Eur. Phys. J. B 56, 209-215 (2007)
https://doi.org/10.1140/epjb/e2007-00115-6

Structural and elastic properties of Zr₂AlX and Ti₂AlX (X = C and N) under pressure effect

¹ Department of Physics, Faculty of Science, University of Setif, 19000 Setif, Algeria
² Laboratoire de Physique Quantique et de Modélisation Mathématique (LPQ3M), Département de Technologie, Université de Mascara, 29000 Mascara, Algeria

Corresponding author: ^a a_bouhemadou@yahoo.fr

Received: 6 December 2006
Revised: 2 April 2007
Published online: 4 May 2007

Abstract

Using first-principles density functional calculations, the effect of high pressures, up to 20 GPa, on the structural and elastic properties of Zr₂AlX and Ti₂AlX, with X = C and N, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation to the exchange-correlation approximation energy. The lattice constants and the internal parameters are in agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline Zr₂AlX and Ti₂AlX aggregates. We estimated the Debye temperature of Zr₂AlX and Ti₂AlX from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Zr₂AlC, Zr₂AlN and Ti₂AlN compounds, and it still awaits experimental confirmation.