The wave functions and energies of hydrogen and its isotopes, deuterium and tritium, were calculated in stoichiometric palladium hydride (PdH), stoichiometric niobium hydride (NbH), lithium imide (Li2NH) and model potentials. They were used to investigate the importance in including quantum effects in determining the location of hydrogen in these systems.
The relative stability of the two potential sites for hydrogen in palladium hydride, was found to have a large dependence on the zero point energy of the hydrogen atom. Hydrogen in lithium imide was found to be delocalised in sites around the nitrogen atom. The quantum tunnelling rate between these sites was calculated to be many times larger than the classical rate.
An expression for the diffusion coefficient in terms of the wave functions and energies of a system, derived from Kubo theory, was used to calculate the diffusion coefficients of hydrogen and its isotopes in these systems. The different processes which contribute to hydrogen diffusion were studied. It was found that it is necessary to include quantum effects when considering the diffusion of hydrogen though materials.
Processes at energies lower than the classical barrier to diffusion were found to be important in all of the systems investigated. In palladium hydride, these processes usually involved tunnelling from the octahedral to the tetrahedral site. In niobium hydride tunnelling between the ground states in neighbouring wells was found to contribute strongly to diffusion.
Calculation of the diffusion coefficient in a model system of a one-dimensional potential coupled to a harmonic oscillator showed that both coherent and incoherent tunnelling processes contributed to diffusion. Coherent processes occurred without a change in in the harmonic oscillator quantum state, whereas incoherent processes involved gaining or losing phonons during the transition.
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