Premelting-Induced Smoothening of the Ice-Vapor Interface

We perform computer simulations of the quasiliquid layer of ice formed at the ice-vapor interface close to the ice Ih-liquid-vapor triple point of water. Our study shows that the two distinct surfaces bounding the film behave at small wavelengths as atomically rough and independent ice-water and water-vapor interfaces. For long wavelengths, however, the two surfaces couple, large scale parallel fluctuations are inhibited, and the ice-vapor interface becomes smooth. Our results could help explain the complex morphology of ice crystallites.

Figure 1

Snapshot of the ice-vapor interface during the course of our simulations. Top: a quasiliquid layer of disordered molecules is clearly seen on top of the bulk ice. The order parameter allows us to distinguish between an ice-film and a film-vapor surface. Bottom: same figure with the liquidlike atoms removed.

Figure 2

Fluctuations of the premelting film on the primary prismatic plane. The plot displays the effective wave-vector dependent stiffness $\mathrm{\Gamma }(q_x)$ in log scale for (pI)[pII] at $\mathrm{\Delta }T=-2\mathrm{K}$ (a), and (pI)[basal] at $\mathrm{\Delta }T=-2\mathrm{K}$ (b) and $\mathrm{\Delta }T=-8\mathrm{K}$ (c). Results for the quasiliquid layer are shown with filled symbols, with ${\mathrm{\Gamma }}_{\text{if}}(q_x)$ for the ice-film (blue circles) and ${\mathrm{\Gamma }}_{\mathrm{fv}}(q_x)$ for the film-vapor surfaces (red squares). The open symbols are the results for the ice-water (blue circles) and water-vapor (red squares) interfaces, which are fitted to $\mathrm{\Gamma }(q_x)=\gamma +\kappa q_x^2+\epsilon q_x^4$ (dashed lines) for the purpose of extrapolation (cf. Refs. [44] and [27]). The colored arrows indicate the extrapolation to $q_x=0$, which provides the ice-water stiffness ${\tilde{\gamma }}_{\mathrm{iw}}$ and the water-vapor surface tension ${\gamma }_{\mathrm{wv}}$, respectively. The black arrow points to $\mathrm{\Sigma }={\tilde{\gamma }}_{\mathrm{iw}}+{\gamma }_{\mathrm{wv}}$, where the effective stiffness of the quasiliquid film would converge were the interface rough. The dashed vertical line indicates approximately the regime of $q_x$ where the quasiliquid surfaces cease to behave independently. The green triangles indicate the results for the coupled fluctuations of the ice-film and film-vapor surfaces, ${\mathrm{\Gamma }}_{\mathrm{iv}}(q_x)$. The full lines are the results from a fit to the model of Eq. (4).

Figure 3

Structure of the ice-vapor (full lines) and ice-liquid (dashed lines) interfaces of the primary prismatic plane along the perpendicular direction. The density of the solidlike molecules is shown in full red for the solid-vapor interface and in dashed indigo for the solid-liquid interface. The density of the liquidlike molecules is shown in full blue for the solid-vapor interface and in dashed green for the solid-liquid interface.