Nonclassical Nucleation Pathways Research Articles

Atomic‐level structure evolution of calcium silicate hydrate nucleation process, the amorphous‐to‐crystalline pathway

AbstractCalcium silicate hydrate (C‐S‐H) synthesis follows multistep nucleation processes ranging from amorphous globules to nanocrystals. This type of nonclassical nucleation pathway attracts extensive interest and yet related molecular processes are mostly unexplored. Herein, atomic‐level structure evolution during this process is unveiled. From inside to outside of the globule, the atomic arrangement evolves from amorphous configuration to layered stacking of calcium silicate layers with layers spaced by 1.1 nm. Numerous cations surrounding the globules provide extra calcium ions to form nano C‐S‐H foils at the edge of the globule. The polymerization to form calcium silicate chains has almost been completed before 5 min reaction, and the C‐S‐H structure formation is basically based on the self‐assembly to be calcium silicate layers and then lamellar crystal inside the globule. Silicate chain defects inhibit a‐ and c‐axes crystallization, but promote b‐axes one, leading to anisotropic growth of crystalline C‐S‐H. The defects lead to the crystallization pathways conversion from Si–O–Si bonds formation to Ca2+ electrostatic linking.

Formation Onset of Flat-Perylene Prenucleation Clusters in Vacuum

Our current understanding of the prenucleation processes involved in the growth of perylene-based organic nanocrystals is still limited. In this study, we utilized molecular dynamics simulations, employing various flat perylene molecules, to investigate these processes. Our findings reveal that, while cluster formation is primarily driven by molecular aggregation, the Ostwald ripening phenomenon also occurs in a vacuum environment. The presence of a methoxy group influences both the rate and structure of clustering. Interestingly, the preferred initial clusters, as determined by their molar Gibbs free energies, do not align with the crystal units or nuclei observed in herringbone perylene crystals. Overall, this study enhances the understanding of organic nanocrystal formation, specifically nonclassical nucleation pathways, and guides the manipulation of perylene-based organic crystals.

Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models

Using a hierarchy of three sigmoid growth models with increasing complexity, i.e., number of parameters, we reanalyzed kinetic data for heterogeneous nucleation—the number of nuclei N(t) vs. time t—from archetypical experiments on the electrodeposition of mercury on platinum by I. Markov and E. Stoycheva, to obtain two scales: Nmax and τ. The universal character of the studied phenomenon was revealed when replotting the original data as α ≡ N(t)/Nmax vs. t/τ. Yet the simplest model, the recently introduced α21 model which is aimed to describe diffusion-limited growth in 2D, α21 = tanh2(2t/τ21), fits all datasets with an R2 ≥ 0.989. This can be rationalized by attracting the non-classical notion of two-step nucleation—the nuclei form in a metastable phase which, in this case, grows on the electrode surface. Beyond the universality, we find the dependence of the two obtained scales on the overvoltage, which is increased systematically from 83 to 88 mV to generate the six N(t) datasets for each of the two electrode types—planar and hemispherical. Surprisingly, for one of them, the planar electrode, there is a discontinuity in the dependence—an almost horizontal jump from 85 to 86 mV, while for the hemispherical electrode, τ decreases smoothly.

The nucleation of C-S-H via prenucleation clusters.

The nucleation and growth of calcium-silicate-hydrate (C-S-H) is of fundamental importance for the strength development and durability of the concrete. However, the nucleation process of C-S-H is still not fully understood. The present work investigates how C-S-H nucleates by analyzing the aqueous phase of hydrating tricalcium silicate (C3S) by applying inductively coupled plasma-optical emission spectroscopy as well as analytical ultracentrifugation. The results show that the C-S-H formation follows non-classical nucleation pathways associated with the formation of prenucleation clusters (PNCs) of two types. Those PNCs are detected with high accuracy and reproducibility and are two species of the 10 in total, from which the ions (with associated water molecules) are the majority of the species. The evaluation of the density and molar mass of the species shows that the PNCs are much larger than ions, but the nucleation of C-S-H starts with the formation of liquid precursor C-S-H (droplets) with low density and high water content. The growth of these C-S-H droplets is associated with a release of water molecules and a reduction in size. The study gives experimental data on the size, density, molecular mass, and shape and outlines possible aggregation processes of the detected species.

Nucleation experiments on a titanium-carbon system imply nonclassical formation of presolar grains.

Just as the shapes of snowflakes provide us with information on the temperature and humidity of the upper atmosphere, the characteristics of presolar grains in meteorites place limits on their formation environment in a stellar outflow. However, even in the case of well-characterized presolar grains consisting of a titanium carbide core and a graphitic carbon mantle, it is not possible to delimit their formation environment. Here, we have demonstrated the formation of core-mantle grains in gravitational and microgravity environments and have found that core-mantle grains are formed by a nonclassical nucleation pathway involving the three steps: (i) primary nucleation of carbon at a substantially high supersaturation, (ii) heterogeneous condensation of titanium carbide on the carbon, and (iii) fusion of nuclei. We argue that the characteristics of not only core-mantle grains but also other presolar and solar grains might be accurately explained by considering a nonclassical nucleation pathway.

Nonclassical Nucleation of Zinc Oxide from a Physically Motivated Machine-Learning Approach

Observing nonclassical nucleation pathways remains challenging in simulations of complex materials with technological interests. This is because it requires very accurate force fields that can capture the whole complexity of their underlying interatomic interactions and an advanced structural analysis able to discriminate between competing crystalline phases. Here, we first report the construction and particularly thorough validation of a machine-learning force field for zinc oxide interactions using the Physical LassoLars Interaction Potentials approach which allows us to be predictive even for high-temperature dynamical systems such as ZnO melt. Then, we carried out several types of crystallization simulations and followed the formation of ZnO crystals with atomistic precision. Our results, which were analyzed using a data-driven approach based on bond order parameters, demonstrate the presence of both prenucleation clusters and two-step nucleation scenarios, thus retrieving seminal predictions of nonclassical nucleation pathways made on much simpler models. Dedicated calculations of high-temperature ZnO free energy within a newly developed automated nonequilibrium thermodynamic integration method revealed the existence of a thermodynamic bias for the predicted nonclassical nucleation scenarios.

A Deep Learning Framework Discovers Compositional Order and Self-Assembly Pathways in Binary Colloidal Mixtures.

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of rA/rB = 0.8 to rA/rB = 0.95) can promote the self-assembly of defect-free BSLs much more effectively than systems of identically sized particles, as nearly defect-free BCC-CsCl, FCC-CuAu, and IrV crystals are observed in the former case. The framework additionally reveals that size-disparate colloidal mixtures can undergo nonclassical nucleation pathways where BSLs evolve from dense amorphous precursors, instead of directly nucleating from dilute solution. These findings illustrate that the presented characterization framework can assist in enhancing mechanistic understanding of the self-assembly of binary colloidal mixtures, which in turn can pave the way for engineering the growth of defect-free BSLs.

Signatures of sluggish dynamics and local structural ordering during ice nucleation.

We investigate the microscopic pathway of spontaneous crystallization in the ST2 model of water under deeply supercooled conditions via unbiased classical molecular dynamics simulations. After quenching below the liquid-liquid critical point, the ST2 model spontaneously separates into low-density liquid (LDL) and high-density liquid phases, respectively. The LDL phase, which is characterized by lower molecular mobility and enhanced structural order, fosters the formation of a sub-critical ice nucleus that, after a stabilization time, develops into the critical nucleus and grows. Polymorphic selection coincides with the development of the sub-critical nucleus and favors the formation of cubic (Ic) over hexagonal (Ih) ice. We rationalize polymorphic selection in terms of geometric arguments based on differences in the symmetry of second neighbor shells of ice Ic and Ih, which are posited to favor formation of the former. The rapidly growing critical nucleus absorbs both Ic and Ih crystallites dispersed in the liquid phase, a crystal with stacking faults. Our results are consistent with, and expand upon, recent observations of non-classical nucleation pathways in several systems.

Seeds of imperfection rule the mesocrystalline disorder in natural anhydrite single crystals

In recent years, we have come to appreciate the astounding intricacies associated with the formation of minerals from ions in aqueous solutions. In this context, a number of studies have revealed that the nucleation of calcium sulfate systems occurs nonclassically, involving the aggregation and reorganization of nanosized prenucleation species. In recent work, we have shown that this particle-mediated nucleation pathway is actually imprinted in the resultant micrometer-sized CaSO4 crystals. This property of CaSO4 minerals provides us with the unique opportunity to search for evidence of nonclassical nucleation pathways in geological environments. In particular, we focused on large anhydrite crystals extracted from the Naica Mine in Mexico. We were able to shed light on this mineral's growth history by mapping defects at different length scales. Based on this, we argue that the nanoscale misalignment of the structural subunits, observed in the initial calcium sulfate crystal seeds, propagates through different length scales both in morphological, as well as in strictly crystallographic aspects, eventually causing the formation of large mesostructured single crystals of anhydrite. Hence, the nonclassical nucleation mechanism introduces a "seed of imperfection," which leads to a macroscopic "single" crystal whose fragments do not fit together at different length scales in a self-similar manner. Consequently, anisotropic voids of various sizes are formed with very well-defined walls/edges. However, at the same time, the material retains in part its single crystal nature.

A new perspective of inorganic crystallization: Non-classical nucleation and growth

<p indent=0mm>Inorganic crystals surround us and play important roles in our daily life. They form integral parts of our body (e.g., bones), make up all the ground we stand on (ours and any other rocky planet consist of crystals), as well as show significant necessity for industrial processes and technologies (from table salt over concrete to biomedical nanoparticles). Accordingly, the formation mechanisms and properties of crystals have been extensively studied over the past decades. While there are longstanding theories on both the birth of crystals (nucleation) and their subsequent evolution (growth, recrystallization, and/or transformation), a vast amount of evidence suggests that the classical view on crystallization is over-simplified. In addition to the monomer-by-monomer (i.e., atoms, ions, or molecules) addition described in the classical theories, the particle attachment has been recognized as one of the most important pathways to inorganic crystallization. These particles range from the ion pairs to well-crystallized nanoparticles, such as amorphous precursors, magic-size clusters, nanocrystals, etc. The complexity of both the free-energy landscapes and reaction kinetics leads to diverse crystallization pathways. While experimental observations clearly demonstrate the non-classical crystallization pathways, many fundamental aspects remain unknown—Particularly the interaction of solution structure, interfacial forces, and particle motion. Thus, a predictive description linking molecular details to ensemble behavior is lacking. As such description develops, long-term interpretations of inorganic crystal formation should be revisited, which is important to broaden the scope of research across various disciplines such as geological events, biomineralization mechanisms, environmental remediation, and the development of environmentally functional materials. Based on several exemplary spotlights, the current state of the art in non-classical nucleation has been firstly illustrated in our review. Specifically, two non-classical nucleation pathways (i.e., the prenucleation clusters (PNCs) and aggregation pathway) in the current crystal research field are summarized. According to the PNCs pathway, PNCs were considered as the stable solute species with chainlike structural that are precursors to nucleation. Once system reaches the equilibrium ion activity product, the change in the chemistry of linkages within PNCs causes PNCs aggregation, as a consequence of nucleus formation. Another non-classical view (aggregation pathway) pointed that the fine crystalline nuclei first form in solution and then aggregate into a larger and more stable nucleus. Besides, the non-classical oriented attachment (OA) and random attachment (RA) growth pathways are also elucidated. OA and RA growth are similar in involving the self-assembly of primary nanocrystals. However, their main difference is the orientation of the crystal lattice at the grain boundary. For RA growth pathway, there is no particular preference for the attachment whereas for the OA growth, there is a common crystallographic alignment of the attachment to occur, which is allowing for continuous crystallographic planes. Finally, the implications and perspective of non-classical crystallization research are proposed. The aim of this review is to guide the readers through the complex world of crystallizing systems, highlighting a new perspective on non-classical crystallization of inorganic materials, which drives a true renaissance in the field and provides completely new perspectives on the underlying crystallization mechanisms. Additionally, through a mechanism-based understanding, we believed that non-classical crystallization processes can be used to produce innovative structures that retain the dimensional properties of their nanoscale building blocks and create materials with enhanced or novel physical and chemical properties.

Three-step nucleation of metal–organic framework nanocrystals

Metal-organic frameworks (MOFs) are crystalline nanoporous materials with great potential for a wide range of industrial applications. Understanding the nucleation and early growth stages of these materials from a solution is critical for their design and synthesis. Despite their importance, the pathways through which MOFs nucleate are largely unknown. Using a combination of in situ liquid-phase and cryogenic transmission electron microscopy, we show that zeolitic imidazolate framework-8 MOF nanocrystals nucleate from precursor solution via three distinct steps: 1) liquid-liquid phase separation into solute-rich and solute-poor regions, followed by 2) direct condensation of the solute-rich region into an amorphous aggregate and 3) crystallization of the aggregate into a MOF. The three-step pathway for MOF nucleation shown here cannot be accounted for by conventional nucleation models and provides direct evidence for the nonclassical nucleation pathways in open-framework materials, suggesting that a solute-rich phase is a common precursor for crystallization from a solution.

Kinetic pathways of crystallization at the nanoscale.

Nucleation and growth are universally important in systems from the atomic to the micrometre scale as they dictate structural and functional attributes of crystals. However, at the nanoscale, the pathways towards crystallization have been largely unexplored owing to the challenge of resolving the motion of individual building blocks in a liquid medium. Here we address this gap by directly imaging the full transition of dispersed gold nanoprisms to a superlattice at the single-particle level. We utilize liquid-phase transmission electron microscopy at low dose rates to control nanoparticle interactions without affecting their motions. Combining particle tracking with Monte Carlo simulations, we reveal that positional ordering of the superlattice emerges from orientational disorder. This method allows us to measure parameters such as line tension and phase coordinates, charting the nonclassical nucleation pathway involving a dense, amorphous intermediate. We demonstrate the versatility of our approach via crystallization of different nanoparticles, pointing the way to more general applications.

Non-classical nucleation pathways revealed by scanning tunneling microscopy of epitaxy of covalent materials

Identifying atomic/molecular mechanism is crucial for understanding crystallization and epitaxial growth and to enable controlled synthesis of high-quality devices and desired crystalline structures. Using scanning tunneling microscopy, we studied early stages of Si epitaxy on a Si(1 1 1) surface mediated by a Pb monolayer. A type of highly mobile magic clusters was observed only when they were trapped at boundary or defect sites. Magic clusters also formed cluster aggregates temporarily. Adding more Si transformed the aggregates into immobile metastable or stable structures. Here we propose a scenario involving concerted chemical reactions of multiple, co-localized magic clusters with the activation energies decreasing with increasing number of clusters. This scenario may be modified to understand nucleation and growth of many covalent materials as well as crystallization in numerous synthetic and natural systems.

Polymorphic transition and nucleation pathway of barium dititanate (BaTi2O5) during crystallization from undercooled liquid

The nucleation pathway plays an important role in vitrification, preparation of glass-ceramic composites and synthesis of metastable materials. In this paper, we studied the nucleation pathway of a novel ferroelectric BaTi2O5 (BT2) during crystallization from undercooled liquid by aerodynamic levitation (ADL) containerless processing and structural analysis. An interesting polymorphic transition of BT2 regulated by the undercooling was observed during the crystallization process: the ferroelectric monoclinic phase (γ-BT2) was fabricated at low undercoolings and the paraelectric orthorhombic metastable phase (β-BT2) was obtained from hypercooled liquid. This polymorphic transition phenomenon corresponds to a non-classical nucleation pathway: metastable β-BT2 preferentially nucleates from undercooled melt and γ-BT2 is generated from β phase by solid-state phase transition. The two-step nucleation pathway stems from the structural heredity between the undercooled liquid and crystals. A stronger structural homology exists between the undercooled melt and β-BT2 than γ-BT2 based on diffraction data and atomic configurations analysis. This structural homology coupled with nucleation barrier calculation was used to elucidate the non-classical nucleation pathway of BT2 crystallization: the similarity of the structural unit (Ti-O polyhedra) between the undercooled liquid and the metastable β-BT2 reduces the nucleation barrier and contributes to the preferential precipitation of β-like clusters. This work reveals the formation route of BT2 from cooling melt, which not only benefits the synthesis and application of this novel functional material but also provides a guideline of the crystallization process of titanates from melt at atomic level.

Coarse-Grained Simulation of CaCO3 Aggregation and Crystallization Made Possible by Nonbonded Three-Body Interactions

Calcium-containing minerals are key model systems for investigating fundamental principles of nucleation and mineral formation both experimentally and by simulation. Due to the rare event character of nucleation, the different dimensions of pre- and postnucleation stages and the possible relevance of nonclassical nucleation pathways, such investigations require advanced sampling techniques and simulation models on a range of resolution levels. To this end, we have developed coarse-grained (CG) models for calcium carbonate. We present a strategy to devise CG parameters, including nonbonded angular-dependent terms such that the model correctly represents the calcite phase along with properties of the constituents in solution. We show how the CG interactions affect the crystallization pathways by stabilizing different intermediates, spanning a wide range of degrees of crystallinity and water content. This will allow us to investigate contributions to crystallization transitions and link them to experimentall...

Physical origin underlying the prenucleation-cluster-mediated nonclassical nucleation pathways for calcium phosphate.

The involvement of prenucleation clusters (PNCs) in crystallization from a supersaturated solution has been recently admitted within the framework of nonclassical nucleation theory; however, little is known about PNCs, at the quantitative level, for their formation mechanism and stability, the new phase formed by them, as well as their impact on nucleation barriers. Herein, using the sophisticated free energy calculations with a cumulative simulation time of over 5 μs, we identify a thermodynamically favored pathway of the PNC-mediated nucleation for calcium phosphate, starting with the ion pair association in solution. We demonstrate that such an ion association occurs not only between cations and anions, but also for the polyatomic species with charges of the same sign, which, in fact, leads to PNC formation via the consecutive coordination of the phosphate ions to calcium. The free energy decomposition calculations illustrate that the water phase is capable to either hinder or promote ion association for the abovementioned processes, and its specific role is intricately related to the characteristics of the hydration shell around calcium ions. The favorable interactions between the highly charged species play a crucial role in stabilizing the PNC complexes and the aggregates formed by PNCs. Furthermore, our present work reveals that the uptake of an extra calcium ion is the first and mandatory step to trigger PNC aggregation into amorphous calcium phosphate (ACP) by eliminating the related free energy barriers. Our theoretical study successfully provides quantitative explanations to a large set of experimental data in the field, which is currently under intense discussions associated with the nonclassical nucleation mechanism. The combination of computational methods developed in our present work offers a feasible and general solution to quantitatively and systematically study ion associations and crystal nucleation/growth in an aqueous solution at the atomic level, which are normally inaccessible to most of the existing experimental acquisitions.

Two-Step to One-Step Nucleation of a Zeolite through a Metastable Gyroid Mesophase.

The importance of nonclassical nucleation pathways in the formation of complex crystals has become apparent in recent years. Nonclassical pathways were unraveled for, among others, the crystallization of proteins, colloids, and clathrates. In those cases, the formation of a metastable fluid with density close to the crystal decreases the crystallization barrier. Recent simulations indicate that mesophases can facilitate the nucleation of zeolites. Here, we use molecular simulations to investigate the role of a gyroid mesophase on the crystallization of a model zeolite from liquid. The nucleation pathway is always nonclassical. At warmer temperatures, the mechanism proceeds in two well-defined steps: nucleation of a metastable gyroid followed by its crystallization into a zeolite. At colder temperatures, the second barrier becomes negligible, and the crystallization occurs in one step. This second scenario is also nonclassical, as the critical nucleus for the crystallization has the structure of the gyroid and seamlessly transforms into a zeolite as it grows past its critical size. To our knowledge, this is the first report of a nonclassical mechanism of crystallization mediated by a mesophase.

General framework for nonclassical nucleation

A great deal of experimental evidence suggests that a wide spectrum of phase transitions occur in a multistage manner via the appearance and subsequent transformation of intermediate metastable states. Such multistage mechanisms cannot be explained within the realm of the classical nucleation framework. Hence, there is a strong need to develop new theoretical tools to explain the occurrence and nature of these ubiquitous intermediate phases. Here we outline a unified and self-consistent theoretical framework to describe both classical and nonclassical nucleation. Our framework provides a detailed explanation of the whole multistage nucleation pathway showing in particular that the pathway involves a single energy barrier and it passes through a dense phase, starting from a low-density initial phase, before reaching the final stable state. Moreover, we demonstrate that the kinetics of matter inside subcritical clusters favors the formation of nucleation clusters with an intermediate density, i.e. nucleation precursors. Remarkably, these nucleation precursors are not associated with a local minimum of the thermodynamic potential, as commonly assumed in previous phenomenological approaches. On the contrary, we find that they emerge due to the competition between thermodynamics and kinetics of cluster formation. Thus, the mechanism uncovered for the formation of intermediate phases can be used to explain recently reported experimental findings in crystallization: up to now such phases were assumed a consequence of some complex energy landscape with multiple energy minima. Using fundamental concepts from kinetics and thermodynamics, we provide a satisfactory explanation for the so-called nonclassical nucleation pathways observed in experiments.

Surface stabilization determines a classical versus non-classical nucleation pathway during particle formation

In the bottom-up synthesis of nanoparticles, the degree of surface stabilization by the surfactant decides a classical or non-classical formation pathway.

Direct observation of liquid pre-crystallization intermediates during the reduction of aqueous tetrachloroaurate by sulfide ions

Phenomena preceding precipitation of gold(i) sulfide in the reaction of aqueous tetrachloroauric acid with sodium sulfide have been studied applying several time-resolved in situ techniques. As can be deduced from UV-vis absorption spectroscopy, soluble species ("pre-nucleation clusters") emerge within several seconds and slightly change with time; the spectra, along with the previous data for the immobilized products, are indicative of disordered matter with Au(I)-S bonding and the gap of about 1.5 eV. In situ tapping-mode atomic force microscopy (AFM) directly imaged "soft" droplet-like species from 20-50 nm to about 200 nm in the lateral size and the continuous film condensed on the highly oriented pyrolytic graphite (HOPG) support. Small-angle X-ray scattering (SAXS) revealed quasi-particles ("liquid clusters") growing to about 12 nm for 30 min, and slowly afterwards. Dynamic light scattering (DLS) was preferentially due to the larger species, although the liquid clusters within 20 nm comprise more than 80% of the total volume of the fluid products. The entities, which exist in solution for many hours before sudden gold sulfide sedimentation, are considered as "dense liquid" intermediates involved in a non-classical nucleation pathway.