Nucleation of tetrahedral solids: A molecular dynamics study of supercooled liquid silicon

Bridging classical nucleation theory and molecular dynamics simulation for homogeneous ice nucleation

Water freezing, initiated by ice nucleation, occurs widely in nature, ranging from cellular to global phenomena. Ice nucleation has been experimentally proven to require the formation of a critical ice nucleus, consistent with classical nucleation theory (CNT). However, the accuracy of CNT quantitative predictions of critical cluster sizes and nucleation rates has never been verified experimentally. In this study, we circumvent this difficulty by using molecular dynamics (MD) simulation. The physical properties of water/ice for CNT predictions, including density, chemical potential difference, and diffusion coefficient, are independently obtained using MD simulation, whereas the calculation of interfacial free energy is based on thermodynamic assumptions of CNT, including capillarity approximation among others. The CNT predictions are compared to the MD evaluations of brute-force simulations and forward flux sampling methods. We find that the CNT and MD predicted critical cluster sizes are consistent, and the CNT predicted nucleation rates are higher than the MD predicted values within three orders of magnitude. We also find that the ice crystallized from supercooled water is stacking-disordered ice with a stacking of cubic and hexagonal ices in four representative types of stacking. The prediction discrepancies in nucleation rate mainly arise from the stacking-disordered ice structure, the asphericity of ice cluster, the uncertainty of ice-water interfacial free energy, and the kinetic attachment rate. Our study establishes a relation between CNT and MD to predict homogeneous ice nucleation.

Interplay of multiple clusters and initial interface positioning for forward flux sampling simulations of crystal nucleation

Forward flux sampling (FFS) is a path sampling technique widely used in computer simulations of crystal nucleation from the melt. In such studies, the order parameter underpinning the progress of the FFS algorithm is often the size of the largest crystalline nucleus. In this work, we investigate the effects of two computational aspects of FFS simulations, using the prototypical Lennard-Jones liquid as our computational test bed. First, we quantify the impact of the positioning of the liquid basin and first interface in the space of the order parameter. In particular, we demonstrate that these choices are key to ensuring the consistency of the FFS results. Second, we focus on the frequently encountered scenario where the population of crystalline nuclei is such that there are multiple clusters of size comparable to the largest one. We demonstrate the contribution of clusters other than the largest cluster to the initial flux; however, we also show that they can be safely ignored for the purposes of converging a full FFS calculation. We also investigate the impact of different clusters merging, a process that appears to be facilitated by substantial spatial correlations-at least at the supercooling considered here. Importantly, all of our results have been obtained as a function of system size, thus contributing to the ongoing discussion on the impact of finite size effects on simulations of crystal nucleation. Overall, this work either provides or justifies several practical guidelines for performing FFS simulations that can also be applied to more complex and/or computationally expensive models.

Practical guide to replica exchange transition interface sampling and forward flux sampling

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations.

Timescale prediction of complex multi-barrier pathways using flux sampling molecular dynamics and 1D kinetic integration: Application to cellulose dehydration

Reactive molecular dynamics (MD) simulations, especially those employing acceleration techniques, can provide useful insights on the mechanism underlying the transformation of buried organic matter, yet, so far, it remains extremely difficult to predict the time scales associated with these processes at moderate temperatures (i.e., when such time scales are considerably larger than those accessible to MD). We propose here an accelerated method based on flux sampling and kinetic integration along a 1D order parameter that can considerably extend the accessible time scales. We demonstrate the utility of this technique in an application to the dehydration of crystalline cellulose at temperatures ranging from 1900 K to 1500 K. The full decomposition is obtained at all temperatures apart from T = 1500 K, showing the same distribution of the main volatiles (H₂O, CO, and CO₂) as recently obtained using replica exchange molecular dynamics. The kinetics of the process is well fitted with an Arrhenius law with E_a = 93 kcal/mol and k₀ = 9 × 10¹⁹ s^-1, which are somehow larger than experimental reports. Unexpectedly, the process seems to considerably slow down at lower temperatures, severely departing from the Arrhenius regime, probably because of an inadequate choice of the order parameter. Nevertheless, we show that the proposed method allows considerable time sampling at low temperatures compared to conventional MD.

Liquid infused surfaces with anti-icing properties

Ice accretion on solid surfaces, a ubiquitous phenomenon that occurs in winter, brings much inconvenience to daily life and can even cause serious catastrophes. Icephobic surfaces, a passive way of processing surfaces to prevent surface destruction from ice accumulation, have attracted much attention from scientists because of their special ice-repellent properties, and many efforts have been made to rationally design durable icephobic coatings. This review is aimed at providing a brief and crucial overview of ice formation processes and feasible de-icing strategies. Here, the excellent anti-icing performance of liquid infused surfaces (LIS) inspired from Nepenthes is emphatically introduced. After a short introduction, the recent progresses in ice nucleation theory and ice adhesion decrease mechanism are comprehensively reviewed to gain a general understanding of the long freeze process and low ice adhesion on LIS. Subsequently, the anti-icing performance of LIS is systematically evaluated from four aspects regarding water repellence, condensation-frosting, long freeze process, and low ice adhesion. Finally, this review focuses on discussing the advantages and disadvantages of LIS and the potential measures to eliminate and alleviate these drawbacks.

Silicon Liquid Structure and Crystal Nucleation from Ab Initio Deep Metadynamics

Studying the crystallization process of silicon is a challenging task since empirical potentials are not able to reproduce well the properties of both a semiconducting solid and metallic liquid. On the other hand, nucleation is a rare event that occurs in much longer timescales than those achievable by ab initio molecular dynamics. To address this problem, we train a deep neural network potential based on a set of data generated by metadynamics simulations using a classical potential. We show how this is an effective way to collect all the relevant data for the process of interest. In order to efficiently drive the crystallization process, we introduce a new collective variable based on the Debye structure factor. We are able to encode the long-range order information in a local variable which is better suited to describe the nucleation dynamics. The reference energies are then calculated using the strongly constrained and appropriately normed (SCAN) exchange-correlation functional, which is able to get a better description of the bonding complexity of the Si phase diagram. Finally, we recover the free energy surface with a density functional theory accuracy, and we compute the thermodynamics properties near the melting point, obtaining a good agreement with experimental data. In addition, we study the early stages of the crystallization process, unveiling features of the nucleation mechanism.

Free energy landscape and molecular pathways of gas hydrate nucleation

Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p_B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p_B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

Transient Melting and Recrystallization of Semiconductor Nanocrystals Under Multiple Electron-Hole Pair Excitation

Ultrafast optical pump, X-ray diffraction probe experiments were performed on CdSe nanocrystal (NC) colloidal dispersions as functions of particle size, polytype, and pump fluence. Bragg peak shifts related to heating and peak amplitude reduction associated with lattice disordering are observed. For smaller NCs, melting initiates upon absorption of as few as ∼15 electron-hole pair excitations per NC on average (0.89 excitations/nm³ for a 1.5 nm radius) with roughly the same excitation density inducing melting for all examined NCs. Diffraction intensity recovery kinetics, attributable to recrystallization, occur over hundreds of picoseconds with slower recoveries for larger particles. Zincblende and wurtzite NCs revert to initial structures following intense photoexcitation suggesting melting occurs primarily at the surface, as supported by simulations. Electronic structure calculations relate significant band gap narrowing with decreased crystallinity. These findings reflect the need to consider the physical stability of nanomaterials and related electronic impacts in high intensity excitation applications such as lasing and solid-state lighting.

Silicon-wall interfacial free energy via thermodynamics integration

We compute the interfacial free energy of a silicon system in contact with flat and structured walls by molecular dynamics simulation. The thermodynamics integration method, previously applied to Lennard-Jones potentials [R. Benjamin and J. Horbach, J. Chem. Phys. 137, 044707 (2012)], has been extended and implemented in Tersoff potentials with two-body and three-body interactions taken into consideration. The thermodynamic integration scheme includes two steps. In the first step, the bulk Tersoff system is reversibly transformed to a state where it interacts with a structureless flat wall, and in a second step, the flat structureless wall is reversibly transformed into an atomistic SiO₂ wall. Interfacial energies for liquid silicon-wall interfaces and crystal silicon-wall interfaces have been calculated. The calculated interfacial energies have been employed to predict the nucleation mechanisms in a slab of liquid silicon confined by two walls and compared with MD simulation results.

Computational investigation of structure, dynamics and nucleation kinetics of a family of modified Stillinger-Weber model fluids in bulk and free-standing thin films

In recent years, computer simulations have found increasingly widespread use as powerful tools for studying phase transitions in wide variety of systems. In the particular and very important case of aqueous systems, the commonly used force-fields tend to offer quite different predictions with respect to a wide range of thermodynamic and kinetic properties, including the ease of ice nucleation, the propensity to freeze at a vapor-liquid interface, and the existence of a liquid-liquid phase transition. It is thus of fundamental and practical interest to understand how different features of a given water model affect its thermodynamic and kinetic properties. In this work, we use the forward-flux sampling technique to study the crystallization kinetics of a family of modified Stillinger-Weber (SW) potentials with energy (ε) and length (σ) scales taken from the monoatomic water (mW) model, but with different tetrahedrality parameters (λ). By increasing λ from 21 to 24, we observe the nucleation rate increases by 48 orders of magnitude at a supercooling of ζ = T/Tm = 0.845. Using classical nucleation theory, we are able to demonstrate that this change can largely be accounted for by the increase in |Δμ|, the thermodynamic driving force. We also perform rate calculations in freestanding thin films of the supercooled liquid, and observe a crossover from surface-enhanced crystallization at λ = 21 to bulk-dominated crystallization for λ ≥ 22.

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Molecular simulation of homogeneous nucleation of crystals of an ionic liquid from the melt

The homogeneous nucleation of crystals of the ionic liquid [dmim(+)][Cl(-)] from its supercooled liquid phase in the bulk (P = 1 bar, T = 340 K, representing a supercooling of 58 K) was studied using molecular simulations. The string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] was used in combination with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [E. E. Santiso and B. L. Trout, J. Chem. Phys. 134, 064109 (2011)] to sketch a minimum free energy path connecting the supercooled liquid and the monoclinic crystal phases, and to determine the free energy and the rates involved in the homogeneous nucleation process. The physical significance of the configurations found along this minimum free energy path is discussed with the help of calculations based on classical nucleation theory and with additional simulation results obtained for a larger system. Our results indicate that, at a supercooling of 58 K, the liquid has to overcome a free energy barrier of the order of 60 kcal/mol and to form a critical nucleus with an average size of about 3.6 nm, before it reaches the thermodynamically stable crystal phase. A simulated homogeneous nucleation rate of 5.0 × 10(10) cm(-3) s(-1) was obtained for our system, which is in reasonable agreement with experimental and simulation rates for homogeneous nucleation of ice at similar degrees of supercooling. This study represents our first step in a series of studies aimed at understanding the nucleation and growth of crystals of organic salts near surfaces and inside nanopores.

Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation

The prevalence of heterogeneous nucleation in nature was explained qualitatively by the classical theory for heterogeneous nucleation established over more than 60 years ago, but the quantitative validity and the key conclusions of the theory have remained unconfirmed. Employing the forward flux sampling method and the coarse-grained water model (mW), we explicitly computed the heterogeneous ice nucleation rates in the supercooled water on a graphitic surface at various temperatures. The independently calculated ice nucleation rates were found to fit well according to the classical theory for heterogeneous nucleation. The fitting procedure further yields the estimate of the potency factor, which measures the ratio of the heterogeneous nucleation barrier to the homogeneous nucleation barrier. Remarkably, the estimated potency factor agrees quantitatively with the volumetric ratio of the critical nuclei between the heterogeneous and homogeneous nucleation. Our numerical study thus provides a strong support to the quantitative power of the theory and allows understanding ice nucleation behaviors under the most relevant freezing conditions.

Driving ordering processes in molecular-dynamics simulations

Self-organized criticality describes the emergence of complexity in dynamical nonequilibrium systems. In this paper we introduce a unique approach whereby a driven energy conversion is utilized as a sampling bias for ordered arrangements in molecular dynamics simulations of atomic and molecular fluids. This approach gives rise to dramatically accelerated nucleation rates, by as much as 30 orders of magnitude, without the need of predefined order parameters, which commonly employed rare-event sampling methods rely on. The measured heat fluxes suggest how the approach can be generalized.

Ice nucleation at the nanoscale probes no man's land of water

At a given thermodynamic condition, nucleation events occur at a frequency that scales with the volume of the system. Therefore at the nanoscale, one may expect to obtain supercooled liquids below the bulk homogeneous nucleation temperature. Here we report direct computational evidence that in supercooled water nano-droplets ice nucleation rates are strongly size dependent and at the nanoscale they are several orders of magnitude smaller than in bulk water. Using a thermodynamic model based on classical nucleation theory, we show that the Laplace pressure is partially responsible for the suppression of ice crystallization. Our simulations show that the nucleation rates found for droplets are similar to those of liquid water subject to a pressure of the order of the Laplace pressure within droplets. Our findings aid the interpretation of molecular beam experiments and support the hypothesis of surface crystallization of ice in microscopic water droplets in clouds.

Crystalline nucleation in undercooled liquids: a Bayesian data-analysis approach for a nonhomogeneous Poisson process

A Bayesian data-analysis approach to data sets of maximum undercooling temperatures recorded in repeated melting-cooling cycles of high-purity samples is proposed. The crystallization phenomenon is described in terms of a nonhomogeneous Poisson process driven by a temperature-dependent sample nucleation rate J(T). The method was extensively tested by computer simulations and applied to real data for undercooled liquid Ge. It proved to be particularly useful in the case of scarce data sets where the usage of binned data would degrade the available experimental information.

Morphology and temperature dependence of the thermal conductivity of nanoporous SiGe

Using molecular dynamics simulations, we show that the thermal conductivity (κ) of Si(0.5)Ge(0.5) can be reduced by more than one order of magnitude by etching nanometer-sized holes in the material, and it becomes almost constant as a function of temperature between 300 and 1100 K for samples with 1 nm wide pores. In nanoporous SiGe, thermal conduction is largely determined by mass disorder and boundary scattering, and thus the dependence of κ on pore distance and on structural, atomistic disorder is much weaker than in the case of nanoporous Si. This indicates that one may minimize κ of the alloy with less stringent morphological constraints than for pure Si.