First-principles calculations of the structural, mechanical, electronic and bonding properties of (CrB 2 ) n CrAl with n ¼ 1, 2, 3 Xiaohong Li a, b, d, * , Maurício Chagas da Silva b , Dennis R. Salahub b, c a College of Physics and Engineering, Henan University of Science and Technology, Luoyang, 471023, China b Department of Chemistry and Center for Molecular Simulation, University of Calgary, Calgary, Alberta, T2N1N4, Canada c Department of Chemistry, Henan University of Technology, Zhengzhou, 450001, China d Department of Chemistry, Nanjing University of Science and Technology, Nanjing, 210094, China article info Article history: Received 1 November 2016 Received in revised form 14 December 2016 Accepted 16 December 2016 Available online 18 December 2016 Keywords: Electronic structure Mechanical properties Band crossing (CrB 2 ) n CrAl First-principles calculations abstract The crystal structure, the electronic structure and the mechanical properties were investigated for (CrB 2 ) n CrAl with n ¼ 1, 2, 3 by using the all-electron projector augmented wave method with the Perdew-Burke Ernzerhof functional. The calculated bulk moduli for Cr 2 AlB 2 , Cr 3 AlB 4 and Cr 4 AlB 6 were 202, 222 and 234 GPa, respectively, and the Young moduli were estimated to be 397, 412 and 434 GPa, respectively. All three materials were identified as stiff and hard materials; however, the density of states and the projected density of states analysis predicted a metallic behavior for all investigated materials. The partially filled d-orbitals of Cr atoms have an important role in attributing metallic behavior to these materials. The hardness of these materials was related to the presence of quite strong BeB covalent bonds and the metallic characteristic arises from CreCr interactions. The chemical interpretation of the physical properties was made with the electron localization function and the investigation of the to- pology of the electron densities was provided, based on the quantum theory of atoms in molecules. Surface properties were explored for slab models, arbitrarily chosen to be along the a-axis. The metallic behavior of the compounds (CrB 2 ) n CrAl continues in the surface model. Using the electron localization function and Bader's charge analysis, a small increase of the number of electronic carriers was observed, due to the localization of some AleAl bonds in the slab models. © 2016 Elsevier B.V. All rights reserved. 1. Introduction The borides are a very large group of high-melting-temperature compounds and some of them are among the hardest and most heat-resistant materials reported as well. In recent years, many transition-metal boron (TM-B) compounds have been synthesized successfully such as OsB 2 [1], RuB 2 [2], ReB 2 [2e4], WB 4 [5,6], CrB 4 [7], and FeB 4 [8]. These TM-B compounds have attracted much attention because they are promising ceramic materials with interesting magnetic properties [9,10]. Recently, another layered family called “MAX-phase” with the general formula M nþ1 AX n (or (MX) n MA, where M is a transition metal, X is often C or N, n ¼ 1, 2, or 3) has been investigated intensively. These compounds are found to have a unique combination of metallic and ceramic properties, which may be explained by the layered structure consisting of a hard carbide or nitride part (MX) n with variable thickness and a ductile intermetallic part MA [11]. The M and X atoms form strong directional covalent bonds in the M-X layers. They not only have metallic properties, such as high electrical and thermal conduc- tivity, easy machinability, but they also have properties which are similar to ceramics, such as thermal stability, damage tolerance, reversible plasticity, toughness, etc. [12]. Generally, the macroscopic properties of a compound are related to their electronic structures and structural properties of the compound. Nanolaminated-layered MAX-phase compounds have a hexagonal structure with nearly close-packed layers of the M-elements interleaved with square-planar slabs of pure A-ele- ments which are located at the center of a trigonal prism, where the X-atoms fill the octahedral sites between the M-atoms [13]. Villars et al. [14] and Rogl [15] have shown that the structures of borides are based on trigonal prisms. In 1951, Bertaut et al. [16] determined the structure of CrB to be parallel and congruent. Then the com- bination of the polygons beyond hexagons appears such as YCrB 4 * Corresponding author. College of Physics and Engineering, Henan University of Science and Technology, Luoyang, 471023, China. E-mail address: lorna639@126.com (X. Li). Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom http://dx.doi.org/10.1016/j.jallcom.2016.12.219 0925-8388/© 2016 Elsevier B.V. All rights reserved. Journal of Alloys and Compounds 698 (2017) 291e303