Structural and elastic properties of Zr<Subscript>2</Subscript>AlX and Ti<Subscript>2</Subscript>AlX (X=C and N) under pressure effect

Using first-principles density functional calculations, the effect of high pressures, up to 20 GPa, on the structural and elastic properties of Zr<Subscript>2</Subscript>AlX and Ti<Subscript>2</Subscript>AlX, 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 Zr<Subscript>2</Subscript>AlX and Ti<Subscript>2</Subscript>AlX aggregates. We estimated the Debye temperature of Zr<Subscript>2</Subscript>AlX and Ti<Subscript>2</Subscript>AlX from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Zr<Subscript>2</Subscript>AlC, Zr<Subscript>2</Subscript>AlN and Ti<Subscript>2</Subscript>AlN compounds, and it still awaits experimental confirmation. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007