Contribution of Optical Phonons to the Elastic Moduli of PdHX and PdDX
Sound velocity measurements carried out between 10 and 300K on α’-phase PdHx and PdDx show that the temperature coefficients dCij/dT of the elastic moduli Cij are significantly more negative in PdDx than in PdHx. 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 γt and γℓ. The Einstein temperatures are θ t H = 650K, θ ℓ H = 910K in PdH0.66, θ t D = 450K and θ ℓ D = 640K in PdD0.652. Our analysis implies that |γℓ−γt| is large compared to the average optical phonon Grüneisen parameter γ̅ = (γℓ + 2γt)/3 determined from thermal expansion measurements. For CL, 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.
KeywordsElastic Modulus Optical Phonon Phonon Dispersion Curve Longitudinal Optical Phonon Ultrasonic Absorption
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