Anomalous isotope dependence of hydrogen diffusion rates on tungsten (110) surfaces: Implications for lattice–hydrogen interactions

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Abstract
A theoretical analysis is provided of the anomalous isotope effects observed for the diffusion of hydrogen on the W(110) surface in the limit of zero coverage. Low temperature tunneling diffusion shows an isotope effect several orders of magnitude smaller than predicted by simple rigid lattice models, while the higher temperature activated diffusion displays an inverse isotope effect several orders of magnitude larger than the rigid lattice predictions. It is shown here that both effects can be explained consistently by a single model of hydrogen–tungsten interactions in which there is a large separation in time scales between the hydrogen and tungsten motions. Tunneling is described with a small polaron model. Large phonon overlap factors are found to diminish the role of the tunneling matrix element and thereby to decrease the isotope effect. Activated diffusion is described as a many-phonon process in which the vibron is thermally excited as a result of phonon–vibron coupling. The same coupling parameter explains both the tunneling and activated diffusion results. This coupling parameter is shown to be dependent on adsorbate mass.