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 PdH_x, PdD_x, and PdT _x single crystals at 300 K. For 0.1 < x < 0.62 our PdH _x crystals are two-phase mixtures of coherent α. and β hydride phases. For increasing x in this range, C₄₄ decreases monotonically whereas C′ = 1/2(C₁₁ - C₁₂) has a concave parabolic dependence. This difference is because C′ is softened by an anelastic relaxation resulting from acoustic-stress-induced changes in the shape of the coherent lenticular-shape precipitates (β-hydride precipitates in α-hydride matrix and α-hydride precipitates in β-hydride matrix). In the β-phase C′ and C₄₄ decrease with increasing hydrogen (or deuterium or tritium) content. Furthermore, C′ 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.