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Gold (Au) catalysts exhibit a significant size effect, but its origin has been puzzling for a long time. It is generally believed that supported Au clusters are more or less rigid in working condition, which inevitably leads to the general speculation that the active sites are immobile. Here, by using atomic resolution in situ environmental transmission electron microscopy, we report size-dependent structure dynamics of single Au nanoparticles on ceria (CeO₂) in CO oxidation reaction condition at room temperature. While large Au nanoparticles remain rigid in the catalytic working condition, ultrasmall Au clusters lose their intrinsic structures and become disordered, featuring vigorous structural rearrangements and formation of dynamic low-coordinated atoms on surface. Ab initio molecular-dynamics simulations reveal that the interaction between ultrasmall Au cluster and CO molecules leads to the dynamic structural responses, demonstrating that the shape of the catalytic particle under the working condition may totally differ from the shape under the static condition. The present observation provides insight on the origin of superior catalytic properties of ultrasmall gold clusters.

The interactions between dislocations (dislocations and deformation twins) and boundaries (grain boundaries, twin boundaries and phase interfaces) during deformation at ambient temperatures are reviewed with focuses on interaction behaviors, boundary resistances and energies during the interactions, transmission mechanisms, grain size effects and other primary influencing factors. The structure of boundaries, interactions between dislocations and boundaries in coarse-grained, ultrafine-grained and nano-grained metals during deformation at ambient temperatures are summarized, and the advantages and drawbacks of different in-situ techniques are briefly discussed based on experimental and simulation results. The latest studies as well as fundamental concepts are presented with the aim that this paper can serve as a reference in the interactions between dislocations and boundaries during deformation.

Structural components with different scales normally show different fatigue behaviors, which are virtually dominated by defects originated from multiple sources, including manufacturing processes. This paper reviews three types of size effects (statistical, geometrical, technological) as well as their recent advances in metal fatigue, aiming to provide a guide for fatigue strength assessment of engineering components containing defects, inclusions and material inhomogeneity. Firstly, the background of inherent defects and defect-based failure mechanism are briefly outlined, and fatigue failure analysis based on fracture mechanics as well as statistics theory are emphasized. Then, two approaches commonly applied in statistical size effect modeling, i.e. critical defect method and weakest link method, are elaborated. In addition, the highly stressed volume method is introduced for considering the geometrical size effects, and the technological (production and surface) size effect is briefly overviewed. Finally, further directions on size effect in metal fatigue under defects are explored.

In prevention science and related fields, large meta-analyses are common, and these analyses often involve dependent effect size estimates. Robust variance estimation (RVE) methods provide a way to include all dependent effect sizes in a single meta-regression model, even when the exact form of the dependence is unknown. RVE uses a working model of the dependence structure, but the two currently available working models are limited to each describing a single type of dependence. Drawing on flexible tools from multilevel and multivariate meta-analysis, this paper describes an expanded range of working models, along with accompanying estimation methods, which offer potential benefits in terms of better capturing the types of data structures that occur in practice and, under some circumstances, improving the efficiency of meta-regression estimates. We describe how the methods can be implemented using existing software (the “metafor” and “clubSandwich” packages for R), illustrate the proposed approach in a meta-analysis of randomized trials on the effects of brief alcohol interventions for adolescents and young adults, and report findings from a simulation study evaluating the performance of the new methods.

Particle size strongly influences the shear strength of granular materials. However, previous studies of the particle size effect have focused mainly on the macroscopic behavior of granular materials, neglecting the associated micro-mechanism. In this study, the effect of particle size on the shear strength of uncrushable granular materials in biaxial testing is investigated using the discrete element method (DEM). First, a comprehensive calibration against experimental results is conducted to obtain the DEM parameters for two types of quartz sand. Then, a series of biaxial tests are simulated on sands with parallel particle size distributions to investigate the effect of particle size on macro- and microscopic behaviors. Finally, by adopting the rolling resistance method and the clump method, irregular-shaped particles are simulated to investigate how the particle size effect will be influenced by the particle shape. Simulation results demonstrate that (1) the peak shear strength increases with particle size, whereas the residual shear strength is independent of particle size; (2) the thickness of the shear band increases with the particle size, but its ratio decreases with particle size; (3) the particle size effect can be explained by the increase of friction utilization ratio with particle size; and (4) the particle size effect is more significant in granular materials that consist of particles with higher angularity.

In the present study, the buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study is made of functionally graded materials in the longitudinal direction and the cross-section of the microcolumn varies continuously throughout the axial direction. The Bernoulli–Euler beam theory in conjunction with modified strain gradient theory are employed to model the structure by considering the size effect. The Rayleigh–Ritz numerical solution method is used to solve the eigenvalue problem for various conditions. The influences of changes in the cross-section and Young’s modulus, size dependency, and non-classical boundary conditions are examined in detail. It is observed that the size effect becomes more pronounced for smaller sizes and differences between the classical and non-classical buckling loads increase by increasing the taper ratios.

A transversely isotropic rock, slate, was utilized to investigate the size effect and anisotropy on its deformation, tensile strength, and failure mechanism. A series of Brazilian tests were conducted on slate samples of six different sizes from 25 to 100 mm in diameter at seven different loading-foliation angles from 0° to 90°. The results indicate that the Young’s modulus in the plane of transverse isotropy increases, while the Young’s modulus and shear modulus perpendicular to the plane of transverse isotropy decrease with specimen size. The tensile strength of the slate increases with increasing loading-foliation angle, the variation of which is well captured by the Nova–Zaninetti criterion. Furthermore, the tensile strength of the slate increases with specimen size at loading-foliation angles from 0° to 45°, while it increases first and then decreases with specimen size at loading-foliation angles from 60° to 90°. A unified size-effect relation including two equations is proposed and verified against the experimental data on slate. The size-effect relation reveals the relationship among the tensile strength, specimen size, and loading-foliation angle for the transversely isotropic rock. Finally, the slate samples exhibit an increased brittle failure with specimen size, which is consistent with the observations in various isotropic rocks. It is also found that the specimen size, loading-foliation angle, and loading configuration together control the failure mechanism of transversely isotropic rocks in the Brazilian test.

The origin of the indentation size effect has been extensively researched over the last three decades, following the establishment of nanoindentation as a broadly used small-scale mechanical testing technique that enables hardness measurements at submicrometer scales. However, a mechanistic understanding of the indentation size effect based on direct experimental observations at the dislocation level remains limited due to difficulties in observing and quantifying the dislocation structures that form underneath indents using conventional microscopy techniques. Here, we employ precession electron beam diffraction microscopy to “look beneath the surface,” revealing the dislocation characteristics (e.g., distribution and total length) as a function of indentation depth for a single crystal of nickel. At smaller depths, individual dislocation lines can be resolved, and the dislocation distribution is quite diffuse. The indentation size effect deviates from the Nix–Gao model and is controlled by dislocation source starvation, as the dislocations are very mobile and glide away from the indented zone, leaving behind a relatively low dislocation density in the plastically deformed volume. At larger depths, dislocations become highly entangled and self-arrange to form subgrain boundaries. In this depth range, the Nix–Gao model provides a rational description because the entanglements and subgrain boundaries effectively confine dislocation movement to a small hemispherical volume beneath the contact impression, leading to dislocation interaction hardening. The work highlights the critical role of dislocation structural development in the small-scale mechanistic transition in indentation size effect and its importance in understanding the plastic deformation of materials at the submicron scale.

The impact of the size effect on the color and photoluminescence (PL) of quantum dots (QDs) has sparked a revolutionary field of research, culminating in the prestigious Nobel Prize in 2023. Prior to their widespread popularization and large-scale commercialization, it is of paramount importance to effectively manipulate and optimize their optical properties. In this review, we place specific emphasis on the striking correlation between the optical characteristics of QDs and their size, structure, composition, and interface environment. We commence by tracing the evolution of quantum dot technology and subsequently categorizing QDs while outlining their typical synthesis methods. This is followed by a deep dive into the pivotal roles of size, composition, structure, and interfacial ligands in fine-tuning, optimizing, and enhancing the optical properties of QDs. Additionally, we illustrate the luminescence enhancement and charge transfer phenomena stemming from the heterojunction between semiconductor QDs and metal nanomaterials, which contribute to improved performance. Lastly, we introduce the burgeoning field of chiral QDs and their innovative applications. Armed with this knowledge, QDs can be readily tailored to exhibit adjustable luminous characteristics across the entire spectrum, boasting high luminous efficiency through multifaceted regulation. These advancements render QDs even more enticing and promising for a wide array of applications.

An effect size (ES) provides valuable information regarding the magnitude of effects, with the interpretation of magnitude being the most important. Interpreting ES magnitude requires combining information from the numerical ES value and the context of the research. However, many researchers adopt popular benchmarks such as those proposed by Cohen. More recently, researchers have proposed interpreting ES magnitude relative to the distribution of observed ESs in a specific field, creating unique benchmarks for declaring effects small, medium or large. However, there is no valid rationale whatsoever for this approach. This study was carried out in two parts: (1) We identified articles that proposed the use of field-specific ES distributions to interpret magnitude (primary articles); and (2) We identified articles that cited the primary articles and classified them by year and publication type. The first type consisted of methodological papers. The second type included articles that interpreted ES magnitude using the approach proposed in the primary articles. There has been a steady increase in the number of methodological and substantial articles discussing or adopting the approach of interpreting ES magnitude by considering the distribution of observed ES in that field, even though the approach is devoid of a theoretical framework. It is hoped that this research will restrict the practice of interpreting ES magnitude relative to the distribution of ES values in a field and instead encourage researchers to interpret such by considering the specific context of the study.