Elastic moduli of the C15 Laves-phase materials TaV₂, TaV₂H(D)_x and ZrCr₂

Abstract

The elastic moduli of the C15 Laves-phase materials TaV₂, TaV₂H(D),_x and ZrCr₂ have been measured using the technique of resonant ultrasound spectroscopy. The temperature dependences of the shear modulus and Young's modulus of TaV₂ were found to be anomalous; the moduli increase with increasing temperature over the entire temperature range 4-345 K. In contrast, the shear modulus and Young's modulus of TaV₂H_0.34, TaV₂H_0.53 and TaV₂D_{0 17} all decrease with increasing temperature. The bulk moduli of these materials are only weakly temperature dependent. The elastic moduli of the C15 Laves-phase compound ZrCr₂ exhibit a normal temperature dependence over the range 20-300 K. The unusual elastic behaviour of these materials is accounted for by a model involving electronic contributions to the elastic constant c₄₄. The symmetry of the C15 structure results in doubly degenerate electronic energy levels at the X point of the Brillouin zone. The strain dependence of these levels affects the elastic constant c₄₄, which in turn contributes to the measured moduli of the polycrystalline samples. The predictions of the model depend critically on the distance of the Fermi level from the double-degeneracy point. The experimental results for TaV₂, are qualitatively accounted for if the Fermi level passes very near this special point. It is suggested that the extra electrons contributed by H(D) raise the Fermi level in TaV₂H(D)_x and result in a more normal temperature dependence of the elastic moduli over the observed temperature range. Similarly, C15 ZrCr₂ with its extra electron per formula unit may have a higher Fermi level and hence a more normal temperature dependence of the moduli.