First-principles investigation of the ternary scandium based inverse-perovskite carbides Sc 3 AC(A ¼ Al, Ga, In and Tl) K. Haddadi a , A. Bouhemadou a, * , F. Zerarga a , S. Bin-Omran b a Laboratory for Developing New Materials and their Characterization, Department of Physics, Faculty of Science, University of Setif, 19000 Setif, Algeria b Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia article info Article history: Received 12 August 2011 Received in revised form 21 April 2012 Accepted 23 April 2012 Available online 30 April 2012 Keywords: Inverse-perovskite Ab initio calculations Elastic properties Electronic structure Thermal and pressure effects abstract Based on first-principles approach, we present a comparative study of structural, electronic, elastic and thermo-dynamical properties of the series of inverse-perovskites Sc 3 AC, with A ¼ Al, Ga, In and Tl. The calculated equilibrium lattice constants are in excellent agreement with the experimental and available theoretical data. The electronic band structures and densities of states profiles show that the studied compounds are conductors. Analysis of atomic site projected local density of states and charge densities reveals that a mixture of covalenteionicemetallic characterizes the chemical bonding of the considered inverse-perovskites. Pressure dependence up to 40 GPa of the single-crystal and polycrystalline elastic constants has been investigated in details. The computed B/G ratios show that all Sc 3 AC compounds are brittle. We have estimated the sound velocities in the principal directions. Through the quasi-harmonic Debye model, in which the phononic effects are taken into account, the temperature and pressure effects on the lattice constant, bulk modulus, heat capacity and Debye temperature are performed. Ó 2012 Elsevier Masson SAS. All rights reserved. 1. Introduction Inverse-perovskite type crystals with M 3 AX composition (where M are s-d metals, A are divalent or trivalent elements and X are nitrogen or carbon atoms) are of scientific interest due to their versatile physical/chemical properties such as a giant magnetore- sistance [1], nearly zero temperature coefficient of resistivity [2] and depending on their chemical composition, can also display a wide variety of physical properties ranging from semiconducting to magnetic and superconducting properties [3e8]. The discovery of superconductivity in the inverse-perovskite Ni 3 MgC compound [9] has generated interest in the inverse-perovskite family. Recently, new Sc-based cubic inverse-perovskite nitrides (CIPNs) compounds have been reported. Kirchner and collaborators [10] reported on the preparation, crystal structure and some physical properties of the inverse-perovskite Sc 3 InN. Höglund and co-workers [11] synthesized for the first time Sc 3 AlN with the inverse-perovskite structure. Mattesini et al. [14] predicted Sc 3 GaN with the inverse-perovskite structure by means of ab initio calcu- lations. These new reports have generated interest in the Sc-based CIPNs compounds in order to take advantages of their properties for eventual technological applications. Electronic properties and structural stability of the ternary inverse-perovskites Sc 3 BN, Sc 3 AlN, Sc 3 GaN and Sc 3 InN have been thoroughly investigated using ab initio calculations [11e 14]. Contrarily to the Sc-based cubic inverse-perovskite nitrides compounds, the Sc-based cubic inverse-perovskite carbides (CIPCs) present an unexplored family of inverse-perovskites. Experimen- tally, Gesing and his collaborators [15] reported the synthesis of Sc- based CIPCs systems. From the theoretical side, only the Sc 3 AlC compound has been investigated, to the best of our knowledge. Electronic properties of Sc 3 AlC have been explored by Shein and Ivanovskii [16] using a first-principles method. Recently, Medkour et al. [17] reported a theoretical study on the structural, electronic and elastic properties of this compound at zero pressure. Therefore, from the above one can remark that some physical properties of the Sc-based CIPCs systems are not yet explored. The aim of the present paper is to study the structural, elec- tronic, chemical bonding, elastic and thermodynamic properties of Sc 3 AlC, Sc 3 GaC, Sc 3 InC and Sc 3 TlC using pseudo-potential plane- wave method based on the density functional theory. The rest of the paper has been divided in three parts. In Section 2, we briefly describe the computational techniques used in this study. The most relevant results obtained for the structural, elastic, electronic, chemical bonding and thermodynamic properties of the Sc 3 AC compounds are presented and discussed in Section 3. Finally, in Section 4 we summarize the main conclusions of our work. * Corresponding author. Tel.: þ213 365128; fax: þ213 36925101. E-mail address: a_bouhemadou@yahoo.r (A. Bouhemadou). Contents lists available at SciVerse ScienceDirect Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie 1293-2558/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2012.04.028 Solid State Sciences 14 (2012) 1175e1185