PHYSICAL REVIEW B 83, 094119 (2011) Energy landscape of small clusters of self-interstitial dumbbells in iron M.-C. Marinica, 1 F. Willaime, 1 and N. Mousseau 2 1 CEA, DEN, Service de Recherches de M´ etallurgie Physique, F-91191 Gif-sur-Yvette, France 2 D´ epartement de Physique and Regroupement Qu´ eb´ ecois Sur les Mat´ eriaux de Pointe, Universit´ e de Montr´ eal, Case Postale 6128, Succursale Centre-ville, Montr´ eal, Qu´ ebec H3C 3J7, Canada (Received 2 September 2010; revised manuscript received 15 January 2011; published 17 March 2011) The activation-relaxation technique nouveau (ARTn), a method for the systematic search of the minima and saddle-point conﬁgurations, is applied to the study of interstitial-cluster defects in iron. Some simple modiﬁcations to improve the efﬁciency of the ARTn method for these types of applications are proposed. The energy landscapes at 0 K of defect clusters with up to four self-interstitial atoms obtained using the Ackland-Mendelev potential for iron are presented. The efﬁciency of the method is demonstrated in the case of monointerstitials. The number of different bound conﬁgurations increases very rapidly with cluster size from di- to quadri-interstitials. All these clusters can be analyzed as assemblies of dumbbells mostly with 〈110〉 orientation. The lowest-energy conﬁgurations found with the present method and potential are made of parallel dumbbells. The mechanisms associated with the lowest saddle-point energies are analyzed. They include local rearrangements that do not contribute to long-range diffusion. The translation-rotation mechanism is conﬁrmed for the migration of mono- and di-interstitials. For the tri-interstitial the migration is dominated by three mechanisms that do not involve the lowest-energy conﬁguration. The migration of quadri-interstitials occurs by an on-site reorientation of the dumbbells in the 〈111〉 direction, followed by the conventional easy glide. Finally, the minimum energy paths are investigated for the transformation toward the lowest-energy conﬁguration of two speciﬁc clusters, including a quadri-interstitial cluster with a ring conﬁguration, which was shown to exhibit an unexpected low mobility in previous molecular-dynamics simulations. DOI: 10.1103/PhysRevB.83.094119 PACS number(s): 68.43.Fg, 68.43.Hn, 68.43.Jk I. INTRODUCTION The evolution of defects in materials is governed by events that range from nearly athermal to highly infrequent, i.e., with activation energies from meV to eV. 1 The atomistic simulation of such processes becomes even more challenging for irradiated materials owing to the increased diversity of lattice defects. In the past few years substantial efforts have been made to improve the efﬁciency in the simulation of such thermally activated events. Several ﬁnite-temperature methods have been proposed in the framework of molecular dynamics (MD): hyperdynamics, 2 parallel replica dynamics, 3 temperature accelerated dynamics, 4 action-derived molecu- lar dynamics, 5,6 or properly obeying probability activation- relaxation technique (ART). 7 These methods, which provide recipes to accelerate the activated transition between local minima of the system at ﬁnite temperature, have proven to be very useful in radiation damage studies. 8–11 Other followed approaches are based on the reduction, at 0 K, of the energy landscape to the local minima conﬁgurations and the ﬁrst-order saddle points that link them. This information is sufﬁcient, away from melting, to fully determine the system’s thermodynamics and kinetics using transition-state theory within, for example, the quasiharmonic approximation. Algorithms for ﬁnding saddle points at 0 K can be divided into two classes: (i) the ones based on an interpolation between two known minima and (ii) those using only local information around a given minimum. In the ﬁrst class, an initial diffusion pathway is ﬁrst constructed and then optimized thanks to algorithms such as the nudged elastic band (NEB) method. 12,13 A review of such methods can be found in Refs. 14 and 15. Algorithms for the second class are more complex because they combine uphill climbs to escape from the minimum and relax- ations in the perpendicular direction to ﬁnd valleys bringing to saddle points. The saddle point is generally found by following the eigenvector corresponding to the lowest eigenvalue of the Hessian. The efﬁciency of the initial algorithms 15–18 has been recently improved mainly by replacing the calculation of the full Hessian matrix and its spectrum—which is a prohibitive task for large systems—by that of only the lowest eigenvalue and corresponding eigenvector. This includes the ART 19 or ART nouveau (ARTn), 20–22 and the dimer 18,23 and the hybrid eigenvector-following methods. 15,24 Interstitial-type defects formed by the clustering of self- interstitials produced under irradiation have rather peculiar properties in α-iron in comparison with other bcc metals, where all interstitial-type defects are predominantly 〈111〉. In α-iron, isolated self-interstitial atoms (SIAs) have a rather large migration energy, ∼0.3 eV, 25 instead of tens of meV in other bcc metals. Density-functional theory (DFT) calculations 26–28 show that in bcc Fe, the 〈110〉 dumbbell conﬁguration is adopted while in all the other bcc transition metals the 〈111〉 crowdion conﬁguration has the lowest formation energy. 29 Nanometer size clusters—or dislocation loops—have either 〈111〉 or 〈100〉 orientation in Fe. 30–32 The structure of interstitial clusters with an intermediate size is largely unknown, although they play a key role in the loop growth mechanism. 31,33,34 The 〈111〉 loops can glide very easily, as observed in MD simulations, 33–35 with an activation energy lower than 0.1 eV, whereas the 〈100〉 loops are very weakly mobile, with an estimated activation energy larger than 2.5 eV. 33 The competition between these various orientations raises the question of their relative stabilities as functions of cluster size and temperature. Dudarev et al. indeed 094119-1 1098-0121/2011/83(9)/094119(14) ©2011 American Physical Society