Study on the formation of rhenium borides by density functional calculations G. Soto * , M.G. Moreno-Armenta, A. Reyes-Serrato Universidad Nacional Autónoma de México, CNyN, Km 107 carretera Tijuana-Ensenada, Ensenada Baja California, Mexico article info Article history: Received 23 November 2007 Received in revised form 12 March 2008 Accepted 1 May 2008 Available online 26 June 2008 Keywords: Transition metal alloys and compounds Rhenium boride Density functional calculations Computer simulation abstract The searching of hard and superhard materials is a hot topic in material science. Two known factors are fundamental to get high hardness: (1) high valence-electron density; and (2) high number of electron in covalent bonds. The 5d-transition metals comply with requirement (1); so, the task is to fulfill condition (2) without expanding its native structure. Supposedly this is possible by developing interstitial alloys with elements of moderate electronegativity, like boron and/or carbon. This idea materializes in the very hard ReB 2 , which scratches the surface of diamond. This work is a study in the formation of rhenium bor- ides by density functional calculations. Here, we want to reveal the changes that would occur in the hex- agonal close packed lattice of Re as B is inserted into its interstitial sites. We cover compositions in ReB x from x = 0 to x = 3 in x steps of 0.125. B is positioned in octahedral and tetrahedral interstices of Re, and for each arrangements we have calculated cell volume, cohesive energy, bulk modulus, valence electron concentration, and energy density. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction The ab initio methods are a very powerful tool to study new al- loys and compounds [1]. However, often happen that we do not have an identified structure for the compound, then it is required a trial structure to base computations on it. The typical approach to deal with this problem is to propose quite a few atomic arrange- ments, and by their calculated energies infer the most likely struc- ture, as exemplified in Ref. [2]. Clearly, the chances to get correct structures are significant only in straightforward cases – like bin- ary cubic systems – but for complex structures this procedure is impractical. To progress in this direction is crucial to develop pro- cedures to provide seed structures as close as possible to the un- known structure. In this study, we expose an initiative in which the starting structure for rhenium borides is taken from its parent metal. The subsequent structures are derived by successive approximations using the supercell method in which boron was introduced as impurity in interstitial sites. An important effort in material science is directed to find or de- sign new ultra- and super-hard materials to fulfill many technolog- ical necessities [3,4]. The heavy metals, like W, Re, Os, Ir and Pt, are very promising for the reason that they possess a key attribute, that is, a high valence-electron density [5,6]. As a result they have an intrinsic high bulk modulus and are thus highly incompressible [7]. However, due to its omnidirectional metallic bonding they do not resist plastic deformations. In practice the hardness of most metals is certainly enhanced by providing covalent bonds within the lattice. If the number of covalent bonds of heavy metals is in- creased without expanding their native structures it would be likely to reach superhardness values [8]. The above idea is work- able by making interstitial alloys with elements of fair electroneg- ativity, like boron and/or carbon. Recently this premise was tested in rhenium–boron alloys. It was claimed that ReB 2 is superhard be- cause it was able to scratch natural diamond [9]. The structures of most superhard materials are isotropic, and that makes the rhe- nium borides peculiar because they are anisotropic [10]. We will show that the valence electron density and covalency increases from ReB 2 to ReB 3 , but the bulk modulus decreases. The main goal of this work is to present our approach to calcu- late interstitial alloys with variable composition by density func- tional calculations, as we recently did with related alloys [12– 14]. Even if this work is just a test for our procedure, we consider that this approach is innovative and we found interesting results as the compounds between rhenium and boron is produced. 2. Considerations The intention of our work is to develop procedures to find struc- tures of unknown alloys. At this stage of investigation we just want to test a successive approximation approach, and with this aim we selected the rhenium borides as study project. This problem is proper for our intention because the structures of rhenium borides are somewhat intricate. Two identified structures of rhenium bor- ides, ReB 3 and ReB 2 , share a hexagonal configuration of Re atoms [10,11]. They are layered in c-direction by alternating Re and B planes. The main difference between them is the usage of intersti- 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.05.012 * Corresponding author. Address: CCMC-UNAM, P.O. Box 439036, San Ysidro, CA, USA. Tel.: +52 646 1744602; fax: +52 646 1744603. E-mail address: gerardo@cnyn.unam.mx (G. Soto). Computational Materials Science 44 (2008) 628–634 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci