First-principles calculations of (Y, Ti, O) cluster formation in body centred cubic iron-chromium Antoine Claisse ⇑ , Pär Olsson Reactor Physics, KTH, AlbaNova University Centre, 106 91 Stockholm, Sweden article info Article history: Received 13 July 2012 Received in revised form 10 January 2013 Accepted 10 January 2013 Available online 23 January 2013 Keywords: Density functional theory ODS steels Binding energy abstract In the present work, the ab initio parametrization necessary for a Monte Carlo study of the (Y, Ti, O) clus- ters in a FeCr matrix is done. The cohesive, binding and migration energies of all the solutes have been calculated in the dilute limit in the framework of density functional theory. The special case of the strong interaction between an Y atom and a vacancy has been considered. In the dilute limit, Cr is transparent with respect to Y, Ti, O or vacancies. On the contrary, Y binds O strongly in 2NN configuration while not in 1NN. Ti binds O in 1NN and 2NN configurations. A vacancy binds strongly with Y and O in 1NN position which is resulting in a low diffusion coefficient for Y. The peculiar case of the binding attraction between two interstitial oxygen atoms has been studied and is believed to be the main reason for the planar (2D) symmetry of the cluster nuclei. A preferential cluster shape is determined for the early nucleation stage, up to 12 atoms. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction The limitation of nuclear fuel resources and the issue of manag- ing the long lived waste from light water reactors demands new technologies to be used. The GEN IV fission reactors and the poten- tial future fusion reactors are considered in that perspective. These operate at high temperatures and yield high fluxes of high energy neutrons. Under these conditions, materials undergo swelling, thermal creep and a ductile to brittle transition temperature (DBTT) shift [1]. To overcome the limitations of the austenitic and ferritic–martensitic steels, a new class of materials has been developed: the Oxide Dispersion Strengthened (ODS) steels. These new materials meet with reasonably good success on these three main issues; the DBTT and the swelling decrease, and the thermal creep resistance increases [2–6]. It can be explained by the ultra high density of oxide nanoclusters in the ODS steels [7] that ensure trapping of helium atoms in small bubbles and prevent disloca- tions from moving. However, the formation and behaviour of these clusters is not yet well understood. The (Y, Ti, O) clusters have been observed in a near stoichiom- etric form, such as Y 2 TiO 5 or Y 2 Ti 2 O 7 or in the simpler oxide form Y 2 TiO 3 [2]. It is reasonable to assume that the smallest of these clusters is the stem for the other ones and should therefore be studied and understood. In addition to the experimental work showing that titanium- free Y 2 O 3 clusters do not seem to exist in Ti containing steels [8] and that titanium reduces the size of the clusters and confirming the existence of Y 2 Ti 2 O 7 or Y 2 TiO 5 [9,10], it is necessary to create a model that can reproduce the observed behaviours. Previous ab initio studies have provided data of the cohesive energies of the self interstitial atoms (SIA) [11–13], of the solution energy of oxy- gen, yttrium and titanium [13,14] and their binding energies with a vacancy [14]. Jiang et al. have also calculated the binding energy between Y, Ti and O in interstitial and substitutional positions up to the second nearest neighbour. The formation of the clusters has been considered as impossible without a vacancy to stabilize them [15] but the contrary has been stated in a later work, showing that they could be formed in a vacancy-free lattice [13]. The possi- bility that the clusters could have an incoherent structure even at an early stage of the nucleation has also been investigated [16]. Also using density functional theory and the nudged elastic band method, the diffusion coefficients of Fe, Y, Ti and Zr by the vacancy mechanism using the nine frequencies model of Le Claire [17] have been calculated [18]. The limited scope of these studies warrants further efforts in the subject area. Considering that all candidate ODS steels contain large amounts of Cr, it is necessary to include this element in the calculations in a more extensive way than previous authors have [14,13,15]. Increasing the interaction range considered in the study up to the fifth nearest neighbour (one diagonal of the primary body-centred cubic (bcc) cell) is also of prime importance, as the interaction between a SIA and an oxygen atom will be shown not to be negligible at these distances, and the Cr–Cr interaction is also long-ranged [19,20]. The reference cases useful to calculate the binding energy of different configurations are firstly presented in this study. The 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2013.01.016 ⇑ Corresponding author. E-mail address: claisse@kth.se (A. Claisse). Nuclear Instruments and Methods in Physics Research B 303 (2013) 18–22 Contents lists available at SciVerse ScienceDirect Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb