Pergamon PII: SOO22-3697(97)00211-4 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP J. Phw . Chem Sohds Vol 59. No. 5, pp. 743-146. I998 0 I998 Elsevier Science zyxwvutsrqp Ltd Printed in Great Britain. All rights reserved 0022-3697i98 $19.00 + 0.00 ELECTRONIC STRUCTURE OF /3-Be3Nz A. REYES-SERRATOa, G. SOTOa, A. GAMIETEAb and M. H. FARiASb “Institute de Fisica, Universidad National Aut6noma de Mexico Posgrado en Fisica de Materiales, CICESE Apartado Postal 2681, Ensenada, Baja California, 22800 Mexico bInstituto de Fisica, Universidad National Autonoma de Mexico Postal 2681. Ensenada, Baja California, 22800 Mexico (Received 11 July 1991; accepted 22 August 1997) zyxwvutsrqponmlkjihgfedcbaZYXWVU Abstract-Ab inirio all electron Hat-tree-Fock periodical calculations were performed on the hexagonal phase of Be,N*. The electronic structure was studied and the structural parameters were determined. By performing total energy calculations, equilibrium lattice parameters, bulk modulus and its derivative, and cohesion energy were determined. The lattice parameters obtained, a = 2.847 A and c = 9.714 A, differ by less than 1% from the corresponding experimental values. The calculated bulk modulus, 2.61 Mbar, locates this compound among the hard materials. Based on the band structure and density of states obtained, the hexagonal Be3N2 is a wide band gap semiconductor with an indirect gap of 12SOeV. The charge density difference along the Be-N bonds indicates that the character of the bond is more covalent than ionic. 0 1998 Elsevier Science Ltd. All rights reserved. Keywords: A. inorganic compounds, C. ab initio calculations, D. electronic structure 1. INTRODUCTION There is a great deal of interest in developing new materials with high yield structural, optical and electro- nical applications. Lately, a special effort has been directed towards ceramic materials that could be obtained from the second period elements of the periodic table, which can be bound with strong chemical bonds, and then give hard materials with tribological appli- cations [ 11. Very often, these materials present wide band gaps, with interesting dielectric properties or possible electro- optical applications. In particular, in this last field, it is desirable to have a refractory material with wide band gap and high thermal conductivity in order to produce high power UV solid state devices. Among the known materials, only the AlN wurtzite structure, with a 6.2 eV gap, has a direct gap in this energy interval [2]. On the other hand, a feasible compound of this type is the one suggested by Lambrecht and Segall [2], BeCN*, with possibly chalcopyrite structure and an almost direct estimated gap of 5.7 eV. However, this compound has not been synthetized so far [3]. Also, although Lee et al. [4] suggest Be&Zas a starting material for the synthesis of BeCN?, they indicate as possible problems the tendency of Be& to hydrolyse to Be(OH)2 and to react with 0 and N. Another possible compound that could be used as a starting point for the synthesis of the above-mentioned material is beryllium nitride (BesN& on whose proper- ties there is not much information, and even less on its electronic characteristics. Nevertheless, reliable crystal- lographic studies on Be3N2 have been performed 151 and it is known that thin films of this material can be formed on beryllium [6]. There are two crystallographic structures of beryllium nitride [7], o-Be3N2, cubic with 40 atoms per cell, and hexagonal with 10 atoms per cell, fl-Be3N2. The last structure is obtained by heating up the cubic phase at 1400°C. In Fig. 1 the cell of fi-BesNr is shown. In this theoretical work we study the structural and electronic properties of &BeJNZ phase and report its hardness and band gap as obtained by the ab initio all electron Hartree-Fock method. To our best knowledge, this is the first ab initio theoretical work on this compound. 2. CALCULATIONMETHOD The study was performed by means of the ab initio all electron Hartree-Fock method, with a lineal combination of atomic orbitals (HF-LCAO), modified for periodic systems and implemented in the CRYSTAL-92 [8] program. A detailed description of this program is in 191. The base set utilized for all calculations is named 3-21G and was obtained from Tables 4.35.1 and 7.74.1 of [lo] for Be and N. respectively. Besides, for total energy calculations only, the base set 6.21G* from Tables 4.39.1 and 7.77.1 of the same reference was utilized. In order to make the base set more adequate for crystal calcu- lations [9], the last exponent of each base set was reoptimized calculating the total energy cell as a function of variations of the exponents, using the experi- mental lattice parameters. For the 3-21G base, the 743