Elementary steps at the surface of ice crystals visualized by advanced optical microscopy

Abstract

Due to the abundance of ice on earth, the phase transition of ice plays crucially important roles in various phenomena in nature. Hence, the molecular-level understanding of ice crystal surfaces holds the key to unlocking the secrets of a number of fields. In this study we demonstrate, by laser confocal microscopy combined with differential interference contrast microscopy, that elementary steps (the growing ends of ubiquitous molecular layers with the minimum height) of ice crystals and their dynamic behavior can be visualized directly at air-ice interfaces. We observed the appearance and lateral growth of two-dimensional islands on ice crystal surfaces. When the steps of neighboring two-dimensional islands coalesced, the contrast of the steps always disappeared completely. We were able to discount the occurrence of steps too small to detect directly because we never observed the associated phenomena that would indicate their presence. In addition, classical two-dimensional nucleation theory does not support the appearance of multilayered two-dimensional islands. Hence, we concluded that two-dimensional islands with elementary height (0.37 and 0.39 nm on basal and prism faces, respectively) were visualized by our optical microscopy. On basal and prism faces, we also observed the spiral growth steps generated by screw dislocations. The distance between adjacent spiral steps on a prism face was about 1/20 of that on a basal face. Hence, the step ledge energy of a prism face was 1/20 of that on a basal face, in accord with the known lower-temperature roughening transition of the prism face.

Ice is one of the most abundant materials on earth, and its phase transition governs a wide variety of phenomena, such as weather, environment-related issues, life in a cryosphere, and cosmic evolution, etc. Hence the molecular-level understanding of ice crystal surfaces is crucially important. For example, ice crystal surfaces play a key role in heterogeneous physical/chemical reactions, such as the degradation of ozone and organic compounds adsorbed on ice crystal surfaces by UV light irradiation (1–4), the suppression of the growth of ice in living things by antifreeze proteins adsorbed on ice crystal surfaces (5–8), etc., as well as in the growth and sublimation/melting of ice crystals.

A crystal bounded by flat crystal faces grows layer by layer (9, 10), utilizing laterally growing molecular layers that have the minimum height determined by the crystal structure. Hence, growing ends of such molecular layers, so-called “elementary steps,” which ubiquitously exist on a crystal surface, play a key role during the physical/chemical reactions and the growth and sublimation/melting of ice crystals. Therefore to clarify such phenomena at the molecular level, first one has to observe elementary steps on ice crystal surfaces.

Many optical microscopy studies have been carried out to date to observe the surface morphology of ice crystals, such as steps (11–15), height topography (16–23) and quasi-liquid layers (QLLs) (24, 25), by ordinary bright-field microscopy (11, 15, 16), differential interference contrast microscopy (12–14, 17, 21–23, 25), two-beam interferometry (18–20), and laser reflection microscopy (24). However, none of these studies could prove, by their optical observations, that they could visualize individual elementary steps, mainly due to the small reflectivity (1.8%) of air-ice interfaces. Although elementary steps of mineral crystals were visualized by traditional optical microscopy as early as the 1950s (26, 27), in such cases the coating of crystal surfaces with thin films of silver (nearly 100% reflectivity) was indispensable. However, after coating crystal surfaces, one cannot observe the dynamic behavior of elementary steps on such dead crystal surfaces. Hence, direct in situ observation of elementary steps on “bare ice crystal surfaces” is still needed.

Atomic force microscopy (AFM) is the most popular technique used to observe solid surfaces at the molecular level. However, it is generally acknowledged that the molecular-level AFM observation of ice crystal surfaces is very difficult (28–33). Such difficulty is partly due to QLLs, although the cause of this difficulty is not yet fully clarified. The presence of QLLs at air-ice interfaces prevents the precise scan of cantilevers in the lateral directions, because of strong surface tension existing between the cantilevers and QLLs. However, some studies have measured the thickness of QLLs by measuring force curves, scanning cantilevers in the vertical direction. To our knowledge, so far, only Zepeda and coworkers have succeeded in the AFM observation of elementary steps on ice crystal surfaces by covering the ice crystal surfaces with octane (a hydrophobic solvent) (33). Because of the difficulty in utilizing AFM at air-ice interfaces, we decided that advanced optical microscopy is probably a promising alternative to directly observe elementary steps on ice crystal surfaces.

From among the various kinds of advanced optical microscopy, we chose laser confocal microscopy combined with differential interference contrast microscopy (LCM-DIM). We have previously directly visualized elementary steps of protein crystals (> several nm in height) in aqueous protein solutions (∼1% reflectivity) with a sufficient contrast level by this technique (34–37). Using LCM-DIM, we could also visualize dislocations in protein crystals during growth (38). Because LCM-DIM has a high detection sensitivity and is not affected by the observation environment, we were able to visualize elementary steps of protein crystals even in a gel (39) and under high pressure (40). Such high detection sensitivity coupled with an insensitivity to the environment makes this technique look very promising, in particular for observing air-ice interfaces at a temperature just below the melting point of ice. In this study, we further improved the detection sensitivity of LCM-DIM, and attempted the visualization of elementary steps at air-ice interfaces.

Results and Discussion

Basal Faces Grown by Two-Dimensional Nucleation and Subsequent Lateral Growth.

We grew Ih ice single crystals heteroepitaxially on a cleaved {0001} face of an AgI crystal from supersaturated water vapor in a nitrogen environment. We set the temperature of the ice single crystals (T_sample) at -15.0 °C, at which temperature basal ({0001}) faces of ice crystals develop most widely (41). To supply water vapor to the sample ice crystals, we prepared other ice crystals (as a source of water vapor) on a copper plate that was 16 mm distant from the AgI crystal, and then separately set the temperature of the source ice crystals (T_source) at -13.0 °C. By changing T_sample and T_source, we adjusted the growth temperature of the sample ice crystals and the supersaturation of water vapor (the driving force for crystallization) separately. In our experiments, the exact evaluation of supersaturation was difficult, because of the uncertainty in the temperature of water vapor in the vicinity of the sample ice crystals. The details of all these operations are explained in the Materials and Methods section. Hence, hereafter, to notate the growth conditions, we list values of T_sample and T_source, rather than try to estimate the actual degree of supersaturation.

Fig. 1 shows typical examples of the surface morphology of the basal face of a sample ice crystal observed by our improved LCM-DIM, by which steps with subnanometer height on a transparent crystal surface could be visualized, as explained in the Materials and Methods section. T_sample and T_source were -10.0 and -9.3 °C, respectively. Photomicrographs of 720 × 208 pixels were acquired over a 0.57 s scan time. To obtain the images shown in Fig. 1, raw images were processed according to the recipe explained in (Fig. S1). We subtracted the time-averaged image (Fig. S1B), in which motionless objects such as defects (a white arrowhead in Fig. S1B) and the inhomogeneous background level were recorded, from the original image (Fig. S1A). After the adjustment of a gain and an offset (Fig. S1C), a Gaussian filter of one pixel size was used to smooth the image (Fig. S1D).

Fig. 1.

Photomicrographs of the surface morphology on the basal face of a Ih ice crystal. The sequence of micrographs show the time course of a two-dimensional nucleation growth of birth-and-spread type: 0 s (A), 0.57 s (B), 1.14 s (C) and 1.72 s (D). Cross marks in B and D show the regions at which contrast between the coalesced steps disappeared. Growth conditions: T_sample = -10.0 and T_source = -9.3 °C. To obtain these images, raw images were processed according to the recipe explained in Fig. S1.

As shown in Fig. 1 A–D taken at 0.57 s intervals, the basal face of the ice crystal grew by a two-dimensional nucleation growth mode of birth-and-spread type. The two-dimensional islands appeared and then spread laterally with growth time. The isotropic round shape of the two-dimensional islands agrees with that observed for sublimation steps at temperatures above -20 °C (15). When the steps of neighboring two-dimensional islands coalesced, contrast of the steps always disappeared completely, as in the regions indicated by cross marks in Fig. 1 B and D. Videos of the appearance and lateral growth of two-dimensional islands are available in (Movies S1 and S2), in which the image processing shown in Fig. S1 was not performed (Movie S1: just the gain and offset of original images were adjusted) and was performed (Movie S2), respectively.

From the time course of the surface morphology observed during 100 s, we determined the positions at which two-dimensional islands were formed and coalesced, as shown in Fig. 2. Asterisk marks (Fig. 2A) indicate the positions where two-dimensional islands were newly formed. In the central region of the basal face, two-dimensional islands appeared at random locations, demonstrating that in these regions two-dimensional islands were formed by two-dimensional nucleation. In contrast, in the peripheral region, the two-dimensional islands did not appear, probably suggesting that strain energy induced by defects, which generally tend to remain in the central region of a crystal surface, promoted the two-dimensional nucleation in the central region (42, 43).

Fig. 2.

Positions at which the two-dimensional nucleations (asterisk marks in A) and the coalescences of adjacent two-dimensional islands (cross marks in B) occurred, during 100 s, on top of the basal face of the ice crystals shown in Fig. 1. Growth conditions: T_sample = -10.0 and T_source = -9.3 °C. The asterisk and cross marks were placed on the time-averaged image shown in Fig. S1B.

In Fig. 2B, cross marks correspond to the positions where the step contrast disappeared completely after the coalescence of neighboring two-dimensional islands during 100 s of observation. Due to the spatial randomness of the two-dimensional nucleation, the disappearances of the step contrast also occurred at random locations on the crystal surface. Fig. 2B shows such a typical example observed during 100 s at T_sample = -10.0 and T_source = -9.3 °C. We could commonly observe such disappearances of the step contrast on ice crystal surfaces grown under various T_sample, although at ΔT ≡ T_source - T_sample > 1.5 °C the disappearances of the step contrast became difficult to observe because of the high densities and high lateral growth rates of two-dimensional islands. Noteworthy is that no step contrast remained after the coalescence of neighboring two-dimensional islands, indicating that no bunched (multilayered) step was being produced.

Verification of the Visualization of Elementary Steps.

As a first step, it is important to prove whether or not the steps we observed were elementary steps, those which have the minimum height determined by the crystal structure. To discuss this issue quantitatively, we assumed two cases. The first is in which all steps that existed on the ice crystal surface could be fully visualized. The second is where there were invisible steps on the ice crystal surface: i.e., LCM-DIM could not visualize steps whose heights were smaller than a critical value h_crit.

In the first case, the complete disappearance of the step contrast after the coalescences shown in Figs. 1 and 2 indicates that the height of the steps of the two-dimensional islands observed was identical: i.e., such steps can be described as elementary steps with the minimum height.

In the second case, we have to take into account the coalescence of a detectable step (whose height h≥h_crit) and an undetectable step (whose height h^′ < h_crit). When the height difference Δh ≡ h - h^′ is less than h_crit, the detectable step apparently disappears after the coalescence. Such apparent disappearance of the step contrast becomes more frequent with increasing h, as explained quantitatively in our previous paper (40). However, we never found such apparent disappearance of the step contrast throughout all of the experiments. This result strongly supports our hypothesis that h_crit is smaller than the height of the smallest steps: i.e., LCM-DIM could visualize elementary steps on the ice crystal surface.

In addition, the second case violates the tenets of classical two-dimensional nucleation theory, whose validity has been widely confirmed by many experiments (9, 10, 37, 44, 45). The two-dimensional nucleation rate J^2D(i) of multilayered islands, where i is the number of layers, can be expressed as follows (9, 10):

[1]

Here ϖ is the attachment frequency of a monomeric molecule to a critical nucleus, Γ the Zeldovich factor, C₁ the density of monomeric molecules on a crystal surface, ΔG(1) the activation free energy barrier of the two-dimensional nucleation of single-layered (elementary) islands, k_B the Boltzmann constant, and T the absolute temperature. Hence the ratio of J^2D(i) to J^2D(1) [the two-dimensional nucleation rate of single-layer (elementary) islands] is given by

[2]

where C(1)^∗ is the density of single-layered critical nuclei on a crystal surface. Because C(1)^∗ is astronomically smaller than C₁, J^2D(i) is negligibly small compared to J^2D(1). Hence, we can conclude that the two-dimensional islands visualized by LCM-DIM were single (elementary) layers.

So far, there are many papers that observed steps on ice crystal surfaces (11–15). However, these studies observed spiral growth steps, and hence failed to prove the observation of elementary steps. In this study, we have clearly observed two-dimensional nucleation growth and verified that we are visualizing elementary steps. The keys to this achievement are the improvement to LCM-DIM explained in the Materials and Methods section and the preparation of high quality ice crystals.

Height of Elementary Steps.

A schematic cross section of an ice crystal (Fig. 3) indicates that a basal face has a bilayer structure (46). The distance between adjacent bilayers is 0.37 nm, which is a half of a unit cell height in the C direction. Because of the tetrahedral bonding of water molecules in an ice crystal, the density of intrabilayer hydrogen bonding is three times higher than that between bilayers, strongly suggesting that a bilayer structure forms a topmost layer of a basal face. Therefore one could expect that the height of elementary steps on a basal face is 0.37 nm.

Fig. 3.

A schematic drawing of a cross section of a Ih ice crystal. Gray and red atoms correspond to oxygen and hydrogen, respectively. Bilayers made of water molecules are stacked in the C direction at 0.37 nm intervals.

To our knowledge, Zepeda and coworkers are the only workers so far who have visualized elementary steps on ice crystal surfaces covered with octane by AFM, and reported that the measured height of elementary steps of basal faces was 0.29 nm (33). Taking into account the large error of AFM measurements in the height direction, this height coincides well with the interbilayer height of 0.37 nm. Hence, we concluded that LCM-DIM could successfully visualize elementary steps of 0.37 nm height at the interface between air and a basal face.

Two-Dimensional Nucleation Growth on Prism Faces.

In addition to the ice crystals grown heteroepitaxially on the cleaved AgI crystal, we also found that a small number of ice crystals had randomly nucleated and grown with their prism () faces (by chance) placed perpendicular to the optical axis. This fortunate occurrence meant that such prism faces could be observed by LCM-DIM.

Fig. 4 shows the time course of a prism face taken by LCM-DIM. Photomicrographs of 512 × 448 pixels were acquired over a 0.99 s scan time. T_sample and T_source were -2.2 and -2.2 °C, respectively (the supersaturation was very small). The crystallographic orientation of the crystal was determined from an image taken by ordinary bright-field optical microscopy (see Materials and Methods). As shown in Fig. 4 A–D, the prism face also grew by a two-dimensional nucleation growth mode of birth-and-spread type. The two-dimensional islands appeared randomly on the prism face and spread in the lateral direction with growth time. Then, after the coalescence of neighboring two-dimensional islands, the contrast of the steps disappeared completely, as in the regions indicated by cross marks in Fig. 4 B and D. Such disappearances of the step contrast were consistently observed all over the prism faces examined. Therefore, following the same line of argument used for the basal face, we also concluded that LCM-DIM could visualize elementary steps on the prism face.

Fig. 4.

Photomicrographs of the surface morphology on the prism face of a Ih ice crystal. The sequence of micrographs show the time course of a two-dimensional nucleation growth of birth-and-spread type: 0 s (A), 0.99 s (B), 1.98 s (C) and 2.97 s (D). Cross marks in B and D show the regions at which contrast between the coalesced steps disappeared. Growth conditions: T_sample = -2.2 and T_source = -2.2 °C. To obtain these images, raw images were processed according to the recipe explained in Fig. S1.

The height of elementary steps on a prism face is expected to be 0.39 nm from their crystallographic structure (also consisting of a bilayer structure), although no AFM measurement has yet been reported.

Spiral Growth.

Besides two-dimensional nucleation growth, another important and ubiquitous growth mechanism is spiral growth (9, 10). In situ observations of elementary spiral steps on basal and prism faces provide intrinsic information on this growth mode on these faces. Fig. 5 presents a basal face (A) and a prism face (B) growing by the spiral growth mechanism induced by screw dislocations (indicated by white arrowheads). Although the steps shown in Fig. 5A do not look like spiral steps because of the low step density (large step separation), growth under higher supersaturation provided much higher step density (smaller step separation), as shown in Fig. S2. Hence, we could be sure that these features were really spiral steps.

Fig. 5.

Photomicrographs of a basal face (A) and a prism face (B) of Ih ice crystals grown by the spiral growth mechanism induced by screw dislocations (indicated by white arrowheads). These two crystals were located adjacently on the same AgI crystal. As a result, it can be expected that the supersaturations provided for both crystal surfaces were almost the same. Growth conditions: T_sample = -15.0 and T_source = -16.0 °C. Although T_sample was slightly higher than T_source, the growth of elementary spiral steps indicated that water vapor was still supersaturated. Details are explained in the Materials and Methods section. To obtain these images, the series of image processing used in Figs. 1 and 4 was not performed. Just the gain and offset of the original images were adjusted.

The two crystals shown in Fig. 5 A and B were adjacently located on the same AgI crystal. Hence, we can assume that the supersaturations provided for both crystal surfaces were almost the same. Nevertheless, the distance between the adjacent spiral steps on the basal face (l^basal ≅ 100 μm) was much longer than that on the prism face (l^prism ≅ 5 μm). The distance between adjacent spiral steps l can be expressed as follows (9, 10):

[3]

Here ρ_c is the radius of a critical two-dimensional nuclei, s the area one molecule occupies inside a two-dimensional nucleus, κ the free energy of a step ledge, and Δμ the driving force for crystallization (supersaturation). Therefore, the ratio of interstep distances corresponds to the ratio of the step ledge energies:

[4]

Much smaller κ^prism than κ^basal qualitatively coincides with the fact that the prism face roughens more easily (at a lower temperature) than the basal face (47).

Long-Standing Questions That will Be Explored by LCM-DIM.

In this study, we demonstrated that LCM-DIM can visualize elementary steps on ice crystal surfaces directly with sufficient contrast levels in real time. Hence, we believe that LCM-DIM can become a promising means in the near future to explore many long-standing questions regarding ice crystals, such as the role of ice crystal surfaces in the heterogeneous physical/chemical reactions, the formation mechanisms and growth kinetics of QLLs induced by surface melting, roughening transitions of steps and crystal surfaces, and evaluation of the step ledge free energy from the measurement of two-dimensional nucleation rates, etc., in addition to the growth kinetics of elementary steps.

Materials and Methods

Observation System.

A confocal system (FV300 [discontinued], Olympus Optical Co. Ltd.) was attached to an inverted optical microscope (IX70 [discontinued], Olympus Optical Co. Ltd.), as shown in Fig. 6A. A super luminescent diode (Amonics Ltd., model ASLD68-050-B-FA: 680 nm), whose coherent length and full-width at half-maximum were about 10 μm and 23 nm, was used for LCM-DIM observation to avoid the appearance of interference fringes. LCM significantly reduces the noise originating from outside of the focal depth. In addition, DIM changes the phase difference between the two light beams reflected at both sides of a step (upper and lower terraces) into an intensity difference. By combining these two effects, LCM-DIM exhibits a high sensitivity in z-direction (34). In this study, a polarizer made of aligned silver nanoparticles (colorPol VISIR CWO2, CODIXX AG Co. Ltd.) and a polarization beam splitter (BL9004, Olympus Optical Co. Ltd.) were newly adopted to increase the illumination intensity and hence to further improve the signal-noise ratio of LCM. Also an analyzer used in our previous system was removed, since the polarization beam splitter provides the same function. A new low magnification objective (UPlanFl 10X P, Olympus Optical Co. Ltd.) was also used to avoid deterioration of the degree of polarization and hence to improve the DIM contrast further. Other details were reported in our previous studies (34, 36).

Fig. 6.

Schematic drawings of the experimental setups: (A) the LCM-DIM system, the observation chamber, and the water-vapor supply system; (B) a cross sectional view of the observation chamber; (C) and (D) ordinary bright-field optical microscopy images and crystallographic orientations of ice crystals nucleated heteroepitaxially (C) and randomly (D) on the cleaved AgI crystal at -15 °C. In B, the top right inset shows a close up view of the cleaved AgI crystal attached to the top Cu plate; the top center inset presents a photomicrograph of the Ih ice crystals grown heteroepitaxially on the AgI crystal; the top left inset depicts the morphology of the Ih ice crystal. The surface of the cleaved AgI crystal was observed from below through a triple window made of three glass plates of 150 µm thickness and rubber O-rings. In D, white arrowheads indicate prism faces, which are connected to the targeted prism face and are used to identify the crystallographic orientation.

To prove the efficiency of the improved LCM-DIM system, a cleaved surface of a transparent gypsum crystal was observed by both LCM-DIM and AFM (Fig. S3). The comparison of the same field of view observed by both methods clearly shows that steps of 0.75 nm height on a cleaved gypsum crystal could be visualized with sufficient contrast level by LCM-DIM.

Fig. 6B presents a sectional view of the observation chamber. The chamber was made of a teflon plate sandwiched between two copper plates. The temperatures of the upper and lower Cu plates were separately controlled using four Peltier elements (an exploded diagram of the chamber is shown in Fig. S4). At the center of the lower side of the upper Cu plate, a cleaved AgI crystal, which is known as an ice nucleating agent, was attached using heat grease. AgI crystals were a kind gift provided by emeritus professor Gary Layton of Northern Arizona University.

Growth of Seed Ice Crystals.

Temperatures of the upper and lower Cu plates were set at T_sample = 20.0 and T_source = -15.0 °C, respectively. Then water vapor was supplied to the inside of the chamber by nitrogen gas bubbled through water (flow rate: 500 mL/ min). After source ice crystals were grown on the lower Cu plate for 1 h, two valves on the chamber were closed to stop the water-vapor supply and to keep the chamber airtight. The temperatures of the upper and lower Cu plates were then kept at T_sample = -15.0 and T_source = -13.0 °C, respectively, for 2 h to nucleate sample ice crystals on the cleaved AgI crystal. Most of the ice crystals that appeared on the AgI crystal had the same orientation (inset of Fig. 6B), indicating that they were grown heteroepitaxially. Then at T_sample = -15.0 and T_source = -14.0 °C, the sample ice crystals were grown overnight until their lateral size and height reached several hundred μm.

Fig. 6 C and D respectively show the images of basal and prism faces of ice crystals observed by ordinary bright-field optical microscopy. In the case of a basal face, two facets with a dihedral angle of 120° clearly indicate their crystallographic orientation (Fig. 6C). However, in the case of a prism face, the crystallographic orientation is determined utilizing other prism faces (marked by white arrowheads in Fig. 6D) that are connected to the targeted prism face. As the shape of ice crystals became rounded close to the melting point (as shown in Fig. 4), the crystallographic orientation was determined at -15 °C, at which temperature well faceted crystals were obtained.

In the observation chamber the sample ice crystals were 16 mm away from the source ice crystals. As water vapor diffused away from the source ice crystals in N₂ gas at atmospheric pressure, its temperature increased. Hence the temperature of water vapor in the vicinity of the sample ice crystals was unclear, and in our observations, the degree of supersaturation could not be quantified exactly. The temperature increase of water vapor during the diffusion is evidenced by the fact that even when T_sample was slightly higher than T_source, like the case shown in Fig. 5, the growth of elementary steps was observed.