Equilibrium Grain Boundary Segregation and Clustering of Impurities in Colloidal Polycrystalline Monolayers

Dumbbell Impurities in 2D Crystals of Repulsive Colloidal Spheres Trap Dislocations

Impurity-induced defects play a crucial role for the properties of crystals, but little is known about impurities with anisotropic shape. Here, we study how colloidal dumbbells distort and interact with a hexagonal crystal of charged colloidal spheres at a fluid interface. We find that subtle differences in the dumbbell length determine whether it induces a local distortion of the lattice or traps a dislocation, and determine how the dumbbell moves inside the repulsive hexagonal lattice. Our results provide new routes toward controlling material properties and understanding fundamental questions in phase transitions through particle-bound dislocations.

Nonadditive Interactions Unlock Small-Particle Mobility in Binary Colloidal Monolayers

We examine the organization and dynamics of binary colloidal monolayers composed of micron-scale silica particles interspersed with smaller-diameter silica particles that serve as minority component impurities. These binary monolayers are prepared at the surface of ionic liquid droplets over a range of size ratios (σ = 0.16-0.66) and are studied with low-dose minimally perturbative scanning electron microscopy (SEM). The high resolution of SEM imaging provides direct tracking of all particle coordinates over time, enabling a complete description of the microscopic state. In these bidisperse size mixtures, particle interactions are nonadditive because interfacial pinning to the droplet surface causes the equators of differently sized particles to lie in separate planes. By varying the size ratio, we control the extent of nonadditivity in order to achieve phase behavior inaccessible to additive 2D systems. Across the range of size ratios, we tune the system from a mobile small-particle phase (σ < 0.24) to an interstitial solid (0.24 < σ < 0.33) and furthermore to a disordered glass (σ > 0.33). These distinct phase regimes are classified through measurements of hexagonal ordering of the large-particle host lattice and the lattice's capacity for small-particle transport. Altogether, we explain these structural and dynamic trends by considering the combined influence of interparticle interactions and the colloidal packing geometry. Our measurements are reproduced in molecular dynamics simulations of 2D nonadditive disks, suggesting an efficient method for describing confined systems with reduced dimensionality representations.

Mechanical strength enhancement by grain size reduction in a soft colloidal polycrystal

It has long been known that the mechanical strength of finely grained solid state polycrystals could be enhanced when the grain size is reduced. Indeed, the equation linking the yield stress and the inverse square root of grain size was introduced in the 1950s by Hall and Petch. Since then this relationship has been widely used to engineer structural metals and alloys. To date, no similar behavior has been reported in materials other than atomic systems where the grain size usually lies in the nanometric range. The purpose of the present work is to study the influence of grain size on the mechanical strength enhancement of a soft colloidal 'alloy' made of micellar polycrystalline grains and silica nanoparticles. The nanoparticles act as nucleation sites and their concentration promotes the variation of the polycrystalline grain size. This system bears resemblance to solid state polycrystals; however the achieved grain length scale is situated in the micrometric domain. We show that the grain size evolves non-monotonically, first decreasing then increasing, when the nanoparticle concentration increases. Our main result is that the yield stress rigorously obeys the Hall-Petch law and follows a linear variation as a function of the inverse square root of the grain diameter. We believe that our experimental approach offers new possibilities to study the poorly understood mechanical aspects of polycrystalline and nanocrystalline structures, such as their plasticity, using non-destructive techniques.

Disconnection-Mediated Transition in Segregation Structures at Twin Boundaries

Twin boundaries play an important role in the thermodynamics, stability, and mechanical properties of nanocrystalline metals. Understanding their structure and chemistry at the atomic scale is key to guide strategies for fabricating nanocrystalline materials with improved properties. We report an unusual segregation phenomenon at gold-doped platinum twin boundaries, which is arbitrated by the presence of disconnections, a type of interfacial line defect. By using atomistic simulations, we show that disconnections containing a stacking fault can induce an unexpected transition in the interfacial-segregation structure at the atomic scale, from a bilayer, alternating-segregation structure to a trilayer, segregation-only structure. This behavior is found for faulted disconnections of varying step heights and dislocation characters. Supported by a structural analysis and the classical Langmuir-McLean segregation model, we reveal that this phenomenon is driven by a structurally induced drop of the local pressure across the faulted disconnection accompanied by an increase in the segregation volume.

Pattern detection in colloidal assembly: A mosaic of analysis techniques

Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.

Competing factors in grain boundary loop shrinkage: Two-dimensional hard sphere colloidal crystals

A grain boundary (GB) loop in a two-dimensional solid is the boundary of a domain or grain whose lattice orientation is mismatched with its uniform surroundings. Understanding the factors that influence the rate at which the interior of a GB loop relaxes to the orientation of its surroundings is an important step toward control and predictability of grain coarsening in general. Recent computational and experimental studies looking at the rate of GB loop shrinkage in two-dimensional colloidal hard sphere solids have uncovered contradictory trends: in experiments, GB loops with low misorientation angles shrank the fastest, while in simulations, they persisted the longest. In this study, the computational system's behavior is brought into qualitative agreement with the experimental results through increasing the lateral packing pressure, decreasing the domain size, and mimicking the experimental protocol used to form the GB loop. Small GB loops with the same misorientation, but displaying either a hexagonal or starlike grain shape depending on the orientation of their six dislocations, are shown to differ in their rates of shrinkage by two orders of magnitude. The evidence suggests that both the barrier to generating new dislocations as well as the pattern of dislocations formed by different GB loop preparation methods will determine which trend is observed.

Ordering of colloidal hard spheres under gravity: from monolayer to multilayer

The phase behaviour of hard spheres confined by a gravitational potential to a thin layer (up to several monolayers) near a hard, flat surface is investigated using grand canonical Monte Carlo simulation. Depending on the strength of the gravitational field, the bottom monolayer of spheres may adopt uniform hexagonal order before, during, or after the growth of the second layer of particles. The crossover from ordering with a sparsely populated overlayer to ordering with almost one-third of the system's particles forming a second layer is observed upon decreasing the dimensionless Péclet number Pe = mgσ/kBT from 18 to 16. The particular sensitivity of the nature of the transition to particle size in this range is interpreted in terms of competing influences on the base layer structure by particles in the overlayer: promotion of order through increased pressure, versus stabilization of defects through occupation of low-lying sites on top of them. Simulations of grain boundaries between 2-D ordered domains of different orientation are used to correlate the degree of overlayer coverage to its effects on grain boundary stiffness as an indicator of defect free energy. Finally, we examine the structure of the ordered phases at coexistence over a range of gravitational strengths and find that orientational ordering of the second monolayer occurs along with first-order transition of the base layer at Pe = 8 but not at Pe = 10.

Partitioning of Size-Mismatched Impurities to Grain Boundaries in 2d Solid Hard-Sphere Monolayers

Computational studies have been carried out to investigate the equilibrium partitioning of size-mismatched impurities between the bulk solid and grain boundary (GB) environments in 2d hard-sphere monolayers. The solvent repacking Monte Carlo method and a new variation were used to exchange varying numbers and types of particles under conditions of fixed particle fugacities, allowing efficient sampling of impurity particle distributions even within the bulk solid. Measurements of GB stiffness depression arising from the impurities were made via the capillary fluctuation method and found to agree with calculations based on the Gibbs adsorption isotherm, providing a test of the internal consistency of the results. The dependence of the excess concentration at the GB on factors, including impurity size (diameter ratios λ = 0.5-4 times the majority host particle diameter), impurity concentration, grain misorientation angle, and packing pressure, was studied. In general, the affinity of impurity particles for GB increased with the difference between their size and the host particles, and varied with grain misorientation angle with a dependence reflecting the excess free area at the GB. Impurities with λ = 4 were exceptions to both these trends, due to their ability to substitute efficiently for six-coordinate host particles within the bulk and for five-coordinate host particles at dislocations in the grain boundaries. Comparison with results from an experimental study of mixed colloidal monolayers raises questions about how kinetic effects during grain coarsening might produce less impurity segregation to the GB than equilibrium exchange.

Pattern Formation in Binary Colloidal Assemblies: Hidden Symmetries in a Kaleidoscope of Structures

In this study, we present a detailed investigation of the morphology of binary colloidal structures formed by self-assembly at air/water interface of particles of two different sizes, with a size ratio such that the larger particles do not retain a hexagonal arrangement in the binary assembly. While the structure and symmetry of binary mixtures in which such hexagonal order is preserved has been thoroughly scrutinized, binary colloids in the regime of nonpreservation of the hexagonal order have not been examined with the same level of detail due also to the difficulty in finding analysis tools suitable to recognize hidden symmetries in seemingly amorphous and disordered arrangements. For this purpose, we resorted to a combination of different analysis tools based on computational geometry and computational topology to get a comprehensive picture of the morphology of the assemblies. By carrying out an extensive investigation of binary assemblies in this regime with variable concentration of smaller particles with respect to larger particles, we identify the main patterns that coexist in the apparently disordered assemblies and detect transitions in the symmetries upon increase in the number of small particles. As the concentration of small particles increases, large particle arrangements become more dilute and a transition from hexagonal to rhombic and square symmetries occurs, accompanied also by an increase in clusters of small particles; the relative weight of each specific symmetry can be controlled by varying the composition of the assemblies. The demonstration of the possibility to control the morphology of apparently disordered binary colloidal assemblies by varying experimental conditions and the definition of a route for the investigation of disordered assemblies are important for future studies of complex colloidal patterns to understand self-assembly mechanisms and to tailor the physical properties of colloidal assemblies.