Direct Measurements of Activation Energies for Surface Diffusion of CO and CO2 on Amorphous Solid Water Using In Situ Transmission Electron Microscopy

The importance of the activation energy of surface diffusion (Esd) of adsorbed molecules on amorphous solid water (ASW) has been widely discussed in terms of chemical reactions on ASW at low temperatures. However, in previous work, Esd has not been measured directly but estimated from indirect experiments. It has been assumed in chemical network calculations that Esd is between 0.3 and 0.8 of the desorption energies of a molecule. It remains important to obtain direct measurements of Esd. We performed in situ observations of the deposition process of CO and CO2 on ASW using transmission electron microscopy (TEM) and deduced the Esd of CO and CO2 on ASW to be 350 ± 50 and 1500 ± 100 K, respectively. The value of Esd of CO is approximately 0.3 of the total adsorption energy of CO on ASW, i.e., much smaller than assumed in chemical network calculations, where the corresponding figure is 575 K, assuming approximately 0.5 of the desorption energy. We demonstrated that TEM is very useful not only for the observation of ices but also for the measurement of some physical properties that are relevant in astrochemistry and astrophysics. Using the Esd of CO measured in the present study (350 K), we have updated the chemical network model of Furuya et al., confirming that CO2 could be efficiently formed by the reaction CO + OH → CO2 + H in the initial stages of the evolution of molecular clouds.


Introduction
In molecular clouds and dense cores where star formation occurs, the most abundant molecules, such as H 2 O, CO 2 and CH 3 OH, are present mainly on grain surfaces, including ice. These molecules are formed by two-body reactions on surfaces through the Langmuir-Hinshelwood mechanism (e.g., Watanabe & Kouchi 2002;Hama & Watanabe 2013). One of the most important parameters for determining the rates of surface twobody reactions is the activation energy of the surface diffusion of adsorbed species, but this is poorly quantified. It is, therefore, usually assumed that the activation energy of the surface diffusion of a molecule is 0.3-0.8 of the desorption energies of that molecule (Iqubal et al. 2018).
Some experimental attempts have been made to clarify the surface diffusion of CO and CO 2 . Öberg et al. (2009) conducted segregation experiments using mixed ices, H 2 O:CO, and H 2 O:CO 2 , and obtained activation energies of surface-segregation. Mispelaer et al. (2013), Karssemeijer et al. (2014), Lauck et al. (2015), and He et al. (2018) measured the diffusion of CO in amorphous solid water (ASW). In these studies, it was assumed that diffusion of CO or CO 2 occurs at the surface of pores and/or cracks in ASW and that the measured activation energies were not due to bulk diffusion but due to surface diffusion. He et al. (2017) conducted annealing experiments of CO 2 deposited on the surface of ASW and obtained the activation energy of surface diffusion for CO 2 on ASW. Because all of the studies referred above (Öberg et al. 2009;Mispelaer et al. 2013;Karssemeijer et al. 2014;Lauck et al. 2015;He et al. 2017He et al. , 2018 used infrared spectroscopy to observe change of composition, models (e.g., rate equations) are required in order to estimate diffusion coefficients or activation energies of surface diffusion. It is thus concluded that all values obtained in these studies are model dependent.
In theoretical works, Karssemeijer et al. (2014) obtained activation energies of surface diffusion of CO on ASW, finding that the CO mobility is highly dependent on the morphology of ASW. Because the values obtained are very widely distributed (48-114 meV or 557-1320 K) and because the maximum value of 114meV is larger than the activation energy of adsorption (Collings et al. 2003), using their results in chemical network calculations is difficult. It is, therefore, necessary to perform direct measurements of the surface diffusion coefficient of CO or CO 2 on ASW or activation energy for surface diffusion.
To overcome some of the difficulties experienced in past studies, direct observations using a transmission electron microscope (TEM) are highly valuable. Although some observations of pure H 2 O ice using TEM have been performed, the primary focus of these observations included the structures formed (e.g., Honjo et al. 1956;Vertsner & Zhdanov 1966), the structural transition between high-density ASW and lowdensity ASW (e.g., Heide 1984;Jenniskens & Blake 1994), and the crystallization of ASW to form ice (e.g., Jenniskens & Blake 1996). Further, there have been no observations of CO and CO 2 using TEM.
In the present study, we have performed in situ observations of the deposition process of CO and CO 2 on ASW using an ultrahigh-vacuum transmission electron microscope (UHV-TEM) and obtained the activation energies for surface diffusion of CO and CO 2 on ASW.

Experiment
We used a UHV-TEM (JEOL JEM-2100VL) for in situ observation of ices (Kouchi et al. 2016;Tachibana et al. 2017). A column of the UHV-TEM was evacuated using five ion pumps and two Ti sublimation pumps. The pressure between the specimen chamber and the ion pump was set at 1×10 −6 Pa. The pressure near the specimen might be lower than 1×10 −6 Pa as the specimen is surrounded by a liquid nitrogen shroud.
We used a liquid He cooling holder (Gatan ULTST) for sample cooling (Figure 1). A non-porous amorphous Si film with a thickness of 5nm (SiMPore Inc. US100-A05Q33) was used as the substrate for sample deposition. We observed the Si film using high-resolution field emission TEM (JEM-2100F), and observed no pores or cracks. We also used a 0.4 mm inner diameter Ti gas inlet tube for sample deposition, which was directed at the specimen surface with an incident angle of 55°( Figure 1).
First, a ∼10 nm thick layer of ASW was deposited at ∼10 K. We measured the thickness of the ice samples as follows. First, a thick ice sample (e.g., 200-300 nm) was deposited at a constant deposition rate. Then, we observed the sample via TEM. By adjusting the foci at the bottom and the surface sides of the ice sample, we could measure the thickness of ices. We also measured the pressure of a gas reservoir prior and subsequent to the ice deposition. From these measurements, we obtained the relationship between the amount of deposited gas and the ice thickness. The use of thin ASW (10 nm thick) has an advantage that the contrast of the newly deposited CO or CO 2 on ASW is stronger than that of ASW. ASW deposited at low temperatures is very porous (e.g., Stevenson et al. 1999); thus, we termed it porous ASW (p-ASW). We used the p-ASW without annealing for CO deposition. For CO 2 deposition, p-ASW deposited at approximately 10 K was annealed at 70 K. Then, CO or CO 2 was deposited onto ASW with a deposition rate of ∼1nm minute −1 . We confirmed that crystalline CO (α-CO) was formed when deposition rate is larger than this value as stated by Kouchi (1990). We observed the entire deposition process using UHV-TEM. To avoid electron beam damage to the samples, a low dose (Tachibana et al. 2017) was applied, using an 80 kV accelerating voltage, very weak electron beam intensity (∼2×10 −3 electrons Å −2 at the sample position), and low-magnification observation (×25,000) using a CCD camera (Gatan ES500W). It is usually assumed that most 80 kV electrons will not interact with 10 nm thick ASW, implying that the ASW will not be damaged by an electron beam.

Results and Discussion
Figures 2(a) and (b) show the temperature dependence of the deposition processes of CO and CO 2 on ASW, respectively. It is noted that TEM observation was made during the gas deposition in situ. Electron diffraction patterns show that crystalline CO (α-CO) and CO 2 (CO 2 I) were formed at temperatures higher than 18 and 50 K, respectively. At lower temperatures (broken lines in Figure 2), amorphous CO (a-CO) and amorphous CO 2 (a-CO 2 ) were formed. These transition temperatures depend on the rate of deposition and are not determined uniquely (Kouchi et al. 1994), differing from the crystallization temperatures of a-CO and a-CO 2 (Watanabe & Kouchi 2008). TEM images clearly show that crystals did not grow as a uniform film but as three-dimensional islands, sometimes referred to as the Volmer-Weber growth mode. With decreasing substrate temperature, the number of crystals increased, and crystalline sizes decreased. In the case of a-CO and a-CO 2 , on the other hand, uniform films were formed. Figure 3 shows the change in the number densities of the CO and CO 2 crystals as measured via visual counting. It is clear that the number densities increased suddenly after certain incubation times, reaching saturated values. The heterogeneous nucleation rate, J, is given by the following equation (Hirth & Pound 1963, Figure 1. Newly developed UHV-TEM. Three ports are directed at the sample surface (the short blue bar) with an incident angle of 55°; these ports are used for an ultraviolet (UV) lamp, a variable leak valve connected to a Ti tube for gas deposition, and a quadrupole mass spectrometer.
Chapter C): where Z is the non-equilibrium factor, ΔG * is the free energy for the formation of the critical nucleus, k B is the Boltzmann constant, and ω=n 2πr * a sinθ, where n is the number of adsorbed molecules, r * is the radius of the critical nucleus, a is the diffusion jump distance, and θ is the contact angle between the substrate and the nucleus. Because the incubation time for nucleation, τ, is defined as τ=1/J, τ is proportional to ΔG * and q −1 . Therefore, the fact that the τ value of the CO 2 crystals (less than 2 minutes) was shorter than that of the CO crystals (2-6 minutes) indicates that the ΔG * of CO 2 is lower than that of CO and/or that the θ of CO 2 is smaller than that of CO ( Figure 3). The thicknesses of the CO crystals at 21.5 and 24 K in Figure 2 are larger than those of CO 2 at 55 K and 60 K, respectively; therefore, the θ value of CO 2 is smaller than that of CO, suggesting the latter possibility. In the case of CO, τ In general, the contrast of TEM images increases from bright (gray) to dark (black) with the increasing atomic numbers (scattering contrast). The contrast of crystal samples is much stronger (darker) than that of amorphous sample owing to the diffraction contrast. Therefore, the detection of CO or CO 2 crystals on ASW is easier than that of a-CO or a-CO 2 on ASW. At temperatures higher than the critical temperatures shown by broken lines, crystalline CO (α-CO) and CO 2 (CO 2 I) were formed. At temperatures lower than the critical temperature, on the other hand, amorphous CO and CO 2 were deposited. White blurred images recorded in some TEM photographs are residual images in the charge-coupled device (CCD) detector.
clearly decreases with decreasing temperature. Conversely, in the case of CO 2 , such a temperature dependence has not been observed. This is likely because nucleation is the stochastic phenomenon and the observed temperature range defined by 1/T of CO is wider than that of CO 2 (see Figure 4). When the nucleation ceases, the growth of crystalline islands is limited by the surface diffusion of monomers, not by that of dimers or trimmers (clusters). This is verified by the following reasons.
(1) At a constant incident flux and temperature, the nucleation rate should decrease with the increasing the number of crystalline islands that are larger than the critical size, because the growth of islands via the diffusion of monomers should be the dominant process rather than the nucleation.
(2) During the growth stage of stable crystalline islands, growth via cluster-cluster collision can be ignored compared with that via the attachment of monomers. In this case, we were able to obtain information on surface diffusion from the distance between islands. From the saturated number densities, N s , mean distances between crystalline islands, L, were derived using the relation L=(π N s ) −1/2 . The mean diffusion distance, X, of CO or CO 2 on ASW is defined to be half of L. According to Smith (1995) (Chapter 5.2), when desorption of molecules is ignored, X is expressed by where a is hop distance, ν is the frequency factor, n 0 the number of adsorption sites, F the deposition flux, E sd the activation energy of surface diffusion, R the gas constant, and T is the temperature. The above assumption that the desorption of molecules could be ignored is supported because a sticking coefficient of CO 2 onto non-porous ASW (np-ASW) is unity at temperatures lower than 80 K (He et al. 2016a). Although there has been no direct measurement of the sticking coefficient of CO onto p-ASW, this may also be unity because the sticking coefficient of N 2 onto p-ASW is unity at temperatures below 26.5 K (Kimmel et al. 2001) and because the sticking coefficient of CO onto np-ASW is unity at temperatures lower than 50 K (He et al. 2016a). The behavior of Equation (2) appears as a straight line with a negative slope of −E sd /2R on   the plot of ln X versus 1/T in Figure 4. We obtained an E sd of CO (E sd (CO)) on p-ASW and E sd of CO 2 (E sd (CO 2 )) on np-ASW of 350±50 and 1500±100 K, respectively. He et al. (2016b) measured the surface coverage dependence of the binding energy of CO on p-ASW. If we assume that the surface coverage of CO on p-ASW is unity, the adsorption energy of CO on p-ASW would be 1028 K. E sd (CO) on p-ASW obtained in this study is 0.34 of this value. E sd (CO 2 ) on annealed ASW is 0.66 of the adsorption energies of CO 2 on np-ASW (Noble et al. 2012). Because p-ASW is acknowledged as a very porous material with a large surface area (e.g., Stevenson et al. 1999), the surface of p-ASW is not molecularly flat but might be rough. Therefore, true diffusion distances are much larger than the projected distances obtained in the present study. If true, the plot in Figure 4 should be moved upward as shown by the broken line. Since annealed ASW at 70 K may be less porous than p-ASW, a slight correction might be needed, as shown by the dotted line. It is noted that the slopes of the plots, E sd , do not change after correction. In addition, the Arrhenius plots were found to be linear throughout the temperature regions of 18-24 K for CO and 50-60 K for CO 2 . These results suggest that the growth of crystalline islands is dominated by the diffusion of monomers rather than clusters because the diffusion of large clusters should be effective at high temperatures, which would cause the data to deviate from the Arrhenius plot. He et al. (2018) pointed out from the observation of dangling OH that the structure of p-ASWdeposited at 10 K changes from 10 to 30 K. However, this possible structural change does not influence diffusion of CO significantly as the Arrhenius plot of CO can be reproduced by a single linear component.We, therefore, conclude that the values of E sd determined in the present study are unique.
This study presents the first direct measurements of E sd (CO) and E sd (CO 2 ) on ASW. Some previous studies have reported values of E sd for CO on ASW using indirect methods such as infrared spectroscopy and temperature programmed desorption (TPD) mass spectrometry, e.g., 116±174 K (Mispelaer et al. 2013), 302±174 K (Karssemeijer et al. 2014), 158±12 K (Lauck et al. 2015, and 490±12 K (He et al. 2018). E sd values have certain uncertainties when the experiments are performed at high temperatures such as 35-40 K (Mispelaer et al. 2013) or 32-50 K (Karssemeijer et al. 2014) because the desorption and diffusion of CO simultaneously occur and it is difficult to separate the two effects. Furthermore, Karssemeijer et al. (2014) reported a significantly small pre-exponential factor (D 0 ) of 9.2×10 −10 (cm 2 s −1 ). For reference, D 0 is roughly estimated to be 9×10 −4 (cm 2 s −1 ), assuming D 0 =a 2 ν, where a and ν are the typical hopping distance (a=0.3 nm) and frequency factor (ν=10 12 s −1 ), respectively. A minor D 0 value was also reported in Lauck et al. (2015), D 0 =3.1×10 −12 (cm 2 s −1 ). These small D 0 values imply that there may be problems when calculating D 0 and E sd in surface diffusion on amorphous ices using rate equation models. He et al. (2018) reported D 0 =10 −6.47 and E sd = 490 K and proposed that the frequency for diffusion (ν) could be several orders of magnitude smaller than that for desorption, i.e., ν=1.5×10 9 s −1 . The difference in E sd between this study (350 K) and that of He et al. (2018) can be explained by the ice preparation method, i.e., He et al. (2018) annealed ASW at 70 K for 30 minutes. As a next step, measurements of D (D 0 and E sd ) on various ices, such as annealed p-ASW at 70 K, compact ASW, and crystalline ices, are required to comprehend the diffusion mechanism on ices. In addition, if we can simultaneously measure the nucleation rate and growth rate of CO or CO 2 crystals, the surface energy of these crystals can be obtained as well as D (D 0 and E sd ).
It is important to discuss the morphologies of CO and CO 2 deposited on ASW after the surface reactions, as well as the nonthermal desorption of molecules and the sticking of icy grains. However, this study makes its focus on the E sd since the morphologies of CO and CO 2 require further information on the morphologies of CO and CO 2 crystals formed by the crystallization of amorphous CO and CO 2 . This will form the subject of forthcoming work. Furthermore, the method developed in this study could be applicable to infrared inactive molecules, such as N 2 , O 2 , and Ar.
This study demonstrates that TEM is extremely useful and promising not only for the observation of the deposition process but also for the measurement of E sd . TEM images include various information concerning the texture, number, and form of grains, all of which cannot be obtained via infrared spectroscopy or TPD methods. Electron diffraction provides detailed information concerning the crystallinity, amorphous, or crystalline nature, and size of the crystals. Our UHV-TEM instrument includes an electron energy-loss spectrometer (Gatan Imaging Filter Tridium), which enables us to measure atomic compositions and to detect various functional groups. In particular, the detection of radicals (OH, O, and HO 2 ) is the most remarkable feature of electron energy-loss spectroscopy; such detections are nearly impossible via infrared spectroscopy or TPD. This Letter is a first report of results using UHV-TEM; other examples demonstrating the usefulness of UHV-TEM will be published in forthcoming papers.

Efficient Formation of CO 2 in Molecular Clouds
CO 2 is one of the most abundant components of interstellar ice after H 2 O; the median CO 2 /H 2 O abundance ratio is 26% in molecular clouds and cores (see Boogert et al. 2015 for a review). The main formation pathway of CO 2 in the interstellar medium (ISM) remains under debate. Infrared ice observations in star-forming regions indicate that the polar component of CO 2 dominates over the apolar component, suggesting that most CO 2 (approximately 80% of the overall CO 2 ) is embedded in H 2 O within the interstellar ice (Öberg et al. 2011 (e.g., Garrod & Pauly 2011). In such a scenario, the formation of CO 2 ice competes with that of H O 2 ice, i.e., CO diffusion competes with the hydrogenation of OH. Note that Reaction (3) in the gas phase has an activation energy barrier of 176 K (Song et al. 2006;Li et al. 2012), whereas Oba et al. (2010) found that the reaction proceeds on the ASW surface at 10 K, suggesting that the surface reaction has effectively no or very small energy barrier. Therefore, the ratelimiting step of Reaction (3) at the surface would be the diffusion of CO to OH.