Surface phase transitions and crystal habits of ice in the atmosphere

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Science Advances  20 May 2020:
Vol. 6, no. 21, eaay9322
DOI: 10.1126/sciadv.aay9322
  • Fig. 1 Growth of ice crystals at low supersaturation.

    (Middle) As temperature ΔT = TTt decreases below the triple point, Tt, the habit of hexagonal ice prisms grown in the atmosphere changes sharply from platelike to columnar at ca. −4 K, from columnar to platelike at −10 K, and somewhat less sharply from platelike to columnar at −40 K (8). The facet which grows faster as indicated by the arrows, dictates the prevalence of plates or columns. The change of crystal habits results from a crossover in the growth rates of the basal and prism facets. (Top and bottom) Sketch of surface structural evolution with temperature as found in our work. Blue lines represent the i/f surface, and red lines represent the f/v surface. The basal surface (top row) is a high-temperature reconstructed flat (HT-RF) phase from ΔT = 0 to −4 K. It becomes a DOF phase in the range between ca. −4 and −47 K and is transformed into an OF phase at lower temperatures. In this phase, surface disorder resulting from patches of liquid-like molecules remains. The prism surface (bottom row) is an HT-RF phase all the way from 0 to −17 K but is very close to the roughening transition at ΔT > − 2 K in our model. In the range from −17 to −57 K, it is a DOF phase and becomes an OF phase below −57 K. At the transition from DOF-like to HT-RF phases, step free energies increase anomalously and result in the crossover of crystal growth rates. The shaded areas illustrate the temperature range where melting of full bilayers has been accomplished. Blue, less than one full bilayer; white, less than two full bilayers; yellow, more than two full bilayers.

  • Fig. 2 Characterization of the premelting layer.

    After placing a slab of perfect ice in vacuum, a premelting layer of disordered water molecules is formed spontaneously in a few nanoseconds as shown in the snapshot. Using a suitable order parameter, it is possible to distinguish liquid-like (red) from solid-like (blue) molecules. The state of the premelting film may be described in terms of two different surfaces, zif(r) and zfv(r), separating the film from bulk ice and vapor phases, respectively. A film thickness, h(r), may be defined as the difference between ice/film and film/vapor surfaces such that h(r) =zfv(r) zif(r)∣.

  • Fig. 3 Surface fluctuations on the basal facet.

    (A) Probability distribution of ice/film (blue) and film/vapor (red) surface fluctuations, as measured by the deviations of the interface position zα(x) about the average surface z¯α, for α = {if, fv}. Results are shown for different temperatures as indicated in the legend. (B) Snapshots of the basal surface at the same four temperatures. Red lines show the connected hydrogen bond network of all solid-like and liquid-like water molecules. The violet patches represent disordered liquid-like molecules. At low temperature, the surface is mainly a regular hexagonal honeycomb with a few patches of liquid-like molecules sitting on interstitial positions (as indicated by the yellow circles). The extent of filled interstitial positions increases as the premelting layer covers the surface. (C) Plot showing a snapshot of local surface height fluctuations δzif(r) (bottom, blue frame) and δzfv(r) (top, red frame) on the basal ice face. Notice the emergence of large-scale correlated patches for the DOF phase in the temperature range ΔT = −32 to −9 K (see movies S1 and S2). The patches disappear at high temperature as the surface flattens again. (D) Wave vector–dependent stiffness coefficients, as obtained from the inverse surface structure factor for i/f correlations (blue), f/v correlations (red), and crossed i/f -f/v correlations (green). Crosses are results from simulation; full lines are fits to the SG-CW model. The results show that all surfaces are smooth, as indicated by the divergence of Γ(qx) as qx → 0. Note that the sharp minimum appears at intermediate length scales in the temperature range ΔT = −32 to −9 K, where the DOF phase is present.

  • Fig. 4 Surface fluctuations on the prism facet.

    Content displayed as in Fig. 3. (A) A bimodal distribution in this facet is only visible at temperature ΔT = −32 K. (B) Here, the snapshots show the characteristic rectangular mesh of the prism facet. At low temperature, the liquid-like molecules form patches on the solid surface as in the basal face. (C) Emergence of large correlated domains signals a DOF phase that is clearly visible at ΔT = −32 K and vanishes at notably lower temperatures than for the basal facet (see movies S4 and S5). (D) Likewise, the sharp minimum of the stiffness coefficient is visible only at and below ΔT = − 32 K.

  • Fig. 5 Fluctuations of premelting thickness.

    Results are shown for basal (A and C) and prism (B and D) facets. (A and B) Distribution of average film thickness, h, as a function of undercooling, with ΔT = −82 K (blue), −32 K (green), −9 K (yellow), and −2 K (red). Dashed vertical lines represent full layers in units of the molecular diameter. The transition of premelting layer thickness across integer multiples of the molecular diameter occurs at broadly the same temperature for the basal and prism facets. (C and D) Surface plot of the instantaneous premelting thickness, h(r), for basal (C) and prism (D) surfaces (see movies S3 and S6). Notice the absence of large correlated domains at all temperatures, in marked contrast with the δzif(r) and δzfv(r) surfaces shown in Figs. 3 and 4.

  • Fig. 6 Calculated step free energies.

    Step free energies as obtained from a fit of the mean field SG-CW model to the regular (Gaussian) part of the stiffness coefficients in Figs. 3D and 4D for the basal (blue) and prism (red) facets. Results (squares with dashed lines) are compared to experimental data (circles with full lines) (17) and displayed on two different figures to avoid crowding. Notice that the scale in both figures is the same. The step free energies from the fit exhibit a crossover at ca. −6 K, 2 K above that found in the accepted Nakaya diagram, and display overall a trend similar to the experimental data.

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