We present a combined experimental and theoretical study of the self-diffusion of ammonia on exfoliated graphite. Using neutron time-of-flight spectroscopy we are able to resolve the ultrafast diffusion process of adsorbed ammonia, NH$_3$, on graphite. Together with van der Waals corrected density functional theory calculations we show that the diffusion of NH$_3$ follows a hopping motion on a weakly corrugated potential energy surface with an activation energy of about 4 meV which is particularly low for this type of diffusive motion. The hopping motion includes further a significant number of long jumps and the diffusion constant of ammonia adsorbed on graphite is determined with $D=3.9 cdot 10^{-8}~mbox{m}^2 /mbox{s}$ at 94 K.
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