[Paper Review] Toward a Comprehensive Model of Snow Crystal Growth: 3. The Correspondence Between Ice Growth from Water Vapor and Ice Growth from Liquid Water

Kenneth G. Libbrecht|arXiv (Cornell University)|Jul 2, 2014

nanoparticles nucleation surface interactions3 citations

TL;DR

This paper proposes a unified physical mechanism for ice crystal growth from water vapor and from liquid water, showing that both processes are governed by the same nucleation barrier on the basal ice surface due to comparable molecular step energies. Near the melting point, the step energy at the quasiliquid layer (solid/quasiliquid) matches that at the solid/liquid interface, indicating a fundamental correspondence in growth dynamics governed by equilibrium surface energetics.

ABSTRACT

We examine ice crystal growth from water vapor at temperatures near the melting point, when surface premelting creates a quasiliquid layer at the solid/vapor interface. Recent ice growth measurements as a function of vapor supersaturation have demonstrated a substantial nucleation barrier on the basal surface at these temperatures, from which a molecular step energy can be extracted using classical nucleation theory. Additional ice growth measurements from liquid water as a function of supercooling exhibit a similar nucleation barrier on the basal surface, yielding about the same molecular step energy. These data suggest that ice growth from water vapor and from liquid water are both well described by essentially the same underlying nucleation phenomenon over a substantial temperature range. A physical picture is emerging in which molecular step energies at the solid/liquid, solid/quasiliquid, and solid/vapor interfaces create nucleation barriers that dominate the growth behavior of ice over a broad range of conditions. Since the step energy is an equilibrium quantity, just as surface melting is an equilibrium phenomenon, there exists a considerable opportunity to use many-body simulations of the ice surface structure and energetics at equilibrium to better understand many dynamical aspects of ice crystal growth.

Motivation & Objective

• To investigate the physical correspondence between ice growth from water vapor and from liquid water near the melting point.
• To determine whether the same nucleation barrier governs growth in both vapor and liquid phases.
• To explore the role of surface premelting and quasiliquid layers in mediating ice crystal growth dynamics.
• To assess the potential of equilibrium many-body molecular dynamics simulations to predict non-equilibrium growth behavior via step energy calculations.
• To reconcile discrepancies in growth rate prefactors between vapor and liquid growth data.

Proposed method

• Application of classical nucleation theory to extract molecular step energy from measured growth rate dependencies on supersaturation (σ) and supercooling (ΔT).
• Use of the Wilson-Frenkel growth law (vₙ ∝ σ exp(−σ₀/σ)) to model nucleation-limited growth from vapor, with σ₀ derived from experimental data.
• Comparison of growth rate data from water vapor (σ₀ ≈ 0.4% at −2°C on basal plane) and liquid water (ΔT₀ ≈ 0.24°C) to infer equivalent step energies.
• Extrapolation of σ₀ data toward the melting point to estimate step energy near T = 0°C, assuming a smooth transition.
• Use of thermodynamic relationships to connect chemical potential jumps (Δμ) in vapor and liquid growth to growth velocity and nucleation barriers.
• Evaluation of kinetic prefactor A₀ in the growth law to assess discrepancies between vapor and liquid growth rates, suggesting possible systematic errors or surface-specific effects.

Experimental results

Research questions

• RQ1 Do ice growth from water vapor and from liquid water exhibit the same underlying nucleation mechanism on the basal ice surface near the melting point?
• RQ2 Is the molecular step energy at the solid/quasiliquid interface comparable to that at the solid/liquid interface, implying a physical correspondence?
• RQ3 Can equilibrium many-body molecular dynamics simulations accurately predict step energies that govern non-equilibrium ice crystal growth?
• RQ4 Why is the kinetic prefactor A₀ significantly lower in vapor growth (A_vap ≈ 0.2 m/s) than in liquid growth (A_liq > 2 m/s), and what does this imply about growth limitations?
• RQ5 How does surface premelting influence the transition between growth mechanisms from vapor and liquid phases?

Key findings

• The measured nucleation barrier (σ₀ ≈ 0.4% at −2°C) for ice growth from water vapor on the basal surface corresponds to a molecular step energy consistent with that derived from liquid water growth (ΔT₀ ≈ 0.24°C).
• Extrapolation suggests the step energy at the quasiliquid interface approaches that of the solid/liquid interface as temperature nears 0°C, indicating a smooth transition.
• The step energy on the prism surface is negligible in both vapor and liquid growth, consistent with faster growth and less nucleation limitation.
• The kinetic prefactor A_vap ≈ 0.2 m/s for basal growth from vapor is significantly lower than A_liq > 2 m/s for liquid growth, suggesting kinetic limitations at the quasiliquid/vapor interface.
• The data imply that growth from vapor near the melting point is limited by nucleation at the quasiliquid layer, not by vapor-side kinetics, and that step energy is the dominant control parameter.
• The physical consistency between vapor and liquid growth supports the use of equilibrium many-body simulations to compute step energies and predict growth dynamics.