James J. De Yoreo

Crystallization by particle attachment in synthetic, biogenic, and geologic environments

Growing crystals by attaching particles Crystals grow in a number a ways, including pathways involving the assembly of other particles and multi-ion complexes. De Yoreo et al. review the mounting evidence for these nonclassical pathways from new observational and computational techniques, and the thermodynamic basis for these growth mechanisms. Developing predictive models for these crystal growth and nucleation pathways will improve materials synthesis strategies. These approaches will also improve fundamental understanding of natural processes such as biomineralization and trace element cycling in aquatic ecosystems. Science, this issue 10.1126/science.aaa6760 Materials nucleate and grow by the assembly of small particles and multi-ion complexes. BACKGROUND Numerous lines of evidence challenge the traditional interpretations of how crystals nucleate and grow in synthetic and natural systems. In contrast to the monomer-by-monomer addition described in classical models, crystallization by addition of particles, ranging from multi-ion complexes to fully formed nanocrystals, is now recognized as a common phenomenon. This diverse set of pathways results from the complexity of both the free-energy landscapes and the reaction dynamics that govern particle formation and interaction. Whereas experimental observations clearly demonstrate crystallization by particle attachment (CPA), many fundamental aspects remain unknown—particularly the interplay of solution structure, interfacial forces, and particle motion. Thus, a predictive description that connects molecular details to ensemble behavior is lacking. As that description develops, long-standing interpretations of crystal formation patterns in synthetic systems and natural environments must be revisited. Here, we describe the current understanding of CPA, examine some of the nonclassical thermodynamic and dynamic mechanisms known to give rise to experimentally observed pathways, and highlight the challenges to our understanding of these mechanisms. We also explore the factors determining when particle-attachment pathways dominate growth and discuss their implications for interpreting natural crystallization and controlling nanomaterials synthesis. ADVANCES CPA has been observed or inferred in a wide range of synthetic systems—including oxide, metallic, and semiconductor nanoparticles; and zeolites, organic systems, macromolecules, and common biomineral phases formed biomimetically. CPA in natural environments also occurs in geologic and biological minerals. The species identified as being responsible for growth vary widely and include multi-ion complexes, oligomeric clusters, crystalline or amorphous nanoparticles, and monomer-rich liquid droplets. Particle-based pathways exceed the scope of classical theories, which assume that a new phase appears via monomer-by-monomer addition to an isolated cluster. Theoretical studies have attempted to identify the forces that drive CPA, as well as the thermodynamic basis for appearance of the constituent particles. However, neither a qualitative consensus nor a comprehensive theory has emerged. Nonetheless, concepts from phase transition theory and colloidal physics provide many of the basic features needed for a qualitative framework. There is a free-energy landscape across which assembly takes place and that determines the thermodynamic preference for particle structure, shape, and size distribution. Dynamic processes, including particle diffusion and relaxation, determine whether the growth process follows this preference or another, kinetically controlled pathway. OUTLOOK Although observations of CPA in synthetic systems are reported for diverse mineral compositions, efforts to establish the scope of CPA in natural environments have only recently begun. Particle-based mineral formation may have particular importance for biogeochemical cycling of nutrients and metals in aquatic systems, as well as for environmental remediation. CPA is poised to provide a better understanding of biomineral formation with a physical basis for the origins of some compositions, isotopic signatures, and morphologies. It may also explain enigmatic textures and patterns found in carbonate mineral deposits that record Earth’s transition from an inorganic to a biological world. A predictive understanding of CPA, which is believed to dominate solution-based growth of important semiconductor, oxide, and metallic nanomaterials, promises advances in nanomaterials design and synthesis for diverse applications. With a mechanism-based understanding, CPA processes can be exploited to produce hierarchical structures that retain the size-dependent attributes of their nanoscale building blocks and create materials with enhanced or novel physical and chemical properties. Major gaps in our understanding of CPA. Particle attachment is influenced by the structure of solvent and ions at solid-solution interfaces and in confined regions of solution between solid surfaces. The details of solution and solid structure create the forces that drive particle motion. However, as the particles move, the local structure and corresponding forces change, taking the particles from a regime of long-range to short-range interactions and eventually leading to particle-attachment events. Field and laboratory observations show that crystals commonly form by the addition and attachment of particles that range from multi-ion complexes to fully formed nanoparticles. The particles involved in these nonclassical pathways to crystallization are diverse, in contrast to classical models that consider only the addition of monomeric chemical species. We review progress toward understanding crystal growth by particle-attachment processes and show that multiple pathways result from the interplay of free-energy landscapes and reaction dynamics. Much remains unknown about the fundamental aspects, particularly the relationships between solution structure, interfacial forces, and particle motion. Developing a predictive description that connects molecular details to ensemble behavior will require revisiting long-standing interpretations of crystal formation in synthetic systems, biominerals, and patterns of mineralization in natural environments.

In situ TEM imaging of CaCO3 nucleation reveals coexistence of direct and indirect pathways

Watching nucleation pathways in calcite The initial stage of crystallization, the formation of nuclei, is a critical process, but because of the length and time scales involved, is hard to observe. Nielsen et al. explored the crystallization of calcium carbonate, a well-studied material but one with multiple nucleation theories. Different calcium and carbonate solutions were mixed inside a fluid cell and imaged using a liquid cell inside a transmission electron microscope. Competing pathways operated during nucleation, with both the direct association of ions into nuclei from solution and the transformation of amorphous calcium carbonate into and between different crystalline polymorphs. Science, this issue p. 1158 Calcium carbonate crystal nucleation occurs via direct formation from solution and transformation from less stable phases. Mechanisms of nucleation from electrolyte solutions have been debated for more than a century. Recent discoveries of amorphous precursors and evidence for cluster aggregation and liquid-liquid separation contradict common assumptions of classical nucleation theory. Using in situ transmission electron microscopy (TEM) to explore calcium carbonate (CaCO3) nucleation in a cell that enables reagent mixing, we demonstrate that multiple nucleation pathways are simultaneously operative, including formation both directly from solution and indirectly through transformation of amorphous and crystalline precursors. However, an amorphous-to-calcite transformation is not observed. The behavior of amorphous calcium carbonate upon dissolution suggests that it encompasses a spectrum of structures, including liquids and solids. These observations of competing direct and indirect pathways are consistent with classical predictions, whereas the behavior of amorphous particles hints at an underlying commonality among recently proposed precursor-based mechanisms.

Calcium carbonate nucleation driven by ion binding in a biomimetic matrix revealed by in situ electron microscopy

The characteristic shapes, structures and properties of biominerals arise from their interplay with a macromolecular matrix. The developing mineral interacts with acidic macromolecules, which are either dissolved in the crystallization medium or associated with insoluble matrix polymers, that affect growth habits and phase selection or completely inhibit precipitation in solution. Yet little is known about the role of matrix-immobilized acidic macromolecules in directing mineralization. Here, by using in situ liquid-phase electron microscopy to visualize the nucleation and growth of CaCO3 in a matrix of polystyrene sulphonate (PSS), we show that the binding of calcium ions to form Ca-PSS globules is a key step in the formation of metastable amorphous calcium carbonate (ACC), an important precursor phase in many biomineralization systems. Our findings demonstrate that ion binding can play a significant role in directing nucleation, independently of any control over the free-energy barrier toxa0nucleation.

Direct observation of mineral–organic composite formation reveals occlusion mechanism

Manipulation of inorganic materials with organic macromolecules enables organisms to create biominerals such as bones and seashells, where occlusion of biomacromolecules within individual crystals generates superior mechanical properties. Current understanding of this process largely comes from studying the entrapment of micron-size particles in cooling melts. Here, by investigating micelle incorporation in calcite with atomic force microscopy and micromechanical simulations, we show that different mechanisms govern nanoscale occlusion. By simultaneously visualizing the micelles and propagating step edges, we demonstrate that the micelles experience significant compression during occlusion, which is accompanied by cavity formation. This generates local lattice strain, leading to enhanced mechanical properties. These results give new insight into the formation of occlusions in natural and synthetic crystals, and will facilitate the synthesis of multifunctional nanocomposite crystals.

Nucleation Pathways in Electrolyte Solutions

The nucleation of a solid crystalline phase from an electrolyte solution is a long-standing subject of scientific investigations; however, neither pathways nor rates can be confidently predicted from classical nucleation theory (CNT). Moreover, results from recent experimental and theoretical studies call into question underlying assumptions of that theory, such as the nature of the species that form a stable nucleus and whether that process occurs directly from solution or following a liquid–liquid separation process. Here we provide a framework for how to interpret current investigations of solid formation from electrolyte solutions by reviewing the findings of some recent investigations. These experimental and computational studies probe nucleation pathways and rates in both homogeneous and heterogeneous environments and the processes of liquid–liquid phase separation and cluster aggregation.

Liquid Phase TEM Investigations of Crystal Nucleation, Growth, and Transformation

The scarcity of high-resolution, in situ tools has left many fundamental questions regarding crystallization processes unanswered. Recent years have seen many advances in transmission electron microscopy (TEM) approaches that allow TEM observations of liquid environments. These liquid phase TEM techniques provide an in situ platform for investigating the early events in materials formation and understanding the mechanisms by which crystals develop. In this chapter, we provide an overview of the liquid phase TEM experimental platforms and discuss recent studies that use the technique to address open questions in crystallization. We first highlight liquid phase TEM investigations into the calcium carbonate system, where the technique provides insights into the formation pathways that take the mineral from its solvated state to one of various solid phases and the effect that an organic additive can have on such processes. In the following section, we discuss studies of metal nanoparticle formation that investigate the mechanisms of nucleation and growth from a precursor solution, as well as the development into faceted nanocrystals in the presence of an organic ligand. We close the chapter with a discussion of areas for future development that would broaden the utility of liquid phase TEM.

A classical view on nonclassical nucleation

Significance Nucleation is the process by which constituent building blocks first assemble to form a new substance. In the case of mineral formation from initially free ions in solution, the emergence of intermediary phases often determines the thermodynamics and kinetics of formation for the most stable phase. Our work on CaCO3 mineralization reevaluates a topic of intense discussion: Can nucleation be explained by theories established over a century ago, or should new physical concepts, as recently proposed, be adopted? Our data show that classical theories can indeed be used to describe complex mechanisms of crystallization. In addition, we provide information about the properties of intermediate phases, which will aid in the design of additives to control mineralization. Understanding and controlling nucleation is important for many crystallization applications. Calcium carbonate (CaCO3) is often used as a model system to investigate nucleation mechanisms. Despite its great importance in geology, biology, and many industrial applications, CaCO3 nucleation is still a topic of intense discussion, with new pathways for its growth from ions in solution proposed in recent years. These new pathways include the so-called nonclassical nucleation mechanism via the assembly of thermodynamically stable prenucleation clusters, as well as the formation of a dense liquid precursor phase via liquid–liquid phase separation. Here, we present results from a combined experimental and computational investigation on the precipitation of CaCO3 in dilute aqueous solutions. We propose that a dense liquid phase (containing 4–7 H2O per CaCO3 unit) forms in supersaturated solutions through the association of ions and ion pairs without significant participation of larger ion clusters. This liquid acts as the precursor for the formation of solid CaCO3 in the form of vaterite, which grows via a net transfer of ions from solution according to z Ca2+ + z CO32− → z CaCO3. The results show that all steps in this process can be explained according to classical concepts of crystal nucleation and growth, and that long-standing physical concepts of nucleation can describe multistep, multiphase growth mechanisms.

Supersaturated calcium carbonate solutions are classical

Ions and ion pairs are the species that lead to CaCO3 nucleation. Mechanisms of CaCO3 nucleation from solutions that depend on multistage pathways and the existence of species far more complex than simple ions or ion pairs have recently been proposed. Herein, we provide a tightly coupled theoretical and experimental study on the pathways that precede the initial stages of CaCO3 nucleation. Starting from molecular simulations, we succeed in correctly predicting bulk thermodynamic quantities and experimental data, including equilibrium constants, titration curves, and detailed x-ray absorption spectra taken from the supersaturated CaCO3 solutions. The picture that emerges is in complete agreement with classical views of cluster populations in which ions and ion pairs dominate, with the concomitant free energy landscapes following classical nucleation theory.

The energetics of prenucleation clusters in lattice solutions

According to classical nucleation theory, nucleation from solution involves the formation of small atomic clusters. Most formulations of classical nucleation use continuum droplet approximations to describe the properties of these clusters. However, the discrete atomic nature of very small clusters may cause deviations from these approximations. Here, we present a self-consistent framework for describing the nature of these deviations. We use our framework to investigate the formation of polycube atomic clusters on a cubic lattice, for which we have used combinatoric data to calculate the thermodynamic properties of clusters with 17 atoms or less. We show that the classical continuum droplet model emerges as a natural approach to describe the free energy of small clusters, but with a size-dependent surface tension. However, this formulation only arises if an appropriate site-normalized definition is adopted for the free energy of formation. These results are independently confirmed through the use of Monte Carlo calculations. Our results show that clusters formed from sparingly soluble materials (μM solubility range) tend to adopt compact configurations that minimize the solvent-solute interaction energy. As a consequence, there are distinct minima in the cluster-size-energy landscape that correspond to especially compact configurations. Conversely, highly soluble materials (1M) form clusters with expanded configurations that maximize configurational entropy. The effective surface tension of these clusters tends to smoothly and systematically decrease as the cluster size increases. However, materials with intermediate solubility (1 mM) are found to have a balanced behavior, with cluster energies that follow the classical droplet scaling laws remarkably well.

Trends in mica–mica adhesion reflect the influence of molecular details on long-range dispersion forces underlying aggregation and coalignment

Significance Crystal growth through nanoparticle assembly appears to be a common phenomenon in synthetic, biological, and geochemical settings, and can lead to formation of hierarchical structures with unique properties tied to this nonclassical assembly process, but the underlying forces driving assembly are poorly understood. Using custom-made single-crystal atomic force microscopy tips, we measured the adhesion force between mica surfaces in the solvent-separate regime as a function of crystallographic orientation and solution parameters. The observed dependencies are predicted using a continuum description of the electrostatic and electrodynamic interactions that includes short-range molecular details. The findings show that the attractive interaction driving nanoparticle assembly and orientation results from the coupling between the short-range solution response and the long-range van der Waals interactions. Oriented attachment of nanocrystalline subunits is recognized as a common crystallization pathway that is closely related to formation of nanoparticle superlattices, mesocrystals, and other kinetically stabilized structures. Approaching particles have been observed to rotate to achieve coalignment while separated by nanometer-scale solvent layers. Little is known about the forces that drive coalignment, particularly in this “solvent-separated” regime. To obtain a mechanistic understanding of this process, we used atomic-force-microscopy-based dynamic force spectroscopy with tips fabricated from oriented mica to measure the adhesion forces between mica (001) surfaces in electrolyte solutions as a function of orientation, temperature, electrolyte type, and electrolyte concentration. The results reveal an ∼60° periodicity as well as a complex dependence on electrolyte concentration and temperature. A continuum model that considers the competition between electrostatic repulsion and van der Waals attraction, augmented by microscopic details that include surface separation, water structure, ion hydration, and charge regulation at the interface, qualitatively reproduces the observed trends and implies that dispersion forces are responsible for establishing coalignment in the solvent-separated state.