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Systematic study on the microstructural evolution, interfacial diffusion and mechanical properties of ultra-thin stainless steel–copper composites (50 µm) after annealing treatment was conducted in the present study. The results show that the as-received specimen exhibits low elongation (0.031) as well as high strength (891.346 MPa) by work hardening, thus requires heat treatment to improve the plasticity. With the increase of annealing temperature from 700 to 1000 °C, the dislocation/grain boundary strengthening is weakened while the surface grains which exhibit fewer constraints is increasing, resulting in lower strength. Moreover, a uniform and refined microstructure with high recrystallization rate is formed inside stainless steel and copper matrixes for the specimens annealed at 900 °C, thereby improving the plasticity of ultra-thin stainless steel–copper composites. Additionally, an obvious strain gradient exists at the interface of ultra-thin stainless steel–copper composites, and the interdiffusion process between stainless steel and copper matrixes is primarily governed by the diffusion of Cu atoms. The influence of diffusion layer thickness on the strength of ultra-thin stainless steel–copper composites is negligible. Overall, an optimal annealing temperature of 900 °C is obtained with the improved plasticity of ultra-thin stainless steel–copper composites. [ABSTRACT FROM AUTHOR]

The fatigue of adhesive joints in offshore wind turbine blades is a critical and widespread challenge, necessitating an urgent focus on adhesive bond reliability. Given the constraints of full-scale testing, this research explores the fatigue endurance of carbon fiber–epoxy adhesive composites, integral to blade construction. Recognizing the fatigue characteristics' sensitivity to environmental factors and joint dimensions, an innovative approach to fatigue modelling and evaluation is introduced. This method incorporates the influence of different environmental stresses and size effects. Specifically, a degradation coefficient and size impact factor (SIF) are introduced into the cyclic cohesive zone model, and a simulation-based analytic approach is proposed for analyzing adhesive fatigue. Furthermore, we introduce a reliability modelling procedure that integrates performance degradation theory to address the deteriorative characteristics inherent in adhesive fatigue. Subsequently, the specimens' damage accumulation increased by 75% because of the stresses and escalated to 85% with adhesive joint size effects, causing carbon fiber Reinforced Polymer/epoxy adhesive joints to fail interfacially rather than in a mixed-mode manner. This study provides valuable insights for the safety analysis and assessment of adhesive joint performance in offshore wind turbine blades. [ABSTRACT FROM AUTHOR]

Dams fragment stream habitats and fishways around dams typically serve few species that are strong swimmers or jumpers. We tested a prototype wetted ramp designed to allow upstream passage of small-bodied fishes while blocking upstream movement of invasive sea lampreys in the Laurentian Great Lakes. We tested short, smooth ramps with 5–10 mm water depth in various combinations of ramp angle, water flow, and swim channel width with the aim to selectively block adult migrating sea lampreys (Petromyzon marinus) while passing sub-adult white suckers (Catostomus commersonii) and creek chubs (Semotilus atromaculatus). Sea lampreys easily passed a 0.75 ramp at a 5° angle, but very few individuals passed a similar ramp at a 10° angle, and none passed a longer ramp at a 5° angle. Limiting the amplitude of tailbeats in a narrow channel did not hamper lampreys or the other species. Greater water flow, and thereby greater immersion depth on the ramp, fostered passage for all species. Smaller-bodied individuals of creek chubs and white suckers performed best on the ramp. We showed that wetted ramps could be incorporated into fishways at low-head dams to aid the passage of smaller-bodied fishes while also blocking the spawning migration of adult sea lampreys. [ABSTRACT FROM AUTHOR]

Non-uniform deformation of the dielectric subjected to external forces can induce the flexoelectric effect, a phenomenon that couples electrical polarization to strain gradients. However, limited by the size effects, flexoelectricity is not significant at the macroscale and only becomes catchable at the microscale and nanoscale. In recent work, we obtained a considerable flexoelectric-like response by crumpling the dielectric embedded with charges, i.e., the electret, which significantly improved the flexoelectric effect at the macroscale. In this work, we further optimize the macroscopic performance of the flexoelectric response by applying gradient treatment to the electret films. Specifically, we analytically derive the electromechanical coupling of crumpled electret films with gradients of different thicknesses, charge densities, and Young's moduli as key design variables. It is shown that the gradient-oriented electret film can be tuned to nearly five times that of a uniform electret film. [ABSTRACT FROM AUTHOR]

Evaporation deposition of gold nanoparticles (AuNPs) on a glass surface textured by cellulose nanofibers (CNFs) provides an effective substrate for surface-enhanced Raman spectroscopy (SERS). The performance enhancement of such a SERS substrate hinges upon the quality and quantity of nanostructured surfaces, which are strongly correlated to the AuNP particle size. Unfortunately, the size effect of AuNPs on the Raman activity of CNF-textured SERS substrates remains unclear. Here, we investigate the Raman activity of CNF-textured SERS substrates constructed by evaporating sessile drops of AuNPs with diameters of 40 nm and 16 nm on CNF-textured surfaces, respectively. Both experimentation and computation analysis reveal that the use of 40 nm AuNPs exhibits more effective Raman activity and traps larger amounts of analyte molecules than 16 nm AuNPs. Moreover, the existence of the CNF-textured surface significantly enhances the Raman signals of analyte molecules in all regions of SERS substrates when compared with AuNPs deposited on the bare glass surface. These findings provide insights into the particle size selection for fabricating effective SERS substrates and advance applications of CNF-textured SERS substrates. [ABSTRACT FROM AUTHOR]

The fatigue of adhesive joints in offshore wind turbine blades is a critical and widespread challenge, necessitating an urgent focus on adhesive bond reliability. Given the constraints of full-scale testing, this research explores the fatigue endurance of carbon fiber–epoxy adhesive composites, integral to blade construction. Recognizing the fatigue characteristics’ sensitivity to environmental factors and joint dimensions, an innovative approach to fatigue modelling and evaluation is introduced. This method incorporates the influence of different environmental stresses and size effects. Specifically, a degradation coefficient and size impact factor (SIF) are introduced into the cyclic cohesive zone model, and a simulation-based analytic approach is proposed for analyzing adhesive fatigue. Furthermore, we introduce a reliability modelling procedure that integrates performance degradation theory to address the deteriorative characteristics inherent in adhesive fatigue. Subsequently, the specimens’ damage accumulation increased by 75% because of the stresses and escalated to 85% with adhesive joint size effects, causing carbon fiber Reinforced Polymer/epoxy adhesive joints to fail interfacially rather than in a mixed-mode manner. This study provides valuable insights for the safety analysis and assessment of adhesive joint performance in offshore wind turbine blades.

The present paper investigates flaw strength distributions established using various flexural tests on batches of SiC bar test specimens, namely four-point bending as well as three-point bending tests with different span lengths. Flaw strength is provided by the elemental stress operating on the critical flaw at the fracture of a test specimen. Fracture-inducing flaws and their locations are identified using fractography. A single population of pores was found to dominate the fracture. The construction of diagrams of p-quantile vs. elemental strengths was aimed at assessing the Gaussian nature of flaw strengths. Then, empirical cumulative distributions of strengths were constructed using the normal distribution function. The Weibull distributions of strengths are then compared to the normal reference distributions. The parameters of the Weibull cumulative probability distributions are estimated using maximum likelihood and moment methods. The cumulative distributions of flexural strengths for the different bending tests are predicted from the flaw strength density function using the elemental strength model, and from the cumulative distribution of flexural strength using the Weibull function. Flaw strength distributions that include the weaker flaws that are potentially present in larger test pieces are extrapolated using the p-quantile diagrams. Implications are discussed regarding the pertinence of an intrinsically representative flaw strength distribution, considering failure predictions. Finally, the influence of the characteristics of fracture-inducing flaw populations expressed in terms of flaw strength interval, size, dispersion, heterogeneity, and reproducibility with volume change is examined.

Although various simplified models can capture size effects of composite laminated micro beam and plate by combining new modified couple stress theory, there is no benchmark to access the accuracy of predicting size effects in those models. Therefore this paper develops a quasi-3D model based on new modified couple stress as a benchmark for analyzing thermal size effects of composite laminated micro plate, and also proposes two simplified quasi-3D models with assumptions out of computational cost at the same time. By a classical example of simply-supported micro laminated square plate, several conclusions can be got from numerical results. For the present quasi-3D model under non-uniform temperature loading, (i): the model is capable to capture size effects of composite laminated micro plate, (ii): discovering a law to define the boundary size between micro and macro laminated plate, which is important for the engineering applications; For the simplified quasi-3D models under uniform temperature loading, (i): As the material length parameter l decreases, the accuracy of both of models is rising gradually, (ii): The first simplified quasi-3D model may substitute the present quasi-3D model to predict thermal size-dependent behaviors of composite laminated micro plate, whereas the second simplified quasi-3D model is suitable to laminated micro plate for which span-to-thickness ratio is no less than 14. [ABSTRACT FROM AUTHOR]

In this work, nonlocal strain gradient integral model is applied to investigate the free damping vibration analysis of functionally graded (FG) viscoelastic Timoshenko microbeam with immovable boundary conditions in thermal environment. The microbeam is assumed to be viscoelastic and modeled by Kelvin–Voigt model. The differential governing equations and corresponding boundary conditions are derived with the Hamilton's principle. Combining nonlocal strain gradient integral model and Kelvin–Voigt viscoelastic model, the integral constitutive equations of nonlocal stress with thermal effect are derived and then converted into differential form plus constitutive constraints. The size-dependent axial force due to thermal expansion is explicitly derived through the immovable boundary conditions. The bending deflection and moment, cross-sectional rotation as well as shear force are explicitly derived with Laplace transformation for linear thermo-elastic vibration. Taking into account the boundary conditions as well as constitutive constraints, one gets a nonlinear equation with complex coefficients, from which one can determine the complex characteristic frequency. A two-step numerical method is proposed to solve the elastic vibration frequency and damping ratio. The influence of length scale parameters, viscos coefficient, FG index, thermal effect, vibration order and ratio between beam length and thickness on the vibration frequencies and damping ratio is investigated numerically for FG viscoelastic Timoshenko microbeams under different immovable boundary conditions. [ABSTRACT FROM AUTHOR]

Copper with equiaxed grains (EG Cu), copper with columnar nanotwinned grains (C‐NT Cu), and copper with mixed equiaxed and columnar grains (MG Cu) are electroplated on pads and redistributed layers (RDLs) with different dimensions. When the diameters of pads increase from 40 to 105 μm, the flatness of pads decreases from 34.5% to 24.0%. The flatness gradually deteriorates from 16.5% to 34.4% with the increase of RDL width from 8 to 20 μm. In contrast, the flatness of C‐NT Cu and MG Cu fluctuates between 1% and 5%, showing a weak correlation on the dimension. In terms of microstructure, the EG Cu and MG Cu has a weak correlation with size change, and the grain orientation shows a randomness. However, the (111) texture component of C‐NT Cu differs greatly with different dimensions, especially in transition layer. The (111) texture component changes from 9.6% to 38.1% for ϕ 40–105 μm pad and from 14.3% to 18.9% for 8–20 μm‐wide RDL. The study reveals the significant size effect on the deposited profile and microstructure of electrodeposited copper materials, which should give insights of the materials design in advanced packaging technology. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) is often used to create designs inspired by topology optimization and biological structures, yielding unique cross-sectional geometries spanning across scales. However, manufacturing defects intrinsic to AM can affect material properties, limiting the applicability of a uniform material model across diverse cross-sections. To examine this phenomenon, this paper explores the influence of specimen size and layer height on the compressive modulus of polycarbonate (PC) and thermoplastic polyurethane (TPU) specimens fabricated using fused filament fabrication (FFF). Micro-computed tomography imaging and compression testing were conducted on the printed samples. The results indicate that while variations in the modulus were statistically significant due to both layer height and size of the specimen in TPU, variations in PC were only statistically significant due to layer height. The highest elastic modulus was observed at a 0.2 mm layer height for both materials across different sizes. These findings offer valuable insights into design components for FFF, emphasizing the importance of considering mechanical property variations due to feature size, especially in TPU. Furthermore, locations with a higher probability of failure are recommended to be printed closer to the print bed, especially for TPU, because of the lower void volume fraction observed near the heated print bed. [ABSTRACT FROM AUTHOR]

The present paper investigates flaw strength distributions established using various flexural tests on batches of SiC bar test specimens, namely four-point bending as well as three-point bending tests with different span lengths. Flaw strength is provided by the elemental stress operating on the critical flaw at the fracture of a test specimen. Fracture-inducing flaws and their locations are identified using fractography. A single population of pores was found to dominate the fracture. The construction of diagrams of p-quantile vs. elemental strengths was aimed at assessing the Gaussian nature of flaw strengths. Then, empirical cumulative distributions of strengths were constructed using the normal distribution function. The Weibull distributions of strengths are then compared to the normal reference distributions. The parameters of the Weibull cumulative probability distributions are estimated using maximum likelihood and moment methods. The cumulative distributions of flexural strengths for the different bending tests are predicted from the flaw strength density function using the elemental strength model, and from the cumulative distribution of flexural strength using the Weibull function. Flaw strength distributions that include the weaker flaws that are potentially present in larger test pieces are extrapolated using the p-quantile diagrams. Implications are discussed regarding the pertinence of an intrinsically representative flaw strength distribution, considering failure predictions. Finally, the influence of the characteristics of fracture-inducing flaw populations expressed in terms of flaw strength interval, size, dispersion, heterogeneity, and reproducibility with volume change is examined. [ABSTRACT FROM AUTHOR]

Herein, we prepared Pd nanoparticle (NP) catalysts using XC-72 carbon supports through a tailored deposition–precipitation method. Our primary objective was to unravel the size effects of Pd NPs on hydrogenation of tetraacetyldibenzylhexaazaisowurtzitane (TADBIW), a pivotal intermediate for synthesis of high energy density materials hexanitrohexaazaisowurtzitane (CL-20). The controlled modulation of Pd NP size ranged from a mere 1.8 nm to 7.4 nm. Remarkably, our investigations into TADBIW hydrogenation unveiled a fascinating trend: the ultrasmall-sized Pd NPs with a diameter of 1.8 nm exhibited excellent yield and reaction rates. In stark contrast, their larger-sized counterparts demonstrated diminished catalytic activities. To disclose the size-dependent nature, various characterization techniques were employed, including XRD, TEM, XPS, CO and H2 pulse chemisorption. The comprehensive analysis revealed that the ultrasmall-sized Pd possessed more positively charged sites and exhibited higher dispersion. This unique configuration facilitated an accelerated adsorption of hydrogen and the electron-rich substrate TADBIW. Notably, this phenomenon led to a reduction in the activation energy through a thermodynamic effect, thereby enhancing overall catalytic performance. Our results strongly suggested that the ultrasmall-sized Pd NPs can exert a dominated influence on the physical and chemical states of the active sites, playing a key role in triggering the adsorption and activation of the substrate TADBIW. These findings not only deepen our understanding of the intricate connections between Pd NP size and catalytic activity but also open new avenues for advancing the design and optimization of catalysts in the hydrodebenzylation methodologies and synthesis of related compounds. [ABSTRACT FROM AUTHOR]

Context: Mixed-metal clusters have long been studied because of their peculiar properties and how they change with cluster size, composition, and charge state and their potential roles in catalysis. The characterization of these clusters is therefore a very important issue. One of the main experimental tools for characterizing their electronic structure is photoelectron spectroscopy. Theoretical computation completes the task by fully determining the structural properties and matching the theoretical predictions to the measured spectra. We present density functional theory computations of the structural, magnetic, and electronic properties of negatively charged mixed AlnNi- clusters with up to 13 Al atoms. The lowest energy structures of the anionic clusters with up to 7 atoms are also found to be low-energy isomers of the neutral counterparts found in the literature. The 13-atom cluster is found to be a quartet and a perfect icosahedron. The predicted photoelectron spectra are also presented and can be used to interpret future experimental data. We also presented indicators that can be used to determine the potential of these systems for single-atom catalysis. These indicators point to smaller clusters to be more reactive as the gap between the Fermi energy and the center of the d-band increases with cluster size and that Ni occupies an internal site for n = 11–13. We speculate that reactivity can be enhanced if one adds an additional Ni atom. Methods: The DFT calculations were performed using the Becke exchange and Perdew-Wang/91 correlation functionals (BPW91), a DFT-optimized all-electron basis set for the aluminum atom, and the Stuttgart small core pseudopotential for the Ni atom. All of the computations used the Gaussian 03 software. [ABSTRACT FROM AUTHOR]

Based on the hyperbolic tangent parabola mixed shear deformation theory, the paper studied the sound radiation and the sound insulation of the functionally graded (FG) sandwich microplates under thermal-electric effects. The sandwich plate is composed of piezoelectric skin layers and FGM core layer. By using Hamilton's principle, a size-dependent model considering the thermal-piezoelectric effects are established. The acoustic response and sound insulation are calculated with Rayleigh integral and solid-fluid coupling conditions. The accuracy of the presented method is verified by the numerical simulations. Then the effects of various parameters on the vibro-acoustic characteristics are analyzed and discussed. Numerical results show that the temperature variations, the length scale parameter to thickness ratio and the gradient index have great impacts on the FG sandwich microplates. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on ultra-high-performance concrete (UHPC) beams without stirrups, where the test data of 487 beams were collected, and an experimental database was established. Four distinct shear strength calculation models for UHPC beams were examined in the study. These models were created from national specification guides. The results indicate that while the code equation is useful for predicting UHPC beam shear capacity, it consistently underestimates actual values, with a mean experimental-to-calculated ratio above 1.5. The database was also used to study the impacts of the compressive strength of UHPC, the shear span-to-depth ratio, the fiber volume fraction, and the reinforcement ratio on the shear strength of UHPC beams. The findings showed that the shear span-to-depth ratio significantly affected the shear load-bearing capacity of UHPC beams. The increase in the compressive strength of UHPC, fiber volume fraction, and reinforcement ratio positively affected the shear strength of UHPC beams to varying degrees. Additionally, there were size effects for beams with a shear span-to-depth ratio of less than 1.5 and an effective depth of more than 300. In addition, coefficients accounting for fiber influence and the shear span-to-depth ratio were incorporated to develop an enhanced formula for UHPC beams. The empirical data from the database tests revealed that the average ratio of the beams' experimental shear capacity to the values predicted by the modified equation is 1.3, with a standard deviation of 0.74. These results suggest that the refined equation offers improved calculation precision and broader applicability. Eventually, a summary of the issues pertaining to the shear performance of UHPC beams and the key future research directions is provided to facilitate a clearer comprehension and awareness of emerging concepts for scholars within the discipline. [ABSTRACT FROM AUTHOR]

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Abstract The dimensionality of dynamic interfaces—domain walls (DWs) —is greatly influenced by symmetry and physical dimensions, irrespective of the microscopic details of the system. To address this fundamental question for the ferroelectric model system, the DW scaling criticality and dimensionality is investigated in ultrathin films of varied ferroelectric materials, compositions, and electrode–ferroelectric interfaces, grown on nominally flat and vicinal substrates. In spite of significant variations among ferroelectric systems, the observed prevalence of 1D DWs is consistent with a random bond disorder, elucidated through a scenario of 2D nucleation and growth‐driven DW creep. These findings highlight the thickness size‐dominated universal behavior of ferroelectric DWs, uncovering fascinating prospects for dimensionally engineered DW‐based nanoelectronics.

A hybrid planar micro-lattice made of functionally graded materials is proposed where the active and passive constituents are constructed by functionally graded beams with and without partially distributed piezoelectric attachments respectively. The analytical model for predicting complex band structure is presented via the spectral element method in combination with the modified couple stress theory and power law, whose accuracy is validated by the finite element method. By adjusting size dependence, feedback control gain, material gradient and arrangement of piezo-patches, controllable wave propagation and attenuation is achieved, which further advances the implementation of optimizations to obtain ultra-wide low frequency stop bands. [ABSTRACT FROM AUTHOR]

It is now well established that, upon decreasing system sizes down to a few μ m or below, the nature of plasticity of metallic materials is changing. Two important features of this small-sizes plasticity are two size effects, which can be summed up as "smaller is stronger" and "smaller is wilder", this last observation meaning that the jerkiness of plastic deformation becomes prominent at small enough system sizes. In FCC and HCP materials, this is now rather well understood within the framework of obstacle-controlled plasticity, from the key role of a scaling ratio between the system size L and an internal scale l mainly dictated by dislocation patterning in pure materials, or by the nature of extrinsic disorder in alloys. The situation is more complex in BCC materials, for which screw dislocation motion becomes lattice-controlled, i.e. is thermally activated, below a transition temperature T a . Therefore, in small-sized BCC systems, temperature, size and strain-rate effects combine to give rise to a complex landscape. We show, from an analysis of the literature as well as micropillar compression tests on Molybdenum performed with different sample sizes, under different temperatures and different applied strain-rates, that (i) near or above T a , the plasticity of pure BCC metals is athermal and obstacle-controlled, much like at bulk scales, therefore mimicking that of pure FCC metals; (ii) below T a and for sample sizes larger than ∼ 1 μ m, BCC plasticity becomes lattice-controlled, this damping dislocation avalanches and thus reducing wildness; but (iii) for very small systems, still below T a , the role of screw dislocations on plasticity vanishes, i.e. is no more lattice-controlled, opening again the door for wild plastic fluctuations and jerkiness. [ABSTRACT FROM AUTHOR]

Demand for micro-deep-drawn complex-shaped parts in biomedical, chemical analysis and microsystem technologies has been growing. Micro-deep drawing is a micro-plastic forming used to produce micro-parts from different materials. Researchers have worked upon several aspects of micro-deep drawing (MDD), namely the scaling effects, handling of micro-parts and process intermittency. The present work reviews some of these experimental and numerical studies on the MDD considering the size effects, forming limit diagram, parametric effect, lubrication and coating on punch and die surfaces. The topology modification of the deep drawing tool surface using macro/microstructured coated tool shows substantial potential for the lubricant-free micro-deep drawing. Further, micro-structuring of the blank via laser has emerged as another approach in the MDD process to reduce the effective contact area between tool and sheet and, hence, the friction forces. Finally, challenges and scope for further research in MDD are listed to implement these processes commercially. [ABSTRACT FROM AUTHOR]

The microalloyed high-strength aviation alloy of the Al-Si-Cu system obtained using additional pressure on the melt during crystallization is studied in the work. The technology and design features of laminar filling of the mould are developed in order to minimize the formation of technological casting defects. The peculiarities of the structure and crystallization conditions of the AK9M2 alloy are studied. The level of physical-mechanical properties of obtained alloy and its fracture behaviour are determined. Mechanisms of heat transfer are analysed and determined, which allow the promising use of obtained alloys as a material for heat-exchange applications. [ABSTRACT FROM AUTHOR]

Bifunctional metal/zeolite materials are some of the most suitable catalysts for the direct hydroalkylation of benzene to cyclohexylbenzene. The overall catalytic performance of this reaction is strongly influenced by the hydrogenation, which is dependent on the metal sizes. Thus, systematically investigating the metal size effects in the hydroalkylation of benzene is essential. In this work, we successfully synthesized Ru and Pd nanoparticles on Sinopec Composition Materials No.1 zeolite with various metal sizes. We demonstrated the size-dependent catalytic activity of zeolite-supported Ru and Pd catalysts in the hydroalkylation of benzene, which can be attributed to the size-induced hydrogen spillover capability differences. Our work presents new insights into the hydroalkylation reaction and may open up a new avenue for the smart design of advanced metal/zeolite bi-functional catalysts. [ABSTRACT FROM AUTHOR]

The use of supported Co-based catalysts is widespread in various catalytic reactions due to their unique structures. The structural sensitivity of these catalysts is closely linked to their particle size and crystal form. Consequently, comprehending the structure-activity relationship requires the development of well-defined Co-based catalysts. Herein, we employed a colloidal wet chemical process and a heterogeneous nucleation method to prepare well-defined Co-based catalysts supported by inert carbon nanospheres. The nanospheres' surface possesses abundant functional groups that efficiently capture metal complexes and facilitate the nucleation and growth of CoO nanoparticles. By adjusting the Co source concentration, solvent molar ratio, and nucleation growth kinetics, we successfully prepared CoO/carbon sphere (CS) catalysts with different particle sizes and crystal forms. The influence of metallic face-centered cubic (fcc)-Co0 particle size in the range of 6.6–17.6 nm on the performance of Fischer-Tropsch synthesis (FTS) using well-defined CoO/CS catalysts has been investigated. The result demonstrated that the turnover frequency (TOF) remained constant for CoO/CS catalysts with metallic fcc-Co0 particle size larger than 7.7 nm. However, both the selectivity and the activity changed for CoO/CS catalysts with smaller particles (< 7.7 nm). Significantly, when metallic fcc-Co0 particle size was reduced from 17.6 to 7.7 nm, the cobalt time yield increased to 6.7 µmolCO·gCo−1·s−1, indicating improved catalytic activity. At the same time, the CH4 selectivity decreased to 4.9%, suggesting a higher preference for hydrocarbon production. These findings demonstrate the importance of particle size in Co catalyzed Fischer-Tropsch synthesis. The use of well-defined CoO/CS catalysts offers valuable insights into the structure-activity relationship, leading to a better understanding of Co catalyzed Fischer-Tropsch synthesis. [ABSTRACT FROM AUTHOR]

Numerical modeling of concrete fractures is of prime importance in the durability assessment of civil engineering structures. The phase field model has been demonstrated as a promising framework to simulate crack propagation in brittle material while using the many existing techniques. In this paper, we discuss choosing the most appropriate phase field model for describing the fracture behavior of concrete. More specifically, we present a detailed analysis of the existing models, which have been created by combining different spectral decompositions and crack density functions. The numerical simulation predictions are confronted with the experimental observation of a benchmark problem from the literature. The obtained results showed that the extensive/ compressive decomposition and the quadratic crack density function are the most suitable models to study concrete cracking behavior. The investigation's size effects demonstrated heterogeneities played an important role in concrete's post-cracking behavior and softening branches, especially for the small concrete structure. [ABSTRACT FROM AUTHOR]

The discovery of deepwater oil and gas sources has altered the scenario of world production of oil products, attracting even more attention to nickel superalloys. However, this class of materials can be used in several applications. Furthermore, nickel superalloys are highly dependent on their processing history, and the manner in which superalloys react to machining can directly affect the finished product. This work aims to evaluate the surface integrity of two different materials after cryogenic side-milling in conditions that stimulate severe plastic deformation (SPD) and high heat generation. The results show that the material response to machining depends strongly on the pre-processing route instead of most assumptions. While cryogenic cooling led to significant sub-surface hardness and microstructural changes in wrought Inconel 625 alloy, such changes were not observed for clad Inconel 625. Therefore, in order to achieve significant surface integrity changes, process parameters need to be selected and optimized accordingly. Also, the findings indicate that some new factors established significant affect/change surface integrity: (a) SPD through a high rβ/h ratio; (b) the specific pre-processing thermomechanical history of the workpiece material; and (c) and cryogenic cooling, by changing material properties, reducing temperature and altering cutting phenomena and chip formation. [ABSTRACT FROM AUTHOR]

Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT) stands out among lead‐free ferroelectric oxides under consideration to replace state‐of‐the‐art high‐sensitivity piezoelectric Pb(Zr,Ti)O3, for a range of energy conversion ceramic technologies. However, the best performances have been reported for very coarse‐grained materials, and attempts to refine microstructure below 10 µm grain size consistently result in significant property degradation. Here a comprehensive study of the grain size effects on the properties of BCZT across the micron scale is reported, down to the verge of the submicron one. Results show a distinctive early evolution of properties for grain sizes between 1 and 5 µm. For the larger sizes in this range, an opposite effect is found for the piezoelectric charge coefficient and electric field‐induced strain with respect to the very coarse‐grained material, while very good overall performance is maintained. For the lower sizes, relaxor features appear, yet materials can still be poled indicating their ferroelectric nature. This strongly resembles size effects in the Pb(Mg1/3Nb2/3)O3‐PbTiO3 system, driven by the slowing down of the relaxor to ferroelectric transition with size reduction, though kinetics seem to slow down across much larger grain sizes for BCZT. Concomitant changes in the polymorphic phase coexistence are described and discussed by synchrotron X‐ray diffraction. [ABSTRACT FROM AUTHOR]

We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Struct. 38 (26-27): 4585-4608 '01). Depending on how different characteristic lengths of the domain scale with respect to the Cosserat intrinsic length, we obtain either an effective classical Cauchy continuum or an effective Cosserat continuum. Moreover, we provide some corrector type results for each case. [ABSTRACT FROM AUTHOR]

The corrugated sheet is a crucial component of the metal honeycomb structure. This study investigates the size effects on the deformation behavior of ultra-thin-walled corrugated sheets in the roll bending process using experimental and simulation methods. A precision roll bending device was developed, which incorporated a specifically designed eccentric fine-tuning module and a pneumatic module to prevent the distortion and insufficient deformation of the ultra-thin-walled corrugated sheets. The experimental results showed that micro-scratches and orange peel phenomenon appeared in the bending region of ultra-thin-walled corrugated sheets due to the lack of grain deformation coordination. Decreasing the ratio of foil thickness to grain diameter (t/d value) resulted in a slight increase in edge lengths, but a sharp decrease in the thickness of the bending region of ultra-thin-walled corrugated sheets. For the ultra-thin-walled corrugated sheet with a t/d value of 1.2, its thickness was reduced by 14%, leading to a high risk of rupture. Consequently, a finite element model of the roll bending process was established with consideration of the heterogeneity of grain shape and grain orientation. The simulation results indicate that the prediction error of the model for the springback angle was less than 15%. The random distribution of elastic deformation and plastic penetration zones is responsible for the great scatter of the springback angle of ultra-thin-walled corrugated sheets. This research provides a theoretical foundation for the precision manufacturing of ultra-thin-walled corrugated sheets. [ABSTRACT FROM AUTHOR]

Сучасні технології електроніки і сенсорної техніки дозволяють отримувати плівкові матеріали нанометрової товщини із унікальними властивостями, які не є типовими для масивного стану. Експериментально встановлено, що перехід від масивного до плівкового матеріалу призводить до змін його фізичних властивостей. Основні причини цього пов’язані: з різною структурою матеріалів; розмірними ефектами, які виникають у результаті обмеження середньої довжини вільного пробігу носіїв електричного струму зовнішніми поверхнями плівки або геометричними розмірами кристалітів; зміною частотних і енергетичних характеристик атомів кристалічної решітки під дією температурного фактору. На основі температурних залежностей питомого опору одношарових металевих плівок благородних металів (Pd, Pt і Ag) проаналізовані особливості високотемпературної електрон-фононної взаємодії. Нами установлено, що кутовий коефiцiєнт лiнiйної дiлянки температурних залежностей питомого опору одношарових плiвок зростає при зменшеннi їх товщини. При зменшенні товщини плівки середня енергія фонона збільшується, що призводить до підвищення ефективності електрон-фононного розсіювання і, як наслідок цього, – зростання питомого опору. [ABSTRACT FROM AUTHOR]

Size effects, influencing a material's strength, elongation, fatigue limit, and longevity, depend on the operative and dominant deformation and failure mechanisms. This study explores the size effects in additive manufactured (AM) GRCop-42 (Cu-4at%Cr-2at%Nb) thin wall structures fabricated via laser-powder bed fusion (L-PBF) and their impact on fatigue life. The influence of internal defects and surface topography on the fatigue life of specimens in both as-built and hot isostatic pressed (HIP) conditions across different thicknesses is investigated. Where micro-computed tomography (μCT) was used to quantify the internal porosity of as-built, pristine HIP'd, and fatigued HIP'd specimens, and laser microscopy was employed to quantify the surface topography of specimens prior to fatigue. Additionally, quasi-static tests were used to establish baseline mechanical properties (i.e. yield strength (YS), ultimate tensile strength (UTS), and elongation) to frame fatigue testing conditions. Results indicate a significant enhancement in fatigue life for HIP'd specimens for both thicknesses, with internal defects depicting a greater impact than surface topography. Furthermore, fractographic analysis suggests that thicker specimens exhibit higher resistance to crack propagation during fatigue testing in the absence of substantial porosity. Thus, the size effects observed on the fatigue life of L-PBF GRCop-42 appears to be dominated by internal defects.

Abstract Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT) stands out among lead‐free ferroelectric oxides under consideration to replace state‐of‐the‐art high‐sensitivity piezoelectric Pb(Zr,Ti)O3, for a range of energy conversion ceramic technologies. However, the best performances have been reported for very coarse‐grained materials, and attempts to refine microstructure below 10 µm grain size consistently result in significant property degradation. Here a comprehensive study of the grain size effects on the properties of BCZT across the micron scale is reported, down to the verge of the submicron one. Results show a distinctive early evolution of properties for grain sizes between 1 and 5 µm. For the larger sizes in this range, an opposite effect is found for the piezoelectric charge coefficient and electric field‐induced strain with respect to the very coarse‐grained material, while very good overall performance is maintained. For the lower sizes, relaxor features appear, yet materials can still be poled indicating their ferroelectric nature. This strongly resembles size effects in the Pb(Mg1/3Nb2/3)O3‐PbTiO3 system, driven by the slowing down of the relaxor to ferroelectric transition with size reduction, though kinetics seem to slow down across much larger grain sizes for BCZT. Concomitant changes in the polymorphic phase coexistence are described and discussed by synchrotron X‐ray diffraction.

Dams fragment stream habitats and fishways around dams typically serve few species that are strong swimmers or jumpers. We tested a prototype wetted ramp designed to allow upstream passage of small-bodied fishes while blocking upstream movement of invasive sea lampreys in the Laurentian Great Lakes. We tested short, smooth ramps with 5–10 mm water depth in various combinations of ramp angle, water flow, and swim channel width with the aim to selectively block adult migrating sea lampreys (Petromyzon marinus) while passing sub-adult white suckers (Catostomus commersonii) and creek chubs (Semotilus atromaculatus). Sea lampreys easily passed a 0.75 ramp at a 5° angle, but very few individuals passed a similar ramp at a 10° angle, and none passed a longer ramp at a 5° angle. Limiting the amplitude of tailbeats in a narrow channel did not hamper lampreys or the other species. Greater water flow, and thereby greater immersion depth on the ramp, fostered passage for all species. Smaller-bodied individuals of creek chubs and white suckers performed best on the ramp. We showed that wetted ramps could be incorporated into fishways at low-head dams to aid the passage of smaller-bodied fishes while also blocking the spawning migration of adult sea lampreys.

Additive manufacturing (AM) is often used to create designs inspired by topology optimization and biological structures, yielding unique cross-sectional geometries spanning across scales. However, manufacturing defects intrinsic to AM can affect material properties, limiting the applicability of a uniform material model across diverse cross-sections. To examine this phenomenon, this paper explores the influence of specimen size and layer height on the compressive modulus of polycarbonate (PC) and thermoplastic polyurethane (TPU) specimens fabricated using fused filament fabrication (FFF). Micro-computed tomography imaging and compression testing were conducted on the printed samples. The results indicate that while variations in the modulus were statistically significant due to both layer height and size of the specimen in TPU, variations in PC were only statistically significant due to layer height. The highest elastic modulus was observed at a 0.2 mm layer height for both materials across different sizes. These findings offer valuable insights into design components for FFF, emphasizing the importance of considering mechanical property variations due to feature size, especially in TPU. Furthermore, locations with a higher probability of failure are recommended to be printed closer to the print bed, especially for TPU, because of the lower void volume fraction observed near the heated print bed.

Benefiting from the ultra-high specific energy that is even comparable to gasoline, metal-air batteries (MABs) showcase great promising practical prospects in next-generation battery technologies that beyond the commercial Li-ion batteries. Even though the advances witnessed in MABs in the last decades, there are still numerous critical scientific challenges that need to be solved for their future practical applications. Especially, ascribed to the sluggish reaction kinetics and high overpotentials of air cathodes, the performances of MABs are less than ideal, which also makes its industrialization prospect unclear. Noble metal-based catalysts often show the superior catalytic activity in MABs, but the corresponding systematic review is still not given. Our review mainly focuses on the relationship between the MABs performances and the composite and structure of the noble metal catalysts regarding their size from nano to atom levels. In this review, we first introduced the synthesis strategies of the noble metal-based nano-catalysts followed up by discussing the influences of the size, morphology, and support of noble metal-based catalysts as well as their applications in a variety of MABs. In the following sections, the main advanced characterization techniques for single atom catalysts (SACs) and the roles and recent progress of the noble metal-based SACs were also discussed in detail. Finally, we provided personal outlook and perspectives towards the challenges and future development of MABs and noble metal-based catalysts.

Discrete dislocation dynamics (DDD) simulations reveal the evolution of dislocation structures and the interaction of dislocations. This study investigated the compression behavior of single-crystal copper micropillars using few-shot machine learning with data provided by DDD simulations. Two types of features are considered: external features comprising specimen size and loading orientation and internal features involving dislocation source length, Schmid factor, the orientation of the most easily activated dislocations and their distance from the free boundary. The yielding stress and stress-strain curves of single-crystal copper micropillar are predicted well by incorporating both external and internal features of the sample as separate or combined inputs. It is found that the machine learning accuracy predictions for single-crystal micropillar compression can be improved by incorporating easily activated dislocation features with external features. However, the effect of easily activated dislocation on yielding is less important compared to the effects of specimen size and Schmid factor which includes information of orientation but becomes more evident in small-sized micropillars. Overall, incorporating internal features, especially the information of most easily activated dislocations, improves predictive capabilities across diverse sample sizes and orientations.

This paper presents a comprehensive study on ultra-high-performance concrete (UHPC) beams without stirrups, where the test data of 487 beams were collected, and an experimental database was established. Four distinct shear strength calculation models for UHPC beams were examined in the study. These models were created from national specification guides. The results indicate that while the code equation is useful for predicting UHPC beam shear capacity, it consistently underestimates actual values, with a mean experimental-to-calculated ratio above 1.5. The database was also used to study the impacts of the compressive strength of UHPC, the shear span-to-depth ratio, the fiber volume fraction, and the reinforcement ratio on the shear strength of UHPC beams. The findings showed that the shear span-to-depth ratio significantly affected the shear load-bearing capacity of UHPC beams. The increase in the compressive strength of UHPC, fiber volume fraction, and reinforcement ratio positively affected the shear strength of UHPC beams to varying degrees. Additionally, there were size effects for beams with a shear span-to-depth ratio of less than 1.5 and an effective depth of more than 300. In addition, coefficients accounting for fiber influence and the shear span-to-depth ratio were incorporated to develop an enhanced formula for UHPC beams. The empirical data from the database tests revealed that the average ratio of the beams’ experimental shear capacity to the values predicted by the modified equation is 1.3, with a standard deviation of 0.74. These results suggest that the refined equation offers improved calculation precision and broader applicability. Eventually, a summary of the issues pertaining to the shear performance of UHPC beams and the key future research directions is provided to facilitate a clearer comprehension and awareness of emerging concepts for scholars within the discipline.

Many studies have shown that direct tensile tests are fraught with numerous challenges. The Double Punch Test (DPT) is considered a more reliable alternative for evaluating tensile properties among the indirect tensile methods. While DPT is efficient and reliable, its size effect should not be overlooked. Previous studies on DPT size effects have primarily focused on specimen size, with little discussion on the impact of punch size variations. Additionally, with the evolution of construction materials, the applicability of the generalized DPT formula to new materials, such as Ultra-High-Performance Concrete (UHPC), with its exceptional strength, toughness, durability, and crack resistance, needs to be evaluated. This study conducts experimental research on UHPC, focusing on the relationship between specimen and punch sizes and their impact on tensile strength measurements. By designing experiments with 12 different specimen sizes and punch ratios, we explore the differences between actual experimental results and simplified formula calculations. Bažant's theoretical methods are also applied to analyze the size effects of specimen and punch dimensions on DPT. The results indicate that, with appropriate specimen size and punch ratio, DPT can provide tensile strength measurements closer to those of Direct Tensile Tests (DTT). It was also found that tensile strength, strain, and toughness decrease with increasing specimen size. When the ratio of UHPC specimen to punch size (d/D) is 1/3, the results align well with the predictions of the simplified formula. This indicates that the optimal punch ratio is not fixed for different specimen sizes. These findings offer valuable references for designing related experiments and improving quality control and structural performance in various engineering fields. ● The effect of specimen and punch sizes were examined on the Double Punch Test (DPT). ● Size effect affects tensile property; smaller sizes show higher d/D sensitivity. ● Smaller specimens show higher internal friction angle ϕ and stress concentrations. ● Smaller specimens crack faster; larger ones need more energy but fail earlier. ● DPT results with d/D=1/3 closely match the simplified formula predictions. [ABSTRACT FROM AUTHOR]

A recent arrival in the open literature is the scaling theory finite similitude bringing into existence a countably infinite number of new similitude rules. The application of the theory to fracture mechanics has revealed that the first-order similitude rule is applicable in the sense that information gleaned from two fractured scaled components can be combined to capture the response of a third. This paper examines an unexplored aspect of the finite similitude theory, in that, it is shown how it can be re-configured for the purposes of scaling analysis. This is achieved by retaining the first derivative (with respect to scale) in the first-order rule and on involving an additional transport equation. The approach assumes the first-order rule to be exact, which is confirmed here, but in addition, has the advantage of automatically accounting for any defect-size related size effects that are present. It is a top-down scheme with analysis performed under the constraint of an imposed rule. To instigate the methodology, fracture mechanics for the first time is defined on a new scaling space, where all physical quantities are deemed dependent on a single dimensional scaling parameter β. This approach is demonstrated to facilitate the imposition of similitude rules and has led to the discovery of new relationships that connect fatigue responses at two sizes. Although analysis here is limited to linear elastic fracture mechanics (LEFM), it is demonstrated through proof, analytical, and experimentally validated numerical models, that the approach provides an exact scaling theory for fatigue. • A new analytical method is established for the analysis of fracture and fatigue. • New similitude rules are established involving derivatives with respect to scale. • The rules provide constraints on enrichment, cohesive zone models, and J-integrals. • New identities for fatigue are shown to be consistent with the Paris empirical law. [ABSTRACT FROM AUTHOR]

Using density functional theory, we determine the magnetic properties and the size effects of iron, cobalt and nickel nanoparticles and their alloys with platinum. Some weak oscillations of the spin magnetic moment are found due to the relaxation acting on the distances between the shells of the nanoparticles. The magnetic moment of the pristine nanoparticles depends mainly on the coordination. In the nanoalloys, due to a localization resulting from the variation of the atomic potential by assembling two different species, the magnetic moment of the nanoalloys is less dependent on the coordination and is more uniformly distributed at the surface. • A descriptor shows that the energy of the nanoalloys is closer to the energy of bulk materials compared to pristine metal nanoparticles. • The relaxation effects tend to produce a weak oscillation of the spin magnetic moment especially for large size nanoparticles. • The spin magnetic moment does not depend much on the coordination in the nanoalloys because of a localization due to the variation of the atomic potential by assembling two different species. • The significant difference between the atomic potentials of iron and platinum causes an uniform distribution of the spin magnetic moment at the surface of the FePt nanoalloys compared to the other nanoalloys. [ABSTRACT FROM AUTHOR]

To account for or neglect the defect position, i.e. the fatigue initiating defect location, both radially and axially, is evaluated for hourglass-shaped ultrasonic fatigue specimen. The commonly used analytical equations to calculate the stress is compared against a finite element (FE) based approach, which is able to fully considering the stress state at the defect position. Notably, the effects on several common fatigue analyses are evaluated: the fatigue strength distribution, the stress–life and the stress–defect relationships. Fracture mechanical assessment is also performed, for a comprehensive VHCF characterization of the EN-GJS-500-7 ductile cast iron used in the study. The VHCF properties are characterized up to 3 ⋅ 1 0 8 cycles, using the Step-Stress fatigue testing method under fully reversed loading. The FE-model and Weibull distribution as the choice of fatigue strength distribution, enables size effect evaluation by Weakest-link effective volume with the highly stressed volume method as benchmark. The work shows that it is imperative to use the local stress state at the defect position, as the distribution of failures can diverge largely from the center of the specimen, and that neglecting this causes systematic error and flawed potentially results. • In-depth VHCF characterization of an EN-GJS-500-7 ductile cast iron. • Effect of accounting for the defect position, radially and axially, is evaluated. • Evaluation is performed over a variety of common fatigue analyses techniques. • Systematic errors in the analytical equations for stress determination are alleviated. [ABSTRACT FROM AUTHOR]

With the rapid advancement of 5 G technology, the demand for surface acoustic wave (SAW) devices is experiencing exponential growth. Precisely forecasting the speed at which Rayleigh waves propagate, taking into account size effects and flexoelectric properties, is vital for enhancing SAW device design. To address this need, the study explores Rayleigh wave propagation in a stratified system consisting of a nanoscale piezoelectric guiding layer atop an isotropic elastic substrate. The governing equations, boundary conditions, and interface continuity conditions between the guiding layer and substrate are established through the Hamiltonian principle. Following this, the dispersion equations for Rayleigh waves under electric open-circuit and electric short-circuit conditions are derived and solved numerically. Additionally, the effects of flexoelectricity, inertial gradients, strain gradients, electric field gradients, and the piezoelectric guiding layer thickness on the phase velocity of Rayleigh waves are extensively explored. Our findings indicate that flexoelectricity and strain gradients elevate the phase velocity, while inertial gradients and electric field gradients result in a decrease in the phase velocity. As the frequency of Rayleigh waves increases, the impact of these factors becomes more prominent. In addition, it is observed that electric field gradients play a less significant role compared to inertial gradients and strain gradients. The findings of this study could offer valuable insights for the advancement of miniaturized SAW devices designed for high-frequency service. • Investigation of piezoelectric layer guided in-plane surface waves. • Consideration of size effects in nanoscale piezoelectric thin film. • Study of both electrically open- and short-circuit cases. • Findings show that flexoelectricity and strain gradients increase the phase velocity. • Discovery that inertial and electric field gradients decrease the phase velocity. [ABSTRACT FROM AUTHOR]

In this study, 15 % w/w polyvinylidene fluoride (PVDF)–Fe3O4 nanoparticle (NP) nanocomposite scaffolds were prepared using coaxial electrospinning with a high-speed conductive rotating collector to obtain aligned fibers. The effects of varying the Fe 3 O 4 NP size (6, 9, and 14 nm in diameter) on the fiber morphology, mechanical response, and piezoelectric phase content were investigated. In situ X-ray diffraction measurements during heating-cooling and tensile tests were carried out using synchrotron radiation to study the charge in the β-phase content and polymer chain orientation under different conditions. At zero strain, the presence of smaller NPs seems to impede the β-phase crystallization in PVDF. However, heating-cooling cycles revealed that the NPs acted as nucleation agents, promoting a higher β-phase content after cooling compared to pure PVDF. The mechanical response showed that nanocomposites with smaller NPs exhibited higher stiffness. While the initial degree of polymer chain orientation was higher in the nanocomposites, the presence of NPs hindered the α-to-β phase transformation and chain alignment under tensile deformation compared to pure PVDF. This study highlights the complex interplay among NP size, β-phase formation, mechanical properties, and chain orientation in PVDF-Fe 3 O 4 nanocomposites, providing insights into tailoring their piezoelectric performance for various applications. Graphical abstract: Comparison of two electrospun fibers: pure PVDF and PVDF + Fe₃O₄ nanoparticles. The pure PVDF fibers are thicker than the nanocomposite fiber, suggesting that pure PVDF fibers have a greater margin for deformation and alignment of polymer chains within the fiber structure. In contrast, the nanocomposite fibers, incorporating Fe₃O₄ nanoparticles, show reduced thickness, indicating less margin for deformation and orientation of polymer chains. However, both types of fibers exhibit a limit to polymer chain orientation before breakage occurs. [Display omitted] • We analyzed the microstructure at different length scales. We investigated the distribution of NPs as a function of their size. • A detailed description of the crystalline structure as a function of the NP size is provided under different conditions (mechanical and thermal loading). • This analysis provides details on the interaction at the NP length scale and the distribution of crystalline phases in the presence of the surrounding iron oxide NPs. [ABSTRACT FROM AUTHOR]

[Display omitted] • An unexpected size effect of precursor on graphene films was found in submicron range. • Commonly overlooked through-plane thermal conductivity was taken into consideration. • Submicron precursor surpasses micron one in preparing high-performance graphene films. • Thermally induced gases and gas-sheet interactions may lead to negative size effect. Graphene films assembled from graphene nanosheets have achieved a wide range of applications in thermal management due to their ultra-high thermal conductivity. Although it is well established in the micron range that increasing the lateral size of graphene sheets enhances the thermal conductivity of graphene films. However, the preparation of large-size graphene sheets and their assembly into ordered film structures remain challenging, which impedes the development of high-performance thermally conductive graphene films. Herein, by unifying the properties of graphene sheets and preparation processes, we correlate the thermal conductivity of graphene films and the lateral size of starting sheets ranging from 0.32 to 20.32 μm and probe the underlying mechanism from the perspectives of macroscopic and microscopic structural defects. Surprisingly, decreasing lateral size to 0.32 μm achieved as high in-plane thermal conductivity (K // , 1550.06 ± 12.99 W/mK) and significantly higher through-plane thermal conductivity (K ⊥ , 8.11 ± 0.08 W/mK) of graphene films as the case of 20.32 μm. Besides, the commonly overlooked size effect of K ⊥ shows an unexpected negative correlation, and the size effect of K // is also not monotonically increasing. These phenomena are correlated with micro-structure defects and lattice defects. Mechanism analysis reveals that thermally induced gas generation and the complex gas-sheet interactions during micro-structure evolution play a critical role in the size effect and may explain the unexpected negative size effect in the sub-micro range. These findings in size effects provide theoretical guidance for the selection of raw materials in fabricating highly thermally conductive graphene films. [ABSTRACT FROM AUTHOR]

Current research on the inverse design of phononic crystals, which aim to retrieve optimal structures according to given band gaps, is limited to controlling elastic waves at the macro-scale. This work extends the concept to nano-scale and implements this concept with phononic nanobeam made up of functionally graded materials by applying the nonlocal strain gradient theory and the probabilistic tandem network (PTN), which is responsible for detecting size effects and unveiling implicit relationships between band gaps and nanostructures. An analytical model that has not been published before is proposed based on the plane wave expansion method to predict band structures within size, thickness and porosity effects, enabling quick preparation for composing a dataset to train the network. Acting as an auto-encoder-like framework, the component of PTN in the reverse path allows to effectively encode required band gaps into a latent space, while the network in the forward path serves as a surrogate model to map the candidates from the latent space to band gaps. Numerical results not only show the influences of size effects on band gaps but also verify the accuracy, diversity, and generalization ability to meet different requirements of the inverse design. The proposed PTN can fulfill the on-demand design by generating multiple phononic nanobeams possessing same man-made band gaps. Undoubtedly, the framework proposed in the present work makes it a promising approach to provide flexible and diversified solutions, paving the way to discovering innovative phononic crystals at nano-scale. • A nonclassic model is developed to predict band gaps with size and thickness effects. • The inverse design is realized for FGM PnCs at the nanoscale by DL-based framework. • Diversified feasible designs regarding same requirement of band gaps are obtained. • Accurate FGM nano-PnCs are produced corresponding to band gaps tailored on-demand. [ABSTRACT FROM AUTHOR]