Maximum Likelihood Analysis of Reaction Coordinates during Solidification in Ni

Harvesting nucleating structures in nanoparticle crystallization: The example of gold, silver, and iron

The thermodynamics and kinetics of nanoparticle crystallization, as opposed to bulk phases, may be influenced by surface and size effects. We investigate the importance of such factors in the crystallization process of gold, silver, and iron nanodroplets using numerical simulations in the form of molecular dynamics combined with path sampling. This modeling strategy is targeted at obtaining representative ensembles of structures located at the transition state of the crystallization process. A structural analysis of the transition state ensembles reveals that both the average size and location of the critical nucleation cluster are influenced by surface and nanoscale size effects. Furthermore, we also show that transition state structures in smaller nanodroplets exhibit a more ordered liquid phase, and differentiating between a well-ordered critical cluster and its surrounding disordered liquid phase becomes less evident. All in all, these findings demonstrate that crystallization mechanisms in nanoparticles go beyond the assumptions of classical nucleation theory.

Stochastic computer experiments of the thermodynamic irreversibility of bulk nanobubbles in supersaturated and weak gas-liquid solutions

Spontaneous gas-bubble nucleation in weak gas-liquid solutions has been a challenging topic in theory, experimentation, and computer simulations. In analogy with recent advances in crystallization and droplet formation studies, the diffusive-shielding stabilization and thermodynamic irreversibility of bulk nanobubble (bNB) mechanisms are revisited and deployed to characterize nucleation processes in a stochastic framework of computer experiments using the large-scale atomic/molecular massively parallel simulator code. Theoretical bases, assumptions, and limitations underlying the irreversibility hypothesis of bNBs, and their computational counterparts, are extensively described and illustrated. In essence, it is established that the irreversibility hypothesis can be numerically investigated by converging the system volume (due to the finiteness of interatomic forces) and the initial dissolved-gas concentration in the solution (due to the single-bNB limitation). Helium nucleation in liquid Pb17Li alloy is selected as a representative case study, where it exhibits typical characteristics of noble-gas/liquid-metal systems. The proposed framework lays down the bases on which the stability of gas-bNBs in weak and supersaturated gas-liquid solutions can be inferred and explained from a novel perspective. In essence, it stochastically marches toward a unique irreversible state along out-of-equilibrium nucleation/growth trajectories. Moreover, it does not attempt to characterize the interface or any interface-related properties, neither theoretically nor computationally. It was concluded that bNBs of a few tens of He-atoms are irreversible when dissolved-He concentrations in the weak gas-liquid solution are at least ∼50 and ∼105 mol m-3 at 600 and 1000 K (and ∼80 MPa), respectively, whereas classical molecular dynamics -estimated solubilities are at least two orders of magnitude smaller.

Divergence among Local Structure, Dynamics, and Nucleation Outcome in Heterogeneous Nucleation of Close-Packed Crystals

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use path sampling simulations of two model systems to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of the heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly, wherein low-coordinated crystalline particles outpace their liquid-like counterparts. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies and present suitable structural heuristics within the metastable fluid for CV prescreening. Employing such optimized CVs is pivotal for properly characterizing the mechanism of heterogeneous nucleation in metallic and colloidal systems.

An exploration of machine learning models for the determination of reaction coordinates associated with conformational transitions

Determining collective variables (CVs) for conformational transitions is crucial to understanding their dynamics and targeting them in enhanced sampling simulations. Often, CVs are proposed based on intuition or prior knowledge of a system. However, the problem of systematically determining a proper reaction coordinate (RC) for a specific process in terms of a set of putative CVs can be achieved using committor analysis (CA). Identifying essential degrees of freedom that govern such transitions using CA remains elusive because of the high dimensionality of the conformational space. Various schemes exist to leverage the power of machine learning (ML) to extract an RC from CA. Here, we extend these studies and compare the ability of 17 different ML schemes to identify accurate RCs associated with conformational transitions. We tested these methods on an alanine dipeptide in vacuum and on a sarcosine dipeptoid in an implicit solvent. Our comparison revealed that the light gradient boosting machine method outperforms other methods. In order to extract key features from the models, we employed Shapley Additive exPlanations analysis and compared its interpretation with the "feature importance" approach. For the alanine dipeptide, our methodology identifies ϕ and θ dihedrals as essential degrees of freedom in the C7ax to C7eq transition. For the sarcosine dipeptoid system, the dihedrals ψ and ω are the most important for the cisαD to transαD transition. We further argue that analysis of the full dynamical pathway, and not just endpoint states, is essential for identifying key degrees of freedom governing transitions.

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.

Explaining reaction coordinates of alanine dipeptide isomerization obtained from deep neural networks using Explainable Artificial Intelligence (XAI)

A method for obtaining appropriate reaction coordinates is required to identify transition states distinguishing product and reactant in complex molecular systems. Recently, abundant research has been devoted to obtaining reaction coordinates using artificial neural networks from deep learning literature, where many collective variables are typically utilized in the input layer. However, it is difficult to explain the details of which collective variables contribute to the predicted reaction coordinates owing to the complexity of the nonlinear functions in deep neural networks. To overcome this limitation, we used Explainable Artificial Intelligence (XAI) methods of the Local Interpretable Model-agnostic Explanation (LIME) and the game theory-based framework known as Shapley Additive exPlanations (SHAP). We demonstrated that XAI enables us to obtain the degree of contribution of each collective variable to reaction coordinates that is determined by nonlinear regressions with deep learning for the committor of the alanine dipeptide isomerization in vacuum. In particular, both LIME and SHAP provide important features to the predicted reaction coordinates, which are characterized by appropriate dihedral angles consistent with those previously reported from the committor test analysis. The present study offers an AI-aided framework to explain the appropriate reaction coordinates, which acquires considerable significance when the number of degrees of freedom increases.

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,...