Measurements of the Activation Energies for Atomic Hydrogen Diffusion on Pure Solid CO

When H atoms are deposited onto the surface, the time evolution of the number density of the H atoms and of the H signal are determined by a competition between the deposition, monoatomic desorption, and H–H recombination following the H-atom diffusion on the surface of the solid CO, and is therefore described by the following equation:

$$\begin{eqnarray}&&\displaystyle \frac{{{dI}}_{{\rm{H}}}}{{dt}}\propto \displaystyle \frac{{{dn}}_{{\rm{H}}}}{{dt}}={{fP}}_{\mathrm{CO}}-{k}_{{\rm{H}}}{n}_{{\rm{H}}}-{k}_{{\rm{H}}-{\rm{H}}}\,{n}_{{\rm{H}}}^{2}-{k}_{{\rm{H}}\mbox{--}\mathrm{CO}}{n}_{{\rm{H}}}{{\rm{N}}}_{\mathrm{CO}}\end{eqnarray} \tag{ 1 }$$

where n_H (cm⁻²) is the surface number density of the H atoms, f is the flux of the H atoms, P_co is the adsorption coefficient of the H atoms onto the pure solid CO, k_H is the atomic desorption rate, and k_H–H is the H–H recombination-rate constant. The P_co may change by the coverage of undissociated H₂ provided from the source. However, this effect was found to be minor in the present low-flux experiment (Kuwahata et al. 2015, see the supplemental material). The final term on the right-hand side corresponds to a pseudo first-order approximation reaction of H and CO for a constant CO number density, because it is known that H atoms react with CO to produce HCO via tunneling on pure solid CO (Hidaka et al. 2007). As the H atoms were deposited on the solid CO surface, I_H, the intensity of the H-atom REMPI signal (Figure 2) increased linearly and then became saturated, as shown in Figure 3. The observed linear increase indicates that the first term on the right-hand side of Equation (1) dominates the number density of H atoms on the surface. During the linear phase, all of the terms that correspond to H-atom losses at the surface are negligible when compared with fP_co. This implies that the slope of the linear part in Figure 3 (I_H versus time) is strongly dependent on the P_co value at a given temperature.

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In the time evolution of the REMPI signal for a substrate temperature of 8 K, saturation starts after about 300 s (Figure 3). Assuming that the value of P_co is unity at 8 K, then the relative adsorption coefficients can be derived as 0.068 and 0.005 at 12 and 15 K, respectively, from the slopes of the linear parts in Figures 3(b) and (c). The temperature dependence of the adsorption coefficient appears to be much larger for CO than for ASW, where the relative coefficients are 1, 0.4, and 0.2 at 8, 15, and 20 K, respectively (Watanabe et al. 2010).

When the H signal starts to saturate, H-atom losses due to processes such as recombination become efficient, and finally (when the coverage is high enough) balances with the supply via deposition; the number density of H atoms on the surface remains constant.

After the H atoms had accumulated on the solid CO surface for a certain amount of time, the gate valve to the atomic source was closed to prevent further H-deposition. After a suitable waiting period the H atoms were then measured. The n_H, and hence I_H, started to decrease due to monoatomic desorption, recombination, and/or reactions with the CO (Figure 4). The accumulation times of the pulsed H beam were 360, 1800, and 21000 s at 8, 12, and 15 K, respectively. The flux of the H beam, f, is ∼1 × 10¹² cm⁻² s⁻¹. Assuming an adsorption coefficient of unity for the H atoms at 8 K, and the relative coefficients obtained in Section 3.1, the maximum coverages of H atoms, θ, are ∼2.5 × 10⁻⁴, ∼8.6 × 10⁻⁵, and ∼7.7 × 10⁻⁵ for the experiments at 8, 12, and 15 K, respectively, when the number of sites on the CO surface was 10¹⁶ cm⁻², such as for ASW. In reality, because H–H recombination may occur even during accumulation, the measured coverages are rather small.

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Although atomic desorption should be minor at 8 K, it was nevertheless evaluated by TPD after the H-atom deposition. During heating the H-atom deposited sample at a rate of 6 K minute⁻¹ from 8 to 30 K, we attempted to detect H-atomic and H₂-molecular desorption at a height of about 1.5 mm above the surface by the REMPI method, which is more sensitive and reliable than a quadrupole mass analyzer for H-atom detection. We find that no H atoms were detected regardless of the amount of H-atom deposition, while significant H₂ desorption was detected. We repeated the same measurement for the molecular H₂ deposition, which was conducted with the same H₂-gas flow rate as that used for the H-atom source, but instead this time the microwave was turned off. The detected H₂ amount when using the TPD method was equivalent to that obtained for the H-atom deposition case within the difference of 3%. These measurements indicate that atomic desorption is minor, and the accommodation coefficient at 8 K is similar between H and H₂, where most of the H atoms were consumed by recombination and remain on the surface as H₂. This also shows that the H-atom loss is dominantly caused by recombination.

Further investigations were performed to test for any decrease in the amount of H atoms arising from a tunneling reaction with CO, which has been studied for CO on ASW (Watanabe & Kouchi 2002) and pure solid CO (Watanabe et al. 2004). HCO can be dissociated by photons of the PSD laser at 532 nm (van Ijzendoorn et al. 1983). If HCO exists on the surface, any H atoms photolyzed from the HCO by the PSD laser can be detected by the REMPI. As the tunneling reaction rate between H and CO should be much lower than the diffusion coefficient of H atoms, H-atom consumption by HCO formation should be minor. Nevertheless, for a long period of time after H-atom deposition, the H atoms could finally react with CO. We therefore evaluated the possibility that the detected H atoms result from HCO photolysis. For a waiting time of 6.7 × 10⁴ s at 8 K, the sample was heated at 20 K, and it was subsequently confirmed that the H-atom intensities diminished immediately (Figure 5). This indicates that any remaining H atoms immediately recombined when the sample was heated to 20 K. If the detected H atoms are dominated by the photolysis of HCO rather than physisorbed H atoms, they should be detected even at 20 K, which is lower than the desorption temperature of HCO. Therefore, we conclude that the detected H atoms result solely from physisorbed H atoms.

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As described above, H–H recombination mainly dominates over monoatomic desorption and CO hydrogenation after H-atom deposition in the present experiment. Therefore, the rate Equation (1) is reduced to

$$\begin{eqnarray}&&\displaystyle \frac{{{dI}}_{{\rm{H}}}}{{dt}}\propto \displaystyle \frac{{{dn}}_{{\rm{H}}}}{{dt}}=-{k}_{{\rm{H}}-{\rm{H}}}\,{n}_{{\rm{H}}}^{2}.\end{eqnarray} \tag{ 2 }$$

To examine the effect of isotopes on the diffusion, measurements identical to those performed for H atoms were undertaken for deuterium (D) atoms at 8 K. As can be seen in Figure 4, the attenuation behavior of the D atoms does not show any significant difference from that for H atoms, which indicates that the diffusion is dominated by thermal hopping rather than tunneling.

If we analytically integrate Equation (2), we have

$$\begin{eqnarray}&&\displaystyle \frac{{I}_{{\rm{H}}}}{{I}_{0}}=\displaystyle \frac{{n}_{{\rm{H}}}}{{n}_{0}}=\displaystyle \frac{1}{({k}_{{\rm{H}}\mbox{--}{\rm{H}}}{n}_{0}t+1)},\end{eqnarray} \tag{ 3 }$$

where I₀ (arb. units) and n₀ (cm⁻²) are the initial values of I_H and n_H, respectively, and t is the waiting time after the H-atom accumulation is terminated. The time evolution curves of I_H for the three temperatures are shown in Figure 4. Fitting these curves with Equation (3) gives the values of the parameters k_H–Hn₀. The term k_H–Hn₀ can be expressed in terms of thermal hopping as follows:

$$\begin{eqnarray}&&{k}_{{\rm{H}}\mbox{--}{\rm{H}}}{n}_{0}=\theta \nu \exp \left(-\displaystyle \frac{{E}_{\mathrm{diff}}}{{k}_{{\rm{B}}}T}\right),\end{eqnarray} \tag{ 4 }$$

where ν is a frequency factor, 10¹²–10¹³ s⁻¹, E_diff is the activation energy for the diffusion of H, k_B is the Boltzmann constant, and T is the surface temperature. Using ν = 5 ×10¹² s⁻¹ and θ = 2.5 × 10⁻⁴ for 10¹⁶ sites cm⁻² on the surface at 8 K, E_diff is determined to be ∼22 meV. Similarly, we obtain ∼30 and ∼37 meV for E_diff at 12 and 15 K, respectively. When we consider a 10× larger coverage for the assumed 10¹⁵ sites cm⁻², the activation energies rise by ∼2 meV for each temperature. That is, the uncertainty originating from the coverage is quite small. In this temperature region, the values of the activation barriers dominating thermal hopping increase almost linearly. At higher temperatures, the H atoms tend to be accommodated in deeper potential sites, suggesting that the diffusion of the H atoms is limited by the larger activation energies. It should be noted that a rough surface generally has various potential sites; therefore, our obtained activation energies should be regarded as average values. There must be shallower potential sites that lead to lower activation barriers than the obtained ones. The rapid diffusion for shallower sites should be reflected in the steep decrease of I_H just after the termination of H-atom accumulation. From Figure 3, the accumulation times used for 8, 12, and 15 K give I_H intensities of about 7 × 10⁻¹⁰, 2 × 10⁻¹⁰, and 2 × 10⁻¹⁰, respectively, while the first plots of I_H obtained after 100–250 s in Figure 4 have similar values (within 50%) for each temperature. These small differences indicate that the fraction of shallower potential sites is of the same order or less than those for the obtained activation energies.

The thermal hopping frequency, N_diff, of the dominant potential site at each temperature can be calculated as follows:

$$\begin{eqnarray}&&{N}_{\mathrm{diff}}=\nu \exp \left(\displaystyle \frac{-{E}_{\mathrm{diff}}}{{k}_{{\rm{B}}}T}\right),\end{eqnarray} \tag{ 5 }$$

and is found to be 0.07, 1.3, and 1.9 s⁻¹ at 8, 12, and 15 K, respectively. Then, the diffusion coefficient, D, is about 1.8 × 10⁻¹⁷, 3.3 × 10⁻¹⁶, and 4.8 × 10⁻¹⁶ cm² s⁻¹ at 8, 12, and 15 K, respectively, assuming a two-dimensional random walk expressed as follows:

$$\begin{eqnarray}&&D=\displaystyle \frac{1}{4}{N}_{\mathrm{diff}}{d}_{\mathrm{site}}^{2},\end{eqnarray} \tag{ 6 }$$

where ${{d}_{\mathrm{site}}}^{2}$ is 10⁻¹⁵ cm², which is a unit area of the adsorption site.