Double Spiral Steps on Ih Ice Crystal Surfaces Grown from Water

Apr 7, 2014 - We present a model structure of spiral steps on basal and prism faces of Ih ice crystals grown from water vapor just below 0 °C. At the...
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Double Spiral Steps on Ih Ice Crystal Surfaces Grown from Water Vapor Just below the Melting Point Gen Sazaki,* Harutoshi Asakawa, Ken Nagashima, Shunichi Nakatsubo, and Yoshinori Furukawa Institute of Low Temperature Science, Hokkaido University, N19-W8, Kita-ku, Sapporo 060-0819, Japan S Supporting Information *

ABSTRACT: During the growth of ice crystals, spiral growth is one of the important growth mechanisms that dominate their growth. However, the structure of spiral steps on ice crystal surfaces at temperatures near the melting point has not been identified. Here we show a possible model structure of spiral steps on basal and prism faces of Ih ice crystals grown from water vapor just below 0 °C. We observed in situ the coalescences of spiral steps and steps of two-dimensional (2D) islands by our advanced optical microscopy, which can visualize individual elementary steps (single-bilayer height) of 2D islands on ice basal faces. We found that both spiral steps and 2D island steps on basal and prism faces show single-bilayer heights, though Burgers’ vectors of screw dislocations on both faces need to have double-bilayer heights because of a crystallographic requirement. These results suggest that at the center of a spiral growth hillock, steps of two adjacent single bilayers coincide and then form a double-bilayer step and that the steps of two single bilayers gradually detach themselves with increasing radii of their spiral steps. We observed the appearance of double spiral steps, which strongly supports our model structure, at −15.0 °C (the lowest temperature of our setup).

1. INTRODUCTION

Among the various kinds of defects, screw dislocations also play important roles in the growth of ice crystals:1 we found that basal and prism faces of ice crystals grow also by the spiral growth mechanism in addition to the 2D nucleation growth mechanism. However, the structure of spiral steps at temperatures near the melting point has still not been determined. As shown in Figure 1, both basal and prism faces are made up of bilayers.7 Two adjacent bilayers (A and B) constitute a unit structure in both faces. Hence, to grow Ih ice crystals by the spiral growth mechanism, the minimum length of a Burgers’ vector of a screw dislocation needs to be a double-bilayer height (0.74 and 0.78 nm on basal and prism faces, respectively), keeping the stacking sequence of ABAB... for Ih ice crystals. Thürmer and Bartelt8,9 reported that Ic ice crystals grow at 120−150 K when the length of a Burgers’ vector on a basal face is a single-bilayer height. In this study, we attempted to reveal whether spiral steps on basal and prism faces of Ih ice crystals (grown from water vapor) exhibit a double-bilayer or singlebilayer height at a temperature just below 0 °C, although steps of 2D islands formed by 2D nucleation show single-bilayer heights on both faces.1 The use of atomic force microscopy (AFM) is the most direct method for measuring the height of spiral steps. However, it is generally acknowledged that molecular-level AFM observation of bare ice crystal surfaces just below the

Because of the abundance of ice on earth, crystal growth of ice plays crucially important roles in a wide variety of fields. Hence, a molecular-level understanding of crystal growth of ice holds the key to unlocking the secrets of various phenomena. Recently, we succeeded in visualizing elementary steps of twodimensional (2D) islands on basal and prism faces (0.37 and 0.39 nm in thickness, respectively) of hexagonal (Ih) ice crystals grown from water vapor, by utilizing improved laser confocal microscopy combined with differential interference contrast microscopy (LCM-DIM).1 The LCM-DIM’s molecular-level resolution in the thickness direction opened up opportunities to perform new-generation studies on quasi-liquid layers (QLLs)2,3 and the growth kinetics of spiral steps on ice crystal surfaces. In the growth of ice crystals, it is widely acknowledged that defects play important roles. A recent molecular dynamics (MD) study by Pirzadeh and Kusalik4 revealed that five- and eight-membered rings (5-8 rings) are formed during the growth of Ih ice crystals at 24 K and that the 5-8 rings induce the formation of stacking faults and cubic (Ic) ice crystals. In contrast, an MD study by Moore and Molinero5 showed that the 5-8 rings are not formed at 180 K but that Ih and Ic ice crystals (formed by spontaneous nucleation) are consolidated, and then polycrystals (including Ih and Ic ice crystals, stacking faults, and random grain boundaries) are formed. An MD study by Li et al.6 also demonstrated that sequential formations of twin boundaries on Ic ice crystals produce ice crystals with 5fold symmetry. © 2014 American Chemical Society

Received: September 27, 2013 Revised: April 3, 2014 Published: April 7, 2014 2133

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Professor G. Layton of Northern Arizona University), known as an ice nucleating agent, was attached using heat grease. On this AgI crystal, Ih sample ice crystals were grown at −15 °C from supersaturated water vapor in a nitrogen environment. To supply water vapor to the sample ice crystals, other ice crystals were prepared on the lower Cu plate as a source of water vapor. Other details of the observation chamber were given in our recent report.1 By separately controlling the temperatures of the sample and source ice crystals, growth temperature of the sample ice crystals and supersaturation of the water vapor were adjusted independently. After the lateral size and height of the sample ice crystals had reached several hundred micrometers at −15 °C, the temperature was increased to a given value. Throughout this process, growth of the sample ice crystals was maintained by carefully changing the supersaturation and confirming the growth by LCM-DIM observations. Then the advancements of spiral steps and 2D island steps were observed. To obtain images, raw LCM-DIM images were processed according to the method explained in Figure S2 of the Supporting Information. The differential interference contrast was adjusted to appear as if the ice crystal surface was illuminated by a light beam slanted from the upper-left to the lower-right direction, as explained in Figure S3 of the Supporting Information.

3. RESULTS AND DISCUSSION We have observed several hundred ice crystals grown from water vapor in situ by LCM-DIM. Among such in situ observations, we could observe ice crystals growing only by the spiral growth mechanism with a probability of about 90%. We also found ice crystals growing only by the 2D nucleation growth mechanism with a probability of about 9%. Then with a probability of about only 1% (only 4 times), ice crystals were growing by both the spiral growth mechanism and the 2D nucleation growth mechanism in parallel. Hence, the spiral growth and 2D nucleation growth mechanisms are common growth mechanisms of ice crystals under our experimental conditions. As shown in our previous paper3 (also as shown in Figure 4), in all cases of ice crystals growing by the spiral growth mechanism, outcrops of screw dislocations were always located at edges of basal and prism faces, although its mechanism is still unclear. Hondo reported that screw dislocations that emerged from basal faces do not have energetically stable configurations.15 To determine the height of spiral growth steps, we observed, by LCM-DIM, the coalescence of spiral steps and 2D island steps formed by 2D nucleation on ice basal faces, utilizing the chance of about 1%. Figure 2 shows an example of such coalescence. A black arrowhead in Figure 2A indicates a 2D island that was formed by 2D nucleation newly in this frame. In addition, as shown in Figure 2B−D, many concentric steps emerged from the upper right portion of the images and then advanced in the downward direction. These concentric steps show spiral steps formed by the spiral growth mechanism. Figure 2B demonstrates that after the coalescence of a spiral step and a 2D island step, contrast of the steps disappeared completely, as in the region indicated by a cross mark. This result indicates that the heights of the spiral step and the 2D island step were the same. Since the height of 2D island steps was found to be a single-bilayer height (0.37 nm),1 we can conclude that the height of spiral steps is also a single-bilayer one. In Figure 2, only one example of the coalescence is shown. However, on the basal face shown in Figure 2, we could observe coalescence of spiral steps and 2D island steps 25 times during a period of 142 s. Then in all of the coalescences, the contrast of the steps always disappeared completely. Hence, we can

Figure 1. Schematic illustrations of cross sections of basal (A) and prism (B) faces of Ih ice crystals. Gray and red atoms show oxygen and hydrogen, respectively. Both faces are made up of bilayers. Two adjacent bilayers (A and B) constitute a unit structure on both faces. On both faces, bilayers A and B have the same crystallographic structure. However, on a basal face, bilayers A and B are rotated with respect to each other by an angle of 60°.

melting point is very difficult,10−13 partly because of QLLs that prevent a precise scan of cantilevers in the lateral directions. To determine the height of spiral steps, one of the attempts that can be performed by LCM-DIM is in situ observation of the coalescences of spiral steps and 2D island steps, since the height of the latter steps is known. From such observations, we attempted to reveal the structure of spiral steps.

2. EXPERIMENTAL METHODS A confocal system (FV300, Olympus Optical Co. Ltd.) was attached to an inverted optical microscope (IX70, Olympus Optical Co. Ltd.), as previously explained.1,14 A superluminescent diode (Amonics Ltd., model ASLD68-050-B-FA, 680 nm) was used as an illumination light source. The LCM-DIM system used in this study (Figure S1A of the Supporting Information) included all of the improvements used in our recent study1 in which elementary steps on ice crystal surfaces were observed. LCM-DIM is relatively slow optical microscopy. To acquire information in one pixel, it takes about 4 μs (an image of 816 × 236 pixels needs 0.70 s). Hence, LCM-DIM images in this study show averages over many molecular events, such as relaxation of molecules and fluctuations of interfaces. An observation chamber had upper and lower Cu plates, the temperatures of which were separately controlled using Peltier elements (Figure S1B of the Supporting Information). At the center of the upper Cu plate, a cleaved AgI crystal (a kind gift from Emeritus 2134

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Figure 3. Schematic illustration of the structure of spiral steps on both basal and prism faces of an Ih ice crystal. Steps marked as A and B indicate two adjacent bilayers A and B, respectively, shown in Figure 1. The two adjacent bilayer steps (A and B) exactly coincide at the center of a spiral growth hillock. However, with increasing radii of spiral steps, steps A and B gradually detach themselves.

Figure 2. Sequence of photomicrographs on a basal face of an Ih ice crystal at −3.0 °C. Photomicrographs show the time course of coalescence of a spiral step and a 2D island step (marked by a black arrowhead): 0 s (A), 0.70 s (B), 1.39 s (C), and 2.08 s (D). A cross mark in B indicates the region at which contrast between the coalesced steps disappeared. To obtain these images, raw images were processed according to the recipe explained in Figure S2, Supporting Information.

observation at present. In addition, to remove unnecessary effects of attractive/repulsive interaction between adjacent spiral steps, we carefully sublimated an ice basal face under a very slightly undersaturated condition and prepared a basal face on which no spiral step existed. Then we carefully started to grow the basal face again under a slightly supersaturated condition. Figure 4 shows the result of in situ observation at −15.0 °C. A screw dislocation was located at the position marked by a white arrowhead in Figure 4A. As time elapsed, double spiral steps emerged from the screw dislocation marked by the white arrowhead (Figure 4A). In addition, with increasing radii of the spiral steps from the screw dislocation, the distances between the double spiral steps (steps A and B in Figures 3 and 4D) also increased. These results strongly suggest that the model structure proposed in Figure 3 is plausible: steps A and B coincide at the screw dislocation, and then steps A and B gradually detached themselves as they grew. In this paper, we have so far reported the behavior of spiral steps on a basal face. To reveal the behavior of spiral steps on a prism face, which is another important low-index face of ice crystals grown from water vapor, we attempted to perform similar in situ observations on prism faces. In addition to the ice crystals grown heteroepitaxially on the cleaved AgI crystal, a small number of ice crystals had randomly nucleated and grown with their prism faces (by chance) placed perpendicular to the optical axis. Among such prism faces, we fortunately found the coalescence of spiral steps and 2D island steps. Figure 5 shows the results. Black arrowheads indicate 2D islands that were formed by 2D nucleation newly in these frames. In addition, from the position marked by a white arrowhead in Figure 5A, concentric steps appeared 50 times during a period of 98 s. Hence, we could conclude that these concentric steps were spiral steps that emerged from a screw dislocation. When the spiral steps and the 2D island steps coalesced, contrast of the steps always disappeared completely, as in the regions indicated by cross marks in Figure 5B,C,D. This result strongly suggests that the spiral steps and the 2D island steps on the prism face also have the same single-bilayer

conclude that the disappearance of step contrast after coalescence of spiral steps and 2D island ones is a common phenomenon. A video of the 25 disappearances of step contrast is available in Video S1, Supporting Information. To grow Ih ice crystals, Burgers’ vectors of screw dislocations have to be a double-bilayer height because of the crystallographic requirement for keeping the ABAB... stacking sequence. Despite this, the spiral steps observed on basal faces (Figure 2) exhibit a single-bilayer height, as in the case of 2D island steps. Figure 3 presents a possible model structure of spiral steps that can explain the observations. Since a Burgers’ vector of a screw dislocation (whose outcrop is marked by a white arrowhead in Figure 3) has a double-bilayer height, two bilayer steps (A and B) have to exactly coincide at the center of a spiral growth hillock. However, with increasing radii of these spiral steps, steps A and B gradually detach themselves. As shown in Figure 1A, the structures of steps A and B are exactly the same (The bilayers A and B are rotated by an angle of 60°). Hence, steps A and B have no reason to coincide, other than at the center of the spiral growth hillock. The detachment of steps A and B would rather be beneficial for obtaining entropic free energy gain. The formation of such double spiral steps has been found in a wide variety of crystals.16−18 To examine whether the model structure proposed in Figure 3 is plausible, we attempted to observe in situ the “double spiral structure” formed by gradual detachment of steps A and B. In Figure 2 (at −3.0 °C), we could not observe such a double spiral structure: steps A and B were fully detached immediately after they emerged. However, we expected that at a lower temperature, the detachment of steps A and B with increasing radii would become slower because of smaller thermal fluctuation. Hence, we carried out observation at −15.0 °C, which is the lowest temperature at which we can perform the 2135

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As explained in the beginning of the Results and Discussion section, we observed coalescence of spiral steps and 2D island steps on only about 1% of the ice crystals. In contrast, on the ice surfaces shown in Figures 2 and 5, we frequently observed such coalescences of both types of steps. In addition, in Figure 5, three of the four 2D islands that were newly formed on the prism face appeared to originate from almost the same positions. These results suggest that 2D nucleation was enhanced for some reason on the ice surfaces shown in Figures 2 and 5. One possible reason for such enhancement is heterogeneous 2D nucleation caused by impurities. In the case of protein crystals, Van Driessche and co-workers reported that impurities adsorbed on protein crystal surfaces significantly enhanced heterogeneous 2D nucleation and sometimes induced repeated 2D nucleation from the same position.19 In this study, such heterogeneous 2D nucleation might also have occurred, though the identity of the impurity is unclear. Since screw dislocations play crucially important roles in the growth of ice crystals, it would be worthwhile discussing how dislocations are formed in ice crystals. MD studies performed by Pirzadeh and Kusalik4 and also by Moore and Molinero5 showed that stacking faults and random grain boundaries are spontaneously formed in ice crystals during their growth. It has been widely acknowledged that stacking faults buried in crystals can produce partial dislocations of Frank and Shockley types and that the combination of such partial dislocations can form perfect dislocations.20 It is also generally known that strain formed on random grain boundaries induces the generation of dislocations in crystals.21 These findings support the fact that ice crystals include many dislocations.7 Hence, as observed in this study, the growth of ice crystals would be mainly governed by the spiral growth mechanism. At present, the system size of MD calculations is not sufficient to simulate the generation of dislocations in ice crystals. However, in the future, such studies will become an important research challenge.

Figure 4. Sequence of photomicrographs on a basal face of an Ih ice crystal at −15.0 °C. Photomicrographs show the time course of emergence of double spiral steps A and B (also shown in Figure 3). Before taking the photomicrographs, the basal face was carefully sublimated, and then no spiral step existed on the basal face. With increasing radii of spiral steps, the distance between adjacent spiral steps (A and B) increased. To obtain these images, raw images were processed according to the recipe explained in Figure S2, Supporting Information.

4. CONCLUSIONS In this study, we carried out in situ observations on Ih ice crystals by LCM-DIM. We found that on both basal and prism faces, spiral steps have single-bilayer heights (0.37 and 0.39 nm in thickness, respectively). We also proposed a model structure that explains Burgers’ vectors of double-bilayer heights and spiral steps of single-bilayer heights. Then at −15.0 °C (the lowest temperature for our experimental setup), we observed the appearance of double spiral steps, which strongly supports our model proposed in this study.

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ASSOCIATED CONTENT

S Supporting Information *

Schematic drawings of the experimental setup, image processing performed to obtain the LCM-DIM images, differential interference contrast, description of Video S1, and Video S1 in AVI format. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 5. Sequence of photomicrographs on a prism face of an Ih ice crystal at −2.4 °C. Photomicrographs show the time course of coalescence of spiral steps and 2D island steps (marked by black arrowheads): 0 s (A), 0.99 s (B), 1.99 s (C), and 2.98 s (D). Cross marks in B, C, and D indicate the regions in which contrast between the coalesced steps disappeared. To obtain these images, raw images were processed according to the recipe explained in Figure S2, Supporting Information.

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AUTHOR INFORMATION

Corresponding Author

*Dr. Gen Sazaki. E-mail: [email protected]. Phone and fax: +81-11-706-6880. Author Contributions

height (0.39 nm in thickness) and that the spiral steps on the prism face also show the structure presented in Figure 3.

G.S. and Y.F. designed the research performed by G.S., H.A., and K.N. S.N. produced the experimental system. G.S. and Y.F. 2136

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wrote the paper. All authors have given approval to the final version of the manuscript.

(15) Hondo, T. An overview of microphysical processes in ice sheets: Toward nanoglaciology. Low Temp. Sci. 2009, 68 (Supplement), 1−23. (16) Sunagawa, I.; Koshino, Y. Growth Spirals on Kaolin Group Minerals. Am. Mineral. 1975, 60 (5−6), 407−412. (17) van der Hoek, B.; van der Eerden, J. P.; Tsukamoto, K. Interpretation of Double Spirals on Silicon-Carbide. J. Cryst. Growth 1982, 58 (3), 545−553. (18) Stoica, C.; van Enckevort, W. J. P.; Meekes, H.; Vlieg, E. Interlaced spiral growth and step splitting on a steroid crystal. J. Cryst. Growth 2007, 299 (2), 322−329. (19) Van Driessche, A. E. S.; Sazaki, G.; Otalora, F.; Gonzalez-Rico, F. M.; Dold, P.; Tsukamoto, K.; Nakajima, K. Direct and noninvasive observation of two-dimensional nucleation behavior of protein crystals by advanced optical microscopy. Cryst. Growth Des. 2007, 7 (10), 1980−1987. (20) Hirth, J. P.; Lothe, J. Theory of Dislocations; Wiley: New York, 1982. (21) Chernov, A. A. Modern Crystallography III; Springer-Verlag: Berlin, 1984.

Funding

G.S. acknowledges support from JSPS KAKENHIs (Nos. 23246001 and 24656001). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Y. Saito and S. Kobayashi (Olympus Engineering Co., Ltd.) for their technical support of LCMDIM, G. Layton (Northern Arizona University) for the provision of AgI crystals, K. Thürmer (Sandia National Laboratories) and K. Kutsukake (Tohoku University) for valuable discussions, and H. Nada (National Institute of Advanced Industrial Science and Technology) for the preparation of Figure 1.

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ABBREVIATIONS LCM-DIM, laser confocal microscopy combined with differential interference contrast microscopy; QLL, quasi-liquid layer

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REFERENCES

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