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The effects of nonstoichiometry in the lattice dynamics of the system PdAₗ, where A is H or D, have been simulated by performing a Born-von K\'arm\'an 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 PdD₀. ₆₃, the frequency spectrum and incoherent cross section for the hydrogen vibrations in PdH₀. 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 PdD₀. ₆₃ has also been investigated.
Rahman et al. (Fri,) studied this question.