[Paper Review] The Surface Diffusion Length of Water Molecules on Faceted Ice: A Reanalysis of "Roles of Surface/Volume Diffusion in the Growth Kinetics of Elementary Spiral Steps on Ice Basal Faces Grown from Water Vapor", by Asakawa et al

Kenneth G. Libbrecht|arXiv (Cornell University)|Sep 22, 2015

nanoparticles nucleation surface interactions3 references3 citations

TL;DR

This paper reanalyzes experimental data on water molecule diffusion on faceted ice surfaces, challenging prior conclusions about surface diffusion length and attachment coefficients. Using improved assumptions about bulk diffusion and a realistic attachment coefficient (α ≈ 1), the authors derive a surface diffusion length of approximately 10 nm at −8.4 °C—about 500 times lower than the 5 μm reported in the original study—while showing that step velocity measurements cannot constrain the Ehrlich-Schwoebel barrier height.

ABSTRACT

We reanalyzed the measurements made by Asakawa et al. [1] of the growth velocities of single-molecule-high steps on basal ice surfaces, as we believe the authors made a number of incorrect assumptions regarding ice growth parameters and bulk diffusion in their experiments. Applying what we believe are more accurate assumptions, we used the data in [1] to derive a surface diffusion length of approximately 10 nm for water molecules on basal ice surfaces at -8.4 C, about 500 times lower than what was reported in [1]. Moreover, in our analysis we found that no information about the height of the Ehrlich-Schwoebel barrier could be obtained from these measurements.

Motivation & Objective

• To reevaluate the surface diffusion length of water molecules on faceted basal ice surfaces using corrected assumptions about bulk diffusion and molecular attachment.
• To challenge the original study’s estimate of α ≈ 10⁻⁵, which is inconsistent with other experimental measurements showing α ≈ 1.
• To demonstrate that the original analysis underestimated the influence of bulk diffusion in the air, leading to erroneous diffusion length estimates.
• To show that step velocity measurements alone cannot determine the height of the Ehrlich-Schwoebel barrier on ice surfaces.
• To provide a self-consistent model explaining the same experimental data with a diffusion length of ~10 nm and α ≈ 1.

Proposed method

• Reanalyzed step growth velocity data from Asakawa et al. (2015) using a one-dimensional diffusion model with a simplified geometry.
• Applied the diffusion equation to model vapor transport between a top source (with supersaturation σ_top) and a bottom faceted ice surface with steps spaced by L.
• Used the relation v_step ≈ (x_s / a) α v_kin σ_bottom to link step velocity to surface diffusion length (x_s), attachment coefficient (α), and kinetic velocity (v_kin).
• Assumed α ≈ 1 based on consistency with other ice growth experiments, rejecting the original value of α ≈ 10⁻⁵.
• Accounted for the effect of surface coverage by steps via an effective attachment coefficient 〈α_bottom〉, which reduces σ_bottom relative to σ_top.
• Used analytic solutions for diffusion from a cylinder to verify the scaling of σ_bottom with x_s and L.

Experimental results

Research questions

• RQ1 What is the true surface diffusion length of water molecules on a basal ice surface at −8.4 °C, given corrected assumptions about bulk diffusion?
• RQ2 Why does the original study’s estimate of α ≈ 10⁻⁵ contradict other experimental measurements showing α ≈ 1?
• RQ3 To what extent does bulk diffusion in air distort the interpretation of step growth velocity measurements in ice growth experiments?
• RQ4 Can the observed step velocity data be consistently explained with α ≈ 1 and a lower surface diffusion length?
• RQ5 Does the step velocity data provide any information about the Ehrlich-Schwoebel barrier height?

Key findings

• The surface diffusion length of water molecules on basal ice at −8.4 °C is estimated to be approximately 10 nm, significantly lower than the 5 μm reported in the original study.
• The analysis assumes an attachment coefficient α ≈ 1, which is consistent with multiple independent experimental measurements, contradicting the original value of α ≈ 10⁻⁵.
• The discrepancy in the original study arises primarily from underestimating the role of bulk diffusion in the air, which reduces the effective supersaturation at the growth surface.
• Even a 0.1% coverage of active attachment sites (α ≈ 1) on the surface can reduce the supersaturation at the step by a factor of two, explaining the observed data.
• The measured kinetic coefficient β^L ≈ 700 μm/sec is consistent with a small residual α_bottom > 0, not with the original assumption of low α.
• The data provide no useful information about the Ehrlich-Schwoebel barrier height, as the model is insensitive to its value under the given experimental conditions.