Elastic properties of Pd-hydrogen, Pd-deuterium, and Pd-tritium single crystals

We used a resonant-ultrasound-spectroscopy technique to measure the three independent elastic constants of PdHx, PdDx, and PdTx single crystals at 300 K. For 0.1 < x < 0.62 our PdHx crystals are two-phase mixtures of coherent (alpha) and (beta) hydride phases. For increasing x in this range, C44 decreases monotonically whereas Cʹ=1/2 (C11 C12) has a concave parabolic dependence. This difference is because Cʹ is softened by an anelastic relaxation resulting from acoustic-stress-induced changes in the shape of the coherent lenticular-shape precipitates ((beta)-hydride precipitates in (alpha)-hydride matrix and (alpha)-hydride precipitates in (beta)-hydride matrix). In the (beta)-phase Cʹ and C44 decrease with increasing hydrogen (or deuterium or tritium) content. Furthermore, Cʹ exhibits a strong isotope effect whereas C44 does not. This effect is attributed to differences in the excitation of optical phonons in Pd-H, Pd-D and Pd-T.