Diffusive and martensitic nucleation kinetics in solid-solid transitions of colloidal crystals

Rational Phase Control in the Synthesis of Cobalt Sulfides

A library of substituted thioureas was used as sulfur reagents in the synthesis of cobalt sulfides. The substitution pattern of the thioureas controls the decomposition rate of precursors into sulfur monomers and thereby aids in the exploration of decomposition kinetics on cobalt sulfide-phase formation, including phase-pure jaipurite (CoS), cobalt pentlandite (Co8S9), linnaeite (Co3S4), and cattierite (CoS2). We hypothesize that the available transformation pathways between phases during synthesis are dictated by the approximate ccp or hcp stacking of the sulfur lattice. Through gaining a complex understanding of the cobalt sulfide crystal system, phase-pure syntheses of all four naturally occurring crystalline structures in the cobalt sulfide system were achieved.

Direct observation of phase transitions in truncated tetrahedral microparticles under quasi-2D confinement

Colloidal crystals are used to understand fundamentals of atomic rearrangements in condensed matter and build complex metamaterials with unique functionalities. Simulations predict a multitude of self-assembled crystal structures from anisotropic colloids, but these shapes have been challenging to fabricate. Here, we use two-photon lithography to fabricate Archimedean truncated tetrahedrons and self-assemble them under quasi-2D confinement. These particles self-assemble into a hexagonal phase under an in-plane gravitational potential. Under additional gravitational potential, the hexagonal phase transitions into a quasi-diamond two-unit basis. In-situ imaging reveal this phase transition is initiated by an out-of-plane rotation of a particle at a crystalline defect and causes a chain reaction of neighboring particle rotations. Our results provide a framework of studying different structures from hard-particle self-assembly and demonstrates the ability to use confinement to induce unusual phases.

Phase Reentrances and Solid Deformations in Confined Colloidal Crystals

A simple geometric constraint often leads to novel, complex crystalline phases distinct from the bulk. Using thin-film charge colloidal crystals, a model system with tunable interactions, we study the effects of geometric constraints. Through a combination of experiments and simulations, we systematically explore phase reentrances and solid deformation modes concerning geometrical confinement strength, identifying two distinct categories of phase reentrances below a characteristic layer number, N_{c}: one for bcc bulk-stable and another for fcc bulk-stable systems. We further verify that the dominant thermodynamic origin is the nonmonotonic dependence of solids' free energy on the degree of spatial confinement. Moreover, we discover transitions in solid deformation modes between interface-energy and bulk-energy dominance: below a specific layer number, N_{k}, geometric constraints generate unique soft deformation modes adaptive to confinement. These findings on the N-dependent thermodynamic and kinetic behaviors offer fresh insights into understanding and manipulating thin-film crystal structures.

In situ observation of coalescence of nuclei in colloidal crystal-crystal transitions

Coalescence of nuclei in phase transitions significantly influences the transition rate and the properties of product materials, but these processes occur rapidly and are difficult to observe at the microscopic scale. Here, we directly image the coalescence of nuclei with single particle resolution during the crystal-crystal transition from a multilayer square to triangular lattices. The coalescence process exhibits three similar stages across a variety of scenarios: coupled growth of two nuclei, their attachment, and relaxation of the coalesced nucleus. The kinetics vary with nucleus size, interface, and lattice orientation; the kinetics include acceleration of nucleus growth, small nucleus liquefaction, and generation/annihilation of defects. Related mechanisms, such as strain induced by nucleus growth and the lower energy of liquid-crystal versus crystal-crystal interfaces, appear to be common to both atomic and colloidal crystals.

Lithium crystallization at solid interfaces

Understanding the electrochemical deposition of metal anodes is critical for high-energy rechargeable batteries, among which solid-state lithium metal batteries have attracted extensive interest. A long-standing open question is how electrochemically deposited lithium-ions at the interfaces with the solid-electrolytes crystalize into lithium metal. Here, using large-scale molecular dynamics simulations, we study and reveal the atomistic pathways and energy barriers of lithium crystallization at the solid interfaces. In contrast to the conventional understanding, lithium crystallization takes multi-step pathways mediated by interfacial lithium atoms with disordered and random-closed-packed configurations as intermediate steps, which give rise to the energy barrier of crystallization. This understanding of multi-step crystallization pathways extends the applicability of Ostwald's step rule to interfacial atom states, and enables a rational strategy for lower-barrier crystallization by promoting favorable interfacial atom states as intermediate steps through interfacial engineering. Our findings open rationally guided avenues of interfacial engineering for facilitating the crystallization in metal electrodes for solid-state batteries and can be generally applicable for fast crystal growth.

Discrete breathers in square lattices from delocalized nonlinear vibrational modes

Standing and moving discrete breathers (or equally, intrinsic localized modes) in a square β-Fermi-Pasta-Ulam-Tsingou lattice are obtained by applying localizing functions to the delocalized nonlinear vibrational modes (DNVMs) found earlier by Ryabov and Chechin. The initial conditions used in our study do not correspond to exact spatially localized solutions, but make it possible to obtain long-lived quasibreathers. The approach employed in this work can easily be used to search for quasibreathers in three-dimensional crystal lattices, for which DNVMs with frequencies outside the phonon spectrum are known.

Internal-stress-induced solid-solid transition involving orientational domains of anisotropic particles

Colloidal particles with anisotropic interaction, such as Janus particles, are important model systems for anisotropic atoms and molecules. Janus particles in a single crystal can rotate collectively and form polycrystalline orientational domains as the temperature increases, while the lattice structure in the translational degree of freedom is preserved. Such an unusual solid-solid transition preserves the long-range translational order but loses the orientational order, and its mechanism is unclear. We find that the transition is induced by internal strains and the orientation-position coupling plays an essential role in the transition. We explain the mechanism using the anisotropic elasticity theory and derive the transition condition and the directions of the domain boundaries by analyzing the strain energy and the stress. The results of the molecular dynamics simulation are consistent with the theoretical analysis. Such a transition mechanism can exist in other anisotropic particle systems.

Multistep nucleation visualized during solid-state crystallization

Mechanisms of nucleation have been debated for more than a century, despite successes of classical nucleation theory. The nucleation process has been recently argued as involving a nonclassical mechanism (the "two-step" mechanism) in which an intermediate step occurs before the formation of a nascent ordered phase. However, a thorough understanding of this mechanism, in terms of both microscopic kinetics and thermodynamics, remains experimentally challenging. Here, in situ observations using transmission electron microscopy on a solid-state nucleation case indicate that early-stage crystallization can follow the non-classical pathway, yet proceed via a more complex manner in which multiple metastable states precede the emergence of a stable nucleus. The intermediate steps were sequentially isolated as spinodal decomposition of amorphous precursor, mass transport and structural oscillations between crystalline and amorphous states. Our experimental and theoretical analyses support the idea that the energetic favorability is the driving force for the observed sequence of events. Due to the broad applicability of solid-state crystallization, the findings of this study offer new insights into modern nucleation theory and a potential avenue for materials design.

Self-Assembly of Model Triblock Janus Colloidal Particles in Two Dimensions

A simplified two-dimensional effective-solvent model of triblock Janus particles, consisting of three interaction sites in a linear configuration, a core particle, and two particles modeling the attractive patches at the poles, is developed to study the mechanism of nucleation and self-assembly in triblock Janus particles. The potential energy parameters are tuned against phase transition temperatures and free energy barriers to the nucleation of crystalline phases, calculated from our previous detailed model of Janus particles. Vapor-liquid equilibria and critical temperatures are calculated by grand-canonical molecular dynamics simulations for particles of different patch widths. With metadynamics, phase equilibria, mechanism of nucleation, and free energy barriers to nucleation are investigated. The minimum free energy path to nucleation indicates two steps. The first step, with a higher free energy increase, consists of the densification of the fluid into a disordered cluster. In the second step, of a lower free energy barrier, the inner particles of the disordered cluster reorient to form a crystalline nucleus. This two-step mechanism of nucleation of a kagome lattice is in complete agreement with the experiment and with our previous simulations using a detailed model of Janus particles. Large systems at a slight supersaturation generate multiple crystalline domains, which are misaligned at the grain boundaries. In complete agreement with the experiment and with previous simulation results, we observe a two-step mechanism for crystal growth: melting of the smaller (less stable) crystallites to a fluid followed by recrystallization at the surface of neighboring bigger (more stable) crystallites. A comparison of the present softer modeling of a Janus particle with harder models in the literature for self-assembly of Janus particles indicates that softer potentials stabilize open lattices (e.g., kagome) more than dense lattices (e.g., hexagonal). Also, experimental locations of phase transition points and barrier heights to nucleation are better reproduced by the present model than by the existing simple models.

Mean-field model of melting in superheated crystals based on a single experimentally measurable order parameter

Melting is one of the most studied phase transitions important for atomic, molecular, colloidal, and protein systems. However, there is currently no microscopic experimentally accessible criteria that can be used to reliably track a system evolution across the transition, while providing insights into melting nucleation and melting front evolution. To address this, we developed a theoretical mean-field framework with the normalised mean-square displacement between particles in neighbouring Voronoi cells serving as the local order parameter, measurable experimentally. We tested the framework in a number of colloidal and in silico particle-resolved experiments against systems with significantly different (Brownian and Newtonian) dynamic regimes and found that it provides excellent description of system evolution across melting point. This new approach suggests a broad scope for application in diverse areas of science from materials through to biology and beyond. Consequently, the results of this work provide a new guidance for nucleation theory of melting and are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Revealing thermally-activated nucleation pathways of diffusionless solid-to-solid transition

Solid-to-solid transitions usually occur via athermal nucleation pathways on pre-existing defects due to immense strain energy. However, the extent to which athermal nucleation persists under low strain energy comparable to the interface energy, and whether thermally-activated nucleation is still possible are mostly unknown. To address these questions, the microscopic observation of the transformation dynamics is a prerequisite. Using a charged colloidal system that allows the triggering of an fcc-to-bcc transition while enabling in-situ single-particle-level observation, we experimentally find both athermal and thermally-activated pathways controlled by the softness of the parent crystal. In particular, we reveal three new transition pathways: ingrain homogeneous nucleation driven by spontaneous dislocation generation, heterogeneous nucleation assisted by premelting grain boundaries, and wall-assisted growth. Our findings reveal the physical principles behind the system-dependent pathway selection and shed light on the control of solid-to-solid transitions through the parent phase's softness and defect landscape.

Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice

A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular β-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular β-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.

Oscillatory shear-induced bcc-fcc martensitic transformation in a colloidal suspension with long-range repulsive interactions

We perform non-equilibrium Brownian dynamics simulations to investigate the out-of-equilibrium phase behavior of a suspension of charged colloids under external oscillatory shear. We independently vary the frequency f and the maximum strain amplitude γ_max of the oscillations and map out an out-of-equilibrium phase diagram in the f-γ_max plane. Similar to what has been observed in earlier studies on colloidal hard spheres, we find the formation of a twinned face-centered-cubic phase in a specific range of γ_max, which displays a martensitic transition to a body-centered-cubic crystal within half of the oscillation cycle. We provide a comprehensive analysis of these structures and show how the system transforms from one to the other. We also report evidence of a sliding layer phase and a string phase.

Mechanisms of Nucleation and Solid-Solid-Phase Transitions in Triblock Janus Assemblies

A model, including the chemical details of core nanoparticles as well as explicit surface charges and hydrophobic patches, of triblock Janus particles is employed to simulate nucleation and solid-solid phase transitions in two-dimensional layers. An explicit solvent and a substrate are included in the model, and hydrodynamic and many-body interactions were taken into account within many-body dissipative particle dynamics simulation. In order not to impose a mechanism a priori, we performed free (unbiased) simulations, leaving the system the freedom to choose its own pathways. In agreement with the experiment and previous biased simulations, a two-step mechanism for the nucleation of a kagome lattice from solution was detected. However, a distinct feature of the present unbiased versus biased simulations is that multiple nuclei emerge from the solution; upon their growth, the aligned and misaligned facets at the grain boundaries are introduced into the system. The liquid-like particles trapped between the neighboring nuclei connect them together. A mismatch in the symmetry planes of neighboring nuclei hinders the growth of less stable (smaller) nuclei. Unification of such nuclei at the grain boundaries of misaligned facets obeys a two-step mechanism: melting of the smaller nuclei, followed by subsequent nucleation of liquid-like particles at the interface of bigger neighboring nuclei. Besides, multiple postcritical nuclei are formed in the simulation box; the growth of some of which stops due to introduction of a strain in the system. Such an incomplete nucleation/growth mechanism is in complete agreement with the recent experiments. The solid-solid (hexagonal-to-kagome) phase transition, at weak superheatings, obeys a two-step mechanism: a slower step (formation of a liquid droplet), followed by a faster step (nucleation of kagome from the liquid droplet).

Absence of crystals in the phase behavior of hollow microgels

Solutions of microgels have been widely used as model systems to gain insight into atomic condensed matter and complex fluids. We explore the thermodynamic phase behavior of hollow microgels, which are distinguished from conventional colloids by a central cavity. Small-angle neutron and x-ray scattering are used to probe hollow microgels in crowded environments. These measurements reveal an interplay among deswelling, interpenetration, and faceting and an unusual absence of crystals. Monte Carlo simulations of model systems confirm that, due to the cavity, solutions of hollow microgels more readily form a supercooled liquid than for microgels with a cross-linked core.

Extremely Fast Optical and Nonvolatile Control of Mixed-Phase Multiferroic BiFeO3 via Instantaneous Strain Perturbation

Multiferroics-materials that exhibit coupled ferroic orders-are considered to be one of the most promising candidate material systems for next-generation spintronics, memory, low-power nanoelectronics and so on. To advance potential applications, approaches that lead to persistent and extremely fast functional property changes are in demand. Herein, it is revealed that the phase transition and the correlated ferroic orders in multiferroic BiFeO₃ (BFO) can be modulated via illumination of single short/ultrashort light pulses. Heat transport simulations and ultrafast optical pump-probe spectroscopy reveal that the transient strain induced by light pulses plays a key role in determining the persistent final states. Having identified the diffusionless phase transformation features via scanning transmission electron microscopy, sequential laser pulse illumination is further demonstrated to perform large-area phase and domain manipulation in a deterministic way. The work contributes to all-optical and rapid nonvolatile control of multiferroicity, offering different routes while designing novel optoelectronics.

Martensitic transition in molecular crystals for dynamic functional materials

Molecular martensitic materials are an emerging class of smart materials with enormous tunability in physicochemical properties, attributed to the tailored molecular and crystal structures through molecular design. This class of materials exhibits ultrafast and reversible structural transitions in response to thermal and mechanical stimuli, which underlies fascinating properties such as thermoelasticity, superelasticity, ferroelasticity, and shape memory effect. These dynamic properties are not widely explored in molecular crystals and therefore molecular martensitic materials represent a new frontier in the field of solid-state chemistry. In martensitic transitions, the materials not only exhibit substantial shape changes but also remember the functions in the associated polymorphic phases. This suggests promising applicability towards light-weight actuators, lifts, dampers, sensors, shape-/function-memory and ultraflexible optoelectronic devices. In this article, we review characteristics, detailed transition mechanisms, and potential applications of molecular martensitic materials. In particular, we aim to describe transition characteristics by collecting cases with similar transition principles in order to glean insights into further advancement of molecular martensitic materials. Overall, we believe that molecular martensitic materials are emerging as the next generation smart materials that have shown promise in advancing a wide range of domains of applications.

Self-assembly of anisotropic nanoparticles into functional superstructures

Self-assembly of colloidal nanoparticles (NPs) into superstructures offers a flexible and promising pathway to manipulate the nanometer-sized particles and thus make full use of their unique properties. This bottom-up strategy builds a bridge between the NP regime and a new class of transformative materials across multiple length scales for technological applications. In this field, anisotropic NPs with size- and shape-dependent physical properties as self-assembly building blocks have long fascinated scientists. Self-assembly of anisotropic NPs not only opens up exciting opportunities to engineer a variety of intriguing and complex superlattice architectures, but also provides access to discover emergent collective properties that stem from their ordered arrangement. Thus, this has stimulated enormous research interests in both fundamental science and technological applications. This present review comprehensively summarizes the latest advances in this area, and highlights their rich packing behaviors from the viewpoint of NP shape. We provide the basics of the experimental techniques to produce NP superstructures and structural characterization tools, and detail the delicate assembled structures. Then the current understanding of the assembly dynamics is discussed with the assistance of in situ studies, followed by emergent collective properties from these NP assemblies. Finally, we end this article with the remaining challenges and outlook, hoping to encourage further research in this field.

Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites

Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.

Melting and solid-solid transitions of two-dimensional crystals composed of Janus spheres

Colloidal model systems have been extensively used in the studies of various phase transitions, but melting and solid-solid transitions have rarely been explored in monolayer colloidal crystals with anisotropic attractions. Patchy colloidal particles have served as important model systems of atoms and molecules with anisotropic interactions. In this work, we study the melting and solid-solid transitions of two-dimensional crystals composed of Janus colloidal spheres using Langevin dynamics simulation. We discovered a first-order solid-solid transition from a single crystal with uniform stripes to a novel crystal with polycrystalline domains of stripes. The centers of masses of the particles maintain the morphology of a single crystal with long-range translational and bond-orientational orders, but particle orientations form polycrystalline domains of stripes. The stripe domains form by a strain-induced nucleation process via the collective rotation of particles. In addition to this solid-solid transition, the melting transition at a higher temperature follows a two-step Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario, similar to most isotropic particle systems.

Experimental validation of interpolation method for pair correlations in model crystals

Accurate analysis of pair correlations in condensed matter allows us to establish relations between structures and thermodynamic properties and, thus, is of high importance for a wide range of systems, from solids to colloidal suspensions. Recently, the interpolation method (IM) that describes satisfactorily the shape of pair correlation peaks at short and at long distances has been elaborated theoretically and using molecular dynamics simulations, but it has not been verified experimentally as yet. Here, we test the IM by particle-resolved studies with colloidal suspensions and with complex (dusty) plasmas and demonstrate that, owing to its high accuracy, the IM can be used to experimentally measure parameters that describe interaction between particles in these systems. We used three- and two-dimensional colloidal crystals and monolayer complex (dusty) plasma crystals to explore suitability of the IM in systems with soft to hard-sphere-like repulsion between particles. In addition to the systems with pairwise interactions, if many-body interactions can be mapped to the pairwise ones with some effective (e.g., density-dependent) parameters, the IM could be used to obtain these parameters. The results reliably show that the IM can be effectively used for analysis of pair correlations and interactions in a wide variety of systems and therefore is of broad interest in condensed matter, complex plasma, chemical physics, physical chemistry, materials science, and soft matter.

Exploring the colloid-to-polymer transition for ultra-low crosslinked microgels from three to two dimensions

Microgels are solvent-swollen nano- and microparticles that show prevalent colloidal-like behavior despite their polymeric nature. Here we study ultra-low crosslinked poly(N-isopropylacrylamide) microgels (ULC), which can behave like colloids or flexible polymers depending on dimensionality, compression or other external stimuli. Small-angle neutron scattering shows that the structure of the ULC microgels in bulk aqueous solution is characterized by a density profile that decays smoothly from the center to a fuzzy surface. Their phase behavior and rheological properties are those of soft colloids. However, when these microgels are confined at an oil-water interface, their behavior resembles that of flexible macromolecules. Once monolayers of ultra-low crosslinked microgels are compressed, deposited on solid substrate and studied with atomic-force microscopy, a concentration-dependent topography is observed. Depending on the compression, these microgels can behave as flexible polymers, covering the substrate with a uniform film, or as colloidal microgels leading to a monolayer of particles.

Complex crystalline structures in a two-dimensional core-softened system

A transition from a square to a hexagonal lattice is studied in a 2D system of particles interacting via a core-softened potential. Due to the presence of two length scales of repulsion, different local configurations with four, five, and six neighbors are possible, leading to the formation of complex crystals. The previously proposed interpolation method is generalized to calculate pair correlations in crystals whose unit cell consists of more than one particle. The high efficiency of the method is illustrated using a snub square lattice as a representative example. Molecular dynamics simulations show that the snub square lattice is broken upon heating, generating a high-density quasicrystalline phase with 12-fold symmetry (HD12 phase). A simple theoretical model is proposed to explain the physical mechanism responsible for this phenomenon: with an increase in the density (from square to hexagonal phases), the concentrations of different local configurations randomly realized through a plane tiling change, which minimizes the energy of the system. The calculated phase diagram in the intermediate density range justifies the existence of the HD12 phase and demonstrates a cascade of first-order transitions "square - HD12 - hexagonal" solid phases with increasing density. The results allow us to better understand the physical mechanisms responsible for the formation of quasicrystals, and, therefore, should be of interest for broad community in materials science and soft matter.

Tunable two-dimensional assembly of colloidal particles in rotating electric fields

Tunable interparticle interactions in colloidal suspensions are of great interest because of their fundamental and practical significance. In this paper we present a new experimental setup for self-assembly of colloidal particles in two-dimensional systems, where the interactions are controlled by external rotating electric fields. The maximal magnitude of the field in a suspension is 25 V/mm, the field homogeneity is better than 1% over the horizontal distance of 250 μm, and the rotation frequency is in the range of 40 Hz to 30 kHz. Based on numerical electrostatic calculations for the developed setup with eight planar electrodes, we found optimal experimental conditions and performed demonstration experiments with a suspension of 2.12 μm silica particles in water. Thanks to its technological flexibility, the setup is well suited for particle-resolved studies of fundamental generic phenomena occurring in classical liquids and solids, and therefore it should be of interest for a broad community of soft matter, photonics, and material science.