Phonon spectra of nonstoichiometric palladium hydrides

The effects of nonstoichiometry in the lattice dynamics of the system $\mathrm{Pd}{A}_x$, where $A$ is H or D, have been simulated by performing a Born-von Kármán treatment on crystals with periodically repeated "supercells" containing 108 Pd atoms and approximately ($108x$) atoms randomly distributed among the $A$ sites and averaging over a large number of such statistical samples. Using the force constants obtained by Rowe and co-workers, from a coherent-neutron-scattering study of a single crystal of Pd${\mathrm{D}}_{0.63}$, the frequency spectrum and incoherent cross section for the hydrogen vibrations in Pd${\mathrm{H}}_{0.63}$ have been calculated and compared with measurements on this system made with the ZING-P prototype pulsed neutron source at Argonne. The results show that nonstoichiometry dramatically broadens the optic-mode frequency system and also that the Pd-H force constants have to be increased by ∼ 20% relative to the corresponding Pd-D force constants in order to obtain agreement with experiment. The effect of nonstoichiometry on the one-phonon neutron groups seen in the coherent scattering experiments on Pd${\mathrm{D}}_{0.63}$ has also been investigated.