Uncovering the effects of interface-induced ordering of liquid on crystal growth using machine learning

Solid-Liquid Interfacial Free Energy from Computer Simulations: Challenges and Recent Advances

The study of interfacial properties in liquid-liquid and liquid-vapor systems has a history of nearly 200 years, with significant contributions from scientific luminaries such as Thomas Young and Willard Gibbs. However, a similar level of understanding of solid-liquid interfaces has emerged only more recently, largely because of the numerous complications associated with the thermodynamics needed to describe them. The accurate calculation of the interfacial free energy of solid-liquid systems is central to determining which interfaces will be observed and their properties. However, designing and analyzing the molecular dynamics simulations required to do this remains challenging, unlike the liquid-liquid or liquid-vapor cases, because of the unique complications associated with solid-liquid systems. Specifically, the lattice structure of solids introduces spatial directionality, and atomic configurations in solids can be altered by stretching. The primary aim of this review is to provide an overview of the numerical approaches developed to address the challenge of calculating the interfacial free energy in solid-liquid systems. These approaches are classified as (i) direct methods, which compute interfacial free energies explicitly, albeit often through convoluted procedures, and (ii) indirect methods, which derive these free energies as secondary results obtained from the analysis of simulations of an idealized experimental configuration. We also discuss two key topics related to the calculation of the interfacial free energy of solid-liquid systems: nucleation theory and curved interfaces, which represent important problems where research remains highly active.

A quantitative theory and atomistic simulation study on the soft-sphere crystal-melt interfacial properties. I. Kinetic coefficients

By employing non-equilibrium molecular dynamics (NEMD) simulations and time-dependent Ginzburg-Landau (TDGL) theory for solidification kinetics [Cryst. Growth Des. 20, 7862 (2020)], we predict the kinetic coefficients of FCC(100) crystal-melt interface (CMI) of soft-spheres modeled with an inverse-sixth-power repulsive potential. The collective dynamics of the local interfacial liquid phase at the equilibrium FCC(100) CMIs are calculated based on a recently proposed algorithm [J. Chem. Phys. 157, 084 709 (2022)] and are employed as the resulting parameter that eliminates the discrepancy between the predictions of the kinetic coefficient using the NEMD simulations and the TDGL solidification theory. A speedup of the two modes of the interfacial liquid collective dynamics (at wavenumbers equal to the principal and the secondary reciprocal lattice vector of the grown crystal) is observed. With the insights provided by the quantitative predictive theory, the variation of the solidification kinetic coefficient along the crystal-melt coexistence boundary is discussed. The combined methodology (simulation and theory) presented in this study could be further applied to investigate the role of the inter-atomic potential (e.g., softness parameter s = 1/n of the inverse-power repulsive potential) in the kinetic coefficient.

A joint diffusion/collision model for crystal growth in pure liquid metals

The kinetics of atomic attachments at the liquid/solid interface is one of the foundations of solidification theory, and to date one of the long-standing questions remains: whether or not the growth is thermal activated in pure liquid metals. Using molecular dynamics simulations and machine learning, I have demonstrated that a considerable fraction of liquid atoms at the interfaces of Al(111), (110) and (100) needs thermal activation for growth to take place while the others attach to the crystal without an energy barrier. My joint diffusion/collision model is proved to be robust in predicting the general growth behaviour of pure metals. Here, I show this model is able to quantitatively describe the temperature dependence of growth kinetics and to properly interpret some important experimental observations, and it significantly advances our understanding of solidification theory and also is useful for modelling solidification, phase change materials and lithium dendrite growth in lithium-ion battery.

Local Structural Features Elucidate Crystallization of Complex Structures

Complex crystal structures are composed of multiple local environments, and how this type of order emerges spontaneously during crystal growth has yet to be fully understood. We study crystal growth across various structures and along different crystallization pathways, using self-assembly simulations of identical particles that interact via multiwell isotropic pair potentials. We apply an unsupervised machine learning method to features from bond-orientational order metrics to identify different local motifs present during a given structure's crystallization process. In this manner, we distinguish different crystallographic sites in highly complex structures. Tailoring this order parameter to structures of varying complexity and coordination number, we study the emergence of local order along a multistep crystal growth pathway─from a low-density fluid to a high-density, supercooled amorphous liquid droplet and to a bulk crystal. We find a consistent under-coordination of the liquid relative to the average coordination number in the bulk crystal. We use our order parameter to analyze the geometrically frustrated growth of a Frank-Kasper phase and discover how structural defects compete with the formation of crystallographic sites that are more high-coordinated than the liquid environments. The method presented here for classifying order on a particle-by-particle level has broad applicability to future studies of structural self-assembly and crystal growth, and they can aid in the design of building blocks and for targeting pathways of formation of soft-matter structures.

Revealing the hidden structure of disordered materials by parameterizing their local structural manifold

Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold. Applying this approach to a two-dimensional model crystal and a three-dimensional binary model metallic glass results in parameters interpretable as coordination number, composition, volumetric strain, and local symmetry. In particular, we show that a more slowly quenched glass has a higher degree of local tetrahedral symmetry at the expense of cyclic symmetry. While these descriptors require post-hoc interpretation, they minimize bias rooted in crystalline materials science and illuminate a range of structural trends that might otherwise be missed.

Fast crystal growth in deeply undercooled ZrTi melts

We investigate the growth of crystals in Zr50Ti50 melts by classical molecular-dynamics simulations with an embedded atom method and a Stillinger-Weber potential model. Both models display fast solidification rates that can be captured by the transition state theory or the Ginzburg-Landau theory at small undercoolings. Fast crystal-growth rates are found to be affected by the pre-existing ordering in liquids, such as the body-centered cubic-like and icosahedral-like structures. The interface-induced ordering unveiled by the crystal-freezing method can explain the rate difference between these two models. However, these orderings fail to rationalize the temperature evolution of the growth rate at deep undercoolings. We correlate the growth kinetics with the detailed dynamical processes in liquids, finding the decoupling of hierarchic relaxation processes when collective motion emerges in supercooled liquids. We find that the growth kinetics is nondiffusive, but with a lower activation barrier corresponding to the structural relaxation or the cage-relative motion in ZrTi melts. These results explore a new relaxation mechanism for the fast growth rate in deeply undercooled liquids.

Lightweight Extendable Stacking Framework for Structure Classification in Atomistic Simulations

Identifying an atom's local crystal structure is one crucial step in many atomistic simulation analyses. However, many traditional methods are available to only a few limited types of structures, and their performance often relies on manually determined parameters, which may lead to poor classification results in complex material systems. Machine learning models can enhance accuracy and generalizability, but they typically require large amounts of data and computation. This issue could be more severe for deep-learning-based frameworks, especially when confronted with unfamiliar crystal structures. To address this challenge, we propose a lightweight and extendable stacked structure (LESS) classifier, which adopts bond orientational order parameters as features and assembles several efficient machine learning methods as based models. The LESS classifier can recognize a variety of crystal structures, e.g., amorphous, mono, and binary structures, with over 98.8% accuracy on our validation data set, outperforming many current methods even including some deep-learning methods. Our model can also conduct probabilistic classification that aids in the interpretation of atomic structures in complicated environments such as heterogeneous interfaces. Furthermore, when exposed to a completely unknown crystal structure, the LESS framework can efficiently incorporate this new knowledge with generative sampled data from the current model. Overall, our model exhibits great potential as an accurate and flexible atomic structure identification tool featuring high efficiency in both learning and retraining.

Traversing the nucleation-growth landscape through heterogeneous random walks

The nucleation-growth process is a crucial component of crystallization. While previous theoretical models have focused on nucleation events and postnucleation growth, such as the classical nucleation theory and Lifshitz-Slyozov-Wagner model, recent advancements in experiments and simulations have highlighted the inability of classical models to explain the transient dynamics during the early development of nanocrystals. To address these shortcomings, we present a model that describes the nucleation-growth dynamics of individual nanocrystals as a series of reversible chain reactions, with the free energy landscape extended to include activation-adsorption-relaxation reaction pathways. By using the Monte Carlo method based on the transition state theory, we simulate the crystallization dynamics. We derive a Fokker-Planck formalism from the master equation to describe the nucleation-growth process as a heterogeneous random walk on the extended free energy landscape with activated states. Our results reveal the transient quasiequilibrium of the prenucleation stage before nucleation starts, and we identify a postnucleation crossover regime where the dynamic growth exponents asymptotically converge towards classical limits. Additionally, we generalize the power laws to address the dimension and scale effects for the growth of large crystals.

Multi-Prismatic Hollow Cube CeVO4 with Adjustable Wall Thickness Directed towards Photocatalytic CO2 Reduction to CO

Ternary orthovanadate compounds have received increasing attention due to their broad light absorption and diverse crystal structure. However, their multi-assembled crystal morphologies are limited mainly due to their initially polyatomic VO4 groups. In this study, multi-prismatic hollow cubic CeVO4 microstructures were fabricated by a one-step solvothermal method without any organic agents. The increase in wall thickness is in accordance with the radial direction of the quadrangular prism. Moreover, the overdose of the V precursor is favorable for the formation of hollow micro-cubic CeVO4, and the wall thickness changes from 200 to 700 nm. Furthermore, these CeVO4 microstructures were applied to photocatalytic CO2 reduction with a maximum CO generation rate of up to 78.12 μmol g-1 h-1 under visible light irradiation, which was several times higher than that of the other samples. This superior photocatalytic activity might be attributed to its good crystallinity and unique exposed interior structure. This study provides guidelines for the multi-assembled structure fabrication of ternary compounds and expands upon the exploration of the spatial structure of multivariate compounds.

Direct Measurement of Solid-Liquid Interfacial Energy Using a Meniscus

Solid-liquid interactions are central to diverse processes. The interaction strength can be described by the solid-liquid interfacial free energy (γ_{SL}), a quantity that is difficult to measure. Here, we present the direct experimental measurement of γ_{SL} for a variety of solid materials, from nonpolar polymers to highly wetting metals. By attaching a thin solid film on top of a liquid meniscus, we create a solid-liquid interface. The interface determines the curvature of the meniscus, analysis of which yields γ_{SL} with an uncertainty of less than 10%. Measurement of classically challenging metal-water interfaces reveals γ_{SL}∼30-60  mJ/m^{2}, demonstrating quantitatively that water-metal adhesion is 80% stronger than the cohesion energy of bulk water, and experimentally verifying previous quantum chemical calculations.

Limits to Crystallization Pressure

Crystallization pressure drives deformation and damage in monuments, buildings, and the Earth's crust. Even though the phenomenon has been known for 170 years, there is no agreement between theoretical calculations of the maximum attainable pressure and experimentally measured pressures. We have therefore developed a novel experimental technique to image the nanoconfined crystallization process while controlling the pressure and applied it to calcite. The results show that displacement by crystallization pressure is arrested at pressures well below the thermodynamic limit. We use existing molecular dynamics simulations and atomic force microscopy data to construct a robust model of the disjoining pressure in this system and thereby calculate the absolute distance between the surfaces. On the basis of the high-resolution experiments and modeling, we formulate a novel mechanism for the transition between damage and adhesion by crystallization that may find application in Earth and materials sciences and in conservation of cultural heritage.

Local collective dynamics at the equilibrium BCC crystal-melt interfaces

We present a classical molecular-dynamics study of the collective dynamical properties of the coexisting liquid phase at equilibrium body-centered cubic (BCC) Fe crystal-melt interfaces. For the three interfacial orientations (100), (110), and (111), the collective dynamics are characterized through the calculation of the intermediate scattering functions, dynamical structure factors and density relaxation times in a sequential local region of interest. An anisotropic speed up of the collective dynamics in all three BCC crystal-melt interfacial orientations is observed. This trend differs significantly different from the previously observed slowing down of the local collective dynamics at the liquid-vapor interface [Acta Mater 2020;198:281]. Examining the interfacial density relaxation times, we revisit the validity of the recently developed time-dependent Ginzburg-Landau (TDGL) theory for the solidification crystal-melt interface kinetic coefficients, resulting in excellent agreement with both the magnitude and the kinetic anisotropy of the CMI kinetic coefficients measured from the non-equilibrium MD simulations.

Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization

Artificial intelligence and specifically machine learning applications are nowadays used in a variety of scientific applications and cutting-edge technologies, where they have a transformative impact. Such an assembly of statistical and linear algebra methods making use of large data sets is becoming more and more integrated into chemistry and crystallization research workflows. This review aims to present, for the first time, a holistic overview of machine learning and cheminformatics applications as a novel, powerful means to accelerate the discovery of new crystal structures, predict key properties of organic crystalline materials, simulate, understand, and control the dynamics of complex crystallization process systems, as well as contribute to high throughput automation of chemical process development involving crystalline materials. We critically review the advances in these new, rapidly emerging research areas, raising awareness in issues such as the bridging of machine learning models with first-principles mechanistic models, data set size, structure, and quality, as well as the selection of appropriate descriptors. At the same time, we propose future research at the interface of applied mathematics, chemistry, and crystallography. Overall, this review aims to increase the adoption of such methods and tools by chemists and scientists across industry and academia.

Beyond the Average: Spatial and Temporal Fluctuations in Oxide Glass-Forming Systems

Atomic structure dictates the performance of all materials systems; the characteristic of disordered materials is the significance of spatial and temporal fluctuations on composition-structure-property-performance relationships. Glass has a disordered atomic arrangement, which induces localized distributions in physical properties that are conventionally defined by average values. Quantifying these statistical distributions (including variances, fluctuations, and heterogeneities) is necessary to describe the complexity of glass-forming systems. Only recently have rigorous theories been developed to predict heterogeneities to manipulate and optimize glass properties. This article provides a comprehensive review of experimental, computational, and theoretical approaches to characterize and demonstrate the effects of short-, medium-, and long-range statistical fluctuations on physical properties (e.g., thermodynamic, kinetic, mechanical, and optical) and processes (e.g., relaxation, crystallization, and phase separation), focusing primarily on commercially relevant oxide glasses. Rigorous investigations of fluctuations enable researchers to improve the fundamental understanding of the chemistry and physics governing glass-forming systems and optimize structure-property-performance relationships for next-generation technological applications of glass, including damage-resistant electronic displays, safer pharmaceutical vials to store and transport vaccines, and lower-attenuation fiber optics. We invite the reader to join us in exploring what can be discovered by going beyond the average.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Predicting Fracture Propensity in Amorphous Alumina from Its Static Structure Using Machine Learning

Thin films of amorphous alumina (a-Al₂O₃) have recently been found to deform permanently up to 100% elongation without fracture at room temperature. If the underlying ductile deformation mechanism can be understood at the nanoscale and exploited in bulk samples, it could help to facilitate the design of damage-tolerant glassy materials, the holy grail within glass science. Here, based on atomistic simulations and classification-based machine learning, we reveal that the propensity of a-Al₂O₃ to exhibit nanoscale ductility is encoded in its static (nonstrained) structure. By considering the fracture response of a series of a-Al₂O₃ systems quenched under varying pressure, we demonstrate that the degree of nanoductility is correlated with the number of bond switching events, specifically the fraction of 5- and 6-fold coordinated Al atoms, which are able to decrease their coordination numbers under stress. In turn, we find that the tendency for bond switching can be predicted based on a nonintuitive structural descriptor calculated based on the static structure, namely, the recently developed "softness" metric as determined from machine learning. Importantly, the softness metric is here trained from the spontaneous dynamics of the system (i.e., under zero strain) but, interestingly, is able to readily predict the fracture behavior of the glass (i.e., under strain). That is, lower softness facilitates Al bond switching and the local accumulation of high-softness regions leads to rapid crack propagation. These results are helpful for designing glass formulations with improved resistance to fracture.

Dielectric Constant of Liquid Water Determined with Neural Network Quantum Molecular Dynamics

The static dielectric constant ϵ_{0} and its temperature dependence for liquid water is investigated using neural network quantum molecular dynamics (NNQMD). We compute the exact dielectric constant in canonical ensemble from NNQMD trajectories using fluctuations in macroscopic polarization computed from maximally localized Wannier functions (MLWF). Two deep neural networks are constructed. The first, NNQMD, is trained on QMD configurations for liquid water under a variety of temperature and density conditions to learn potential energy surface and forces and then perform molecular dynamics simulations. The second network, NNMLWF, is trained to predict locations of MLWF of individual molecules using the atomic configurations from NNQMD. Training data for both the neural networks is produced using a highly accurate quantum-mechanical method, DFT-SCAN that yields an excellent description of liquid water. We produce 280×10^{6} configurations of water at 7 temperatures using NNQMD and predict MLWF centers using NNMLWF to compute the polarization fluctuations. The length of trajectories needed for a converged value of the dielectric constant at 0°C is found to be 20 ns (40×10^{6} configurations with 0.5 fs time step). The computed dielectric constants for 0, 15, 30, 45, 60, 75, and 90°C are in good agreement with experiments. Our scalable scheme to compute dielectric constants with quantum accuracy is also applicable to other polar molecular liquids.

Crystal growth in deeply undercooled Ni50Al50: Signature of the ordering sequence at the interface

Crystal growth of the intermetallic alloy, Ni₅₀Al₅₀, is investigated by molecular dynamics simulations with two different interatomic potentials. The calculated growth rate can be captured by the Wilson-Frenkel or Broughton-Gilmer-Jackson model at small undercoolings but deviates from the theory at deep undercoolings. Failure of the theory is found to be correlated with the dynamic processes that emerged at the interface, but not apparently with the static interface structure. The chemical segregation of Ni and Al atoms occurs before the geometrical ordering upon crystallization at small undercoolings. In contrast, the geometrical ordering precedes the chemical one at deep undercoolings. These two ordering processes show a collapsed time evolution at the crossover temperature consistent with the onset of the theoretical deviation. We rationalize the delayed chemical segregation behavior by the collective atomic motion, which is characterized by the super-Arrhenius transition of the temperature-dependent diffusivity and structural relaxation time at the crossover point.