Solid–liquid interfacial free energy of ice Ih, ice Ic, and ice 0 within a mono-atomic model of water via the capillary wave method

Hydrogen-bond linking is crucial for growing ice VII embryos

We use molecular dynamics simulations to examine the homogeneous nucleation of ice VII from metastable liquid water. An unsupervised machine learning classification identifies two distinct local structures composing Ice VII nuclei. The seeding method, combined with the classical nucleation theory (CNT), predicts the solid-liquid interfacial free energy, consistent with the value from the mold integration method. Meanwhile, the nucleation rates estimated from the CNT framework and brute force spontaneous nucleations are inconsistent, and we discuss the reasons for this discrepancy. Structural and dynamical heterogeneities suggest that the potential birthplace for an ice VII embryo is relatively ordered, although not necessarily relatively immobile. Moreover, we demonstrate that without the formation of hydrogen-bond links, ice VII embryos do not grow.

Are Neural Network Potentials Trained on Liquid States Transferable to Crystal Nucleation? A Test on Ice Nucleation in the mW Water Model

Neural network potentials (NNPs) are increasingly being used to study processes that happen on long time scales. A typical example is crystal nucleation, which rate is controlled by the occurrence of a rare fluctuation, i.e., the appearance of the critical nucleus. Because the properties of this nucleus are far from those of the bulk crystal, it is yet unclear whether NN potentials trained on equilibrium liquid states can accurately describe nucleation processes. So far, nucleation studies on NNPs have been limited to ab initio models whose nucleation properties are unknown, preventing an accurate comparison. Here we train a NN potential on the mW model of water─a classical three-body potential whose nucleation time scale is accessible in standard simulations. We show that a NNP trained only on a small number of liquid state points can reproduce with great accuracy the nucleation rates and free energy barriers of the original model, computed from both spontaneous and biased trajectories, strongly supporting the use of NNPs to study nucleation events.

Direct Calculation of the Interfacial Free Energy between NaCl Crystal and Its Aqueous Solution at the Solubility Limit

Salty water is the most abundant electrolyte aqueous mixture on Earth, however, very little is known about the NaCl-saturated solution interfacial free energy (γ_{s}). Here, we provide the first direct estimation of γ_{s} for several NaCl crystallographic planes by means of the mold integration technique, a highly efficient computational method to evaluate interfacial free energies with anisotropic crystal resolution. Making use of the JC-SPC/E model, one of the most benchmarked force fields for NaCl water solutions, we measure γ_{s} of four different crystal planes, (100), (110), (111), and (112[over ¯]) with the saturated solution at normal conditions. We find high anisotropy between the different crystal orientations with values ranging from 100 to 150  mJ m^{-2}, and the average value of the distinct planes being γ[over ¯]_{s}=137(20)  mJ m^{-2}. This value for the coexistence interfacial free energy is in reasonable agreement with previous extrapolations from nucleation studies. Our Letter represents a milestone in the computational calculation of interfacial free energies between ionic crystals and aqueous solutions.

Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon's needle, requires the rods to "land," with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.

The seven deadly sins: When computing crystal nucleation rates, the devil is in the details

The formation of crystals has proven to be one of the most challenging phase transformations to quantitatively model-let alone to actually understand-be it by means of the latest experimental technique or the full arsenal of enhanced sampling approaches at our disposal. One of the most crucial quantities involved with the crystallization process is the nucleation rate, a single elusive number that is supposed to quantify the average probability for a nucleus of critical size to occur within a certain volume and time span. A substantial amount of effort has been devoted to attempt a connection between the crystal nucleation rates computed by means of atomistic simulations and their experimentally measured counterparts. Sadly, this endeavor almost invariably fails to some extent, with the venerable classical nucleation theory typically blamed as the main culprit. Here, we review some of the recent advances in the field, focusing on a number of perhaps more subtle details that are sometimes overlooked when computing nucleation rates. We believe it is important for the community to be aware of the full impact of aspects, such as finite size effects and slow dynamics, that often introduce inconspicuous and yet non-negligible sources of uncertainty into our simulations. In fact, it is key to obtain robust and reproducible trends to be leveraged so as to shed new light on the kinetics of a process, that of crystal nucleation, which is involved into countless practical applications, from the formulation of pharmaceutical drugs to the manufacturing of nano-electronic devices.

Acoustic and Microstructural Properties of Partially Molten Samples in the Ice–Ammonia System

We measured the ultrasonic properties and microstructure of two-phase binary mixtures of the ice–ammonia partial melt system, which was selected based on its importance for numerous planetary bodies. The equilibrium microstructure of ice–ammonia melt was examined using a light microscope within a cold room. The measured median dihedral angle between the solid and melt at 256 K is approximately 63°, with a broad distribution of observed angles between 10° and 130°. P-wave velocities in the partially molten samples were measured as a function of temperature (177 < T(K) < 268) and composition (1–6.4 wt % NH3). Vp decreases approximately linearly with increasing temperature and melt fraction. We compare the results of this study to those of other potential binary systems by normalizing the datasets using a vertical lever (TL–TE) and articulating the potential effects on the mechanical behavior and transport capabilities of partially molten ice in icy satellites.

Structure and adhesion energy of the (10.4) calcite/(001) ice Ih and (210) baryte/(001) ice Ih interfaces

Adhesion energies of the (10.4)-calcite/(001)-ice and (210)-baryte/(001)-ice interfaces.

Communication: Computing the Tolman length for solid-liquid interfaces

The curvature dependence of interfacial free energy, which is crucial in quantitatively predicting nucleation kinetics and the stability of bubbles and droplets, is quantified by the Tolman length δ. For solid-liquid interfaces, however, δ has never been computed directly due to various theoretical and practical challenges. Here we perform a direct evaluation of the Tolman length from atomistic simulations of a solid-liquid planar interface in out-of-equilibrium conditions, by first computing the surface tension from the amplitude of thermal capillary fluctuations of a localized version of the Gibbs dividing surface and by then calculating how much the surface energy changes when it is defined relative to the equimolar dividing surface. We computed δ for a model potential, and found a good agreement with the values indirectly inferred from nucleation simulations. The agreement not only validates our approach but also suggests that the nucleation free energy of the system can be perfectly described using classical nucleation theory if the Tolman length is taken into account.

Theoretical prediction of the homogeneous ice nucleation rate: disentangling thermodynamics and kinetics

We computed the homogeneous ice nucleation rate, and disentangled and investigated all the relevant physical quantities.

Extracting the interfacial free energy and anisotropy from a smooth fluctuating dividing surface

Interfaces between different materials and phases play a crucial role in many physical and chemical phenomena. When performing simulations of matter at the atomic scale, however, it is often not trivial to characterize these interfaces, particularly when they are rough or diffuse. Here we discuss a generalization of a construction, due to Willard and Chandler, that allows one to obtain a smooth dividing surface that follows the irregular, ever changing shape of these fluctuating interfaces. We show how this construction can be used to study the surface that separates a solid material from its melt and how analyses of the Fourier modes for the capillary fluctuations of this instantaneous dividing surface can be performed. This particular analysis is useful as one can compute the specific free energy excess of the interface, and its dependence on orientation relative to the bulk phases, from the average amplitude of the Fourier modes. We therefore discuss the efficiency of this approach, both in terms of system size and statistical sampling.

Single-crystal Ih ice surfaces unveil connection between macroscopic and molecular structure

Physics and chemistry of ice surfaces are not only of fundamental interest but also have important impacts on biological and environmental processes. As ice surfaces-particularly the two prism faces-come under greater scrutiny, it is increasingly important to connect the macroscopic faces with the molecular-level structure. The microscopic structure of the ubiquitous ice I_h crystal is well-known. It consists of stacked layers of chair-form hexagonal rings referred to as molecular hexagons. Crystallographic unit cells can be assembled into a regular right hexagonal prism. The bases are labeled crystallographic hexagons. The two hexagons are rotated 30° with respect to each other. The linkage between the familiar macroscopic shape of hexagonal snowflakes and either hexagon is not obvious per se. This report presents experimental data directly connecting the macroscopic shape of ice crystals and the microscopic hexagons. Large ice single crystals were used to fabricate samples with the basal, primary prism, or secondary prism faces exposed at the surface. In each case, the same sample was used to capture both a macroscopic etch pit image and an electron backscatter diffraction (EBSD) orientation density function (ODF) plot. Direct comparison of the etch pit image and the ODF plot compellingly connects the macroscopic etch pit hexagonal profile to the crystallographic hexagon. The most stable face at the ice-water interface is the smallest area face at the ice-vapor interface. A model based on the molecular structure of the prism faces accounts for this switch.