number of helium atoms in a fcc structure. In the present calculations, the box size was set to 10a 0 Â 10a 0 Â 10a 0 , where a 0 is the lattice parameter. For all calculations periodic boundary conditions and constant volume were used. The clusters have been generated with the following procedure. Starting from a single vacancy, the iron atom with the highest potential energy is removed from the system. The formation energy of the divacancy is then calculated. By iterating this scheme, the size of the void V m is successively increased up to m equal 15. For each void size, n helium atoms are introduced randomly up to a helium-to-va- cancy ratio equal to 5. The system is subsequently relaxed using a gradient conjugate algorithm. For each ratio several initial random configurations are tested and the one with the lowest for- mation energy is kept. From the formation energies of the helium– vacancy clusters, the vacancy, helium and self-interstitial iron atom (SIA) binding energies have been calculated as previously 0022-3115/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2008.12.128 * Corresponding author. Tel.: +41 76 310 29 41. E-mail address: guillaume.lucas@psi.ch (G. Lucas). Journal of Nuclear Materials 386–388 (2009) 360–362 Contents lists available at ScienceDirect Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat