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.

Interplay of structural and dynamical heterogeneity in the nucleation mechanism in nickel.

Gaining a fundamental understanding of crystal nucleation processes in metal alloys is crucial for the development and design of high-performance materials with targeted properties. Yet, crystallization is a complex non-equilibrium process and, despite having been studied for decades, the microscopic aspects that govern the crystallization mechanism of a material remain elusive to date. Recent evidence shows that the spatial heterogeneity in the supercooled liquid, characterised by extended regions with distinctive mobility and order, may be a key microscopic factor that determines the mechanism of crystal nucleation. These findings have advanced our view of the fundamental nature of crystallization, as most research has assumed that crystal clusters nucleate from random fluctuations in a 'homogeneous' liquid. Here, by analysing transition path sampling trajectories, we show that dynamical heterogeneity plays a key role in the mechanism of crystal nucleation in an elemental metal, nickel. Our results demonstrate that crystallization occurs preferentially in regions of low mobility in the supercooled liquid, evidencing the collective dynamical nature of crystal nucleation in Ni. In addition, our results show that low mobility regions form before and spatially overlap with pre-ordered domains that act as precursors to the crystal phase that subsequently emerges. Our results show a clear link between dynamical and structural heterogeneity in the supercooled liquid and its impact on the nucleation mechanism, revealing microscopic descriptors that could pave a novel way to control crystallization processes in metals.

Role of pre-ordered liquid in the selection mechanism of crystal polymorphs during nucleation.

We investigate the atomistic mechanism of homogeneous nucleation during solidification in molybdenum employing transition path sampling. The mechanism is characterized by the formation of a pre-structured region of high bond-orientational order in the supercooled liquid followed by the emergence of the crystalline bulk phase within the center of the growing solid cluster. This precursor plays a crucial role in the process as it provides a diffusive interface between the liquid and crystalline core, which lowers the interfacial free energy and facilitates the formation of the bulk phase. Furthermore, the structural features of the pre-ordered regions are distinct from the liquid and solid phases and preselect the specific polymorph that nucleates. The similarity in the nucleation mechanism of Mo with that of metals that exhibit different crystalline bulk phases indicates that the formation of a precursor is a general feature observed in these materials. The strong influence of the structural characteristics of the precursors on the final crystalline bulk phase demonstrates that for the investigated system, polymorph selection takes place in the very early stages of nucleation.

Identification of a multi-dimensional reaction coordinate for crystal nucleation in Ni3Al.

Nucleation during solidification in multi-component alloys is a complex process that comprises competition between different crystalline phases as well as chemical composition and ordering. Here, we combine transition interface sampling with an extensive committor analysis to investigate the atomistic mechanisms during the initial stages of nucleation in Ni3Al. The formation and growth of crystalline clusters from the melt are strongly influenced by the interplay between three descriptors: the size, crystallinity, and chemical short-range order of the emerging nuclei. We demonstrate that it is essential to include all three features in a multi-dimensional reaction coordinate to correctly describe the nucleation mechanism, where, in particular, the chemical short-range order plays a crucial role in the stability of small clusters. The necessity of identifying multi-dimensional reaction coordinates is expected to be of key importance for the atomistic characterization of nucleation processes in complex, multi-component systems.

Maximum Likelihood Analysis of Reaction Coordinates during Solidification in Ni.

Understanding the underlying mechanism of crystal nucleation is a fundamental aspect in the prediction and control of materials properties. Classical nucleation theory (CNT) assumes that homogeneous nucleation occurs via random fluctuations within the supercooled liquid, that the structure of the growing clusters resembles the most stable bulk phase, and that the nucleus size is the sole reaction coordinate (RC) of the process. Many materials are, however, known to exhibit multiple steps during crystallization, forming different polymorphs. As a consequence, more complex RCs are often required to capture all relevant information about the process. Here, we employ transition path sampling together with a maximum likelihood analysis of candidate order parameters to identify suitable RCs for the nucleation mechanism during solidification in Ni. In contrast to CNT, the analysis of the reweighted path ensemble shows that a prestructured liquid region that surrounds the crystal cluster is a relevant order parameter that enhances the RC and therefore plays a key role in the description of the nucleus and the interfacial free energy. We demonstrate that prestructured liquid clusters that emerge within the liquid act as precursors of the crystallization in a nonclassical two-step mechanism, which predetermines the coordination of the selected polymorphs.

Origin of Spectral Band Patterns in the Cosmic Unidentified Infrared Emission.

The cosmic unidentified infrared emission (UIE) band phenomenon is generally considered as indicative of free-flying polycyclic aromatic hydrocarbon molecules in space. However, a coherent explanation of emission spectral band patterns depending on astrophysical source is yet to be resolved under this attribution. Meanwhile astronomers have restored the alternative origin as due to amorphous carbon particles, but assigning spectral patterns to specific structural elements of particles is equally challenging. Here we report a physical principle in which inclusion of nonplanar structural defects in aromatic core molecular structures (π domains) induces spectral patterns typical of the phenomenon. We show that defects in model π domains modulate the electronic-vibration coupling that activates the delocalized π-electron contribution to aromatic vibrational modes. The modulation naturally disperses C=C stretch modes in band patterns that readily resemble the UIE bands in the elusive 6-9 µm range. The electron-vibration interaction mechanics governing the defect-induced band patterns underscores the importance of π delocalization in the emergence of UIE bands. We discuss the global UIE band regularity of this range as compatible with an emission from the delocalized sp^{2} phase, as π domains, confined in disordered carbon mixed-phase aggregates.

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

Nucleation is a key step during crystallization, but a complete understanding of the fundamental atomistic processes remains elusive. We investigate the mechanism of nucleation during solidification in nickel for various undercoolings using transition path sampling simulations. The temperature dependence of the free energy barriers and rate constants that we obtain is consistent with the predictions of classical nucleation theory and experiments. However, our analysis of the transition path ensemble reveals a mechanism that deviates from the classical picture of nucleation: the growing solid clusters have predominantly non-spherical shapes and consist of face-centered-cubic and random hexagonal-close-packed coordinated atoms surrounded by a cloud of prestructured liquid. The nucleation initiates in regions of supercooled liquid that are characterized by a high orientational order with structural features that predetermine the polymorph selection. These results provide atomistic insight not only into the nucleation mechanism of nickel but also into the role of the preordered liquid regions as precursors for crystallization.

Comparison of minimum-action and steepest-descent paths in gradient systems.

On high-dimensional and complex potential energy surfaces, the identification of the most likely mechanism for the transition between local minima is a challenging task. Usually the steepest-descent path is used interchangeably with the minimum-energy path and is associated with the most likely path. Here we compare the meaning of the steepest-descent path in complex energy landscapes to the path integral formulation of a trajectory that minimizes the action functional for Brownian dynamics. In particular, for energy landscapes with bifurcation points and multiple minima and saddle points, there can be several steepest-descent paths associated with specific saddles that connect two predetermined states but largely differ from the path of maximum likelihood. The minimum-action path, however, additionally takes into account the scalar work along the trajectory. Minimizing the scalar work can be less ambiguous in the identification of the most likely path in different gradient systems. It can also be used to distinguish between multiple steepest-descent paths that connect reactant and product states. We illustrate that in systems with complex energy landscapes a careful assessment of the steepest-descent path is thus advisable. Here the evaluation of the action can provide valuable information on the analysis and description of the most likely path.

Path finding on high-dimensional free energy landscapes.

We present a method for determining the average transition path and the free energy along this path in the space of selected collective variables. The formalism is based upon a history-dependent bias along a flexible path variable within the metadynamics framework but with a trivial scaling of the cost with the number of collective variables. Controlling the sampling of the orthogonal modes recovers the average path and the minimum free energy path as the limiting cases. The method is applied to resolve the path and the free energy of a conformational transition in alanine dipeptide.

Domain growth, pattern formation, and morphology transitions in Langmuir monolayers. A new growth instability.

The aims of this study are the following two: (1) To show that in Langmuir monolayers (LM) at low supersaturation, domains grow forming fractal structures without an apparent orientational order trough tip splitting dynamics, where doublons are the building blocks producing domains with a seaweed shape. When supersaturation is larger, there is a morphology transition from tip splitting to side branching. Here, structures grow with a pronounced orientational order forming dendrites, which are also fractal. We observed this behavior in different Langmuir monolayers formed by nervonic acid, dioctadecylamine, ethyl stearate, and ethyl palmitate, using Brewster angle microscopy. (2) To present experimental evidence showing an important Marangoni flow during domain growth, where the hydrodynamic transport of amphipiles overwhelms diffusion. We were able to show that the equation that governs the pattern formation in LM is a Laplacian equation in the chemical potential with the appropriate boundary conditions. However, the underlying physics involved in Langmuir monolayers is different from the underlying physics in the Mullins-Sekerka instability; diffusional processes are not involved. We found a new kind of instability that leads to pattern formation, where Marangoni flow is the key factor. We also found that the equations governing pattern formation in LM can be reduced to those used in the theory of morphology diagrams for two-dimensional diffusional growth. Our experiments agree with this diagram.