Theoretical investigations of the elastic constants in Laves phases

Abstract

The bulk modulus B and the tetragonal shear modulus C′ of the C15 Laves phases AAl2, A = Ca, Sc, Y, La and Gd and ZrB2, B = V, Cr, Fe, Co, Zn and Mo; the C14 Laves phases ZrMn2, ZrAl2, ZrCr2, TiCr2, NbCr2 and TaFe2 and the metals forming these Laves phases are studied theoretically by ab-initio density functional band structure calculations. Additionally, the Poisson ratios, the Young moduli, for cubic systems C11 and C12 and for the hexagonal phases C11 + C12, C13 and C33 are calculated and compared with the experimental data. We also compare the results of B obtained from the augmented spherical wave method using the local density and atomic sphere approximations and the full potential linear muf-fin-tin orbitals procedure with and without the generalized gradient correction for the crystal potential. All procedures give the right trend in B and the differences between experiment and theory are less than 15% for systems without a transition element and up to 25% for systems with a transition metal component. The correlation between B and the electron density ϱI in the interstitial region of the crystal found by Moruzzi et al. for metals can be extended to B for the Laves phases and allows rules of mixture for B. For C′ and the other elastic constants, the agreement between experiment and theory is similar for the non-transition metals but less satisfactory for the transition metals and the Laves phases with a transition metal component.