Quasi-liquid layers on ice crystal surfaces are made up of two different phases

Abstract

Ice plays crucially important roles in various phenomena because of its abundance on Earth. However, revealing the dynamic behavior of quasi-liquid layers (QLLs), which governs the surface properties of ice crystals at temperatures near the melting point, remains an experimental challenge. Here we show that two types of QLL phases appear that exhibit different morphologies and dynamics. We directly visualized the two types of QLLs on ice crystal surfaces by advanced optical microscopy, which can visualize the individual 0.37-nm-thick elementary steps on ice crystal surfaces. We found that they had different stabilities and different interactions with ice crystal surfaces. The two immiscible QLL phases appeared heterogeneously, moved around, and coalesced dynamically on ice crystal surfaces. This picture of surface melting is quite different from the conventional picture in which one QLL phase appears uniformly on ice crystal surfaces.

Ice is one of the most abundant materials on Earth, and its phase transition governs a wide variety of phenomena in nature. Surface melting is one of the first-order phase transitions that occur on ice crystal surfaces and dominates the surface properties of ice crystals at temperatures below the melting point (1–3). It is generally acknowledged that quasi-liquid layers (QLLs) formed by surface melting play crucially important roles in the slipperiness of a skating rink, regelation (pressure-induced change in freezing), frost heave by ice columns, recrystallization and coarsening of ice grains, morphological change of snow crystals, cryopreservation, and electrification of thunderclouds. Hence, the molecular-level understanding of QLLs holds the key to unlocking the secrets of those phenomena.

Although surface melting was first proposed by Faraday in the 1850s (4), it was not until the mid-1980s that QLLs on ice crystal surfaces could be measured experimentally (1). Since then, many studies have measured the thickness of QLLs as a function of temperature by various methods (1–3) (Table S1). All those studies reported that the thickness of QLLs increased significantly with increasing temperature; however, their results showed considerable variations—as much as two orders of magnitude—depending on both measurement methods and researchers (1, 3, 5). Such variations could partly result from a lack of spatial and temporal resolution and variations in ice samples. To effectively study QLLs on ice crystal surfaces, the technique used needs to have sufficient spatial and temporal resolution.

We and Olympus Engineering Co., Ltd. have developed one such technique—namely, laser confocal microscopy combined with differential interference contrast microscopy (LCM-DIM) (6), which can directly visualize the 0.37-nm-thick elementary steps on ice crystal surfaces with a typical frame rate of 0.1–4 s per frame (7). In this study, we directly visualized surface melting processes on ice crystal surfaces to elucidate the dynamic behavior of QLLs and found that QLLs are made up of two different phases (Fig. S1).

Results and Discussion

We grew Ih ice single crystals on an AgI crystal from supersaturated water vapor in a nitrogen environment (Fig. S2). To supply water vapor to the sample ice crystals, we prepared other ice crystals (as a source of water vapor) on a separate copper plate. By separately changing the temperatures of the sample and source ice crystals, we adjusted the growth temperature of the sample ice crystals and the supersaturation of water vapor independently. After we prepared sample ice crystals at a growth temperature of -15.0 °C, we increased the temperature to a final -0.1 °C, at rates of approximately 0.1 °C/ min (from -15.0 to -2.0 °C) and approximately 0.02 °C/ min (from -2.0 to -0.1 °C). All through this process, we kept the sample ice crystals growing, by carefully changing the supersaturation and confirming the growth by LCM-DIM observations. Then we observed the behavior of QLLs on the surfaces of sample ice crystals. LCM-DIM images were processed according to the recipe explained in Fig. S3.

Fig. 1 shows the surface morphology of a basal {0001} face of a sample ice crystal. At -0.6 °C (Fig. 1A), we could observe “elementary steps” (7) (the growing ends of ubiquitous molecular layers with the minimum height: Fig. S4). This result demonstrates that at -0.6 °C, the basal face was flat at the molecular level and was growing layer by layer. In Fig. 1A, elementary steps (black arrowhead) grew from left to right (black arrow).

Fig. 1.

The appearance of round liquid-like droplets (α-QLLs), indicated by white arrowheads, on a basal face of an ice crystal with increasing temperature. The temperature was -0.6 (A), -0.4 (B), and -0.3 °C (C). Black arrowheads and black arrows indicate elementary steps and their growth directions, respectively. (D) An interferogram of α-QLLs taken at -0.3 °C by using a different ice crystal during another run. A movie of the process C is available as Movie S1.

At -0.4 °C (Fig. 1B), round objects (white arrowhead) appeared. Then, at -0.3 °C (Fig. 1C), the number of round objects increased, and their size also grew. In Fig. 1, the differential interference contrast was adjusted as if the ice crystal surface were illuminated by a light beam slanted from the upper left to the lower-right direction, as explained in Fig. S5. Hence, the upper-left and lower-right halves of the round objects appeared white and black, respectively.

These round objects coalesced just like liquid drops (Fig. 2 and Movie S1). Because the round objects were formed below 0 °C, they were QLLs formed by surface melting. Hence, hereafter, we name these round objects “α-QLLs”.

Fig. 2.

The coalescence of bulk liquid-like droplets (α-QLLs) at -0.3 °C. Images A–D were, respectively, taken 29, 30, 31, and 36 s after the temperature was set at -0.3 °C. Blue arrowheads show the coalescence of α-QLLs. α-QLLs coalesced just like liquid droplets. A movie of this process is available as Movie S1.

In 1993, Elbaum and coworkers (5) observed, by optical interference microscopy, that round drops appeared and coalesced at -0.4 to -0.2 °C on basal faces of ice crystals in water vapor. Later, Gonda et al. (8) also observed the appearance of round drops at -0.12 °C by differential interference contrast microscopy. The round drops reported in these studies probably correspond to α-QLLs. In this study, in addition to the appearance of α-QLLs, we found that the elementary steps appeared around α-QLLs (marked by a black arrowhead in Fig. 1C), showing that the α-QLLs function as sources of steps (Movie S1).

We measured the three-dimensional geometry of an α-QLL by using a He-Ne laser (633 nm), as shown in Fig. 1D. The interferogram shows that the shape of the α-QLL was a part of a sphere. The spacing between adjacent interference fringes corresponds to a height difference of a half-wavelength. Hence, the α-QLL, marked by a white arrowhead, had a width of 50 μm and a height of 0.5 μm. Although we identified an α-QLL as a “droplet”, its height/width ratio is very small (approximately 1/100). This result indicates that solid water (ice) and liquid water showed very high wettability, which strongly supports the fact that the α-QLLs functioned as step sources.

Fig. 3 shows the surface morphology observed after we further increased the temperature. At -0.2 °C, a thin layer (red arrowhead) newly appeared (Fig. 3A). α-QLLs were generated from this thin layer and also from the crystal surface. Then, we further increased the temperature to -0.1 °C (Fig. 3 B–D and Movie S2). We could observe that elementary steps, which exhibited bright contrast (black arrowheads), advanced to the left direction. This result confirms that one portion of the crystal surface grew, which demonstrates that the temperature of the crystal surface was surely below 0 °C. Therefore, we could conclude that the surface melting observed in the other portion of the crystal surface occurred below 0 °C. The thin layer eventually covered the whole crystal surface (Fig. 3D).

Fig. 3.

The appearance of thin liquid-like layers (β-QLLs), indicated by red arrowheads, with increasing temperature. The temperature was -0.2 (A) and -0.1 °C (B–D). Images B–D were, respectively, taken 0, 18, and 239 s after the temperature was set at -0.1 °C. Other arrowheads and arrows are the same as those in Fig. 1. A movie of the process B–C is available as Movie S2.

The differential interference contrast of the thin layer was significantly higher than that of an elementary step (Fig. 3). Hence, the thickness of the thin layer was much higher than that of an elementary step. We also tried to measure the thickness of the thin layer by interferometry. However, we could not distinguish interference fringes, which indicates that the thickness of the thin layer was smaller than the detection limit of interferometry (≤ several tens of nanometers).

The temperature of the appearances of α-QLLs and the thin layers respectively varied from -1.5 to -0.4 °C and from -1.0 to -0.1 °C, depending on experimental runs. However, in the same run, the thin layers always appeared at a higher temperature than α-QLLs (Fig. S1), and we could never find an inversion of the appearance temperatures.

The thin layer exhibited a feature that was significantly different from that of ice crystal surfaces. As shown in Fig. 4, the thin layers moved around the ice crystal surface and then coalesced with each other, just like liquid droplets. The decrease in the number of the thin layers with increasing time was not due to Ostwald ripening, by which smaller crystals disappear and larger ones grow, but was rather due to coalescence. Such dynamic movement and coalescence, which occurred on a time scale of several tens of seconds, indicate that the thin layer displays fluidity. These results strongly suggest that the thin layer was not a solid phase (ice) but a liquid phase that appeared below 0 °C. Hence, we refer to the thin layers as β-QLLs.

Fig. 4.

The coalescence of thin liquid-like layers (β-QLLs) at -0.5 °C. Images A–D were, respectively, taken 75, 263, 547, and 808 s after the temperature was set at -0.5 °C. White and red arrowheads correspond to α- and β-QLL phases, respectively. β-QLLs moved around the ice crystal surface and then coalesced with each other just like liquid droplets. Finally, only one β-QLL was observed (D).

To prove that a β-QLL was not solid, we carried out further in situ observations. In Fig. 5A, an α-QLL is located at the center, and a β-QLL exists around the α-QLL. On a bare surface of the ice crystal, we could observe the growth of elementary steps (in black arrow directions). We found that further extreme adjustment of the gain and offset of the image enabled us to visualize elementary steps even “beneath the β-QLL” (black arrowheads) in Fig. 5B. As shown in Fig. 5 B and C (Movie S3), we could observe the advancement of elementary steps even beneath the β-QLL (black arrowheads indicate the movement of the same step).

Fig. 5.

Visualization of elementary steps growing beneath a thin liquid-like layer (β-QLL) at -1.0 °C. The gain and offset of the image A were further extremely adjusted to obtain image B. Image C was taken 3.27 s after image B. (D) A schematic cross-sectional view showing two possible mechanisms (red arrows) discussed in the text for the visualization of elementary steps beneath the β-QLL. (E) Schematic illustration of the appearances of two types of QLL phases (α and β). Other arrowheads and arrows are the same as those in Figs. 1 and 3. A movie of the process B–C is available as Movie S3.

There are two possibilities (shown schematically in Fig. 5D) that could explain these images. The first is that elementary steps could be directly visualized through the β-QLL. The second is that elementary steps could not be visualized directly, but the deformation of the β-QLL due to the advancement of the steps could be visualized. In the first case, the refractive index of the β-QLL has to be different from that of solid ice. Hence, the β-QLL cannot be a solid phase but is a quasi-liquid phase appearing below 0 °C. In the second case, the β-QLL has to be easily deformed by the lateral movement of elementary steps that are only 0.37 nm thick (7). Such an easily deformed phase would be a quasi liquid, rather than a solid, although at present the rigidity of a solid ice film of nanometer thickness is unclear. This expectation is strongly supported by the fluidity of the β-QLL demonstrated in Fig. 4. Therefore, in either case, we concluded that we have observed the appearance of two types of QLL phases (α and β) on an ice crystal surface, as schematically summarized in Fig. 5E.

Elbaum and coworkers estimated the thickness of QLLs and the asperity of ice crystal surfaces, respectively, by ellipsometry and optical interference microscopy. Then they argued that, with increasing temperature, QLLs first appeared homogeneously on ice basal faces and the thickness of QLLs increased, and then after the thickness of QLLs exceeded 20 nm, round drops finally appeared on QLLs. This picture is quite different from the observations made in this study: With increasing temperature, α-QLLs first appeared heterogeneously, and then β-QLLs appeared also heterogeneously, as schematically shown in Fig. 5E (also Fig. S1). The different picture proposed by Elbaum et al. probably resulted from a lower spatial resolution of their observation techniques: They perhaps could not detect the heterogeneous behavior of α- and β-QLL phases in the early stages of their appearances.

We further investigated the stability of the two QLL phases. After we confirmed the appearance of α-QLLs and a β-QLL at -0.5 °C, we decreased the temperature to -1.0 °C and then observed the response. Fig. 6 (Movie S4) shows the resulting changes. As time elapsed, a β-QLL decomposed and changed into α-QLLs (small droplets shown in D, marked by a white arrowheads) and bunched steps. The appearance of the bunched steps (black arrowheads) means that a number of elementary steps were formed at one time (Fig. 6C, Inset) by the decomposition of the β-QLL. These results demonstrate that the β-QLL was the least stable phase that appeared in the highest temperature range, with the α-QLL being more stable and forming in a lower temperature range. It is also clear that the Ih ice was most stable among the three phases and formed in the lowest temperature range. The decrease in the size of the α-QLL located at the center (Fig. 6D) indicates that the α-QLL also partly decomposed into the most stable solid ice.

Fig. 6.

Decomposition of a β-QLL into α-QLLs and solid ice with decreasing temperature. After the appearances of α-QLLs and a β-QLL were confirmed at -0.5 °C, the temperature was decreased to -1.0 °C. Images A–D were, respectively, taken 0, 20, 23, and 49 s later. In this figure, black arrowheads and black arrows, respectively, show bunched steps (C, Inset: cross-sectional view) and their growing direction. Other arrowheads and arrows are the same as those in Figs. 1–3. A movie of this process is available as Movie S4.

On ice crystal surfaces, β-QLLs exhibited a much flatter shape than α-QLLs, which demonstrates that β-QLLs had higher wettability (more favorable interaction—i.e., smaller interfacial free energy) with ice crystal surface than α-QLLs. This result contradicts the lower stability (higher appearance temperature) of β-QLLs than α-QLLs. Resolving this contradiction will require further understanding of the physical/chemical properties of α- and β-QLLs.

In this study, we carried out in situ observation of ice crystal surfaces by LCM-DIM. We found the appearances of two types of QLL phases (α and β) formed by surface melting below 0 °C. So far, it has been thought that QLLs appear uniformly on ice crystal surfaces, and QLLs have been discussed by using a static picture. However, the results found in this study demonstrate that surface melting on ice crystal surfaces proceeds through two immiscible liquid phases (α and β) that are both dynamic and spatially inhomogeneous. The insights into the nature of QLLs obtained from direct visualization (Fig. 5E) may play a crucially important roles in understanding a variety of phenomena in which QLLs play a vital role, from the slipperiness of a skating rink to the electrification of thunderclouds (1–3).

Materials and Methods

We attached a confocal system (FV300; Olympus Corporation) to an inverted optical microscope (IX70; Olympus Corporation), as previously explained (6,7). A superluminescent diode (Amonics Ltd.; model ASLD68-050-B-FA: 680 nm) and a He-Ne laser (Melles Griot 05-LHP-991: 633 nm) were used for LCM-DIM and interferometric observations, respectively. The LCM-DIM system used in this study (Fig. S2A) contained all improvements reported in our recent study (7) of the observation of elementary steps on ice crystal surfaces.

The observation chamber had upper and lower Cu plates, whose temperatures were separately controlled by using Peltier elements (Fig. S2B). At the center of the upper Cu plate, a cleaved AgI crystal (a kind gift from emeritus professor G. Layton of Northern Arizona University), known as an ice nucleating agent, was attached by using heat grease. On this AgI crystal, sample ice crystals were grown at -15 °C. 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 were reported in our recent study (7). After the lateral size and height of the sample ice crystals reached several hundred micrometers, the temperatures of the sample and source ice crystals were increased to a final -0.1 °C. During this temperature rise, QLLs that appeared on the basal faces of the sample ice crystals were observed by LCM-DIM.

To obtain the LCM-DIM images shown in this study, raw images taken by LCM-DIM were processed according to the recipe explained in Fig. S3. This image processing corrected the background intensity inhomogeneity caused by the slight misalignment of the optical axis with the surface normal of an ice crystal.