Overview: Experimental studies of crystal nucleation: Metals and colloids

A molecular dynamics study on the boundary between homogeneous and heterogeneous nucleation

The large discrepancy among the nucleation kinetics extracted from experimental measurements and computer simulations and the prediction of the classical nucleation theory (CNT) has stimulated intense arguments about its origin in the past decades, which is crucially relevant to the validity of the CNT. In this paper, we investigate the atomistic mechanism of the nucleation in liquid Al in contact with amorphous substrates with atomic-level smooth/rough surfaces, using molecular dynamics (MD) simulations. This study reveals that the slightly distorted local fcc/hcp structures in amorphous substrates with smooth surfaces can promote heterogeneous nucleation through a structural templating mechanism, and on the other hand, homogeneous nucleation will occur at a larger undercooling through a fluctuation mechanism if the surface is rough. Thus, some impurities, previously thought to be impotent, could be activated in the homogeneous nucleation experiments. We further find that the initial growth of the nucleus on smooth surfaces of amorphous substrates is one order of magnitude faster than that in homogeneous nucleation. Both these factors could significantly contribute to the discrepancy in the nucleation kinetics. This study is also supported by a recent study of the synthesis of high-entropy alloy nanoparticles assisted with the liquid metal Ga [Cao et al., Nature 619, 73 (2023)]. In this study, we established that the boundary existed between homogeneous and heterogeneous nucleation, i.e., the structural templating is a general mechanism for heterogeneous nucleation, and in its absence, homogeneous nucleation will occur through the fluctuation mechanism. This study provides an in-depth understanding of the nucleation theory and experiments.

An atomically smooth container: Can the native oxide promote supercooling of liquid gallium?

Metals tend to supercool-that is, they freeze at temperatures below their melting points. In general, supercooling is less favorable when liquids are in contact with nucleation sites such as rough surfaces. Interestingly, bulk gallium (Ga) can significantly supercool, even when it is in contact with heterogeneous surfaces that could provide nucleation sites. We hypothesized that the native oxide on Ga provides an atomically smooth interface that prevents Ga from directly contacting surfaces, and thereby promotes supercooling. Although many metals form surface oxides, Ga is a convenient metal for studying supercooling because its melting point of 29.8°C is near room temperature. Using differential scanning calorimetry (DSC), we show that freezing of Ga with the oxide occurs at a lower temperature (-15.6 ± 3.5°C) than without the oxide (6.9 ± 2.0°C when the oxide is removed by HCl). We also demonstrate that the oxide enhances supercooling via macroscopic observations of freezing. These findings explain why Ga supercools and have implications for emerging applications of Ga that rely on it staying in the liquid state.

In Situ Kinetic Observations on Crystal Nucleation and Growth

Nucleation and growth are critical steps in crystallization, which plays an important role in determining crystal structure, size, morphology, and purity. Therefore, understanding the mechanisms of nucleation and growth is crucial to realize the controllable fabrication of crystalline products with desired and reproducible properties. Based on classical models, the initial crystal nucleus is formed by the spontaneous aggregation of ions, atoms, or molecules, and crystal growth is dependent on the monomer's diffusion and the surface reaction. Recently, numerous in situ investigations on crystallization dynamics have uncovered the existence of nonclassical mechanisms. This review provides a summary and highlights the in situ studies of crystal nucleation and growth, with a particular emphasis on the state-of-the-art research progress since the year 2016, and includes technological advances, atomic-scale observations, substrate- and temperature-dependent nucleation and growth, and the progress achieved in the various materials: metals, alloys, metallic compounds, colloids, and proteins. Finally, the forthcoming opportunities and challenges in this fascinating field are discussed.

Kinetic Phase Diagram for Nucleation and Growth of Competing Crystal Polymorphs in Charged Colloids

We determine the kinetic phase diagram for nucleation and growth of crystal phases in a suspension of charged colloids. Exploiting the seeding approach in extensive simulations, we calculate nucleation barrier heights for face-centered cubic (fcc) and body-centered cubic (bcc) phases for varying screening lengths and supersaturations. We determine for the entire metastable fluid region the crystal polymorph with the lowest nucleation barrier, and find a regime close to the triple point where metastable bcc can form due to a lower nucleation barrier, even though fcc is the stable phase. For higher supersaturation, we find that the difference in barrier heights decreases and we observe a mix of hexagonal close-packed, fcc, and bcc structures in the growth of crystalline seeds as well as in spontaneously formed crystals. Our kinetic phase diagram rationalizes the different crystallization mechanisms observed in previous work.

Direct Measurements of Surface Strain-Mediated Lateral Interactions between Adsorbates in Colloidal Heteroepitaxy

Surface strain can alter the dynamics of adsorbates, and often, the adsorbates themselves induce and interact via their surface strain fields. In epitaxy, such strain-mediated effects get further compounded when a misfit strain exists due to lattice mismatch between the growing film and substrate. Here, we carry out particle-resolved imaging of heteroepitaxial growth of multilayer colloidal films where the particles interact via a short-range attraction. Surprisingly, although the misfit strain relaxed systematically with film thickness, the adcolloid diffusivity was nonmonotonic. We show that this nonmonotonicity stems from the competition between the spatial extent of self-induced in-layer strain and the short interaction range. Importantly, we provide direct evidence for long-ranged strain-mediated interactions between adsorbates and show that it alters the growing film's morphology.

Role of diffusion in crystallization of hard-sphere colloids

Vital for a variety of industries, colloids also serve as an excellent model to probe phase transitions at the individual particle level. Despite extensive studies, origins of the glass transition in hard-sphere colloids discovered about 30 y ago remain elusive. Results of our numerical simulations and asymptotic analysis suggest that cessation of long-time particle diffusivity does not suppress crystallization of a metastable liquid-phase hard-sphere colloid. Once a crystallite forms, its growth is then controlled by the particle diffusion in the depletion zone surrounding the crystallite. Using simulations, we evaluate the solid-liquid interface mobility from data on colloidal crystallization in terrestrial and microgravity experiments and demonstrate that there is no drastic difference between the respective mobility values. The insight into the effect of vanishing particle mobility and particle sedimentation on crystallization of colloids will help engineer colloidal materials with controllable structure.

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.

Identification of critical nuclei in the rapid solidification via configuration heredity

The identification and characterization of critical nuclei is a long-standing issue in the rapid solidification of metals and alloys. An ambiguous description for their sizes and shapes used to lead to an overestimation or underestimation of homogeneous nucleation ratesITin the framework of classical nucleation theory (CNT). In this paper, a unique method able to distinguish the critical nucleus from numerous embryos is put forward on the basis of configuration heredities of clusters during rapid solidifications. As this technique is applied to analyze the formation and evolution of various fcc-Al single crystal clusters in a large-scale molecular dynamics simulation system, it is found that the sizen_cand geometrical configuration of critical nuclei as well as their liquid-solid interfacial structure can be determined directly. For the present deep super-cooled system with an undercooling ofTm=0.42Tmcal, the average size of critical nuclei is demonstrated to benc̄≈26, but most of which are non-spherical lamellae. Also, their liquid-solid interfaces are revealed to be not an fcc-liquid duplex-phase interface but an fcc/hcp-liquid multi-phase structure. These findings shed some lights on the CNT, and a good agreement with previous simulations and experiments inITindicates this technique can be used to explore the early-stage of nucleation from atomistic levels.

Effect of prenucleation clusters arising from liquid-liquid phase transition on nucleation in a one-component charged colloidal suspension

It is generally thought that liquid-liquid phase transition (LLPT) in a one-component suspension never or only very rarely happens. If this were true, it would contradict the two nonclassical nucleation models building on either liquid droplets or prenucleation clusters (PNCs). One way out of this paradox is to suppose that LLPT occurs in pathway to nucleation. This study specifies the physical parameters of charged colloids which can bring out LLPT according to the consistent prediction of the DLVO (Derjaguin-Landau-Verwey-Overbeek) potential and the Sogami potential about long-range attraction, and reveals that surface charge is not the only factor to affect attraction, size also plays an essential role. For the first time, we follow exactly the evolution from LLPT to nucleation in which PNCs participate, and characterize pre-ordered liquid-like property of the PNCs and their particle-like and template effect by optical microscopy and light scattering. Furthermore, it is found that when the configuration of the PNCs is changed by a little salt, the pathway to nucleation is altered significantly. Our results demystify LLPT in a one-component suspension and dissolve the paradox, thus extending the range of applicability of the nonclassical nucleation models.

Simulated microgravity in the ring-sheared drop

The ring-sheared drop is a module for the International Space Station to study sheared fluid interfaces and their influence on amyloid fibril formation. A 2.54-cm diameter drop is constrained by a stationary sharp-edged ring at some latitude and sheared by the rotation of another ring in the other hemisphere. Shearing motion is conveyed primarily by the action of surface shear viscosity. Here, we simulate microgravity in the laboratory using a density-matched liquid surrounding the drop. Upon shearing, the drop's deformation away from spherical is found to be a result of viscous and inertial forces balanced against the capillary force. We also present evidence that the deformation increases with increasing surface shear viscosity.

Influence of Softness on the Stability of Binary Colloidal Crystals

Mixtures of two types of nanoparticles can self-assemble into a wide variety of binary colloidal crystals (also called binary nanoparticle superlattices), which are interesting for their structural diversity and potential applications. Although so-called packing models-which usually treat the particles as "hard" with only excluded volume interactions-seem to explain many reported dense crystalline phases, these models often fail to predict the right structure. Here, we examine the role of soft repulsive interparticle interactions on binary colloidal crystals comprising two sizes of spherical particles; such "softness" can arise due to ligand shells or screened electrostatics. We determine the ground state phase diagram of binary systems of particles interacting with an additive inverse power law potential using a basin hopping algorithm to calculate the enthalpy of an extremely large pool of candidate structures. We find that a surprisingly small amount of softness can destabilize dense packings in favor of less densely packed structures, which provides further evidence that considerations beyond packing are necessary for describing many of the observed phases of binary colloidal crystals. Importantly, we find that several of the phases stabilized by softness, which are characterized by relatively few interparticle contacts and a tendency for local icosahedral order, are more likely to be observed experimentally than those predicted by packing models. We also report a previously unknown dense AB₄ phase and conduct free energy calculations to examine how the stability of several crystals will vary with temperature. Our results further our understanding of why particular binary colloidal crystals form and will be useful as a reference for experimentalists working with softly repulsive colloids.

Melting of superheated molecular crystals

Melting dynamics of micrometer scale, polycrystalline samples of isobutane, dimethyl ether, methyl benzene, and 2-propanol were investigated by fast scanning calorimetry. When films are superheated with rates in excess of 10⁵ K s^-1, the melting process follows zero-order, Arrhenius-like kinetics until approximately half of the sample has transformed. Such kinetics strongly imply that melting progresses into the bulk via a rapidly moving solid-liquid interface that is likely to originate at the sample's surface. Remarkably, the apparent activation energies for the phase transformation are large; all exceed the enthalpy of vaporization of each compound and some exceed it by an order of magnitude. In fact, we find that the crystalline melting kinetics are comparable to the kinetics of dielectric α-relaxation in deeply supercooled liquids. Based on these observations, we conclude that the rate of non-isothermal melting for superheated, low-molecular-weight crystals is limited by constituent diffusion into an abnormally dense, glass-like, non-crystalline phase.

Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it

Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.

Free-energy barriers for crystal nucleation from fluid phases

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows us to extract the surface free energy of the nucleus. Neither the knowledge of the (in general nonspherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for colloid-polymer mixtures, which form face-centered cubic colloidal crystals. For a polymer to colloid size ratio of 0.15, the colloid packing fraction in the fluid phase can be varied from melt values to zero by the variation of an effective attractive potential between the colloids. It is found that the approximation of spherical crystal nuclei often underestimates actual nucleation barriers significantly. Nucleation barriers are found to scale as ΔF^{*}=(4π/3)^{1/3}γ[over ¯](V^{*})^{2/3}+const with the nucleus volume V^{*}, and the effective surface tension γ[over ¯] that accounts implicitly for the nonspherical shape can be precisely estimated.

Formation of Cellular Structure on Metastable Solidification of Undercooled Eutectic CoSi-62 at. %

The relationship between emissivity, delay time, and surface growth for metastable solidification of CoSi-62 at. % eutectic alloys is reported from undercooling experiments conducted using electrostatic levitation. A fraction of the undercooled melt is first solidified to CoSi2 with subsequent nucleation in the mushy-zone of CoSi after an observed delay time. During this double recalescence event, the temperature of the secondary recalescence exceeds the liquidus, indicating that the spectral emissivity has changed. This emissivity change increases with longer delay times during solidification and is linked to the growth of cellular structure on the sample surface. Density measurements showed that the cellular structure begins to grow rapidly at a certain time during metastable solidification. This phenomenon is likely associated with the constitutional undercooling of the remaining melt.