Abstract
We apply the capillary wave method, based on measurements of fluctuations in a ribbon-like interfacial geometry, to determine the solid-liquid interfacial free energy for both polytypes of ice I and the recently proposed ice 0 within a mono-atomic model of water. We discuss various choices for the molecular order parameter, which distinguishes solid from liquid, and demonstrate the influence of this choice on the interfacial stiffness. We quantify the influence of discretisation error when sampling the interfacial profile and the limits on accuracy imposed by the assumption of quasi one-dimensional geometry. The interfacial free energies of the two ice I polytypes are indistinguishable to within achievable statistical error and the small ambiguity which arises from the choice of order parameter. In the case of ice 0, we find that the large surface unit cell for low index interfaces constrains the width of the interfacial ribbon such that the accuracy of results is reduced. Nevertheless, we establish that the interfacial free energy of ice 0 at its melting temperature is similar to that of ice I under the same conditions. The rationality of a core-shell model for the nucleation of ice I within ice 0 is questioned within the context of our results.
Highlights
The crystallisation of ice I from liquid water continues to be a benchmark problem for molecular simulation
As yet no simulation has demonstrated a propensity for ice I to crystallise entirely in its hexagonal polytype ice Ih (ABABAB stacking of molecular bilayers) at weak supercooling
These bracket the value of 35.5(3) mJ m 2 obtained by Espinosa et al.[7] for the mW model when extrapolating results of the seeding method to coexistence. Despite these small systematic differences from earlier work, our results confirm that the ice Ih–water interfacial free energy for the mW model lies toward the upper end of the experimental estimates and is somewhat higher than values obtained with detailed atomistic models.[7,25]
Summary
The crystallisation of ice I from liquid water continues to be a benchmark problem for molecular simulation. Heterogeneous nucleation has been probed in a variety of studies.[10–13]. As yet no simulation has demonstrated a propensity for ice I to crystallise entirely in its hexagonal polytype ice Ih (ABABAB stacking of molecular bilayers) at weak supercooling. Simulations consistently produce stacking disordered mixtures of the cubic polytype ice Ic (ABCABC stacking) and ice Ih, as seen experimentally only at very low temperatures. The origin of this stacking disorder, and the preference for ordered hexagonal stacking in ice formed at weak supercooling, has been the subject of much discussion in the literature. We refer the reader to a recent review by Malkin et al.[14]
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