Determination of the Quantum Contribution to the Activated Motion of Hydrogen on a Metal Surface: H/Pt(111)

Measurements of the atomic-scale motion of H and D atoms on the Pt(111) surface, above the crossover temperature to deep tunneling, are presented. The results indicate that quantum effects are significant up to the highest temperature studied (250 K). The motion is shown to correspond to nearest neighbor hopping diffusion on a well defined fcc (111) lattice. The measurements provide information on the adiabatic potential of both the adsorption site and the transition state and give strong empirical support for a dissipative transition-state theory description of the quantum contribution to the motion.

Figure 1

Typical HeSE surface correlation measurements, for 0.1 ML atomic H on Pt(111) (points). The data were obtained at a momentum transfer of $0.86{\AA }^{-1}$ along $[11\overline{2}]$ (a periodic scale of 7.3 Å in real space). In each case the time variation is dominated by a single exponential decay (solid lines). The varying initial levels relate to differing phonon contributions to the ISF.

Figure 2

Plots of the dephasing rate, $\alpha$, obtained from HeSE measurements of H diffusion (blue circles) and D diffusion (red triangles) for temperatures of (a) 220, (b) 140, and (c) 90 K and momentum transfers along the $[11\overline{2}]$ direction. The results are in excellent agreement with the sinusoidal form expected for diffusive hopping between adjacent fcc hollow sites (solid line).

Figure 3

Arrhenius plots of the temperature dependence of the hopping rate for H diffusion (blue circles) and D diffusion (red triangles) at a momentum transfer of $0.86{\AA }^{-1}$ along the $[11\overline{2}]$ direction and a coverage of 0.1 ML. A change in gradient for both H and D is evident. The increased rate of diffusion for both isotopes at low temperatures corresponds to the rate contribution due to quantum tunneling. The solid lines show the quantum-TST model described in the text, while the dashed lines show the corresponding classical rates alone, i.e., $\Xi =1$. The lower panel shows the quantum rate correction, $\Xi$, also described in the text. Quantum effects dominate when $\Xi$ is much larger than 1, but are important over the entire temperature range.