Role of stacking disorder in ice nucleation

Abstract

The freezing of water affects the processes that determine Earth's climate. Therefore, accurate weather and climate forecasts hinge on good predictions of ice nucleation rates. Such rate predictions are based on extrapolations using classical nucleation theory, which assumes that the structure of nanometre-sized ice crystallites corresponds to that of hexagonal ice, the thermodynamically stable form of bulk ice. However, simulations with various water models find that ice nucleated and grown under atmospheric temperatures is at all sizes stacking-disordered, consisting of random sequences of cubic and hexagonal ice layers. This implies that stacking-disordered ice crystallites either are more stable than hexagonal ice crystallites or form because of non-equilibrium dynamical effects. Both scenarios challenge central tenets of classical nucleation theory. Here we use rare-event sampling and free energy calculations with the mW water model to show that the entropy of mixing cubic and hexagonal layers makes stacking-disordered ice the stable phase for crystallites up to a size of at least 100,000 molecules. We find that stacking-disordered critical crystallites at 230 kelvin are about 14 kilojoules per mole of crystallite more stable than hexagonal crystallites, making their ice nucleation rates more than three orders of magnitude higher than predicted by classical nucleation theory. This effect on nucleation rates is temperature dependent, being the most pronounced at the warmest conditions, and should affect the modelling of cloud formation and ice particle numbers, which are very sensitive to the temperature dependence of ice nucleation rates. We conclude that classical nucleation theory needs to be corrected to include the dependence of the crystallization driving force on the size of the ice crystallite when interpreting and extrapolating ice nucleation rates from experimental laboratory conditions to the temperatures that occur in clouds.

The vapor pressure over nano-crystalline ice

“…Below about 200 K, however, water may be encountered in the metastable cubic form ice I c (e.g., Hobbs, 1974). Recently, studies using diffraction measurements and numerical simulations showed that samples were not composed of pure cubic ice, but rather exhibited crystalline sequences of cubic ice interlaced with sequences of hexagonal ice (e.g., Hudait et al, 2016;Kuhs et al, 2012;Lupi et al, 2017;Malkin et al, 2015;Shallcross and Carpenter, 1957;Thürmer and Nie, 2013). This ice polymorph has been termed stacking disordered ice I sd .…”

“…Here, k is the Boltzmann constant, T is the temperature, ν is the molecular volume and σ is the ice-vapor surface tension of the crystalline ice. We assume that the crystalline nano-grains are composed of ice I sd as supported by model studies (Lupi et al, 2017) and X-ray diffraction experiments (Morishige et al, 2009). Since the surface tension of hexagonal and cubic ice are assumed to be very similar, we used the surface tension parameterization of hexagonal ice for ice I sd (σ sd = 0.001 Hale and Plummer, 1974) and assumed an uncertainty of 10 %.…”

A Markov theoretic description of stacking-disordered aperiodic crystals including ice and opaline silica

“…On the basis of quantum mechanical calculations Engel et al (2015) have suggested that the anharmonic vibrational energies favour the hexagonal form as a consequence of differences in the fourth nearest-neighbour protons, related to the occurrence of the topologically different boat and chair forms of the sixmembered water rings in cubic and hexagonal ice. Still, as nucleation (and growth) for supercooled water is kinetically controlled, freezing may well start also with a cubic or a stacking-disordered nucleus (Lupi et al, 2017). The subsequent growth appears experimentally to follow a fast s ¼ 2 Markov chain prescription, before any annealing has time to set in for temperatures below approximately 240 K. It is noteworthy that branching (twinning) has been observed for a significant percentage of snow crystals formed at temperatures higher than about 238 K (Kajikawa et al, 1980), which likely have formed from a cubic (or stacking-faulty) nucleus growing along directions separated by the octahedral angle of 70.53 (i.e.…”

Surface phase-transition dynamics of ice probed by terahertz time-domain spectroscopy

“…Recently, this attention has been motivated by the significant role played by the surface melting of ice in many natural phenomena such as snow and ice disaster and melting glaciers. As a result, the solid-liquid phase transition of water has been the subject of numerous experimental and theoretical investigations [1][2][3][4][5][6].…”