THE MECHANISM OF SURFACE DIFFUSION OF H AND D ATOMS ON AMORPHOUS SOLID WATER: EXISTENCE OF VARIOUS POTENTIAL SITES

We performed experiments with the Reaction Apparatus for Surface Chemistry in Astrophysical environments with Laser spectroscopy (RASCAL) apparatus at the Institute of Low Temperature Science, Hokkaido University, which consists of a vacuum sample chamber, a Fourier-transform infrared (FTIR) spectrometer, an atomic source, and two laser systems (Watanabe et al. 2010; Hama et al. 2011).

The vacuum sample chamber was evacuated to ultra-high vacuum conditions (∼10⁻⁸ Pa) using two turbo molecular pumps. A mirror-polished aluminum alloy 2017 (Al) substrate was installed at the center of the sample chamber, which is connected to the cold head of an He refrigerator. ASW was produced on the Al substrate at 8 K by vapor deposition through a capillary plate with an incident angle of 67.7°. The solid samples were monitored in situ by the FTIR (see Figure 1). The typical deposition time for ice preparation is 420 s to produce ∼32 L at 8 K, where 1 L ≈ 1.3 × 10⁻⁴ Pa s. The column density of ASW was calculated at 2.1 × 10¹⁶ molecules cm⁻² (based on Figure 1(a)). The deposition rate was estimated at approximately 0.04 mg hr⁻¹. This low deposition rate leads to a high-density ASW (∼1.1 g cm⁻³) with micropores (Watanabe & Kouchi 2008), which contains dangling OH bonds, as can be seen at 3721 and 3698 cm⁻¹ in Figure 1(a). The PCI sample was vapor deposited onto the Al substrate at 145 K for ∼420 s and subsequently cooled to 8 K for the experiments. The typical PCI column density was 1.4 × 10¹⁶ molecules cm⁻² (see Figure 1(b)). For calculation of the column density, the integrated absorption coefficients we adopted were 2.0 × 10¹⁶ cm molecule⁻¹ for ASW and 2.1 × 10¹⁶ cm molecule⁻¹ for PCI (Hagen et al. 1981; Hidaka et al. 2007, 2008).

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H and D atoms were produced by dissociation of H₂ and D₂ molecules, respectively, in microwave-discharge plasma in a Pyrex tube. The atoms were cooled through an Al pipe at 100 K, which was connected to another He refrigerator, and the atoms were deposited onto the ice surface through the free-flight region to collimate the beam. The atomic-beam line is composed of three differentially pumped stages. Each chamber was separated by a collimator with an aperture of 1.2 mm in diameter. During the atomic-source operation, the typical pressure of the three stages and that in the sample chamber was 5 × 10⁻³, 2 × 10⁻⁵, 6 × 10⁻⁷, and 2 × 10⁻⁸ Pa, respectively. We estimated a flux of H (D) atoms of about 10¹¹–10¹² cm⁻² s⁻¹ and derived a lower limit to the dissociation fractions of H₂ (D₂) molecules of approximately 66% (and 69% for D₂); see Section 2.3. In the RASCAL, although the pulsed atomic beam can be produced by a chopper disk (Watanabe et al. 2010), it was removed in the present study to allow estimation of the flux and the coverage of H and D atoms, and for our measurements of the time-of-flight (TOF) spectra of the atoms.

Upon adsorption of the atoms on the ASW surface, the surface number density of H (D) atoms, n_H (cm⁻²), decreases with time because of recombination of atoms and/or monoatomic desorption, as expressed by

$$\begin{equation} dn_{\rm H} /{\rm d}t = - k_{{\rm H} - {\rm H}} {\rm }n_{\rm H} ^2 - k_{{\rm des}} {\rm }n_{\rm H} , \end{equation} \tag{ 3 }$$

where k_H−H and k_des are the rate constants for recombination and monoatomic desorption, respectively. Since H–H recombination is a barrierless radical–radical reaction, k_H–H is dominated by H-atom diffusion and can thus be expressed as follows for thermal diffusion:

$$\begin{equation} k_{{\rm H} - {\rm H}} = s\;\nu \;\exp {\rm }(- E_{{\rm diff}} /k_B {\rm }T), \end{equation} \tag{ 4 }$$

where s is the unit area of the surface site. Using the relation that the coverage of the H (D) atom, θ, is θ = s n₀, Equation (4) converts to

$$\begin{equation} k_{{\rm H} - {\rm H}} {\rm }n_0 = \theta {\rm }\nu {\rm }\exp (- E_{{\rm diff}} /k_B {\rm }T), \end{equation} \tag{ 5 }$$

where n₀ is the initial surface number density of H atoms. When diffusion and recombination are sufficiently faster than monoatomic desorption, the E_diff for atoms can be determined from k_H–H n₀ and θ.

The present study combines the PSD and REMPI methods to measure the variation of the number density of H (D) atoms, or H₂ (D₂) molecules present on the surface to obtain k_H–H n₀ and θ. Details of the experimental procedures have been described previously (Watanabe et al. 2010). In brief, Figure 2 is a schematic illustration of the timing chart for the present experiment in which the delay time between photodesorption and probe laser pulses corresponds to the TOF. The atoms or molecules were photodesorbed from the surface by the unfocused second-harmonics radiation (532 nm) of a neodymium–yttrium–aluminum garnet (Nd³⁺:YAG) laser with an irradiated area of about 3 mm in diameter at 10 Hz, with a pulse width of ∼4 ns. The power of the 532 nm laser was ∼20 μJ pulse⁻¹ (∼7 × 10⁴ J s⁻¹ cm⁻²).

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The photodesorbed species was selectively ionized by (2+1) REMPI and subsequently detected with a TOF mass spectrometer aligned perpendicularly to the ice surface. The REMPI laser was focused at approximately 1 mm above the ASW surface. H and D atoms were ionized via the two-photon 2s(²S_1/2) ← 1s(²S_1/2) transition at 243.07 and 243.00 nm, respectively (Zumbach et al. 1997). H₂ and D₂ molecules were ionized via the two-photon E,F¹ (v' = 0, J' = J) ← X¹ (v = 0, J = 0 or 1) transitions in the wavelength range of 201–203 nm (Pomerantz et al. 2004). Radiation of ∼100 μJ pulse⁻¹ at the requisite wavelengths was produced by a dye laser pumped with another Nd³⁺:YAG laser, with subsequent frequency doubling and mixing in potassium dihydrogen phosphate and barium borate crystals

We first measured TOF spectra of the H and D atoms taken as a function of the delay time between the photodesorption and REMPI laser pulses. Figure 3 shows typical TOF spectra of photodesorbed H and D atoms from ASW and PCI at various temperatures. During the TOF measurements, the atoms were continuously deposited onto ASW through continuous irradiation by the photodesorption laser at 10 Hz for PSD. In these continuous deposition and irradiation conditions, the number density of atoms on the surface was found to be constant because of the balance between H-atom supply and loss by recombination and photodesorption (and probably a little monoatomic desorption as well). The typical duration to obtain a TOF spectrum is 120–180 s. TOF spectra of photodesorbed H and D atoms from ASW and PCI were reproduced by a single Maxwell–Boltzmann (MB) distribution with a translational temperature, T_trans, of 35–50 K. Details regarding the analysis of such TOF spectra have been reported in Yabushita et al. (2004) and Hama et al. (2009). T_trans = 35–50 K corresponds to 6–9 meV, assuming that the translational energy is 2k_BT_trans (Zimmermann & Ho 1994, 1995). The signal intensities increased linearly as the power of the 532 nm photodesorption laser increased up to ∼40 μJ pulse⁻¹, while the translational energy was independent of laser power. In our TOF spectral measurements, the ice sample was heated to 30 K each time to flush residual atoms or molecules from the surface after the measurements, and cooled to 8, 12, or 15 K to continue the experiments. We confirmed that this method exhibited reproducibility for the results obtained, indicating that undesired effects like evaporation and/or drastic structural changes of ASW were not induced, neither by 532 nm laser irradiation nor by heating to 30 K. Further discussion of the PSD mechanism is presented in the Appendix.

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Table 1 also summarizes the relative area intensities of TOF spectra for H (D) atoms normalized to that from ASW at 8 K. Figure 3 and Table 1 clearly show decreases of all atomic signals as the temperature increases from 8 to 15 K. The temperature effect on the diffusion of atoms will be further discussed in Section 3.4. The absolute intensity for D atoms from ASW at 8 K is comparable with that for H atoms. However, since we did not determine the absolute dissociation fraction in the atomic beams for both H₂ and D₂, a quantitative comparison between the intensities of H and D atoms may not be appropriate.

The coverage of atoms, θ, can be derived from the deposition time and the beam flux. First, we estimated the flux of the molecular beam from the beam line without microwave discharge. Figure 4 shows photodesorbed (a) H₂ (J = 0 and 1) and (b) D₂ (J = 0 and 1) intensities from the Al substrate at 8 K with continuous deposition of molecules within 120 minutes through the beam line. The REMPI spectra of H₂ (J = 0 and 1) and D₂ (J = 0 and 1) molecules were measured during molecular deposition at TOF (the delay time between the PSD and REMPI lasers) = 1.5 and 2.0 μs, respectively, where the strongest H₂ and D₂ (J = 0 and 1) signals were obtained from the Al substrate. The scan step size of the REMPI laser is 0.001 nm and a typical duration to obtain a spectrum is around 60 s. In Figure 4, the H₂ and D₂ intensities increase and start to become saturated at around 30 minutes (1800 s). Since the multiple layers of solid H₂ cannot be created at 8 K, this saturation indicates that the molecular coverage is reaching unity. Based on this plot, we consider the molecular H₂ (D₂) beam flux of about 1.2 × 10¹⁵ cm⁻²/1800 s ≈ 7 × 10¹¹ cm⁻² s⁻¹ if we assume there is 1.2 × 10¹⁵ Al atoms cm⁻² on the Al substrate (Wyckoff 1931). However, because the actual number of sites on the Al substrate cannot be specified, we approximate the flux to be 5 × 10¹¹ to 1 × 10¹² cm⁻² s⁻¹.

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Next, since the atomic beam contains undissociated H₂ (D₂) molecules, we estimate a lower limit to the dissociation fraction of molecules in the atomic beam as follows (for details, see Watanabe et al. 2010). Figure 5(a) shows time evolutions of the sum of H₂ (J = 0 and 1) intensities photodesorbed from the Al substrate at 8 K as a function of deposition time for the H₂ molecular beam (solid data points) and the H atomic beam (open data points) through the same beam line. The H₂ (J = 0 and 1) intensities for atomic deposition are significantly lower than those for molecular deposition. Since the H₂ intensities obtained in the atomic-beam deposition should result from undissociated H₂ contained in the atomic beam and/or recombined H₂ which remained on the surface, the difference in the H₂ (J = 0 and 1) intensities between atomic and molecular depositions in Figure 5(a) indicates a lower limit to the dissociation fractions of H₂ (D₂) molecules. This was derived to be approximately 66% (and 69% for D₂; unpublished data), and we estimated that the H (D)-atom flux is roughly equivalent to the flux of the molecular beam, 5 × 10¹¹ to 1 × 10¹² cm⁻² s⁻¹.

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On the surface of hexagonal ice, there are about 1.0 × 10¹⁵ molecules cm⁻² considering the lattice parameters (Petrenko & Whitworth 1999). We here assume that ASW has a 5–10 times greater surface area than that of a crystalline surface (Al-Halabi & van Dishoeck 2007; Hidaka et al. 2008). Thus, H (D)-atom deposition times of 30 and 360 s on ASW consequently lead to θ ≈ 1–5 × 10⁻³ and 2–7 × 10⁻², respectively, adopting the calculated sticking probability of 0.8–0.9 (Al-Halabi & van Dishoeck 2007).

Evidence of significant recombination on ASW at 8 K is obtained with the following procedure. We performed the same series of measurements as described in Section 2.3; i.e., detection of H₂ (J = 0 and 1) under continuous molecular or atomic deposition onto ASW. The results obtained at 8 K are shown in Figure 5(b).

As can be seen in Figure 5(b), only a slight difference in the H₂ (J = 0 and 1) intensities was observed between molecular (solid data points) and atomic (open data points) deposition. Since the dissociation fraction of H₂ molecules in the atomic beam was high (⩽∼66%), the slight difference indicates that monoatomic desorption is very minor: H atoms diffuse rapidly, and most of them recombine to form H₂ molecules, and maybe are retrapped on the ASW surface at 8 K during atomic deposition in 30–360 s atomic deposition.

The insets in Figure 5(b) show that H atoms have already recombined to form H₂ molecules even after 30 s of deposition of H atoms (corresponding coverage: θ ≈ 1–5 × 10⁻³) on the ASW surface at 8 K. The transient migration lengths of incident H atoms on the ASW surface (∼10 K) before the atoms are fully thermalized (hot atoms) have been calculated as ∼20, 60 ± 50, and ∼12 Å at T_i = 200 K (Buch & Zhang 1991), 100 K (Masuda et al. 1998), and 100 K (Al-Halabi & van Dishoeck 2007), respectively, where T_i is the translational temperature of the incident H atoms. If this is the case, then the hot-atom mechanism plays little role in H₂ formation on the surface in the measurements for Figure 5(b). The recombination of H atoms to yield H₂ molecules must be dominated by the Langmuir–Hinshelwood process.

In the present study, H₂ (J = 2) was not detected from ASW at 8–15 K. It has been theoretically and experimentally demonstrated that H₂ and HD molecules that are newly formed via recombination on low-temperature surfaces are in highly vibrationally and rotationally excited states for a formation energy of 4.5 eV (Takahashi 1999; Creighan et al. 2006; Yabushita et al. 2008a, 2008b). These two facts suggest that H₂ molecules formed via recombination immediately reach thermal equilibrium with the ice temperature as they are retrapped on the ASW surface, which is consistent with the experimental results of Hornekær et al. (2003).

Atoms were found to recombine efficiently on the ASW surface during deposition at 8 K (see Figure 5). On the other hand, some atoms survived on the ASW surface at 8 K even after atomic deposition. Figure 6 shows the time variations of the signal intensities of H and D atoms (I_H and I_D) photodesorbed from ASW or PCI as a function of the waiting time, t, after a deposition time of 360 s. I_H and I_D were measured at fixed delay times of the two lasers, TOF = 1.2 and 1.5 μs, at which the TOF profile of the two atoms peaked, respectively (see Figure 3). To obtain I_H and I_D, the REMPI spectra were acquired three times for each waiting time and those areas were added up. After the REMPI measurements, the ice sample was heated to 30 K to refresh the surface and cooled to 8 K again to continue the experiments.

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I_H and I_D from ASW at 8 K (solid circles in Figure 6) decreased gradually as waiting time increased, while we successfully detected H and D atoms even after t = 90 minutes. When ASW was left for 90 minutes at 8 K without atomic deposition, the signals obtained due to the residual gas in the vacuum chamber were negligible. I_H and I_D from ASW at 12 K (solid triangles in Figure 6) became more than one order of magnitude lower than the equivalent values at 8 K. The H and D atoms were hardly detected from ASW at 15 K. I_H and I_D from PCI at 8 K also diminished immediately (open circles in Figure 6). The observed temperature and structural effects will be further discussed in Sections 3.4 and 3.5, respectively.

As described in Section 3.1, monoatomic desorption from ASW at 8 K would be very small, so that we consider that the attenuations of I_H and I_D on the ASW surface at 8 K after atomic deposition (solid circles in Figure 6) are caused mainly by recombination of the atoms following diffusion. (We did not observe unimolecular desorption of H₂ molecules from the ASW surface at 8–15 K (see Figures 7 and 9 in the Appendix). These results support the assumption that the loss by monoatomic desorption is small at 8 K, at least for D atoms, if the rate of desorption is determined by the mass of the species.)

When the attenuation of H and D atoms on ASW is dominated by recombination, the surface number density of H (D) atoms, n_H (cm⁻²), obeys the rate Equation (6) as described in Section 2.1,

$$\begin{equation} dn_{\rm H} /{\rm d}t = - k_{\rm H \hbox{--} H} n_{\rm H} ^2. \end{equation} \tag{ 6 }$$

Solving Equation (6), I_H (I_D) in Figures 6(a) and (b) can be fitted by Equation (7),

$$\begin{equation} I_{\rm H} /I_{\rm 0} = n_{\rm H} /n_{\rm 0} = 1/(k_{\rm H \hbox{--} H} n_0 t + 1) + b, \end{equation} \tag{ 7 }$$

where I₀ and n₀ are the initial intensity and number density of H atoms, respectively. An asymptotic value, b, arises from the existence of H atoms that are long-lived even after 90 minutes of waiting time. Although we cannot derive k_H–H and n₀ independently, their product, k_H–H n₀, can be determined by fitting the data using Equation (7).

Observation of a significant isotope effect in the diffusion can be an indicator of quantum tunneling (Lauhon & Ho 2000). This is because the tunneling effect strongly depends on the particle mass. In the present study, both I_H and I_D decreased at a similar rate at 8 K (solid circles in Figure 6), however. Thus, we conclude that the diffusion of atoms that are detectable using the present experimental method is thermal hopping rather than tunneling. Using k_H–H n₀ obtained from Equation (7), θ ≈ 2–7 × 10⁻² and ν = 10¹²–10¹³ s⁻¹, we determined E_diff = 22 ± 1 and 23 ± 1 meV for H and D atoms from Equation (5), respectively, by taking into account the errors on the fitted parameters. Some H and D atoms for a coverage of 2–7 × 10⁻² did not encounter each other within 90 minutes at 8 K (see Figures 6(a) and (b)). These results indicate the existence of energetically deep potential sites on the ASW surface in which the H (D) atoms are trapped. We estimated that the value of E_diff for a deep site should exceed approximately 30 meV, as shown by the dotted lines in Figures 6(a) and (b).

We could not determine the value of E_diff for very shallow sites on ASW at which atoms immediately recombine during deposition, as shown in Figure 5(b), but estimated an upper limit as follows. The diffusion coefficient, D_t (cm² s⁻¹), in a two-dimensional random walk can be expressed by

$$\begin{equation} 4\;D_t {\rm }t_{{\rm obs}} = \langle {|x|^2 } \rangle \end{equation} \tag{ 8 }$$

and

$$\begin{equation} \langle {| x |^2 } \rangle {\rm = }N_{{\rm diff}} {\rm }d_{{\rm site}} ^{\rm 2} {\rm }t_{{\rm obs}} , \end{equation} \tag{ 9 }$$

where t_obs and d_site represent the observation time (s) and the distance to each site (cm), respectively, and 〈|x|²〉 is the mean-squared displacement (cm²). Figure 5(b) shows that H atoms have already recombined to form H₂ molecules even after 30 s of deposition of H atoms (corresponding coverage: θ ≈ 1–5 × 10⁻³) on the ASW surface at 8 K. Assuming that t_obs = 30 s, d_site² = 10⁻¹⁵ cm², 〈|x|²〉 = d_site²/θ = 2 × 10⁻¹³ to 1 × 10⁻¹² cm², the lower limits to D_t and N_diff at 8 K were then about 2–8 × 10⁻¹⁵ cm² s⁻¹ and 7–33 s⁻¹, based on Equations (8) and (9), respectively. Although the origin of this rapid diffusion at the very shallow potential sites is not clear, i.e., whether it is due to tunneling or thermal hopping (see Section 3.3), assuming thermal hopping, an upper limit of E_diff for the very shallow site is estimated at 18 ± 2 meV from N_diff and Equation (2).

As described in the previous sections, there is an energetically wide range of potential sites on ASW, including very shallow potential sites (E_diff ⩽ 18 ± 2 meV) where the deposited H atoms diffuse rapidly and recombine efficiently on the ASW surface during atomic deposition at 8 K (see Figure 5), as well as middle and deep sites with energy depths of E_diff = 22 ± 1 and ⩾ ∼30 meV, respectively (see Figure 6).

To obtain further quantitative information about which of the potential sites is predominant on ASW, we studied the time variations of photodesorbed H₂ (J = 0 and 1) signals from ASW as a function of waiting time after H₂ or H deposition for 360 s was completed (θ ≈ 2–7 × 10⁻²). Figure 7(a) shows typical results obtained at 8 K. We observed a small difference in H₂ (J = 0 and 1) intensities between molecular (solid data points) and atomic (open data points) depositions, which was also observed in Figure 5(b). In addition, the sum of the H₂ (J = 0 and 1) signal intensities is kept almost constant for 10 minutes after H-atom deposition (open squares in Figure 7(a)), in spite of the fact that the H signal decreased within 10 minutes (see Figure 6(a)). Note again that, as described above, in the H-atom deposition, H₂ signals were attributed to H–H recombination on the surface but not to the undissociated H₂ in the atomic beam. Thus, if the detected H₂ intensity arises mainly from the attenuation of H atoms (H₂ formation by recombination) for around 10 minutes, as shown in Figure (6), then the H₂ signal should increase for 10 minutes. However, this is not the case. That is, the H₂ signals in Figure 7 mainly reflect H₂ that was formed very rapidly during H deposition. As a result, we conclude that the ASW surface is dominated by very shallow potential sites where most H atoms can diffuse rapidly and recombine efficiently during atomic deposition (E_diff ⩽ 18 ± 2 meV). The middle- (22 ± 1 meV) and deep- (⩾ ∼30 meV) potential sites would be relatively small on the ASW surface, so that the number of H atoms at such sites should be small too. We were able to detect the H atoms there thanks to the high-detection sensitivity to atoms of the REMPI method. In addition, migration of H atoms into the bulk is unlikely on the ASW surface because the deposited H atoms efficiently diffuse on the ASW surface and recombine to yield H₂ molecules before migration into the bulk. The H₂ molecules that formed were retrapped on the ASW surface as shown in Figures 5(b) and 7(a).

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We also performed the above series of experiments for atomic and molecular deuterium under the same conditions as for hydrogen (see Figure 7(b)). Weaker D₂ (J = 0 and 1) signals were obtained from ASW both in D₂- and D-deposition experiments at 8 K compared to those for the H₂ and H experiments (see Figure 7(a)). This can be explained by the difference in REMPI efficiency between hydrogen and deuterium. The ratio of the square of the two-photon transition moments for REMPI, |M_fo|² _{H2(J = 0 and 1)}/|M_fo|²_{D2(J = 0 and 1),} is approximately 2.14 (Pomerantz et al. 2004). Table 2 summarizes the relative signal intensities of the sum of H₂ or D₂ (J = 0 and 1) obtained from H₂, D₂ and H, D depositions at 8 K. Since the lower limit to the dissociation fraction of D₂ molecules is ∼69%, from Figure 7(b), Table 2, and the discussion above, it is clear that most D atoms diffuse efficiently at the very shallow sites and recombine to form D₂ molecules during D-atom deposition, as well as H atoms. The sum of the D₂ (J = 0 and 1) signal intensities is constant for 10 minutes after D-atom deposition (open squares in Figure 7(b)), indicating that the very shallow potential site is also dominant for diffusion of D atoms on the ASW surface.

N_diff and the diffusion coefficient of D atoms at the very shallow sites may be smaller than for H atoms because of the heavier mass of the D atoms, though the isotopic effect on the very fast diffusion of both H and D atoms could not be evaluated quantitatively in the present experiment. This is because both atoms have already recombined to form molecules during the deposition, and we could not evaluate the possibility of quantum tunneling.

The photodesorbed H₂ intensities for J = 0 and 1 as a function of waiting time after H₂ deposition at 8 K (solid triangles and circles in Figure 7(a)) show that the intensity of H₂ (J = 1) decreases, while that of H₂ (J = 0) increases at 8 K as the residence time on the ASW surface increases. Since the sum of the intensities of H₂ (J = 0 and 1) was constant, these results indicate the nuclear spin conversion of H₂ (J = 0 and 1) on the ASW surface at 8 K. The conversion was also observed at 15 K (see Figure 9 in the Appendix and Watanabe et al. 2010). The nuclear spin conversion of H₂ (J = 0 and 1) will be further investigated in a forthcoming article.

As shown in Figure 6, the signal intensities of H and D atoms from ASW at 12 K (solid triangles) became more than one order of magnitude smaller than those at 8 K (solid circles). This result is significantly different from the relative signal ratio obtained from the TOF spectra of photodesorbed H atoms from ASW at 8–15 K during H-atom deposition (see Figure 3(a) and Table 1). Meanwhile, the relative signal intensities of the TOF spectra between 8 and 12 K are 1:0.42 and 1:0.76 for H and D atoms from ASW, respectively (see Table 1). These results indicate that, after H-atom deposition was halted, the H atoms present on the ASW surface at 12 and 15 K were much more rapidly consumed by recombination following fast diffusion compared with the situation at 8 K and/or when immediate monoatomic desorption became appreciable above 12 K. In the TOF spectra, D atoms tend to remain on the surface longer at relatively high temperatures compared to H atoms, both for ASW and PCI, presumably because of the different binding energies, E_b, between H and D atoms due to the zero-point energies (Buch & Czerminski 1991). To evaluate the recombination efficiency of H atoms on the ASW surface and monoatomic desorption at 15 K, we carried out time-variation experiments for H₂ (J = 0 and 1) from ASW at 8 and 15 K after atomic or molecular deposition for 360 s (corresponding coverage: θ ≈ 2–7 × 10⁻²); the contribution of monoatomic desorption at 15 K can be estimated from the relative recombination efficiencies between 8 and 15 K.

Table 2 summarizes the relative signal intensities of the sum of H₂ and D₂ (J = 0 and 1) obtained at 8 and 15 K. The plots of experimental data at 15 K are shown in Figure 9 in the Appendix. For H₂ deposition experiments, the total H₂ (sum of J = 0 and 1) signal intensities obtained at 15 K were slightly higher than that at 8 K (1.2:1.0), as shown in Table 2. This small difference between 8 and 15 K may be caused by the difference in photodesorption efficiencies at 8 and 15 K. The ratios of the total H₂ signal intensities between H₂ and H depositions at 8 and 15 K are 1 (H₂):0.8 (H) and 1 (H₂):0.6 (H), respectively, as summarized in Table 2. When we take a lower limit to the dissociation fraction of H₂ to be roughly 70% in the atomic beam, the fraction of undissociated H₂ molecules is about 0.3. Thus, from Table 2, the lower limits of recombination efficiencies at 8 and 15 K are estimated at 0.8 − 0.3 = 0.5 and 0.6 − 0.3 = 0.3, respectively, indicating the occurrence of diffusion and recombination of H atoms at 15 K before monoatomic desorption.

These values should be lower limits because ejection of H₂ molecules on recombination using heat of formation (4.5 eV) may occur to some extent. These values are fairly consistent with the recombination efficiencies on high-density amorphous ice reported by Vidali, Pirronello, and their coworkers (e.g., Vidali et al. 2006). The lower value at 15 K may be caused by the loss of H atoms by monoatomic desorption as well as ejection of H₂ molecules upon recombination. The same discussion can be adapted to deuterium. Considering the lower limit to the dissociation fraction of D₂ (∼69%) in the atomic beam, Table 2 and Figure 9 in the Appendix indicate that D atoms can also diffuse and recombine on the ASW surface at 15 K.

In our previous study, the H-atom intensities at 15 K after H-atom deposition on ASW were not as weak (of the same order) compared to those at 10 K (see Figure 3 in Watanabe et al. 2010). We found the reason for this is that the data were measured at the rising edge in the TOF spectrum of the H atoms in the previous experiment (see Figure 10 in the Appendix). In the present study, to obtain more quantitative information about potential sites on the ASW surface, we set the delay time between the PSD and REMPI lasers corresponding to the peak in the TOF spectra of the two atoms in Figure 6. Watanabe et al. (2010) confirmed the presence of H atoms on the ASW surface 90 minutes after H-atom deposition at 15 K, which gave a coverage of 10⁻³, and estimated E_diff for a deep site of 50 meV. The fraction of these very deep sites would be small compared with that of potential sites with an energy depth of E_diff = 30 meV.

Figures 3(b) and (d) show typical TOF spectra of photodesorbed H and D atoms from PCI. H and D signals from PCI almost disappeared at 15 K, indicating that the shallower potential sites where H atoms cannot be trapped at 15 K dominate the PCI surface compared to the ASW surface. When H and D atoms were deposited on PCI at 8 K for 360 s, the number of both H and D atoms on PCI diminished immediately (open circles in Figure 6). We could not obtain significant data for fits using Equation (7). Figure 6, however, also shows that the PCI surface only consists of very shallow potential sites, where more efficient diffusion of H and D atoms is expected.

We also studied the time variations of photodesorbed H₂ (J = 0 and 1) signals as a function of waiting time after H₂ and H deposition for 360 s on PCI. Figure 8(a) shows the typical results obtained at 8 K. The results for isotopic D₂ or D experiments at 8 K are also shown in Figure 8(b). We see a decrease in the total signal intensities of both H₂ (J = 0 and 1) and D₂ (J = 0 and 1) at 8 K by unimolecular desorption after molecular deposition (solid data points in Figure 8), which is in contrast to the results from ASW (Figure 7). The same behavior was observed for the H₂ and D₂ (J = 0 and 1) signals obtained after we deposited H or D atoms on PCI at 8 K (open data points in Figure 8). It is thus difficult to evaluate recombination on PCI quantitatively. The sum of the H₂ or D₂ (J = 0 and 1) signals obtained at t = 0.5 minutes from the atomic depositions is, however, higher compared with the lower limit to the dissociation fraction (66% or 69%, respectively) implying that some recombined H₂ (D₂) remains on PCI for at least 0.5 minutes at 8 K. Hornekær et al. (2003) and Amiaud et al. (2007) investigated H+D or D+D recombination on nonporous ASW. Both studies showed that newly formed molecules on nonporous ASW are ejected into the gas phase. Similar reactions can be expected in PCI.

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Monoatomic desorption of H atoms is closely related to their binding energy, E_b (E_b is equivalent to the activation energy for desorption, E_des). Several theoretical studies of E_b for H atoms adsorbed on crystalline ice exist (Hollenbach & Salpeter 1970; Al-Halabi et al. 2002; Al-Halabi & van Dishoeck 2007). For example, Al-Halabi & van Dishoeck (2007) predicted that the adsorption probability of H atoms onto the crystalline surface is similar to that onto the ASW surface, and the average E_b of the trapped H atoms is 34 meV, with a full width at half-maximum of 10 meV. The residence time on crystalline ice was calculated to be 1.0 × 10⁵ s at 10 K (Al-Halabi & van Dishoeck 2007), which was longer than the present experimental timescale. In view of the observed unimolecular desorption of H₂ and D₂ molecules on PCI, however, monoatomic desorption of H and D atoms would contribute to the loss of H and D atoms on PCI to some extent, both during and after atomic deposition. If the desorption rate depends on the mass of the adsorbate, then the desorption rates may be comparable between H₂ molecules and D atoms.

Since the absorption coefficient of water ice is known to be negligibly small for photons at 532 nm (⩽10⁻³ cm⁻¹) (Grenfell & Perovich 1981), photodesorption may be induced from the Al surface; propagation of phonons from the substrate is a possible source. In fact, ice thickness dependence on the signal intensities of TOF spectra for photodesorbed H atoms from ASW at 8 K was studied for vapor-deposition times of 84–4200 s (6–316 L); the intensities decreased as the ice thickness increased, and almost disappeared for 4200 s deposition (316 L). Several PSD mechanisms have also been proposed for physisorbed molecules on cryogenic surfaces (Fukutani et al. 2005).

We now evaluate the possibility of laser-induced thermal diffusion. The optical depth (the depth to which the transmission drops to 1/e = 37%) of the Al substrate is ∼7 nm (Hagemann et al. 1975). Assuming a square incident laser pulse with a pulse width of τ_in seconds, the maximum temperature rise of the Al substrate surface, ΔT(t_in), can be estimated using Equation (A1) (Osmundsen et al. 1985),

$$\begin{eqnarray} &&\Delta T(t_{{\rm in}}) \,{=}\, 2I(1 \,{-}\, R)(1 \,{-}\, 1/e)({\ss}\tau _{{\rm in}} /\pi)^{1/2} /\kappa , 0 \,{\le}\, t_{{\rm in}} \, {\le}\, \tau _{{\rm in}}.\nonumber\\ \end{eqnarray} \tag{ A1 }$$

I (1 − R) (1 − 1/e) is the laser intensity (J s⁻¹ cm⁻²) absorbed at the Al substrate surface at the optical depth. I and R are the incident laser intensity and the reflectivity of the Al substrate surface, respectively; 2 (βτ_in/π)^1/2/κ (J⁻¹ s cm² K) effectively means the inverse of the heat-transfer coefficient, where β and κ are the thermal diffusivity (cm² s⁻¹) and thermal conductivity (J s⁻¹ cm⁻¹ K⁻¹), respectively. For the Al substrate, the reflectivity R = 0.916 (Hass 1955). From the relation β = κ/ρc, where ρ and c are the density (g cm⁻³) and heat capacity (J g⁻¹ K⁻¹), respectively, we derived β for the Al substrate at 8 K to be 24⁺¹²₋₆ (cm² s⁻¹), when taking κ = 0.1 (J s⁻¹ cm⁻¹ K⁻¹), ρ = 2.8 (g cm⁻³), and c = (1.5 ± 0.5) × 10⁻³ (J g⁻¹ K⁻¹) at 8 K (Woodcraft 2005; Ekin 2006). In the present case, I = 7 × 10⁴ (J s⁻¹ cm⁻²), τ_in = 4 × 10⁻⁹ (s), and the maximum temperature rise was estimated to be about 13⁺³₋₂ K in 7 nm of the Al substrate surface. If the ASW surface immediately reaches thermal equilibrium with the Al substrate from 8 K to ∼24 K, then Equation (2) gives only 1−10 hops of atoms during τ_in = 4 × 10⁻⁹ s at the very shallow site with E_diff = 18 meV, even ignoring desorption of atoms. In fact, since heat is dissipated within bulk ice and the thermal conductivity of ASW is extremely low (Kouchi et al. 1992), the temperature of the ASW surface would not reach 24 K. If E_diff at the very shallow site is less than 18 meV, then atoms recombine within 30 s of deposition before the PSD experiment, as discussed in Section 3.2. Thus, we consider that laser-induced thermal diffusion does not play a dominant role in the recombination of atoms at very shallow sites in Figure 5(b).

Figure 9 shows time variations of photodesorbed (a) H₂ (J = 0 and 1) and (b) D₂ (J = 0 and 1) signals as a function of waiting time after molecular (solid data points) or atomic (open data points) depositions for 360 s on ASW at 15 K. The sum of the H₂ and D₂ (J = 0 and 1) intensities are also plotted.

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We have reproduced the data of Figure 3 in Watanabe et al. (2010) by measuring at TOF = 0.5 μs, corresponding to the rising edge in the TOF profile of H atoms. Figure 10 shows the attenuation of the photodesorption intensities of H atoms from ASW at 8 K (solid circles) and 15 K (solid squares) as a function of the waiting time after deposition for 360 s with a chopper disk. The power of 532 nm for PSD was ∼80 μJ pulse⁻¹, which was the same as used in Watanabe et al. (2010). TOF = 0.5 μs corresponds to the rising edge in the TOF spectra of H atoms. To obtain more quantitative information about potential sites on the ASW surface, we set TOF = 1.2 and 1.5 μs for H and D atoms in the present study, respectively, which corresponds to the peak in the TOF spectra of the two atoms shown in Figure 3.

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