Transmission Electron Microscopy Study of the Morphology of Ices Composed of H₂O, CO₂, and CO on Refractory Grains

We developed a 200 kV ultra-high-vacuum transmission electron microscope (UHV-TEM; JEM-2100VL, JEOL) for in situ deposition and observation of ices following Kondo et al. (1991), as described in our recent papers (Kouchi et al. 2016; Tachibana et al. 2017; Kouchi et al. 2020). Briefly, a microscopic column is evacuated using five sputter ion pumps and two Ti-sublimation pumps. The pressure near the specimen is measured by a nude ionization gauge placed between the sample chamber and the ion pump. Because the sample was surrounded by a liquid nitrogen shroud, the real pressure near the specimen was lower than the measured pressure.

We used a commercially available liquid He cooling holder (ULTST, Gatan) for specimen cooling. Because the temperature sensor's position is not the same as that of the specimen, the temperature of the specimen differs from that of the sensor. The temperature of the specimen is calibrated using the vapor pressures of crystalline Ne, CO, Ar, and CO₂. The temperature difference between the specimen and the temperature sensor at low temperatures, such as 10–20 K, is around 3 K (with the temperature of the specimen being higher than that of the sensor), and at temperatures above 30 K, almost no difference occurs. The errors in temperature measurement at 10–30 K and >30 K are about ±1.2 K and ±0.5 K, respectively. One of the three ICF 70 ports directed at the sample surface with an incident angle of 55° is used for gas deposition, with a variable-leak valve connected to a 0.4 mm inner-diameter Ti-gas inlet tube. A small gas-mixing system is attached to the variable-leak valve.

A nonporous a-Si film of thickness 5 nm sputtered onto the Si single-crystal grid (US100-A05Q33, SiMPore Inc.) was used as a substrate for the deposition of ices, organic matter, and a-silicate for the following reasons: (1) because the thermal conductivity of the Si single crystal at 10–200 K is larger than 10³ W m⁻¹ K⁻¹ (Glassbrenner & Slack 1964), the a-Si film is deposited very firmly on the single Si crystal; (2) the TEM contrast of 5 nm thick a-Si is very weak; and (3) the edge of a Si single crystal could be used as a standard for camera-length calibration in electron diffraction. We observed the nonporous a-Si film using a high-resolution field emission TEM (JEM-2100F, JEOL) and observed neither pores nor cracks (as shown in Figure 1(a)).

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An organic refractory material (organics) was made using the method of Piani et al. (2017). A gas mixture consisting of H₂O:CH₃OH:NH₃ = 6:4:1 was deposited onto the a-Si substrate and simultaneously irradiated with UV rays at around 10 K using the PICACHU setup. After deposition, the substrate was warmed up to room temperature and organic refractory materials remained. Although the organic refractory material was not of uniform thickness (see Figures 3(e) and (f) of Piani et al. 2017), we observed the uniform part in the present study (Figure 1(b)). The electron diffraction pattern shows that organic refractory material is amorphous.

An a-silicate was deposited onto the a-Si substrate at room temperature via magnetron sputtering of an Mg₂SiO₄ polycrystalline target. The thickness measured by the quartz microbalance was 10 nm, and the density of a-silicate was assumed to be the same as that of crystalline Mg₂SiO₄ (forsterite). TEM images and electron diffraction patterns show that the film is reasonably uniform and amorphous (Figure 1(c)), and the atomic composition measured using an energy dispersive X-ray spectrometer equipped with JEM-2100F was Mg:Si:O = 33.2:15.6:51.2 (atm%). Hereafter, we call the a-silicate a-Mg₂SiO_3.3.

For the a-C substrate, we used commercially available C-flat with a thickness of 20 nm (Protochip Inc.; Quispe et al. 2007). As shown in Figure 1(d), the film is amorphous and has many small holes, and there are some tiny graphitic grains on the a-C film.

2.3.1. Deposition of H₂O on the Organics, a-Mg₂SiO_3.3, and a-C

2.3.2. Crystallization of Amorphous Ices

2.3.3. TEM Observation

2.3.4. Infrared Spectroscopy

Figure 2 shows the TEM images of ice I_c deposited onto the organic, a-Mg₂SiO_3.3, and a-C substrates taken after saturation of the crystal number at temperatures between 145 and 130 K. At temperatures below 125 K, uniform films of a-H₂O were formed for all substrates. The number of crystals clearly decreases with increasing temperature. The number densities of ice I_c crystals on a-Mg₂SiO_3.3 and a-C take almost the same values, but those on the organics are smaller at 145 and 140 K.

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Based on the number density of crystals as measured via visual counting, we calculated the mean diffusion distances of H₂O molecules following Kouchi et al. (2020) (Figure 3). According to Smith (1995), the mean surface diffusion distance, X, is expressed by X = a(νn₀/F)^1/2 exp(−E_sd/2RT), where a is the hopping distance, ν the frequency factor, n₀ the number of adsorption sites, F the deposition flux, E_sd the activation energy of surface diffusion, R the gas constant, and T the temperature. When F is constant, this behavior appears as a straight line with a negative slope of −E_sd/2R on the Arrhenius plot of lnX versus 1/T in Figure 3. Consequently, from the slopes of these plots, we found the activation energies (E_sd) of the surface diffusion of H₂O molecules on the organics, a-Mg₂SiO_3.3, and a-C to be 2830 ± 200 K, 1940 ± 150 K, and 2050 ± 500 K, respectively. These values are smaller than the activation energy of the surface diffusion of H₂O on a-H₂O, which was estimated by Berland et al. (1995) to be 3575 K; however, they are almost the same as (or larger than) that estimated by Zondlo et al. (1997; 2115 K). In addition, we confirmed that ice I_c also shows a lower wettability on these substrates in the case of deposition (see the 145 K images in Figure 2). The E_sd values on a-Mg₂SiO_3.3 and a-C are 0.33 and 0.35 of the corresponding desorption energies on H₂O (i.e., 5964 and 5928 K), respectively, as measured by Potapov et al.(2018).

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3.2.1. Crystallization of a-CO

Figure 4 shows the crystallization of a-CO on the a-CO₂, a-H₂O, and a-H₂O:CO₂ substrates. The TEM images of CO at 10 K are uniform, and electron diffraction shows halo patterns, suggesting that these samples are amorphous CO (a-CO; Figure 4(a)). TEM images of CO at 21 K suggest the occurrence of crystals because of the strong diffraction contrast (Kouchi et al. 2021); the electron diffraction pattern confirms that crystalline CO (α-CO) was formed. In the image taken after 2 minutes at 21 K, the crystal size was uniform and ∼50 nm in size. After 8 minutes, coarsening of the crystals was observed. TEM images clearly show that α-CO did not grow as a uniform film but as three-dimensional islands.

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Similar phenomena were observed in the cases of crystallization of a-CO on the a-H₂O (Kouchi et al. 2021) and a-H₂O:CO₂ = 5:1 substrates; however, in these cases, the formation of three-dimensional islands was remarkable (Figures 4(b) and (c)). After 0.2 minutes at 24.5 K (Figure 4(b)), crystals were uniformly around 50 nm in size; after 3 minutes, only specific crystals grew to ∼200 nm in size, with others remaining the same size or becoming smaller. We usually call this phenomenon Ostwald ripening (e.g., Lifshitz & Slyozhov 1961; Bhakta & Ruckenstein 1995).

3.2.2. Crystallization of a-CO₂

Figure 5 shows the crystallization of a-CO₂ on the a-H₂O substrate at 50 and 60 K. In the TEM images of the 50 K samples, almost no change can be observed, but the electron diffraction pattern clearly shows the formation of CO₂ i crystals. The size of the crystals (d) could be calculated from the FWHM of the diffraction peak in terms of the 2θ angle, B(2θ), using

$$\begin{eqnarray}&&d=0.85\lambda /[B(2\theta )\cos \theta ],\end{eqnarray} \tag{ 1 }$$

where λ is the wavelength of an 80 kV electron (Ida et al. 2003). The size of the CO₂ i crystals after 10 minutes at 50 K is 9.3 nm. At 60 K, the size increased to ∼50 nm, showing that the coarsening proceeded in CO₂ i; however, the CO₂ crystals formed did not show a three-dimensional island structure like α-CO, but rather formed an almost uniform film.

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3.2.3. Crystallization of a-CO:CO₂

The changes of the TEM images and corresponding electron diffraction patterns during heating of a-CO:CO₂ = 1:1 are shown in Figure 6. At first glance, TEM images appear not to be changed from 12.8 to 70 K; however, electron diffraction patterns clearly show the occurrence of crystalline phases: α-CO with d > 3.6 nm at 33 K, CO₂ i with d = 4.1 nm at 50 K, and CO₂ i with d > 10 nm at 70 K. We note that the crystallization temperature of a-CO (between 25 and 33 K) is higher than that of pure a-CO (<21 K, Figure 4(a); ∼20 K, Kouchi 1990); this may be due to the slow bulk diffusion of CO in the CO:CO₂ matrix.

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3.2.4. Crystallization of a-H₂O

The crystallization processes of a-H₂O on the organics, a-Mg₂SiO_3.3, and a-C substrates are shown in Figure 7. After 1 minute at 140 K, small three-dimensional crystalline islands of ∼50 nm were formed on all substrates. Then, these islands grew to sizes of 100–200 nm via Ostwald ripening. This is consistent with the observation of the crystallization of a-H₂O on a-C (Jenniskens & Blake 1996: Figure 4). Furthermore, the fact that there is no difference among the three kinds of substrates suggests that the interfacial energies between ice I_c and the three substrates have similar values.

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3.2.5. Crystallization of a-H₂O:CO₂

The changes in the TEM images and corresponding electron diffraction patterns during heating of a-H₂O:CO₂ = 5:1 are shown in Figure 8. At 10 K, a-H₂O:CO₂was a uniform mixture; at around 60 K, CO₂ i started to form as nano-crystals, with some crystalline nuclei growing to 50 nm at 70 K, as shown in Figure 8(b). At around 80 K, CO₂ i sublimated and a-H₂O remained at temperatures above 80 K (Figure 8(c)). The remaining CO₂ may have been included in a-H₂O as an impurity, although TEM could not reveal the CO₂ content. At 140 K, crystallization of a-H₂O started to form 50 nm ice I_c (Figure 8(d)). The present results for the crystallization temperature of a-CO₂ and the sublimation temperature of CO₂ i are consistent with previous studies using infrared spectroscopy (e.g., Sandford & Allamandola 1990a; Hodyss et al. 2008; Öberg et al. 2009b).

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3.2.6. Summary of the Crystallization Observation

Observations of crystallization are schematically summarized in Figure 9. When a-CO crystallized on the a-H₂O and a-CO₂ substrates, three-dimensional islands were formed; then, Ostwald ripening proceeded. When a-H₂O crystallized on the organics, a-Mg₂SiO_3.3, and a-C substrates, similar processes were observed in all cases. The sizes of these crystals became ∼200 nm, which are almost the same scale as icy grains in space, strongly suggesting the occurrence of one crystal of α-CO on the icy grain of a molecular cloud and one ice I crystal on the refractory grain in a protoplanetary disk. On the other hand, when a-CO₂ crystallized on the a-H₂O substrate, filmy nano-crystals were formed; then, coarsening occurred. The wetting of crystalline ices on the substrates varies depending on the combination of ice and substrate. α-CO on a-H₂O shows the lowest wettability, and ice I_c on the organic, a-Mg₂SiO_3.3, and a-C substrates shows a poor wettability. Meanwhile, CO₂ i on a-H₂O shows something between a high wettability and perfect wetting. These wettability and crystalline sizes greatly affect the morphology of icy grains in both molecular clouds and protoplanetary disks, as will be discussed later.

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3.2.7. Timescale of Crystallization

We measured the crystallization timescale of a-CO₂; in general, detecting the onset of crystallization is not so difficult using TEM, but detecting the end point is rather difficult. Therefore, our measurement may have a large error of about one order of magnitude. In the case of CO, measurement was not so difficult using TEM because the size of the crystals is relatively large (Kouchi et al. 2021). Meanwhile, in the case of CO₂, measurement was very difficult (especially at lower temperatures) because determining the end point of the crystallization was complicated by the crystals' nanometer size (Figures 5 and 6). Therefore, we measured the change in the IR spectra of a-CO₂ at 35 and 40 K, as shown in Figure 10, and determined the timescale of crystallization, as shown in Figure 11. At temperatures above 50 K, on the other hand, measurement by the IR spectrum becomes very difficult because it takes a long time to heat the substrate from 10 to 50 K, i.e., crystallization will be completed during heating processes. The crystallization timescale, t_cryst, of a-CO₂ is expressed by t_cryst = A exp(E/kT), where k is Boltzmann's constant, T represents the temperature, and A and E are constants determined from the fitting: A = 5.3 × 10⁻³ s and E/k = 540 K. In Figure 11, t_cryst for a-CO (Kouchi et al. 2021) and a-H₂O (Kouchi et al. 1994) are also shown. By extrapolating these data to lower temperatures, we estimated the timescale of crystallization to be 10³ yr at 10 K for a-CO and 10⁵ yr at 16 K for a-CO₂.

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To discuss the crystal morphology on the grain surface, information concerning the surface diffusion coefficient is essential. Figure 12 shows the surface diffusion coefficients, D_s, of CO on a-H₂O, CO₂ on a-H₂O, and H₂O on organics, a-Mg₂SiO_3.3, and a-C. D_s is expressed as

$$\begin{eqnarray}&&{D}_{{\rm{s}}}={D}_{0}\exp (-{E}_{\mathrm{sd}}/{kT}),\end{eqnarray} \tag{ 2 }$$

where D₀ is the pre-exponential factor, E_sd is the activation energy of the surface diffusion, k is Boltzmann's constant, and T is the temperature. Kouchi et al. (2020) measured the E_sd of CO and CO₂ on a-H₂O to be 350 and 1500 K, respectively. Thus, we can calculate D_s if D₀ is assumed to be a² ν, where a is the hopping distance and ν is the hopping frequency (a = 0.3 nm and ν = 10¹² s⁻¹). Note that our discussion is not affected by the uncertainty of ν, because the error of ν is smaller than a few orders of magnitude. There has been no direct measurement of the surface self-diffusion coefficients of CO and CO₂; therefore, we assume the activation energies of surface diffusion to be 0.3 times those of desorption (Sandford & Allamandola 1988, 1990b), as shown by the dashed lines in Figure 12. The D_s of CO on the (111) face of α-CO (see Figure 15) is calculated based on the theoretical estimation of the adsorption energy for that face (see Section 5.1), as shown by a blue dashed line. The D_s of H₂O on organics, a-Mg₂SiO_3.3, and a-C could also be calculated using the measured activation energies (shown by yellow, brown, and black solid lines in Figure 12). The D_s of H₂O on the (0001) face of ice I_h (Kiefer & Hole 1977) is also shown by a light-blue dashed line. Note that the surface structure of the (0001) face of ice I_h is the same as that of the (111) face of ice I_c (see Figure 15). From these results, we conclude that CO molecules diffuse almost freely on a-H₂O, even in 10 K molecular clouds, while CO₂ molecules do not. CO₂ molecules on a-H₂O and H₂O molecules on organics start to diffuse at temperatures above ∼32 and ∼63 K, respectively.

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Kouchi et al. (1994) present the condition for the formation of amorphous ice during deposition:

$$\begin{eqnarray}&&F\gt {F}_{{\rm{c}}}\equiv {D}_{{\rm{s}}}/{a}^{4},\end{eqnarray} \tag{ 3 }$$

where F is the flux of molecule, F_c is the critical flux above which amorphous ice is deposited, and a is the hopping distance. Figure 13 shows the F_c values for a-H₂O on organics, a-CO₂ on a-H₂O, and a-CO on a-H₂O. Following Kouchi et al. (1994), the fluxes of O atoms (F_O) and CO molecules (F_CO) are described by

$$\begin{eqnarray}&&{F}_{{\rm{O}}}={n}_{{{\rm{H}}}_{2}}{f}_{{\rm{O}}}\ {({kT}/2\pi {\mu }_{{\rm{O}}}{m}_{{\rm{H}}})}^{1/2}\end{eqnarray} \tag{ 4 }$$

and

$$\begin{eqnarray}&&{F}_{\mathrm{CO}}={n}_{{{\rm{H}}}_{2}}{f}_{\mathrm{CO}}\ {({kT}/2\pi {\mu }_{\mathrm{CO}}{m}_{{\rm{H}}})}^{1/2},\end{eqnarray} \tag{ 5 }$$

respectively, where ${n}_{{{\rm{H}}}_{2}}$ is the number density of H₂ molecules, f indicates fractional abundances, μ indicates molecular weight, and m_H is the mass of a hydrogen atom. If we assume that ${n}_{{{\rm{H}}}_{2}}={10}^{4}$ cm⁻³, f_O = 10⁻⁴, and f_CO = 4 × 10⁻⁵, then T = 10 K, F_O = 2.7 × 10³ cm⁻² s⁻¹, and F_CO = 1.1 × 10³ cm⁻² s⁻¹. It is clear that crystalline CO (α-CO) is formed by the deposition of CO in 10 K molecular clouds, because F_CO is about 10 orders of magnitude smaller than the critical flux of CO (Kouchi et al. 2021). Because H₂O and CO₂ molecules are formed by surface-atomic reactions (as discussed in the next section), ${F}_{{{\rm{H}}}_{2}{\rm{O}}}$ and ${F}_{{\mathrm{CO}}_{2}}$ could be assumed to be equal to F_O and 0.5F_CO, respectively. We conclude that a-H₂O and a-CO₂ are formed in 10 K molecular clouds because the effective fluxes of H₂O and CO₂ are much larger than the critical fluxes.

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A spherical (or ellipsoidal) layered structure has been implicitly assumed for icy grains in molecular clouds in most previous works (e.g., Ehrenfreund et al. 1998; Pontoppidan et al. 2008). Only Pontoppidan et al. (2003) suggested that CO is crystalline α-CO and that α-CO takes the form of small, irregularly shaped clumps on top of the H₂O ice mantle. Therefore, it is desirable to find other evidence to check this assumption. Furthermore, there has been no discussion of the morphology of CO₂ ice. We will investigate the formation processes of ices on the refractory grains in molecular clouds based on the calculation results for the chemical evolution of ices (e.g., Garrod & Pauly 2011; Furuya et al. 2015; Ruaud et al. 2016; Kouchi et al. 2020). The compositional changes shown by ices from the inner part to the outer part are as follows: pure H₂O to H₂O:CO:CO₂ (basic cloud model of Garrod & Pauly 2011), H₂O:CO₂ to H₂O:CO:CO₂ (three-phase model of Ruaud et al. 2016), and pure H₂O, through H₂O:CO₂, to CO:H₂O (Furuya et al. 2015; Kouchi et al. 2020). Although the details differ among these studies, one can extract a general tendency: inner layers have H₂O-rich composition, intermediate layers H₂O:CO₂, and outer layers H₂O:CO:CO₂.

At first, the H₂O-rich layer was grown by the accumulation of H₂O molecules formed by the following surface reactions (Ioppolo et al. 2008; Miyauchi et al. 2008; Dulieu et al. 2010; Oba et al. 2012; Hama & Watanabe 2013):

$$\begin{eqnarray}&&\begin{array}{l}{\rm{O}}+{\rm{H}}\,\to \,\mathrm{OH}+{\rm{\Delta }}E(429\,\mathrm{kJ}\,{\mathrm{mol}}^{-1}),\\ \ \ \mathrm{OH}+{\rm{H}}\,\to \,{{\rm{H}}}_{2}{\rm{O}}+{\rm{\Delta }}E(499\,\,\mathrm{kJ}\,{\mathrm{mol}}^{-1}),\end{array}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&\mathrm{OH}+{{\rm{H}}}_{2}\to {{\rm{H}}}_{2}{\rm{O}}+{\rm{H}}+{\rm{\Delta }}E(62\,\mathrm{kJ}\,{\mathrm{mol}}^{-1}),\mathrm{and}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{O}}}_{2}+{\rm{H}}\,\to \,{\mathrm{HO}}_{2}+{\rm{\Delta }}E(203\,\mathrm{kJ}\,{\mathrm{mol}}^{-1}),\\ \ \ {\mathrm{HO}}_{2}+{\rm{H}}\,\to \,{{\rm{H}}}_{2}{{\rm{O}}}_{2}+{\rm{\Delta }}E(354\,\mathrm{kJ}\,{\mathrm{mol}}^{-1}),\\ \ \ \mathrm{and}\ {{\rm{H}}}_{2}{{\rm{O}}}_{2}+{\rm{H}}\,\to \,{{\rm{H}}}_{2}{\rm{O}}+\mathrm{OH}+{\rm{\Delta }}E(285\,\mathrm{kJ}\,{\mathrm{mol}}^{-1}).\end{array}\end{eqnarray} \tag{ 8 }$$

Because H₂O molecules were formed from O atoms as above, the flux of O atoms in 10 K molecular clouds determined the crystallinity of H₂O ice. The flux of O atoms is much larger than the critical flux of H₂O, above which a-H₂O formed (Figure 13), indicating that the H₂O ice formed was a-H₂O. Additionally, the fact that UV irradiation promotes amorphization (Kouchi & Kuroda 1990) also supports this conclusion. Therefore, a-H₂O uniformly covered the refractory grains (Figure 14(a)). Oba et al. (2009) suggested that the ice formed by surface reactions has a compact structure compared to vapor-deposited a-H₂O, because the spectral features due to dangling OH bonds were not observed in the IR spectrum.

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The composition of the next layer is expected to be H₂O:CO₂ = 3:2–5:1. Formation of the CO₂ molecule itself proceeded mainly according to the following grain-surface reaction (Yu et al. 2001; Oba et al. 2010; Garrod & Pauly 2011):

$$\begin{eqnarray}&&\mathrm{CO}+\mathrm{OH}\,\to \,{\mathrm{CO}}_{2}+{\rm{H}}+{\rm{\Delta }}E(96\,\mathrm{kJ}\,{\mathrm{mol}}^{-1}).\end{eqnarray} \tag{ 9 }$$

The fluxes of the CO and O atoms in 10 K molecular clouds are considerably larger than the critical flux of a-CO₂ formation (Figure 13), indicating that the solid CO₂ formed was initially amorphous if it had no effect on the heat of the reaction. Simultaneous formation of H₂O and CO₂ led to the growth of the mixed layer. It has been implicitly assumed that this H₂O:CO₂ mixed ice was amorphous (Pontoppidan et al. 2008); however, the following facts suggest the occurrence of CO₂ crystals, i.e., CO₂ I:

• 1.  
  Even if a-CO₂ was formed, a-CO₂ crystallized within 10⁵ yr at 16 K (Figure 11); UV irradiation promotes crystallization of a-CO₂ (Tsuge et al. 2020); and the heat of the H₂O, CO₂, and H₂ (434 kJ mol⁻¹) formation reactions may promote crystallization. If we assume that the whole layer was formed over 10⁶ yr, there might be a small amount of a-CO₂ on the uppermost layer, as shown in Figure 14.
• 2.  
  Direct formation of crystalline CO₂ was possible because the CO₂ molecule formed by reaction (9) possesses sufficient energy to diffuse momentarily on a-H₂O, leading to crystallization (Tsuge et al. 2020).
• 3.  
  Because CO₂ molecules did not diffuse on a-H₂O at around 10 K (as shown in Figure 12), and because the wetting of CO₂ i to a-H₂O is good (Figures 5 and 9(c)), the CO₂ crystals formed should be of nanometer size and were embedded in a-H₂O, as shown in Figure 14(b).

Pure crystalline CO₂ ice, as well as H₂O:CO₂ ice mixtures, shows a characteristic double-peak profile in the 15 μm bending mode (e.g., Ehrenfreund et al. 1996; Gerakines et al. 1999; Bergin et al. 2005). Such a profile has not been observed in prestellar cores (Bergin et al. 2005; Whittet et al. 2007), suggesting the absence of CO₂ crystals in dense starless cores. On the other hand, Escribano et al. (2013) suggested the occurrence of crystalline CO₂ in dense clouds based on the absence of the 2328 cm⁻¹ band toward Elias 16, where the band traces pure a-CO₂. For further confirmation, Mie scattering by ellipsoidal or irregularly shaped grains, which will change the band profile, needs to be evaluated. Given the estimated timescale of CO₂ crystallization (i.e., 10⁵ yr at 16 K with a sharp temperature dependence; Figure 11), it is unclear whether the crystallization of the CO₂ ice is fully completed in a prestellar stage. The present crystallization process will be applicable to the crystalline CO₂ observed in the line of sight toward embedded young stellar objects (Pontoppidan et al. 2008). In those sources, we anticipate that the crystallized CO₂ will form nano-crystals CO₂ i in a-H₂O as shown in Figure 14. The infrared spectral variation of crystalline CO₂ at various measurement conditions has yet to be investigated, particularly in the 15 μm bending mode region. Because the present IR setup uses an HgCdTe (MCT) detector that covers 2–13 μm, the spectrum in the 15 μm region could not be measured. Future studies incorporating TEM observations, IR spectroscopy, and comparison with astronomical spectra for various crystalline ice samples are awaited. Moreover, high-quality measurements with the upcoming James Webb Space Telescope (JWST) mission may shed more light on the crystallinity of CO₂ ice.

The composition of the outer layer is H₂O:CO:CO₂, becoming CO-rich with time. Pontoppidan et al. (2003) suggested the occurrence of α-CO from an IR observation of embedded young low-mass stars and performed a detailed analysis of the spectra. The experimental results obtained by Kouchi et al. (2021) strongly support their suggestion because (1) the flux of CO in the 10 K molecular clouds is smaller than the critical flux for the deposition of a-CO (Figure 13), (2) the timescale of crystallization of a-CO at 10 K is only 10³ yr (Figure 11), and (3) UV irradiation promotes crystallization of a-CO. Pontoppidan et al. (2003) also suggested that α-CO are small, irregularly shaped clumps on top of the H₂O ice mantle; however, our present study shows that solid CO was deposited as one single crystal, α-CO (Figures 14(c) and (d)), because CO molecules diffused almost freely on a-H₂O owing to the very large diffusion coefficient (Figure 12) and accumulated on the largest crystal. In other words, Ostwald ripening proceeded very efficiently. Because the wetting of α-CO against a-H₂O is bad (as shown in Figures 4(b) and (c) and 9(a)), α-CO is not embedded in a-H₂O, nor does it form a uniform layer. Thus, icy grains would have a morphology where an α-CO crystal is attached on the a-H₂O (Figure 14(d)). The above discussion has been somewhat simplified; we do not deny the occurrence of small amounts of CO and CO₂ in a-H₂O as impurities and very small clusters.

First, we will discuss equilibrium forms of ice crystals to consider the morphology of icy grains in space. The equilibrium form of a crystal is defined as the crystal form at which thermodynamic equilibrium is attained. In this case, the Gibbs free energy of the system (i.e., the summation of volume energy and surface energy) should be minimized. The equilibrium form of the crystal becomes a polyhedron with flat crystalline faces. As shown in Figure 15, the equilibrium forms of ice I_h, ice I_c, and face-centered-cubic (FCC) crystal are a hexagonal prism (Krastanow 1943), a regular octahedron (Takahashi 1982), and a truncated regular octahedron (Toschev 1973), respectively. When the self-diffusion coefficients of respective molecules on the corresponding crystals are sufficiently large, equilibrium forms should be realized. Since the surface self-diffusion coefficients of H₂O on ice I_h, CO₂ on CO₂, and CO on CO are sufficiently large (as shown in Figure 12), the respective crystals become their equilibrium forms. Therefore, it is reasonable to assume that thin-layered ice crystals are unstable because the surface energy of thin-layered ice crystals is a few times larger than that of a small sphere of the same volume. We note that we do not know whether CO₂ i nano-crystals in a-H₂O take on their equilibrium form or not owing to the lack of diffusion data concerning CO₂ in a-H₂O.

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The second factor affecting icy-grain morphology is the wetting of ices against substrates; typically, the degree of wetting is determined by Young's equation,

$$\begin{eqnarray}&&{\gamma }_{\mathrm{sub}}={\gamma }_{\mathrm{sub}-\mathrm{ice}}+{\gamma }_{\mathrm{ice}}\ \cos \theta ,\end{eqnarray} \tag{ 10 }$$

where γ_sub and γ_ice are the surface energies of the substrate and the ice crystal, respectively, γ_sub-ice is the interfacial energy between the substrate and the ice crystal, and θ is the contact angle. When wetting is complete, θ = 0°; the poorer the wetting, the larger θ becomes. However, for the wetting of α-CO on a-H₂O, the situation is not so simple because there is an adsorption layer between α-CO and a-H₂O (Kouchi et al. 2021). We should consider the wetting of an adsorbed CO layer on a-H₂O, as well as that of α-CO on the adsorbed CO layer. Unfortunately, when coverage is larger than one monolayer, there are no quantitative data for CO and CO₂ adsorption on porous a-H₂O, or for H₂O on organics, a-Mg₂SiO_3.3, and a-C. It should be noted that when coverage is smaller than one monolayer, complete wetting of CO on porous a-H₂O was observed (He et al. 2016). This result looks somehow contradictory to the present study, but it could be explained by considering surface energies and interfacial energy of the system, which change greatly depending on the coverage (Kouchi et al. 2021). Therefore, we will discuss the wetting of ices against various substrates qualitatively based on TEM observations. Poor wetting is observed in α-CO on a-H₂O (Figures 4(b) and (c)), and almost complete wetting is observed in CO₂ i on a-H₂O (Figure 5). When ice I_c was formed on organics, a-Mg₂SiO_3.3, and a-C substrates, poor wetting was observed in all cases (Figures 2 and 7). Based on these results, we will discuss, in the next section, the morphologies of ices on various substrates and their evolution in protoplanetary disks.

The third factor is the number of crystals formed on the substrate, which is governed by the surface diffusions of the various molecules on the substrate. If we consider diffusion over 10⁵ yr, CO on a-H₂O, CO₂ on a-H₂O, and H₂O on organics could diffuse sufficiently to form one crystal on the corresponding substrates at temperatures above ∼8, ∼32, and ∼63 K, respectively (Figure 12). The crystallization temperatures of a-CO, a-CO₂, and a-H₂O over 10⁵ yr are ∼9, ∼16, and ∼88 K, respectively (Figure 11); this shows that the Ostwald ripening started simultaneously with the crystallization of a-CO and a-H₂O. In the case of CO₂, nano-crystals remained at temperatures between 10 and 32 K and Ostwald ripening started at temperatures above 32 K. Therefore, we conclude that each component (CO, CO₂, and H₂O) forms a single crystal with its equilibrium form (i.e., α-CO, CO₂ i, and ice I) on the grains at temperatures higher than ∼9, ∼32, and ∼63 K, respectively.

Figure 16 compares the evolution of icy grains in protoplanetary disks between the previous assumption and our new model. It has been assumed that all ices have layered structures regardless of composition (CO, CO₂, H₂O) or crystallinity (amorphous, crystalline). However, it is clear that this assumption is imprecise for the following reasons:

• 1.  
  The flux of CO (Figure 13) and the crystallization timescale of a-CO (Figure 11) suggest the absence of a-CO in molecular clouds. Kouchi et al. (2021) showed that that UV rays and high-energy electron irradiation never cause amorphization of α-CO.
• 2.  
  Escribano et al. (2013) suggested an absence of a-CO₂ in molecular clouds, and this study supports their suggestion from the timescale of crystallization (Figure 11). Tsuge et al. (2020) showed that UV irradiation never causes amorphization of crystalline CO₂.
• 3.  
  A simple calculation shows that the total Gibbs free energy of the thin crystalline layer with large radius is larger than that of a small sphere of equivalent volume, because the surface energy of the former is larger than that of the latter.

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Based on the experimental results of this study, we consequently propose a new model shown in Figure 16. As already discussed above, grains in molecular clouds are composed of a silicate and organics core, a pure a-H₂O layer, an a-H₂O layer including nano-crystalline CO₂ I, and one α-CO crystal attached to the a-H₂O. When temperature exceeded the CO snow line, α-CO sublimated. A further increase in temperature above ∼32 K caused efficient surface diffusion of CO₂ molecules on a-H₂O, resulting in the formation of one CO₂ i thin crystal on the a-H₂O. This picture differs greatly from the simple layered ice model adopted in some previous studies of protoplanetary dust growth (e.g., Musiolik et al. 2016; Pinilla et al. 2017; Okuzumi & Tazaki 2019), which assume icy grains consisting of a refractory core, an inner H₂O mantle, and an outer CO₂ mantle. When the temperature exceeded the CO₂ snow line, CO₂ i sublimated and the a-H₂O grains remained ellipsoidal. A further increase in temperature above ∼88 K caused efficient surface diffusion of H₂O molecules on the organics, resulting in the formation of one ice I crystal. Note that this conclusion did not change when ice I was formed on other refractory substrates, a-silicate, or a-C, because the interfacial energies between ice I and the other materials have similar values. Gärtner et al. (2017) concluded from the scanning electron microscope observation of pure H₂O ice particles of a few micrometers in size that the morphology of a crystalline ice particle is a truncated sphere and that collision experiments using ice spheres are good analogs for protoplanetary environments. However, our present results clearly show that crystalline ice particles are not truncated spheres but polyhedral crystals (Figures 15(a) and (b)) attached to the refractory core (Figure 16), and that collision experiments performed thus far using ice spheres are not good analogs for protoplanetary environments.

In general, the chemical evolution on grains depends on the concentration and mobility of atoms and molecules. These have often been discussed in terms of atomic and molecular adsorption and diffusion energies at the surface of a-H₂O. Here, we present our computational estimate of the adsorption energies of H, C, N, and O atoms (as well as the CO molecule itself) onto the α-CO (111) surface model shown in Figure 17.

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Quantum chemical calculations were performed using the Gaussian 09 program (Frisch et al. 2009), similarly to Shimonishi et al. (2018). We optimized the position of the adsorbing species (H, C, N, O, and CO) using the Møller–Plesset method (Møller & Plesset 1934) with the cc-pVTZ basis set (MP2/cc-pVTZ level of theory), where stationary points on the potential energy surface were searched. For optimized structures, the total energy (i.e., single point energies) of the system, E_system, was calculated using the coupled-cluster method (Scuseria et al. 1988; CCSD(T)/cc-pVTZ level of theory), which correctly incorporates dispersion interactions between atoms and surface CO molecules. With the energies of the α-CO (111) surface model (E_adsorbent) and adsorbing species in vacuum (E_adsorbate), adsorption energies E_ads were calculated as E_ads = −[E_system - (E_adsorbent + E_adsorbate)].

Table 3 summarizes the calculated adsorption energies on the α-CO (111) surface model. On the α-CO (111) surface, it should be noted that sites A and B have an appearance ratio of 1:3. From our results, H, N, O, and CO are weakly bound to the α-CO (111) hollow site owing to physisorption; these adsorption energies are apparently smaller than those for the water-ice surface (Shimonishi et al. 2018), indicating that these atoms and molecules exhibit higher mobilities on the α-CO surface. On the other hand, the adsorption energy of the C atom at site B on the α-CO (111) surface was computed to be quite large (over 20,000 K); this is because the C atom reacts with a surface CO molecule to create a C=C=O molecule, as shown in Figure 18; in other words, the C atom is strongly bound to the α-CO (111) surface owing to chemisorption.

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Consequently, our calculated results suggest that mechanisms of chemical evolution are to be changed on the α-CO surface owing to the higher mobility of atoms and molecules and/or the formation of C=C=O molecules, which would be a source of organic molecules. Furthermore, it should be emphasized that different chemical evolutions proceed simultaneously on a-H₂O and α-CO (Figure 14) in 10 K molecular clouds.

Here, we briefly discuss the effect of the morphology of icy grains proposed in this work on the nonthermal desorption (particularly the photodesorption and chemical desorption) of molecules. It is now widely accepted that photodesorption plays an important role in regulating the partitioning of molecules between gas and ice in molecular clouds/cores (e.g., Caselli et al. 2012) and in the cold outer regions of protoplanetary disks (e.g., Hogerheijde et al. 2011; Öberg et al. 2015), where the dust temperature is low (<20 K). Laboratory experiments and molecular dynamics simulations have shown that photodesorption can desorb molecules only from the surface of the ice (i.e., the topmost several monolayers; e.g., Öberg et al. 2009a; Arasa et al. 2015); therefore, the morphology of icy grains significantly affects the efficiency of molecular photodesorption. If icy grains have a classical onion-like (or layered) structure, H₂O photodesorption would be hindered once CO adsorbs on top of the H₂O ice layers, burying them (see Section 4.3). On the other hand, if icy grains have the morphology proposed in this work, H₂O photodesorption would be efficient even after significant CO adsorption occurs on top of the H₂O ice layers. The latter case may be more consistent with the detection of H₂O vapor in the center of the prestellar core L1544, where significant CO freeze-out has already occurred (Caselli et al. 2012). Indeed, Caselli et al. (2012) successfully reproduced the H₂O emission line observed in L1544 using their radiative transfer and chemical models with H₂O photodesorption, the rate of which was calculated assuming that the surfaces of the ice mantles are fully covered by H₂O (see also Keto et al. 2014). This assumption neglects the fact that interstellar ices contain significant fractions of other molecules, such as CO; our proposed morphology of icy grains suggests that this assumption is reasonable. H₂O photodesorption experiments, whereby CO is deposited on top of H₂O ice, should be conducted.

The importance of chemical desorption (or reactive desorption) in the partitioning of molecules between the gas and solid phases in molecular clouds has also been recognized in chemical modeling studies (Garrod et al. 2007; Cazaux et al. 2010; Wakelam et al. 2017); recently, it has been experimentally demonstrated that various kinds of molecules can desorb upon their formation on icy surfaces at low temperatures (Minissale et al. 2016; Chuang et al. 2018; Oba et al. 2018; Nguyen et al. 2020). Additionally, the desorption efficiency can vary depending on the icy surfaces' structures (Oba et al. 2018, 2019). Although there are no data concerning the chemical desorption efficiency of molecules from CO-covered surfaces, we expect that it will differ from the desorption efficiency from H₂O surfaces, whose differences need to be precisely incorporated into future modeling studies.

In general, the adhesion force between grains in contact is primarily determined by the composition and morphology of their contact surface; therefore, grains with highly heterogeneous surface compositions and morphologies (as depicted in Figure 16) may stick significantly differently from ellipsoidal and uniformly layered grains. For example, simple grain models assuming layered mantles of various volatiles (e.g., Musiolik et al. 2016; Pinilla et al. 2017; Okuzumi & Tazaki 2019) predict that the stickiness of grains in a disk is uniquely determined by their location relative to the relevant snow lines; however, our experimental results offer a more complex picture in which grains can have heterogeneous surface compositions and the combination of materials constituting their contact surface is not unique (consider combinations between icy grains depicted in the bottom of Figure 16). The sticking efficiency of two grains in a disk cannot be uniquely predicted as a function of their location and can instead vary depending on their relative orientations upon collision.

Similarly, the irregular surface morphologies that originated from the existence of single crystals on grains inevitably introduce some randomness to their sticking efficiencies. Models of protoplanetary dust growth conventionally assume that there exists a critical collision velocity, v_c, below which two grains can stick. This is a reasonable assumption for uniformly layered grains; however, no well-defined threshold velocity is likely to exist for crystalline particles with facets and edges. While a contact between faces would apply a large contact area and hence a large binding energy, the opposite would apply for a contact between edges. In fact, Poppe et al. (2000) have already reported a lack of a well-defined maximum sticking velocity for irregularly shaped grains.

However, the above discussion does not necessarily mean that aggregates of uniformly layered or irregular, heterogenous grains should have significantly different sticking properties, because an aggregate generally consists of a number of contact surfaces, and their bulk mechanical properties may be determined by the average properties of the surfaces. Further experiments and modeling efforts are needed to better understand the statistical sticking properties of heterogeneous grains and their aggregates.

The collisional outcome of sintered aggregates differs substantially from that of nonsintered aggregates (Sirono & Ueno 2017), because the contact between constituent grains is strengthened by sintering. When one considers possible combinations of contacts between icy grains depicted in the bottom of Figure 16, sintering should proceed if both sides of a contact are made of the same kind of ice. As discussed in Sirono (2011) the strength of a contact increases by sintering. If the composing materials of two sides of a contact differ, sintering depends on the surface energies of the two composing materials. For example, sintering of CO₂ ice on H₂O ice is more likely to occur than sintering of CO ice on H₂O, due to the difference in the wettabilities of the pair of ices. At this stage, it is difficult to predict whether sintering proceeds or not for a particular pair of ices. The strengths of contacts inside an aggregate would vary; although it is clear that the collisional-growth efficiency of uniformly sintered aggregate is lowered (Sirono & Ueno 2017), the collisional outcome of nonuniformly sintered aggregate is not clear and needs to be studied.