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45645-AC5
Classical and Quantum Diffusion of Hydrogen on Cu Surfaces: An Optical Diffraction Study Using Xe Density Gratings as Templates

Xiangdong Zhu, University of California (Davis)

Using linear optical diffraction from hydrogen density gratings on Cu(111), we studied diffusion of hydrogen atoms on Cu(111) from 85K to 210K where we observed both classical over-barrier hopping at high temperatures and quantum mechanical tunneling of hydrogen atoms at low temperatures.

We used monolayer-thick Xe templates to prepare periodic hydrogen density profiles on Cu(111) to avoid optical damage to the substrate.  We formed the Xe template from a pre-adsorbed Xe monolayer on Cu(111) at 35K using dual-beam laser-induced thermal desorption (LITD).  Adsorbed Xe atoms block the access of gas-phase hydrogen to Cu(111).  The modest dual-beam LITD by the interference pattern of a pair of 7-ns laser pulses at 0.532 μm yielded a periodic Xe coverage pattern.  Using the Xe pattern as the template, we formed a complementary hydrogen density pattern by exposing the Xe-covered Cu(111) to hot hydrogen gas.  We removed the Xe template by quickly heating the sample over 80K at which the Xe desorbed from Cu(111) in a few seconds while the density profile of the adsorbed hydrogen adatoms remained unchanged.

We measured diffusion constants of hydrogen adatoms on Cu(111) by detecting the linear optical diffraction from the periodic hydrogen density pattern on Cu(111).  To measure diffusion constants over 6 orders of magnitude as the substrate temperature varied from 85K to 210K, we used three set-ups to produce hydrogen density gratings with periodicities of a = 10.3 μm, 2 μm, and 0.38 μm.  It enabled us to measure diffusion constants from 2×10^-9 to 2×10^-15 cm²/sec.

The normalized 1^st-order linear optical diffraction signal is given by (Fick's law)

S₁(t) = exp(-α(T)t)                         (1)

The diffusion constant D(T) is related to the exponent by

D(T) = α(T) (a²/8π²)                     (2)

By fitting S₁(t) to Eq. (1) we obtained α(T).  From Eq. (2) we found the hydrogen diffusion constants D(T) from 85K to 210K.  In Fig. 1, we display the Arrhenius plot of D(T).

The measured D(T) as a function of temperature are characterized by two distinct Arrhenius functions, each with a well-defined activation energy E_diff and prefactor D₀,

D(T) = D₀exp(-E_diff/k_BT)                  (3)

From 210K down to 110K, D(T) is described by

D₀(CL) = 162 cm²/sec                     (4)

E_diff(CL) = 0.45 eV                          (5)

In this temperature range, the diffusion of hydrogen adatom on Cu(111) is expectedly the classical over-barrier hopping. From 110K to 85K, D(T) is described by a different kinetic with

D₀(QM) = 6.6×10^-14 cm²/sec           (6)

E_diff(QM) = 0.022 eV                       (7)

This is characteristic of quantum mechanical under-barrier tunneling diffusion.  It is noteworthy that the activation energy E_diff(QM) = 0.022 eV is much less than the excitation energy of 0.1 eV for the in-plane vibration of hydrogen on Cu(111).  As a result, unlike hydrogen adatoms on Ni(111) where the diffusion crossed over from the classical over-barrier hopping to quantum tunneling between the first in-plane vibrational states of neighboring 3-fold hollow sites of adsorption, the diffusion of hydrogen atoms on Cu(111) changes from classical over-barrier hopping to quantum mechanical tunneling between the vibrational ground states of neighboring 3-fold hollow sites.  The small activation energy is well attributed to the small polaron effect.

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