Atomistic insight into the non-classical nucleation mechanism during solidification in Ni

Resolving heterogeneous particle mobility in deeply quenched liquid iron: an ultra-fast assembly-free two-step nucleation mechanism

Despite intensive research, little is known about the intermediate state of phase transforming materials, which may form the missing link between e.g. liquids and solids on the nanoscale. The unraveling of the nanoscale interplay between the structure and dynamics of the intermediate state of phase transformations (through which e.g. crystal nucleation proceeds) is one of the biggest challenges and unsolved problems of materials science. Here we show using unbiased molecular dynamics simulations and spatially resolved atomic displacement maps (d-maps) that upon deep quenching the solidification of undercooled liquid iron proceeds through the formation of metastable pre-nucleation clusters (PNCs). We also reveal that the hitherto hidden PNCs are nearly immobile (dynamically arrested) and the related heterogeneity in atomic mobilities becomes clearly visible on atomic displacement-maps (d-maps) when atomic jumps are referenced to the final crystalline positions. However, this is in contrast to PNCs found in molecular solutions, in which PNCs tend to aggregate, move and crystallize via an activated process. Coordination filtered d-maps resolved in real space directly demonstrate that previously unseen highly ramified intermediate atomic clusters with a short lifetime emerge after incubation of undercooled liquid iron. The supercooled liquid iron is neither a spinodal system nor a liquid and undergoes a transition into a specific state called a quasi-liquid state within the temperature regime of 700-1250 K (0.5Tm > 0.7Tm, where the melting point is Tm ≈ 1811 K). Below 700 K the supercooled system is spinodal-like and above 1300 K it behaves like an ordinary liquid with long incubation times. A two-step process is proposed to explain the anomalous drop in the incubation time in the temperature regime of 700-1250 K. The 1st step is activated aggregation of small atomic clusters followed by assembly-free nearly barrierless ultrafast growth of early ramified prenucleation clusters called germs. The display and characterization of the hidden PNCs in computer simulations could provide new perspectives on the deeper understanding of the long-standing problem of precursor development during crystal nucleation following deep quenching.

Controlling polymorph selection during nucleation by tuning the structure of metallic melts

Controlling the polymorphism of crystals is crucial to the design of novel metallic materials with specific properties; however, the atomistic mechanism underlying polymorph selection during crystallization remains unclear. In this work, molecular dynamics simulations combined with well-tempered metadynamics simulations are employed to explore the atomic mechanisms of polymorph selection during the nucleation process of FCC aluminum and copper. Simulation results suggest that the distinct nucleation pathways of both FCC metals originate from different free-energy surfaces of nucleation processes and diverse symmetries of nucleation precursors. The initially forming phase from undercooled melts is most likely to be the one that has the symmetry closest to the precursors. Besides, tiny seeds with diverse crystal symmetries could induce the formation of preordered precursors for nucleation around the seed, leading to the reduction of free-energy barrier and thus the promotion of nucleation. Controlling polymorph selection with tiny seeds is realized by tuning the symmetry of precursors. Our findings not only shed significant light on understanding polymorph selection, but also provide theoretical guidance for better controlling the nucleation pathway in practice.

Controlling crystallization: what liquid structure and dynamics reveal about crystal nucleation mechanisms

Over recent years, molecular simulations have provided invaluable insights into the microscopic processes governing the initial stages of crystal nucleation and growth. A key aspect that has been observed in many different systems is the formation of precursors in the supercooled liquid that precedes the emergence of crystalline nuclei. The structural and dynamical properties of these precursors determine to a large extent the nucleation probability as well as the formation of specific polymorphs. This novel microscopic view on nucleation mechanisms has further implications for our understanding of the nucleating ability and polymorph selectivity of nucleating agents, as these appear to be strongly linked to their ability in modifying structural and dynamical characteristics of the supercooled liquid, namely liquid heterogeneity. In this perspective, we highlight recent progress in exploring the connection between liquid heterogeneity and crystallization, including the effects of templates, and the potential impact for controlling crystallization processes. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

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.

Template-Induced Precursor Formation in Heterogeneous Nucleation: Controlling Polymorph Selection and Nucleation Efficiency

We present an atomistic study of heterogeneous nucleation in Ni employing transition path sampling, which reveals a template precursor-mediated mechanism of crystallization. Most notably, we find that the ability of tiny templates to modify the structural features of the liquid and promote the formation of precursor regions with enhanced bond-orientational order is key to determining their nucleation efficiency and the polymorphs that crystallize. Our results reveal an intrinsic link between structural liquid heterogeneity and the nucleating ability of templates, which significantly advances our understanding toward the control of nucleation efficiency and polymorph selection.

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.

Homogenous nucleation rate of CO2 hydrates using transition interface sampling

Carbon dioxide and water can form solid clathrate structures in which water cages encapsulate the gas molecules. Such hydrates have sparked much interest due to their possible application in CO₂ sequestration. How the solid structure forms exactly from the liquid phase via a homogenous nucleation process is still poorly understood. This nucleation event is rare on the molecular timescale even under moderate undercooling or supersaturation conditions because of the large free energy barrier toward crystallization, rendering a brute force simulation of hydrate nucleation unfeasible for moderate undercooling or supersaturation. Here, we perform transition interface sampling simulations to quantify the homogenous nucleation rate for CO₂ hydrate formation using accurate atomistic force fields at 500 bars for three different temperatures between 260 and 273 K. Collecting more than 100 000 pathways comprising roughly two milliseconds of simulation time, we computed a nucleation rate in the amorphous phase of ∼10²¹ nuclei s^-1 cm^-3 for a temperature of 260 K and a rate of ∼10¹² nuclei s^-1 cm^-3 for a temperature of 265 K. For a temperature of 273 K, we find that the hydrate forms an sI crystalline phase with a rate of order of ∼10¹ nuclei s^-1 cm^-3. We compare these rates to classical nucleation theory estimates as well as experiments, and to nucleation rate estimates for methane hydrates and discuss possible causes of the observed differences. Our findings shed light on the kinetics of this important clathrate and should assist in future hydrate formation investigation.

Identification of critical nuclei in the rapid solidification via configuration heredity

The identification and characterization of critical nuclei is a long-standing issue in the rapid solidification of metals and alloys. An ambiguous description for their sizes and shapes used to lead to an overestimation or underestimation of homogeneous nucleation ratesITin the framework of classical nucleation theory (CNT). In this paper, a unique method able to distinguish the critical nucleus from numerous embryos is put forward on the basis of configuration heredities of clusters during rapid solidifications. As this technique is applied to analyze the formation and evolution of various fcc-Al single crystal clusters in a large-scale molecular dynamics simulation system, it is found that the sizen_cand geometrical configuration of critical nuclei as well as their liquid-solid interfacial structure can be determined directly. For the present deep super-cooled system with an undercooling ofTm=0.42Tmcal, the average size of critical nuclei is demonstrated to benc̄≈26, but most of which are non-spherical lamellae. Also, their liquid-solid interfaces are revealed to be not an fcc-liquid duplex-phase interface but an fcc/hcp-liquid multi-phase structure. These findings shed some lights on the CNT, and a good agreement with previous simulations and experiments inITindicates this technique can be used to explore the early-stage of nucleation from atomistic levels.

Interplay of structural and dynamical heterogeneity in the nucleation mechanism in Ni

Gaining fundamental understanding of crystal nucleation processes in metal alloys is crucial for the development and design of high-performance materials with targeted properties. Yet, crystallizationis a complex non-equilibrium process and,...

Morphological aspect of crystal nucleation in wall-confined supercooled metallic film

In this paper, we simulate the nucleation and growth of crystalline nuclei in a molybdenum film cooled at different rates confined between two amorphous walls. We also compare the results for the wall-confined and wall-free systems. We apply the same methodology as in the work (Kirova and Pisarev 2019J. Cryst. Growth528125266) which is based on reconstructing the probability density function for the largest crystalline nucleus in the system. The size of the nucleus and the asphericity parameter are considered as the reaction coordinates. We demonstrate that in both the free and confined systems there are two mechanisms of crystal growth: the attachment of atoms to the biggest crystal from the amorphous phase and the merging of the biggest crystal cluster with small ones (coalescence). We show that the attachment mechanism is dominant in the melt cooled down at a slower rate, and the mechanism gradually shifts to coalescence as cooling rate increases. We also observe the formation of long-lived crystal clusters and demonstrate that amorphous walls do not affect their geometric characteristics. However, system confined between walls demonstrates higher glass-forming ability.

Rate Prediction for Homogeneous Nucleation of Methane Hydrate at Moderate Supersaturation Using Transition Interface Sampling

The crystallization of methane hydrates via homogeneous nucleation under natural, moderate conditions is of both industrial and scientific relevance, yet still poorly understood. Predicting the nucleation rates at such conditions is notoriously difficult due to high nucleation barriers, and requires, besides an accurate molecular model, enhanced sampling. Here, we apply the transition interface sampling technique, which efficiently computes the exact rate of nucleation by generating ensembles of unbiased dynamical trajectories crossing predefined interfaces located between the stable states. Using an accurate atomistic force field and focusing on specific conditions of 280 K and 500 bar, we compute for nucleation directly into the sI crystal phase at a rate of ∼10^-17 nuclei per nanosecond per simulation volume or ∼10² nuclei per second per cm³, in agreement with consensus estimates for nearby conditions. As this is most likely fortuitous, we discuss the causes of the large differences between our results and previous simulation studies. Our work shows that it is now possible to compute rates for methane hydrates at moderate supersaturation, without relying on any assumptions other than the force field.

Derivation of an exact, nonequilibrium framework for nucleation: Nucleation is a priori neither diffusive nor Markovian

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a nonequilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, i.e., the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics.

Molecular dynamics investigation of the local structure in iron melts and its role in crystal nucleation during rapid solidification

Nucleation process of a bcc crystal after the formation of an MRO cluster.