Thermal properties of BeX (X = S, Se and Te) compounds from ab initio quasi-harmonic method S. Laref a,b,⇑ , A. Laref b a Université de Lyon, Institut de Chimie de Lyon, Laboratoire de Chimie, Ecole Normale Supérieure de Lyon and CNRS, 46 Allée d’Italie, F-69364 Lyon Cedex 07, France b Physics Department, Science Faculty, University of Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria article info Article history: Received 14 October 2010 Received in revised form 7 July 2011 Accepted 8 July 2011 Available online 28 August 2011 Keywords: Beryllium chalcogenides QHA Thermal and mechanical properties ab initio calculations abstract We report ab initio calculations of the structure, elastic constants, lattice dynamics and thermodynamic properties of BeS, BeSe and BeTe compounds. The fully minimized structure parameters and elastic con- stants of BeS, BeSe and BeTe compounds are in good agreement with previous theoretical and experimen- tal data. The density functional perturbations theory with quasi-harmonic approximation QHA methods are applied to determine the phonon dispersion relations, phonon density of states, phonon decomposi- tion density of states, and thermal quantities. The computed thermodynamic properties such as Debye temperature is in agreement with the previous work. The vibrational entropy and constant-volume spe- cific heat are shown for the first time. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction The new class of beryllium chalcogenides (BeS, BeSe and BeTe) belonging to group II–VI compound semiconductor family, and crystallizing in the four-fold coordinated zinc-blende structure. These compounds have received a considerable attention by exper- imentalist and theoretician in the 20 recent years [1–5]. A charac- teristic aspect of this materials is that the mass and ionic radius of Be atom in beryllium compounds is smallest among the cations (Mg, Zn, Cd and Hg) and anions (S, Se, and Te) of the IIa–VI compounds. Unlike other IIa–VI compounds which are partially io- nic-Be-chalcogenides exhibit a high degree of covalent bonding comparable to III–V compounds [5–8]. As a result, Be-chalcoge- nides have much higher bonding energy, hardness, and thus exhi- bit unusual electronic, elastic, and vibrational properties. These unique properties make them potentially useful for various tech- nological applications including laser diodes, high efficiency p-i-n photo-detectors. These materials are particularly important be- cause they can be grown lattice matched to Si-leading to the pos- sibility of realizing novel low dimensional (quantum-well and superlattices) device [5,8]. The incorporation of transition metal ions of the iron group into II–VIs compounds has also resulted in dilute magnetic (e.g., Be x Mn 1x Te) semiconductors commonly used in spintronics applications [9]. At present paper, we would like to use an ab initio and quasi- harmonic approximations to study a dynamic and thermal proper- ties. We apply a plane-wave pseudopotential method based on density functional theory (DFT), within the local density approxi- mation (LDA) [10], using the QUANTUMESPRESSO package [11]. Our interest is to take a look for common trends for differences in the vibrational and thermal properties on this class of semicon- ductors. We will present a comparative study of the fundamental lattice parameter, elastic constants and vibrational decomposition of the atom-projected density of states (PDOS). Furthermore, the thermal quantities for BeS, BeSe and BeTe will be presented with prediction, among those results as well as there are no experimen- tal data. This paper is structured as follow. The methods used on these efforts are described in Section 2. In Section 3, we present our results. Section 4 is concerning the conclusion. 2. Computational details The ab initio calculations were performed using QUANTUMES- PRESSO [11]. This program package has a basis set of a plane-wave pseudopotential PWPP method. For the exchange-correlation en- ergy of the electrons parts we used ultrasoft Vanderbilt [12] for- malism to a local density approximation LDA [10]. The basis set for many-body interaction were described by Ceperley–Alder func- tional [13] parameterized by Perdew and Zunger [14]. The total- energy calculations were integrated over the Brillouin zone, by using a 4  4  4 Monkhorst–Pack method [15]. This gives 10 sym- metrised k-points in the irreducible Brillouin zone. The pseudo- wave functions were expanded in a plane-wave basis set with an 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.07.016 ⇑ Corresponding author at: Université de Lyon, Institut de Chimie de Lyon, Laboratoire de Chimie, Ecole Normale Supérieure de Lyon and CNRS, 46 Allée d’Italie, F-69364 Lyon Cedex 07, France. E-mail address: laref_s@yahoo.fr (S. Laref). Computational Materials Science 51 (2012) 135–140 Contents lists available at SciVerse ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci