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.

Clathrate hydrates and ice I are the most abundant crystals of water. The study of their nucleation, growth, and decomposition using molecular simulations requires an accurate and efficient algorithm that distinguishes water molecules that belong to each of these crystals and the liquid phase. Existing algorithms identify ice or clathrates, but not both. This poses a challenge for cases in which ice and hydrate coexist, such as in the synthesis of clathrates from ice and the formation of ice from clathrates during self-preservation of methane hydrates. Here we present an efficient algorithm for the identification of clathrate hydrates, hexagonal ice, cubic ice, and liquid water in molecular simulations. CHILL+ uses the number of staggered and eclipsed water-water bonds to identify water molecules in cubic ice, hexagonal ice, and clathrate hydrate. CHILL+ is an extension of CHILL (Moore et al. Phys. Chem. Chem. Phys. 2010, 12, 4124-4134), which identifies hexagonal and cubic ice but not clathrates. In addition to the identification of hydrates, CHILL+ significantly improves the detection of hexagonal ice up to its melting point. We validate the use of CHILL+ for the identification of stacking faults in ice and the nucleation and growth of clathrate hydrates. To our knowledge, this is the first algorithm that allows for the simultaneous identification of ice and clathrate hydrates, and it does so in a way that is competitive with respect to existing methods used to identify any of these crystals.

Zeolites and mesoporous silicas are porous materials with important applications in catalysis, gas storage, and separation. Zeolite crystals form in the presence of cationic surfactants that act as structure directing agents (SDAs). The way SDAs control the nucleation and polymorphs selection in zeolites is not fully understood. The formation of mesoporous silica is templated by liquid crystalline mesophases that result from frustrated attraction between silicates and long-chain SDAs. Experiments indicate that surfactants C n H 2n+1 (CH 3 ) 3 N + with n > 6 yield mesoporous silicas, and the one with n = 6 produces a zeolite. This suggests that the driving force toward mesophase formation is also present for small organocations, but is overcome by the ability of silica to wrap a crystal lattice around them. Here we use molecular dynamics simulations to investigate whether the existence of metastable mesophases can play a role in the nucleation and polymorph selection of zeolitic crystals. As a proof of concept, we investigate the phase behavior of simple mesogenic mixtures of SDAs and a network former T that favors tetracoordinated crystals. We represent the network-former T by Stillinger−Weber models of water and silicon, in lieu of silica, because a computationally efficient silica potential that would allow for the spontaneous nucleation of zeolites in molecular dynamics simulations is not yet available. The mixtures of T and SDA produce a rich phase diagram that encompasses the sII clathrate and at least six zeolites, including sigma-2 (SGT). We find that the nucleation of SGT is not assisted by a mesophase. The nucleation of the other five zeolites of this study, however, is facilitated by the existence of metastable mesophases that decrease the nucleation barriers and direct the selection of the crystal polymorph. Together with the experimental support for mesophases in mixtures of silicates and SDAs, our results for model systems suggest that metastable mesophases could play a prominent role in promoting the nucleation and polymorph selection of some zeolites.

Clathrate hydrates mostly occur in two cubic crystal structures, sI and sII. Cross-nucleation between these clathrate crystals has been observed in simulations and may be relevant to the transformation between clathrate polymorphs reported in experiments. Nevertheless, the mechanism by which clathrate crystals cross-nucleate and the structure of the interface between the distinct crystals have not yet been fully characterized. In this work, we use extensive molecular dynamics simulations to investigate the structure of the clathrate/solution interface for sI and sII guest-free and methane-filled hydrates at different degrees of supercooling and the mechanism of cross-nucleation between clathrate polymorphs. We find that 5 12 6 3 water cages, which are not native to the sI or sII crystals, occur assiduously in their interfaces with the solution and play a central role in the mechanism of cross-nucleation of clathrate hydrates: cross-nucleation between sI and sII requires the formation of an interfacial layer tiled by 5 12 6 3 cages connected by dodecahedra. We characterize the structure of the interfacial layer, estimate the size of the critical surface nucleus required for its formation, and assess the role of other variables in the reaction coordinate of cross-nucleation of clathrate hydrates. In agreement with previous reports of crossnucleation of quite different systems, we observe cross-nucleation of clathrate hydrates both from the stable to the metastable crystal and from the metastable to the stable hydrate. The new crystal that forms is, in all cases, the one that has the fastest growth rate.

Clathrate hydrates are crystals in which water molecules form hydrogen-bonded cages that enclose small nonpolar molecules, such as methane. In the laboratory, clathrates are customarily synthesized from ice and gas guest under conditions for which homogeneous nucleation of hydrates is not possible. It is not known how ice assists in the nucleation of clathrate hydrates or how ice forms on clathrate hydrate in the case of self-preservation. There is no lattice matching between any plane of ice and clathrate hydrates; therefore, an interfacial transition layer has to form to connect the two crystals. Here, we use molecular dynamic simulations to study the structure of ice−clathrate interfaces produced by alignment and equilibration of the crystals, competitive growth of ice and clathrate from a common solution, nucleation of hydrate in the presence of a growing ice front, and nucleation of ice in the presence of clathrate hydrates. We find that the interfacial transition layer between ice and clathrate is always disordered and has a typical width of two to three water layers. Water in the interfacial transition layer has tetrahedral order lower than either ice or clathrate and higher than liquid water under the same thermodynamic conditions. The potential energy of the water in the interfacial transition layer is between those in liquid water and the crystals. Our results suggest that the disordered interfacial transition layer could assist in the heterogeneous nucleation of clathrates from ice and ice from clathrates by providing a lower surface free energy than the ice−liquid and clathrate−liquid interfaces.

Cross-nucleation is a phenomenon where a new crystal nucleates and grows upon the surface of a different polymorph. Previous studies indicate that faster growth rate of the new crystal is a necessary but not sufficient condition for cross-nucleation. The thermodynamic stability of the different polymorphs can also affect cross-nucleation by modulating the rates of crystal growth. The interplay between thermodynamic stability of the polymorphs involved, the growth rate of the crystals, and the need for creation of an interfacial transition layer that seamlessly connects the two structures has not yet been fully elucidated. Predicting cross-nucleation is particularly challenging for clathrate hydrates, for which there are sometimes several polymorphs with similar stability and for which growth rates are not known. In this work, we use molecular dynamics simulations to investigate which factor (stability, growth rate, or formation of interfacial transition layer) controls cross-nucleation between the four known Frank-Kasper clathrate hydrate polymorphs: sI, sII, TS, and HS-I. We investigate the growth and cross-nucleation of these four hydrates filled with a set of guest molecules that produce different order of stabilities for the four crystal structures. We determine that the growth rate of sII clathrate is the fastest, followed by TS, HS-I, and sI. We find that cross-nucleation into or from sII clathrates is preceded by the formation of an interfacial transition layer at the seed crystal/liquid interface because sII does not share a crystal plane with sI, HS-I, or TS. Cross-nucleation between the latter three can occur seamlessly and is determined only by their growth rates. Our results indicate that nucleation of an interfacial transition layer between non-matching polymorphs can control cross-nucleation or lack thereof under conditions of small driving force. Under conditions of sufficient supercooling clathrate hydrate polymorphs cross-nucleate into the fastest growing phase even if that new phase is less stable and does not share a common crystal plane with the initial polymorph.

The total, triplet, and pair contributions to the entropy with increasing tetrahedrality are mapped out for the Stillinger-Weber liquids to demonstrate the qualitative and quantitative differences between triplet-dominated, tetrahedral liquids and pair-dominated, simple liquids with regard to supercooling and crystallization. The heat capacity anomaly of tetrahedral liquids originates in local ordering due to both pair and triplet correlations. The results suggest that structural correlations can be directly related to thermodynamic anomalies, phase changes, and self-assembly in other atomic and colloidal fluids.

Cluster expansion (CE) is effective in modeling the stability of metallic alloys, but sometimes cluster expansions fail. Failures are often attributed to atomic relaxation in the DFT-calculated data, but there is no metric for quantifying the degree of relaxation. Additionally, numerical errors can also be responsible for slow CE convergence. We studied over one hundred different Hamiltonians and identified a heuristic, based on a normalized mean-squared displacement of atomic positions in a crystal, to determine if the effects of relaxation in CE data are too severe to build a reliable CE model. Using this heuristic, CE practitioners can determine a priori whether or not an alloy system can be reliably expanded in the cluster basis. We also examined the error distributions of the fitting data. We find no clear relationship between the type of error distribution and CE prediction ability, but there are clear correlations between CE formalism reliability, model complexity, and the number of significant terms in the model. Our results show that the size of the errors is much more important than their distribution.