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

The elastic moduli of the C15 Laves-phase materials TaV2, TaV2H(D)(x) and Z rCr2 have been measured using the technique of resonant ultrasound spectros copy. The temperature dependences of the shear modulus and Young's modulus of TaV2 were found to be anomalous; the moduli increase with increasing tem perature over the entire temperature range 4-345 K. In contrast, the shear modulus and Young's modulus of TaV2H0.34, TaV2H0.53 and TaV2D0.17 all decre ase with increasing temperature. The bulk moduli of these materials are onl y weakly temperature dependent. The elastic moduli of the C15 Laves-phase c ompound 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 c(44) The symmetry of the C15 structure results in doubly degenerate electronic energ y levels at the X point of the Brillouin zone. The strain dependence of the se levels affects the elastic constant c(44), 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 accou nted for if the Fermi level passes very near this special point. It is sugg ested that the extra electrons contributed by H(D) raise the Fermi level in TaV2H(D), and result in a more normal temperature dependence of the elasti c 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.