Author's personal copy Structural, elastic, electronic and dynamical properties of OsB and ReB: Density functional calculations Yanling Li a,b,c, * , Zhi Zeng b , Haiqing Lin c a Department of Physics, Xuzhou Normal University, Xuzhou 221116, People’s Republic of China b Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China c Department of Physics and Institute of Theoretical Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China article info Article history: Received 23 February 2010 In final form 28 April 2010 Available online 4 May 2010 abstract The structural, elastic, electronic and dynamical properties of ReB and OsB are investigated by first-prin- ciples calculations based on density functional theory. It turns out that ReB and OsB are metallic ultra- incompressible solids with small elastic anisotropy and high hardness. The change of c/a ratio in OsB indi- cates that there is a structural phase transition at about 31 GPa. Phonon spectra calculations show that both OsB and ReB are stable dynamically and there are abnormal phonon dispersions along special direc- tions in Brillouin zone. OsB and ReB do not show superconductivity due to very weak electron–phonon interactions in them. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Recently, the investigation of superhard materials has attracted much interest due to their importance in science, technology, and industrial applications [1–9]. The search for novel and robust superhard materials is of great value to the material science com- munity. Superhard materials often favor short covalent bond or high densities of valence electrons [2]. The former resists plastic or elastic deformation, while the latter resists squeezing. At pres- ent, two groups of materials are believed to be possible superhard candidates. One kind of superhard materials is the strong covalent- bonded solids, such as diamond, c-BN, C 3 N 4 [5], BC 2 N [6],B 6 O [7], and BC 5 [8]. Considering that diamond is not an effective tool for cutting steel and other ferrous metals because of a chemical reac- tion producing iron carbide, the other kind of superhard materials, large, electron-rich transition metal (TM) boride, carbide, and ni- tride, such as OsB 2 [1], ReB 2 [3], WC, OsN 2 , IrN 2 [4], and PtN 2 [9], is suggested [1,2]. Applying this idea, many experimental [3,10– 16] and theoretical [17–32] works are performed to explore the possibility of some TM borides [3,10–25], carbides [26–29], and ni- trides [30–32] as superhard materials. Most recently, Gu et al. syn- thesized some transition metal borides [16] and studied their hardness and incompressibility. They pointed out that OsB pos- sesses strong incompressibility. Gou et al. [17] and Liang et al. [33] studied mechanical property of OsB by first-principles calcula- tions. However, to the best of our knowledge, though the phonon spectra are vital to identify the structural stability, dynamical property for OsB has not been reported so far.We also noticed that, as a neighbor of Os, study for monoboride of Re is scarce. Here, structural, elastic, electronic, and dynamical properties of ReB and OsB are investigated based on first-principles calculations. Firstly, the most stable structure at zero pressure is determined and its incompressibility is discussed. Then, elastic constants are calculated and elastic anisotropy is analyzed. Further, we discuss the correlation between elastic property and electronic property. Fourthly, we calculate phonon spectra and electron–phonon cou- pling parameters of ReB and OsB. Lastly, considering that some ul- tra-incompressible hard materials are found to be superconductors [32], the possibility of superconductivity in ReB and OsB was dis- cussed based on McMillan equation [34]. 2. Computational details Structural, elastic, and electronic properties are calculated by using first-principles plane-wave basis pseudopotential method (PW-PP) based on density-functional theory (DFT) as implemented in CASTEP code [35]. For the exchange correlation energy func- tional, the Perdew–Burke–Ernzerhof parametrization in the gener- alized gradient approximation (GGA) is employed. In the calculation, the interaction between the ions and the electrons is described by using Vanderbilt’s ultrasoft pseudopotential with the cut-off energy of 400 eV. The structural optimization is per- formed by BFGS minimizer [36], which can perform cell optimiza- tion, including optimization at fixed external stress. The BFGS scheme uses a starting Hessian which is recursively updated dur- ing optimization. The CASTEP implementation involves a Hessian in the mixed space of internal and cell degrees of freedom, so that both lattice parameters and atomic coordinates can be optimized. 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.04.074 * Corresponding author. Address: Department of Physics, Xuzhou Normal Uni- versity, Xuzhou 221116, People’s Republic of China. Fax: +86 551 5591434. E-mail address: ylli@theory.issp.ac.cn (Y. Li). Chemical Physics Letters 492 (2010) 246–250 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett