Temperature Dependence of the Growth Kinetics of Elementary Spiral

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Temperature dependence of the growth kinetics of elementary spiral steps on ice basal faces grown from water vapor Masahiro Inomata, Ken-ichiro Murata, Harutoshi Asakawa, Ken Nagashima, Shunichi Nakatsubo, Yoshinori Furukawa, and Gen Sazaki Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01251 • Publication Date (Web): 21 Dec 2017 Downloaded from http://pubs.acs.org on December 23, 2017

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Crystal Growth & Design

Temperature dependence of the growth kinetics of elementary spiral steps on ice basal faces grown from water vapor §

¶

Masahiro Inomata, Ken-ichiro Murata, Harutoshi Asakawa , Ken Nagashima, Shunichi Nakatsubo , Yoshinori Furukawa, Gen Sazaki* Institute of Low Temperature Science, Hokkaido University, N19-W8, Kita-ku, Sapporo 060-0819, Japan § Present address: Graduate School of Sciences and Technology for Innovation, Yamaguchi University, 216-1 Tokiwadai, Ube, Yamaguchi 755-8611, Japan ¶ Present address: Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-11 Yoshinodai, Chuo-ku, Sagamihara City, Kanagawa 252-5210, Japan

Abstract. We measured velocity Vstep of isolated elementary spiral steps and distance Leq between adjacent equivalent spiral steps on ice basal faces by advanced optical microscopy. We determined the step kinetic coefficient β from Vstep measured under various supersaturations. We performed similar experiments under various temperatures T, and determined the temperature dependence of β of ice basal faces, for the first time, in the temperature range of -26.0 to -2.7°C. When -6.2≤T≤-2.7°C, the value of β decreased significantly with decreasing T. In contrast, when -15.0≤T≤-6.2°C, the value of β increased with decreasing T, and had the maximum at T≈-15°C. When -26.0≤T≤-15.0°C, the value of β decreased monotonically with decreasing T. Such complicated temperature dependence of β strongly implies the existence of unknown phenomena in the temperature range examined. To obtain a clue to the complicated behavior of β, we also measured dependence of Leq on surface supersaturation ∆µsurf. When -13.0≤T≤-3.2°C, plots of Leq vs.1/∆µsurf satisfactorily follow the spiral growth model. However, when -26.0≤T≤-15.0°C, the Leq vs. 1/∆µsurf plots do not follow any model: this temperature range agrees with the temperature range in which β decreased monotonically with decreasing T.

Figure. An LCM-DIM image of elementary spiral steps grown on an ice basal face (A), and the temperature dependence of the step kinetic coefficient β (B). The temperature dependence of β shows a complicated behavior, strongly suggesting the existence of unknown phenomena.

*

To whom correspondence should be addressed. E-mail: [email protected] 1 ACS Paragon Plus Environment

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Temperature dependence of the growth kinetics of elementary spiral steps on ice basal faces grown from water vapor Masahiro Inomata, Ken-ichiro Murata, Harutoshi Asakawa§, Ken Nagashima, Shunichi Nakatsubo¶, Yoshinori Furukawa, Gen Sazaki* Institute of Low Temperature Science, Hokkaido University, N19-W8, Kita-ku, Sapporo 0600819, Japan § Present address: Graduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Ube, Yamaguchi 755-8611, Japan ¶ Present address: Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara City, Kanagawa 252-5210, Japan * To whom correspondence should be addressed. E-mail: [email protected] KEYWORDS: in-situ observation, ice crystal, elementary spiral step, step kinetic coefficient, temperature dependence, distance between adjacent equivalent spiral steps

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ABSTRACT (189 words) We measured velocity Vstep of isolated elementary spiral steps and distance Leq between adjacent equivalent spiral steps on ice basal faces by advanced optical microscopy. We determined the step kinetic coefficient β from Vstep measured under various supersaturations. We performed similar experiments under various temperatures T, and determined the temperature dependence of β of ice basal faces, for the first time, in the temperature range of -26.0 to -2.7°C. When -6.2≤T≤-2.7°C, the value of β decreased significantly with decreasing T. In contrast, when -15.0≤T≤-6.2°C, the value of β increased with decreasing T, and had the maximum at T≈-15°C. When -26.0≤T≤-15.0°C, the value of β decreased monotonically with decreasing T. Such complicated temperature dependence of β strongly implies the existence of unknown phenomena in the temperature range examined. To obtain a clue to the complicated behavior of β, we also measured dependence of Leq on surface supersaturation ∆µsurf. When -13.0≤T≤-3.2°C, plots of Leq vs. 1/∆µsurf satisfactorily follow the spiral growth model. However, when -26.0≤T≤-15.0°C, the Leq vs. 1/∆µsurf plots do not follow any model: this temperature range agrees with the temperature range in which β decreased monotonically with decreasing T.



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1. INTRODUCTION Ice is one of the most abundant materials on the earth. Hence, crystal growth of ice governs a wide variety of phenomena in nature. For example, most rains fallen outside tropical regions are formed by the melting of ice crystals (snowflakes) that were grown in the sky and then descended to the ground.1 In addition, the fluctuation in the volumes of ice crystals in glaciers significantly changes the sea level.2 Hence, the quantitative understanding of the growth kinetics of ice crystals is crucially important. Ice crystals grow mainly in two kinds of ambient phases: melt (supercooled water) and vapor (supersaturated water vapor). Many studies so far observed the growth of ice single crystals in melt (supercooled water) by optical microscopy. Then they reported normal growth rates3-8, development of a dendritic shape3, 4, and effects of sugar, antifreeze protein and polymer9-14 on the growth of ice crystals. However, it has been very difficult to observe directly surface microtopographs on ice crystal surfaces and to measure growth kinetics at the molecular level, since the growth rate of ice crystals in melt is significantly faster than that in vapor. In contrast, in the case of the growth of ice single crystals in vapor (supersaturated water vapor), several studies measured the growth kinetics of macrosteps15-18, in addition to the reports on the normal growth rates19-22 and the development of a dendritic shape23, 24 by optical microscopy. Therefore, in this study, we focused on the growth in vapor, in which the growth kinetics of ice single crystals can be more easily measured than in melt. Recently, we improved laser confocal microscopy combined with differential interference microscopy (LCM-DIM)25 further, and then succeeded in visualizing individual elementary steps (0.37 nm in thickness) on ice crystal surfaces growing in supersaturated water vapor by LCM-DIM.26 We reported that in the temperature range of -15 to 0°C, two-dimensionalisland steps and spiral steps on ice basal faces exhibit a circular shape, clearly demonstrating that kink density on elementary steps is extremely high. They also reported that on ice basal


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faces, spiral steps have a double-spiral-step structure.27 In addition, Asakawa et al. of our group very recently measured the velocity of elementary spiral steps Vstep on ice basal faces at -8.4°C by LCM-DIM.28 They found that distance L between adjacent spiral steps show significant fluctuation, and then succeeded in determining migration distance χs of water molecules adsorbed on a terrace (χs=4.5 µm), utilizing the fluctuation of L. Furthermore, they determined a step kinetic coefficient β=700 µm/s from the relation between Vstep and the supersaturation. However, as shown in Fig. S1 in the supporting information, it was difficult to accurately evaluate supersaturation dependence of Vstep in particular in a low supersaturation range. Hence, Asakawa et al. could not accurately determine the step kinetics coefficient β from the Vstep vs. supersaturation plot (Fig. S1). Such difficulty in determining β can be understood as follows. During the growth of ice crystals in supersaturated water vapor, three elementary processes are in series (Fig. S2): (1) the volume diffusion of water vapor molecules to an ice crystal surface, (2) the surface diffusion of admolecules to a step, and (3) the incorporation of water molecules at a kink (the diffusion along a step can be ignored because of the high kink density on a step). Ice crystals for the observation were grown heteroepitaxially on a cleaved AgI crystal placed in supersaturated water vapor. Since Asakawa et al. grew many ice crystals on the AgI crystal (a surface coverage of the AgI crystal by ice crystals: ~1), a large amount of water vapor was necessary to grow these ice crystals.28 Consequently, the volume diffusion of water vapor became the rate-determining step even in the low supersaturation range, leading to the deviation from the linear relation between Vstep and supersaturation (Fig. S1). In this study, to investigate the growth kinetics of elementary spiral steps in detail, we grew considerably smaller number of ice crystals on the AgI crystal (the surface coverage: ~0.2) than the Asakawa et al.28 did, and decreased the effects of the volume diffusion significantly. Then, we accurately determined the kinetic coefficient β, which corresponds to the slope of



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the tangential straight line through the origin in Fig. S1, and also revealed the temperature dependence of β.

2. EXPERIMENTAL PROCEDURES 2.1. Observation System. In this study, LCM-DIM developed recently by Sazaki et al.26 was used to visualize individual elementary spiral steps on ice basal faces. An observation chamber was made to observe ice crystal surfaces from below, since LCM-DIM was equipped with an inverted optical microscope. The observation chamber (schematically shown in Fig. 1) was composed of upper and lower Cu plates, whose respective temperatures T and Tbottom were separately controlled using Peltier elements. At the center of the lower side of the upper Cu plate, a cleaved AgI substrate crystal (a kind gift from Emeritus Professor G. Layton of Northern Arizona University), which is known as an ice nucleating agent, was attached using heat grease. Ice crystals for the LCM-DIM observation were grown heteroepitaxially on the cleaved AgI substrate crystal. Ice crystals for supplying water vapor to the ice crystals for the observation were grown on the lower Cu plates.

Figure 1. The total pressure in the observation chamber was kept at 0.1 MPa (atmospheric pressure) by filling the chamber with pure nitrogen gas. The volume of the ice crystals for supplying water vapor was several orders of magnitude larger than that of the ice crystals for the


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observation. Hence, partial pressure of water vapor P∞ in the observation chamber was determined by Tbottom. In addition, equilibrium partial vapor pressure Pe of the ice crystals for the observation was determined by T. For the details in the measurement of T and Tbottom and the determination of Pe and P∞, see Fig. S3 in the supporting information. As shown in Fig. S3, the correction (calibration) of Tbottom shows the error of ±0.5°C, although T exhibits the error of ±0.02°C. Hence, from the error of Tbottom (±0.5°C) and the slope of the vapor-solid equilibrium curve29, 30, P∞ and Pe show errors of ±5 Pa. 2.2. The Step Kinetic Coefficient β. Supersaturation of the ice crystals for the observation is defined as σ = (P∞ - Pe)/Pe. When the incorporation of water molecules at a kink site on a step is the rate-determining step, Vstep can be expressed as follows31, 32: =

= σ.

(1)

When Vstep is proportional to supersaturation σ, the growth kinetics of steps at a certain T can be evaluated from the value of β. From the error of P∞ and Pe (±5 Pa) and the propagation of error, supersaturation σ shows an error of 5 %.

2.3. Determination of the Step Velocity Vstep, Distance Leq between Adjacent Equivalent Spiral Steps and Distance L between Adjacent Spiral Steps. Figure 2 shows an example of LCM-DIM images of elementary spiral steps grown on an ice basal face at T=-15.0 °C and σ =0.18. Concentric elementary spiral steps emerged from the upper left edge of the basal face, and laterally advanced in the lower right direction. White arrowheads show an identical elementary step. The value of Vstep was determined from the time course of the position of the identical step. In the case of a basal face of a Ih ice crystal, as shown in Fig. S4, two adjacent crystal faces (bilayers) A and B, which are rotated by an angle of 60o to each other, are periodically stacked in the crystallographic c direction.27 Hence, elementary spiral steps also 7 ACS Paragon Plus Environment


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show the ABAB… stacking structure, demonstrating that alternate steps are equivalent, as shown in Fig. 2A. Consequently, the distance Leq between adjacent equivalent spiral steps was determined from the distance between adjacent A-A or B-B equivalent steps, as marked by a white double-head arrow in Fig. 2A. The distance L between adjacent A-B steps was also measured. Note that Leq and L are different.

Figure 2.

3. RESULTS AND DISCUSSION 8 ACS Paragon Plus Environment

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3.1. Temperature Dependence of the Step Kinetic Coefficient β. Under the temperature range (-26.0 to -2.7°C) used in this study, spiral steps on ice basal faces always exhibited a circular shape, showing that the density of kinks on a step was significantly high. We measured the step velocity Vstep of isolated elementary steps and the distance L between adjacent A-B spiral steps on ice basal faces by LCM-DIM. Figure 3 shows an example at T=9.2 °C. Under a constant σ, Vstep presents a constant value regardless of L within an accuracy of experimental errors. Under the constant σ, we measured Vstep 5-10 times. Then by calculating the average of these values, we determined the values of Vstep and its error at the constant σ. Under all temperatures used in this study, we measured Vstep of only isolated elementary steps whose L were longer than 10 µm. Hence, all values of Vstep measured in this study excluded the case in which adjacent steps competed with each other through the surface diffusion of admolecules on a terrace. Vstep in this study corresponds to Vstepint in the study of Asakawa et al.28 At T=-9.2 °C, when σ was smaller than 0.12, we could not measure L since L became longer than the size of the ice basal face, although we could measure Vstep even under such condition.

Figure 3.



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In the temperature range of -26.0 to -2.7°C, we measured Vstep under various supersaturations. Figure 4 shows the summary of all data. At each T, we carefully increased and decreased P∞, and observed the movements of elementary steps and the growth and sublimation of crystal edges by LCM-DIM. From such observations, we determined P∞ at which pressure Vstep became zero (σ=0) (for the details, see Fig. S3). As shown in Fig. 4, when σ was small, Vstep increased linearly with σ. However, as σ increased, the increase in Vstep gradually became smaller, and finally Vstep exhibited a constant value. This result demonstrates that with increasing Vstep the growth of isolated steps consumed larger amount of water vapor, resulting in the severer depletion of water vapor in the vicinity of ice basal faces. Hence, as Vstep increased, the volume diffusion of water vapor to ice crystal surfaces gradually became the rate-determining step: to prove this scenario semi-quantitatively, we performed a one-dimensional steady-state calculation of mass transport, as shown in Fig. S5. From the comparison between the results shown in Figs. 4 and S1, we conclude that in this study we could measure the linear increase in Vstep with σ in the small supersaturation range much more precisely than Asakawa et al.28 By minimizing the surface coverage of the AgI crystal by the ice crystals (~0.2 in this study and ~1 in the study of Asakawa et al.28), we succeeded in accurately determining the step kinetic coefficient β of ice basal faces.


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Figure 4. To obtain the value of β from Fig. 4, we needed to use a fitting function that has the following three features: (1) Vstep increases linearly with σ in the range of small σ; (2) as σ increases, the increase in Vstep gradually becomes smaller; and (3) finally Vstep shows a constant value. The features of (2) and (3) are due to the concern that the volume diffusion of water vapor became the rate-determining step as σ increased. However, the actual geometry of the observation chamber was complex, as shown in Fig. S6. Hence, we could not solve the diffusion equation analytically. Therefore, for convenience we used an error function, although it has no physical meaning. Solid curves in Fig. 4 show the results of the curve fittings, indicating that the data could be fitted well using the error function. From the slope of the error function at σ=0, we determined the value of β. At T=-2.7 and -15.0 °C, the accuracies of the curve fittings are not good besides the small supersaturation range, however, we believe that the curve fittings at these temperatures give plausible values of β at σ=0. At T=-6.2 and -9.2°C, Vstep increased linearly in the whole range of σ, since we could prepare very small number of ice crystals on the AgI crystals. At these two temperatures, we used a straight-line approximation.



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Figure 5 shows the changes in β determined from Fig. 4 as a function of T. The amount of an error of β corresponds to the quality of the curve fitting in Fig. 4: the curve fitting of higher quality gives the smaller error of β. The solid curve is a guide for eyes. When -6.2≤T≤2.7°C, the value of β decreased significantly with decreasing T. In contrast, when -15.0≤T≤6.2°C, the value of β increased with decreasing T, and had the maximum at T≈-15 °C. When 26.0≤T≤-15.0°C, the value of β decreased monotonically with decreasing T. As far as we know, we succeeded in determining the temperature dependence of β of elementary steps of ice basal faces, for the first time.

Figure 5. Hallett,15 Mason et al.,16 and Kobayashi17 so far measured the growth kinetics of ice basal faces in the temperature range of -40 to 0°C. They measured the lateral growth velocity Vbs of bunched steps by optical microscopy, and also measured height of bunched steps using interference colors of ice crystals (Fig. S7 shows a summary of their results). In addition, Mason et al.16 determined the surface diffusion distance χs-bs of water admolecules from the critical distance between adjacent bunched steps, from which distance Vbs started to decrease with decreasing the distance. These three studies reported that Vbs and χs-bs exhibited the maximums at certain temperatures, however these temperatures differed significantly from the result shown in Fig. 5. Such discrepancies suggest that they probably could not take into 12 ACS Paragon Plus Environment

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account the effects of volume diffusion properly, since they measured Vbs only at a certain excess water vapor pressure15, 17 or at a certain supersaturation.16 Furthermore, in the case of bunched steps, no one can eliminate the competition between adjacent elementary spiral steps for water admolecules diffusing on crystal surfaces. This would also become the cause for the discrepancies. Gonda and Sei18 also measured the lateral growth rate of steps observed by differential interference contrast microscopy at -7, -15 and -30°C, although there was no description of step height. They measured step velocities as a function of supersaturation, like this study. However, the values of β that we calculated from their data are two orders of magnitude larger than ours. Gonda and Sei first prepared a vacuum environment (40 Pa air) inside their observation chamber. Then they introduced water vapor of a certain pressure, and measured the growth kinetics of steps on ice crystal surfaces. Hence, the vacuum environment might be the cause for much faster growth kinetics. The biggest advantage of the use of the vacuum environment is the removal of the depletion of water vapor in the vicinity of a growing ice crystal, although a thick glass window necessary for a vacuum chamber will cause significant optical aberration and will make the visualization of elementary steps more difficult. In the case of steps growing from a vapor phase, the step kinetic coefficient can be expressed as follows31, 32:

= −

∗

.

(2)

Here, a is the lattice constant, υ is the thermal vibration frequency, δ0 is the average spacing of kink sites, a/δ0 is the probability of finding a kink site, ∆G* is the activation energy barrier of the incorporation of water molecules at a kink site, and k is the Boltzmann constant. Equation (2) shows that β decreases monotonically with decreasing T. However, as shown in



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Fig. 5, β exhibited the complicated behavior with T. This discrepancy clearly demonstrates that there still exist unsolved phenomena in the lateral growth of elementary steps on ice basal faces. The change in a surface structure of an ice basal face with changing T can be one of the candidates for such unsolved phenomena, although we could not find any difference in the contrast of LCM-DIM images with changing T. Then, we came up with the idea that the investigation of the dependence of Leq on supersaturation under various T might give us a clue to the change in a surface structure. 3.2 The distance Leq between adjacent equivalent spiral steps. We can visualize individual elementary steps on ice basal faces by LCM-DIM (Fig. 2). Hence, we can determine the distance Leq between adjacent equivalent (A-A or B-B) elementary spiral steps. We will later discuss whether the spiral steps observed in this study can follow the spiral growth model. For such discussion, we need to use Leq instead of L, since adjacent equivalent (A-A or B-B) steps have the height difference that corresponds to the minimum size of the Burgers’ vectors of screw dislocations. Figure 6 shows examples of distributions of Leq under various supersaturations at T=-15.4 °C. One distribution of Leq in Fig. 6 consists of the data of about 300-times Leq measurements. As Asakawa et al. reported previously,28 Leq exhibited significantly large dispersion, although the cause is still unclear. As supersaturation increases, the dispersion of the distribution of Leq becomes smaller, and the peak of the distribution of Leq shows the smaller value.


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Figure 6. Next, we calculated an average distance Leqav of the distribution of Leq shown in Fig. 6 under a certain supersaturation. We used a probability density function of a log-normal distribution, and fitted this function to the data. Solid curves in Fig. 6 show the results of the curve fitting, indicating that the data could be fitted well using this function. The value of Leqav determined by the curve fitting decreases with increasing supersaturation. In the case of circular spiral steps originating from a single screw dislocation, the relation between Leq and a driving force for crystallization ∆µ can be generally expressed as follows33: = 19"# = 19

$

%

.

(3)

Here, ρc is the radius of a critical two-dimensional nucleus, s is the area occupied by one water molecule, κ is the step ledge free energy. In this study, eq. (3) corresponds to & = 19"# = 19

$

%'()*

.

(4)

Here, ∆µsurf is a driving force for crystallization at a crystal surface. In the case of vapor growth, ∆µsurf is given by



Δ, -./ = 01 ln

'()*

.

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(5)

Here, Psurf is the water vapor pressure at a crystal surface. Hence, to evaluate ∆µsurf, we needed to determine Psurf instead of P∞ used so far. We determined the value of Psurf as follows. Figure 7 shows an example of the relation between Vstep and σ at T=-15.0 °C. The solid curve shows the result of the curve fitting using the error function. Then, the broken straight line presents the tangential line of the error function at σ=0, corresponding to the behavior of Vstep when there was no effect of the volume diffusion of water vapor. In this study, as proved in Fig. S5, the volume diffusion significantly affected the growth of spiral steps, in particular when σ was not small. Hence, as shown in Fig. 7, when σ=0.34, Vstep exhibited the value of 25.6 µm/s, which is significantly smaller than the value of Vstep on the broken straight line. This result indicates that due to the effect of the volume diffusion, the supersaturation at the crystal surface ((Psurf - Pe)/Pe) decreased to 0.17, which is the value of the horizontal axis of the broken straight line when Vstep=25.6 µm/s. Therefore, from the relation on the broken straight line Vstep=β(Psurf - Pe)/Pe, Psurf can be obtained as 4-./ = 1 +

6'7 8 9

4 .

(6)

Using eq. (6) and then eq. (5), we determined Psurf and ∆µsurf for all of the data points shown in Fig. 4.


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Figure 7. When Leqav follows the model of the spiral growth (eq. (4)), the relation between Leqav and 1/∆µsurf exhibits a straight line through the origin. Figure 8 shows the relation between Leqav and 1/∆µsurf obtained in our experiments. The data can be roughly classified into two groups: T≥-13.0°C (filled plots in Fig. 8A) and T≤-15.0°C (open plots in Fig. 8B).

Figure 8. When T≥-13.0°C (filled plots), although the plots exhibit a significantly large dispersion, all data are roughly distributed around the solid straight line through the origin: this line is the result of the fitting of all filled plots using the eq. (4). This result suggests that these data can



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be basically explained by the spiral growth model of a single screw dislocation. The value of κ determined from the slope of the solid straight line is 5.0±1.9 x10-9 J/m. In contrast, when T≤-15.0°C (open plots), the plots clearly exhibit different behavior. The data taken at a constant T can be well expressed by a dotted straight line, which has a much larger slope (with a negative intercept) than the straight line for the filled plots. However, the dotted straight lines determined at different T do not coincide with each other, although their slopes show similar values irrespective of T. These results clearly demonstrate that the data obtained at T≤-15.0°C (open plots) cannot be explained by the spiral growth model of a single screw dislocation (eq. (4)). When spiral steps are originated from a group of dislocations, the eq. (4) can have an intercept. However, such intercept needs to show a positive sign.33-35 Hence, it is also difficult to explain the data shown in the open plots by the spiral growth model of a group of dislocations. To obtain further progress toward this issue, it is necessary to perform another experiments, such as the imaging of dislocations by x-ray topography. Nevertheless, it would be worthy to point out that the temperature range of T≤15.0°C, in which the open plots were obtained in Fig. 8B, coincides with the temperature range that shows the monotonic decrease in β with decreasing T: Fig. 5 may be represented by two Arrhenius-type (exponential) equations (eq. (2) in -26.0≤T≤-15.0 and -6.2≤T≤-2.7°C) and the transition range between these two (-15.0≤T≤-6.2°C), although we have no experimental evidence at this moment. At temperatures lower than 140 K, Thürmer and coworkers36-39 so far observed ice thin film crystals deposited on Pt substrates by scanning tunneling microscopy and atomic force microscopy. Also Materer and coworkers40, 41 so far studied a surface structure of an ultrathin ice film grown on a Pt(111) substrate at 90 K by low-energy electron diffraction, and reported that the ice film exposes the common basal face of a Ih ice crystal without reconstruction.


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However, near the melting point (0°C), so far no one succeeded in observing a surface structure of an ice crystal at the molecular level by any means. If someone will achieve such molecular-level observation of an ice crystal surface in the near future, it will give a clue for revealing the causes for the strange temperature dependences of β and Leqav.

4. CONCLUSIONS In this study, we directly observed the isolated elementary spiral steps on ice basal faces by LCM-DIM. Then we measured the velocity Vstep of elementary spiral steps and the distance Leq between adjacent equivalent (A-A or B-B) spiral steps on ice basal faces under various temperatures T and supersaturations σ. Then we obtained the following key results. (1) We grew considerably small number of ice crystals on the AgI crystal (the surface coverage: ~0.2) to significantly decrease the effects of the volume diffusion of water vapor. Then, we succeeded in accurately evaluating Vstep in the small σ range, resulting in the determination of the step kinetic coefficient β from the dependence of Vstep on σ. We performed similar measurements under various T, and determined the temperature dependence of β, for the first time, in the temperature range of -26.0 to -2.7°C. (2) When -6.2≤T≤-2.7°C, the value of β decreased significantly with decreasing T. In contrast, when -15.0≤T≤-6.2°C, the value of β increased with decreasing T, and had the maximum at T≈-15 °C. When -26.0≤T≤-15.0°C, the value of β decreased monotonically with decreasing T. Such complicated behavior of β clearly demonstrates that there still exist unsolved phenomena in the lateral growth of elementary steps on ice basal faces.



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(3) We determined the relation between the average distance Leqav of the adjacent equivalent spiral steps and 1/∆µsurf (∆µsurf is a driving force for crystallization at a crystal surface). We found that the data can be classified into two groups. When 13.0≤T≤-3.2 °C, the data follow the model formula of the spiral growth of a single screw dislocation, and gave the value of the step ledge free energy κ=5.0±1.9 x10-9 J/m. In contrast, when -26.0≤T≤-15.0°C, the data do not follow any spiral growth model reported so far: this temperature range corresponds to that in which β decreased monotonically with decreasing T. We believe that in the near future the insights into the growth kinetics of elementary spiral steps on ice basal faces will play a crucially important role in understanding a wide variety of phenomena in nature.

Acknowledgements The authors thank Y. Saito, S. Kobayashi and K. Ishihara (Olympus Corporation) for their technical support of LCM−DIM, G. Layton (Northern Arizona University) for the provision of AgI crystals, P.G. Vekilov (University of Houston) for valuable discussion. G.S. is grateful for the partial support by JSPS KAKENHIs (Grant Nos. 23246001 and 15H02016).

ASSOCIATED CONTENT Supporting information available: Previously obtained data concerning the relation between step velocity and supersaturation, a schematic drawing of three elementary growth processes in series, measurement of T and Tbottom and determination of Pe and P∞, a schematic drawing of a cross section of a basal face of a Ih ice crystal, importance of mass transfer of 20 ACS Paragon Plus Environment

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water vapor by volume diffusion, an actual configuration of an observation chamber, a summary of the previously obtained data on velocity of bunched steps and surface migration distance of water admolecules. This material is available free of charge via the Internet at http://pubs.acs.org.

Web-Enhanced Feature: None

References (1) Pruppacher, H. R.; J.D.Klett, Microphysics of clouds and precipitation. ed.; Springer: 1996; Vol. 18. (2) Benn, D.; David, E. J. A., Glaciers and glaciation. ed.; Oxford University Press Inc.: New York, 1998. (3) Furukawa, Y.; Shimada, W., Three-dimensional pattern-formation during growth of ice dendrites - its relation to universal law of dendritic growth. Journal of Crystal Growth 1993, 128, 234-239. (4) Shimada, W.; Furukawa, Y., Pattern formation of ice crystals during free growth in supercooled water. Journal of Physical Chemistry B 1997, 101, 6171-6173. (5) Zepeda, S.; Nakatsubo, S.; Furukawa, Y., Apparatus for single ice crystal growth from the melt. Review of Scientific Instruments 2009, 80, 115102. (6) Yokoyama, E.; Yoshizaki, I.; Shimaoka, T.; Sone, T.; Kiyota, T.; Furukawa, Y., Measurements of growth rates of an ice crystal from supercooled heavy water under microgravity conditions: basal face growth rate and tip velocity of a dendrite. Journal of Physical Chemistry B 2011, 115, 8739-8745. (7) Adachi, S.; Yoshizaki, I.; Ishikawa, T.; Yokoyama, E.; Furukawa, Y.; Shimaoka, T., Stable growth mechanisms of ice disk crystals in heavy water. Physical Review E 2011, 84, 051605. (8) Yoshizaki, I.; Ishikawa, T.; Adachi, S.; Yokoyama, E.; Furukawa, Y., Precise measurements of dendrite growth of ice crystals in microgravity. Microgravity Science and Technology 2012, 24, 245-253. (9) Gonda, T.; Nakahara, S.; Sei, T., The formation of side branches of dendritic ice crystals growing from vapor and solution. Journal of Crystal Growth 1990, 99, 183-187. (10) Sei, T.; Gonda, T.; Arima, Y., Growth rate and morphology of ice crystals growing in a solution of trehalose and water. Journal of Crystal Growth 2002, 240, 218-229. (11) Gonda, T.; Sei, T., The inhibitory growth mechanism of saccharides on the growth of ice crystals from aqueous solutions. Progress in Crystal Growth and Characterization of Materials 2005, 51, 70-80. (12) Zepeda, S.; Yokoyama, E.; Uda, Y.; Katagiri, C.; Furukawa, Y., In situ observation of antifreeze glycoprotein kinetics at the ice interface reveals a two-step reversible adsorption mechanism. Crystal Growth & Design 2008, 8, 3666-3672.



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(13) Vorontsov, D. A.; Sazaki, G.; Hyon, S. H.; Matsumura, K.; Furukawa, Y., Antifreeze effect of carboxylated epsilon-poly-L-lysine on the growth kinetics of ice crystals. Journal of Physical Chemistry B 2014, 118, 10240-10249. (14) Furukawa, Y.; Nagashima, K.; Nakatsubo, S.; Yoshizaki, I.; Tamaru, H.; Shimaoka, T.; Sone, T.; Yokoyama, E.; Zepeda, S.; Terasawa, T.; Asakawa, H.; Murata, K.; Sazaki, G., Oscillations and accelerations of ice crystal growth rates in microgravity in presence of antifreeze glycoprotein impurity in supercooled water. Scientific Reports 2017, 7, 43157(110). (15) Hallett, J., The growth of ice crystals on freshly cleaved covellite surfaces. Philosophical Magazine 1961, 6, 1073-1087. (16) Mason, B. J.; Bryant, G. W.; Vandenheuvel, A. P., Growth habits and surface structure of ice crystals. Philosophical Magazine 1963, 8, 505-526. (17) Kobayashi, T., On the variation of ice crystal habit with temperature. Physics of Snow and Ice 1967, 1, 95-104. (18) Gonda, T.; Sei, T., The growth-mechanism of ice crystals grown in air at a lowpressure and their habit change with temperature. Journal De Physique 1987, 48, 355-359. (19) Sei, T.; Gonda, T., The growth-mechanism and the habit change of ice crystals growing from the vapor-phase. Journal of Crystal Growth 1989, 94, 697-707. (20) Sei, T.; Gonda, T., Growth rate of polyhedral ice crystals growing from the vaporphase and their habit change. Journal of Meteorological Society of Japan 1989, 67, 495-502. (21) Furukawa, Y.; Kohata, S., Temperature-dependence of the growth from of negative crystal in an ice single-crystal and evaporation kinetics for its surfaces. Journal of Crystal Growth 1993, 129, 571-581. (22) Gonda, T.; Matsuura, Y.; Sei, T., In-situ observation of vapor-grown ice crystals by laser two-beam interferometry. Journal of Crystal Growth 1994, 142, 171-176. (23) Gonda, T.; Nakahara, H., Formation mechanism of side branches of dendritic ice crystals grown from vapor. Journal of Crystal Growth 1996, 160, 162-166. (24) Gonda, T.; Nakahara, S., Dendritic ice crystals with faceted tip growing from the vapor phase. Journal of Crystal Growth 1997, 173, 189-193. (25) Sazaki, G.; Matsui, T.; Tsukamoto, K.; Usami, N.; Ujihara, T.; Fujiwara, K.; Nakajima, K., In situ observation of elementary growth steps on the surface of protein crystals by laser confocal microscopy. Journal of Crystal Growth 2004, 262, 536-542. (26) Sazaki, G.; Zepeda, S.; Nakatsubo, S.; Yokoyama, E.; Furukawa, Y., Elementary steps at the surface of ice crystals visualized by advanced optical microscopy. Proceedings of the National Academy of Sciences of the United States of America 2010, 107, 19702-19707. (27) Sazaki, G.; Asakawa, H.; Nagashima, K.; Nakatsubo, S.; Furukawa, Y., Double spiral steps on I-h ice crystal surfaces grown from water vapor just below the melting point. Crystal Growth & Design 2014, 14, 2133-2137. (28) Asakawa, H.; Sazaki, G.; Yokoyama, E.; Nagashima, K.; Nakatsubo, S.; Furukawa, Y., Roles of surface/volume diffusion in the growth kinetics of elementary spiral steps on ice basal faces grown from water vapor. Crystal Growth & Design 2014, 14, 3210-3220. (29) Murphy, D. M.; Koop, T., Review of the vapour pressures of ice and supercooled water for atmospheric applications. Quarterly Journal of the Royal Meteorological Society 2005, 131, 1539-1565. (30) Sonntag, D., Important new values of the physical constants of 1986, vapour pressure formulations based on the ITS-90, and psychrometer formulae. Meteorol. Z. 1990, 70, 340344. (31) A.A.Chernov., Modern crystallography Ⅲ. ed.; Springer-Verlag: Berlin Heidelberg New York Tokyo 1984.


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(32) Markov, I. V., Crystal growth for beginners fundamentals of nucleation, crystal growth and epitaxy. ed.; World Scientific, 1955. (33) Burton, W. K.; Cabrera, N.; Frank, F. C., The growth of crystals and the equilibrium struecture of their surfaces. Philosophical Transactions of the Royal Society of London .Series A, Mathematical and Physical Sciences 1951, 243, 299-358. (34) Vekilov, P. G.; Kuznetsov, Y. G., Growth-kinetics irregularities due to changed dislocation source activity - (101) ADP face. Journal of Crystal Growth 1992, 119, 248-260. (35) Vekilov, P. G.; Kuznetsov, Y. G.; Chernov, A. A., Interstep interaction in solution growth - (101) ADP face. Journal of Crystal Growth 1992, 121, 643-655. (36) Thurmer, K.; Bartelt, N. C., Nucleation-limited dewetting of ice films on Pt(111). Phys Rev Lett 2008, 100, 186101. (37) Nie, S.; Bartelt, N. C.; Thurmer, K., Observation of surface self-diffusion on ice. Phys Rev Lett 2009, 102, 136101. (38) Nie, S.; Bartelt, N. C.; Thürmer, K., Evolution of proton order during ice-film growth: An analysis of island shapes. Physical Review B 2011, 84, 035420. (39) Thurmer, K.; Nie, S., Formation of hexagonal and cubic ice during low-temperature growth. Proc Natl Acad Sci U S A 2013, 110, 11757-62. (40) Materer, N.; Starke, U.; Barbieri, A.; Vanhove, M. A.; Somorjai, G. A.; Kroes, G. J.; Minot, C., Molecular-surface structure of a low-temperature ice Ih(0001) crystal. Journal of Physical Chemistry 1995, 99, 6267-6269. (41) Materer, N.; Starke, U.; Barbieri, A.; VanHove, M. A.; Somorjai, G. A.; Kroes, G. J.; Minot, C., Molecular surface structure of ice(0001): Dynamical low-energy electron diffraction, total-energy calculations and molecular dynamics simulations. Surface Science 1997, 381, 190-210.



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AUTHOR INFORMATION Corresponding Author Prof. Gen Sazaki: Institute of Low Temperature Science, Hokkaido University, N19-W8, Kita-ku, Sapporo 060-0819, Japan. E-mail: [email protected]. Phone and fax: +81-11-706-6880 Author Contributions M.I., Y.F. and G.S. designed the research performed by M.I., K.M., H.A., K.N. and G.S. S.N. produced the experimental system. M.I. and G.S. wrote the paper. The authors declare no conflict of interest. All authors have given approval to the final version of the manuscript. Funding Sources JSPS KAKENHIs (Nos. 23246001 and 15H02016). ABBREVIATIONS LCM-DIM, Laser Confocal Microscopy combined with Differential Interference contrast Microscopy


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For Table of Contents Use Only Manuscript title: Temperature dependence of the growth kinetics of elementary spiral steps on ice basal faces grown from water vapor Author list: Masahiro Inomata, Ken-ichiro Murata, Harutoshi Asakawa, Ken Nagashima, Shunichi Nakatsubo, Yoshinori Furukawa, Gen Sazaki TOC graphic

Synopsis We directly observed individual elementary spiral steps (A) on ice basal faces by our advanced optical microscopy. Then we determined the temperature dependence of the step kinetic coefficient β (B) of ice basal faces, for the first time. The temperature dependence of β shows a complicated behavior, strongly suggesting the existence of unknown phenomena.



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Figure Captions Fig. 1. A schematic drawing of an observation chamber. The observation chamber was composed of upper and lower Cu plates, whose respective temperatures T and Tbottom were separately controlled using Peltier elements. At the center of the upper Cu plate, a cleaved AgI substrate crystal was attached using heat grease. Ice crystals for the LCM-DIM observation were grown heteroepitaxially on the cleaved AgI crystal. Ice crystals for supplying water vapor to the ice crystals for the observation were grown on the lower Cu plates. The total pressure in the observation chamber was kept at 0.1 MPa (atmospheric pressure) by filling the chamber with pure nitrogen gas. The volume of the ice crystals for supplying water vapor was several orders of magnitude larger than that of the ice crystals for the observation. Hence, partial pressure of water vapor P∞ in the observation chamber was determined by Tbottom. In addition, equilibrium partial vapor pressure Pe of the ice crystals for the observation was determined by T. By separately controlling T and Tbottom, we can control the growth temperature T of the ice crystals for the observation and the supersaturation σ in the observation chamber separately.

Fig. 2. LCM-DIM images of elementary spiral steps grown on an ice basal face at T=-15.0 °C and σ=0.18. (A) A screw dislocation was located at the upper left edge of the ice basal face. All elementary spiral steps generated from the dislocation advanced laterally in the lower right direction. Ice basal faces show a ABAB… stacking structure, in which two adjacent crystal faces A and B are rotated by an angle of 60o to each other (for details see Fig. S4). Hence, elementary spiral steps also exhibit the ABAB… stacking structure, indicating that the distance Leq between adjacent A-A or B-B steps corresponds to the distance between adjacent equivalent spiral steps (marked by the white double-head arrow). Note that the distance L between adjacent A-B steps and Leq are different. We measured both Leq and L. (B and C) Images B and C were taken at 1.08 and 2.15 s after image A, respectively. The velocity Vstep of elementary spiral steps was determined from the time course of the position of the identical step (marked by white arrow heads). 26 ACS Paragon Plus Environment

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Fig. 3. An example of the relation between the velocity Vstep of elementary spiral steps and the distance L between adjacent A-B spiral steps on an ice basal face at T=-9.2 °C. Supersaturation σ: 0.12 (□), 0.16 (∆) and 0.20 (○). Straight lines show the average values of Vstep under each supersaturations. At T=-9.2 °C, when σ was smaller than 0.12, we could not measure L since L became longer than the size of the ice basal face.

Fig. 4. Changes in Vstep on ice basal faces as a function of σ. (A) Temperature T: -2.7 (○), -3.2 (□), -4.1 (▵), -6.2 (▿), -6.5 (◇), -8.0 (▹), -9,2 (◃). (B) Temperature T: -13.0 (●), -15.0 (■), 15.4 (▴), -17.9 (▾), -19.9 (◆), -21.9 (◣) and -26.0°C (◢). Solid curves show the results of the curve fittings using an error function besides T=-6.2 and -9.2°C, at which temperatures we used a straight-line approximation.

Fig. 5. Temperature dependence of the step kinetic coefficient β determined from Fig. 4. The solid curve is a guide for eyes.

Fig. 6. An example of the distribution of Leq on an ice basal face at T=-15.4 °C. The vertical and horizontal axes show the probability density and Leq, respectively. Supersaturation σ: 0.56 (A), 0.43 (B), 0.31 (C) and 0.15 (D). The solid curves show the results of the curve fittings using a log-normal distribution.

Fig. 7. An example of changes in Vstep on an ice basal face as a function of σ at T=-15.0°C. The solid curve shows the result of the curve fitting using an error function. The broken 27 ACS Paragon Plus Environment


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straight line represents the tangential line of the error function at σ=0. For the derivation of Psurf from this figure, see the main text.

Fig. 8. Changes in the average distance Leqav between adjacent equivalent (A-A or B-B) spiral steps as a function of the inverse of the driving force ∆µsurf at ice crystal surfaces. (A) Temperature T: -3.2 (●), -4.1 (■), -6,2 (◆), -6.5 (▴), -8.0 (▾), -9.2 (◣), -13.0°C (◢). (B) Temperature T: -15.0 (○), -15.4 (□), -17.9 (◇), -21.9 (△), and -26.0 (▽). The data could be classified into two groups shown in filled and open plots, respectively. The data shown in the filled plots can be approximately expressed by the solid straight line (eq. (4)), irrespective of T. In contrast, the data shown in the open plots at a constant T can be well expressed by a dotted straight line, which has a much larger slope and much smaller intercept (with a negative sign) than the solid straight line. However, the dotted straight lines determined at different T do not coincide with each other.


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Temperature Dependence of the Growth Kinetics of Elementary Spiral

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