Contribution of Optical Phonons to the Elastic Moduli of PdH_X and PdD_X

Abstract

Sound velocity measurements carried out between 10 and 300K on α’-phase PdH_x and PdD_x show that the temperature coefficients dC_ij/dT of the elastic moduli C_ij are significantly more negative in PdD_x than in PdH_x. This isotope effect is well described by a quasiharmonic model in which the transverse and longitudinal optical phonons are treated as Einstein oscillators with different Grüneisen parameters γ_t and γ_ℓ. The Einstein temperatures are θ ^H_t = 650K, θ ^H_ℓ = 910K in PdH_0.66, θ ^D_t = 450K and θ ^D_ℓ = 640K in PdD_0.652. Our analysis implies that |γ_ℓ−γ_t| is large compared to the average optical phonon Grüneisen parameter γ̅ = (γ_ℓ + 2γ_t)/3 determined from thermal expansion measurements. For C_L, C’ and C₄₄ a maximum in ultrasonic absorption is found around 220K. It is interpreted as arising from a reorientation of pairs (or clusters) of vacancies in the hydrogen sublattice under uniaxial or shear strains.