Classical Size Effect Research Articles

Experimental and mesoscopic simulation study of size effect on splitting tensile performance of spontaneous combustion coal gangue concrete

The spontaneous-combustion coal gangue concrete (SCGAC) demonstrates different mechanical behavior compared to ordinary concrete owing to its distinct porous structure and the presence of fibrous materials in its coarse aggregates. Presently, research on the macroscopic mechanical properties of SCGAC is reasonably comprehensive; however, it falls short of fully understanding its size effect. This study examines the splitting tensile strength of cubic SCGAC specimens with three strength grades, i.e., C30, C35, and C40, and three sizes, i.e., 100 mm, 150 mm, and 200 mm; proposes a mesoscopic modeling approach based on the computer vision; analyzes the intrinsic mechanisms of splitting failure and the size effect of different strength grades on the SCGAC by utilizing mesoscopic simulation methods. Subsequently, an analysis of the size effect on the splitting tensile strength of SCGAC is conducted based on classical size effect laws. The results reveal the following: The method proposed in this study for mesoscopic modeling is recognized for its low cost, high efficiency, and accurate simulations, fulfilling the required standards for mesoscopic mechanical analysis. SCGAC, as a heterogeneous material, demonstrates significant size effect phenomena that become more pronounced with enhancements in strength grades. The Carpinter fractal size effect law is ideally suited to characterize the size effect patterns in SCGAC. This paper enhances the comprehension of the size effect of SCGAC through a combination of macroscopic experiments and mesoscopic simulations, thereby facilitating its engineering applications.

Size effect of compressive performance of concrete under elevated temperatures: Tests and meso-scale analysis

This study investigates the size effect of concrete under ambient and elevated temperatures through tests and numerical simulations. Compressive performance of prismatic and cylindrical concrete specimens with varying dimensions were tested at temperatures ranging from ambient temperature to 600°C. Meso-scale finite element analysis (FEA), assuming that the mechanical properties of matrix and interfacial transition zones (ITZ) followed Weibull distribution, was employed to simulate the tested specimens and to conduct parametric analysis on specimens with larger or smaller sizes and under temperatures up to 800°C. Both experimental and numerical results showed that the cracks on the specimen surface became finer and denser as an increase of specimen sizes under elevated temperatures. A noticeable decrease in concrete compressive strength with increasing specimen dimensions was observed below 600°C, but peak strain and elastic modulus did not exhibit significant size effect. Size effect on strength diminished at temperatures exceeding 800°C. Classic Size Effect Laws (SEL), such as Weibull's and Bažant's SEL, were applicable to characterize the size effect on strength of specimens within common lab test dimensions under elevated temperatures. Based on the results from experiments, FEA and Bažant's SEL, a stress-strain model under elevated temperatures considering size effect was proposed. The predicted results from this model showed good agreement with test results.

Thermal transport and phonon localization in periodich-GaN/h-AlN superlattices.

The widely observed non-diffusive phonon thermal transport phenomenon in nanostructures is largely attributed to classical size effects, which ignore the characteristic of phonon wave. In this context, the crossover transition process from incoherent to coherent phonon transport in two-dimensional heterogeneous periodic h-GaN/h-AlN superlattices is demonstrated using a non-equilibrium molecular dynamics approach, where the localization behavior of thermal phonons is particularly significant. The results show that the thermal transport of the superlattice structure is affected by a combination of structural parameters and temperature. The thermal conductivity (TC) of the superlattice decreases and then increases as the interface density increases. Phonon-interface scattering dominates the incoherent phonon transport, while local phonons modulate the transport in the coherent region. Thus, the competition between phonon wave and particle properties causes the transition from incoherent to coherent phonon transport. In addition, as the TC valley depth slows down with increasing system temperature, the scattering of medium and high frequency phonons is enhanced and the phonon lifetime decreases. Research on localized phonons in superlattices provides theoretical support for thermal transport regulation in basal low-dimensional materials.

Remarkable heat conduction mediated by non-equilibrium phonon polaritons.

Surface waves can lead to intriguing transport phenomena. In particular, surface phonon polaritons (SPhPs), which result from coupling between infrared light and optical phonons, have been predicted to contribute to heat conduction along polar thin films and nanowires1. However, experimental efforts so far suggest only very limited SPhP contributions2-5. Through systematic measurements of thermal transport along the same 3C-SiC nanowires with and without a gold coating on the end(s) that serves to launch SPhPs, here we show that thermally excited SPhPs can substantially enhance the thermal conductivity of the uncoated portion of these wires. The extracted pre-decay SPhP thermal conductance is more than two orders of magnitude higher than the Landauer limit predicted on the basis of equilibrium Bose-Einstein distributions. We attribute the notable SPhP conductance to the efficient launching of non-equilibrium SPhPs from the gold-coated portion into the uncoated SiC nanowires, which is strongly supported by the observation that the SPhP-mediated thermal conductivity is proportional to the length of the gold coating(s). The reported discoveries open the door for modulating energy transport in solids by introducing SPhPs, which can effectively counteract the classical size effect in many technologically important films and improve the design of solid-state devices.

Inverse design in nanoscale heat transport via interpolating interfacial phonon transmission

We introduce a methodology for density-based topology optimization of non-Fourier thermal transport in nanostructures, based upon adjoint-based sensitivity analysis of the phonon Boltzmann transport equation (BTE) and a novel material interpolation technique, the “transmission interpolation model” (TIM). The key challenge in BTE optimization is handling the interplay between real- and momentum-resolved material properties. By parameterizing the material density with an interfacial transmission coefficient, TIM is able to recover the hard-wall and no-interface limits, while guaranteeing a smooth transition between void and solid regions. We first use our approach to tailor the effective thermal conductivity tensor of a periodic nanomaterial; then, we maximize classical phonon size effects under constrained diffusive transport, identifying a promising new thermoelectric material design. Our method enables the systematic optimization of materials for heat management and conversion and, more broadly, the design of devices where diffusive transport is not valid.

Size-Dependent Grain-Boundary Scattering in Topological Semimetals

We assess the viability of topological semimetals for application in advanced interconnect technology, where conductor size is on the order of a few nanometers and grain boundaries are expected to be prevalent. We investigate the electron transport properties and grain-boundary scattering in thin films of the topological semimetals $\mathrm{Co}\mathrm{Si}$ and $\mathrm{Co}\mathrm{Ge}$ using first-principles calculations combined with the nonequilibrium Green's function (NEGF) technique. Unlike conventional interconnect metals such as $\mathrm{Cu}$ and $\mathrm{Al}$, we find that $\mathrm{Co}\mathrm{Si}$ and $\mathrm{Co}\mathrm{Ge}$ conduct primarily through topologically protected surface states in thin-film structures even in the presence of grain boundaries. The area-normalized resistance decreases with decreasing film thickness for $\mathrm{Co}\mathrm{Si}$ and $\mathrm{Co}\mathrm{Ge}$ thin films both with and without grain boundaries; a trend opposite to that of the conventional metals $\mathrm{Cu}$ and $\mathrm{Al}$. The surface-dominated transport mechanisms in thin films of topological semimetals with grain boundaries does not follow the classic resistivity size effect, and suggests that these materials may be promising candidates for applications as nanointerconnects where high electrical resistivity acts as a major bottleneck limiting semiconductor device performance.

Galvanomagnetic and Thermoelectric Properties of Bismuth Films Doped with Tin

This paper presents the experimental study of the galvanomagnetic and thermoelectric properties of thin bismuth films doped with tin. The amount of tin is 0.06 at. % with the thickness ranged within 250-800 nm, and it is deposited on mica-muscovite substrates in vacuum up to 1·10-5 mm Hg. The galvanomagnetic and thermoelectric coefficients of all presented films are measured in the temperature range of 77-300 K in a magnetic field of up to 0.65 T. It is found that the classical size effect in the films occurs due to mobility of electrons being restricted by the thickness of the film. A characteristic maximum of temperature dependence of relative transverse magnetoresistance in the temperature range of 150-200 K is observed. A change in the sign of the Seebeck coefficient at the temperature of 175 K is found. It can be explained by the temperature change ratio of the electron and hole components contributions to galvanomagnetic and thermoelectric phenomena, and the contribution of holes at the L, T points of the Brillouin zone. The positive values of differential thermoelectric power in bismuth films doped with tin can become the basis for searching for the possibility of creating a p-branch of thermoelectric energy converters in the low-temperature area. The obtained results of measurements can be used for creation of a low-dimensional bismuth-based structures with a controlled hole concentration.

Elastic stiffening induces one-dimensional phonons in thin Ta2Se3 nanowires

Compared to extensive studies of thermal transport in two-dimensional materials, very limited attention has been paid to the corresponding phenomenon in quasi-one-dimensional van der Waals crystals. Here, we show that Ta2Se3 can be easily exfoliated into thin nanowires, indicating strong anisotropy in the bonding strength within the basal plane. Systematic thermal property measurements disclose signatures of one-dimensional phonons as the nanowire hydraulic diameter reduces below 19.2 nm with linearly escalating thermal conductivity as temperature increases and size dependence inconsistent with the classical size effect. We further show that these unusual transport properties are induced by elastic stiffening occurring for wires of <30 nm diameter.

Size effect on tensile strength of lightweight aggregate concrete: A numerical investigation

Lightweight aggregate concrete (LWAC) showed an obvious brittleness when subjected to the tensile stress, and the related size effect issue was crucial for the analysis and design of structural LWAC. The random aggregate structure was used to establish finite element models, and materials parameters were calibrated by using existing test data. Influences of the ratio of water-to-binder (W/B) materials, grading of lightweight aggregate (LWA), the strength of LWA and the relative strength of interfacial transitional zone on the tensile strength and the size effect of LWAC were evaluated. Finally, the results of simulations were applied to conduct a regression analysis on classical size effect law. It was concluded that the grading of LWA had a relatively more minor influence on the size effect of LWAC in tension, while the W/B ratio and the strength of LWA significantly affected the size effect due to the alteration of the concrete strength. Formulas for parameters in classical size effect law were developed by using the results of numerical analysis.

From nanowires to super heat conductors

Thermal transport through various nanowires has attracted extensive attention in the past two decades. Nanowires provide an excellent platform to dissect phonon transport physics because one can change the wire size to impose systematically varying boundary conditions that can help to distinguish the contributions of various scattering mechanisms. Moreover, novel confinement phenomena beyond the classical size effect promise opportunities to achieve highly desirable properties. Based on a summary of research progresses in nanowire thermal properties, we discuss more intriguing observations due to the classical size effect, coupling between mechanical and thermal properties, and divergent thermal conductivity as a result of conversion from three-dimensional to one-dimensional phonon transport, showcasing the superdiffusive thermal transport phenomenon. We hope that these discussions could provide a new perspective on further exploring thermal transport in nanowires, which may eventually lead to breakthroughs such as achieving thermal conductivity values higher than that of any known materials.

Anomalous Size Effect of Pt Ultrathin Nanowires on Oxygen Reduction Reaction.

The classical size effect of Pt particles on oxygen reduction reaction (ORR) suggests that the activity and durability would decrease with reducing the particle size, self-limiting the effectiveness in maximizing the Pt utilization efficiency with the particle-size-reduction strategy. Herein, we discover an anomalous size effect based on Pt nanowires (NWs) with tunable diameters, where the monotonically increasing activity and durability for ORR were observed with decreasing the diameter from 2.4 to 1.1 nm. Our results reveal that the dominant role of increased compressive strain induced by decreasing the diameter of NWs in weakening the adsorption and suppressing the Pt dissolution accounts for this anomalous size effect, where the reduced low-coordinated sites on NWs, the intrinsic structural advantage, is the root. Our findings not only expand the knowledge to the classical size effect but also provide new implications to break through the size limit in the design of Pt-based ORR catalysts.

Observation of superdiffusive phonon transport in aligned atomic chains.

Fascinating phenomena can occur as charge and/or energy carriers are confined in one dimension1-4. One such example is the divergent thermal conductivity (κ) of one-dimensional lattices, even in the presence of anharmonic interatomic interactions-a direct consequence of the Fermi-Pasta-Ulam-Tsingou paradox proposed in 19555. This length dependence of κ, also known as superdiffusive phonon transport, presents a classical anomaly of continued interest6-9. So far the concept has remained purely theoretical, because isolated single atomic chains of sufficient length have been experimentally unattainable. Here we report on the observation of a length-dependent κ extending over 42.5 µm at room temperature for ultrathin van der Waals crystal NbSe3 nanowires. We found that κ follows a 1/3 power law with wire length, which provides experimental evidence pointing towards superdiffusive phonon transport. Contrary to the classical size effect due to phonon-boundary scattering, the observed κ shows a 25-fold enhancement as the characteristic size of the nanowires decreases from 26 to 6.8 nm while displaying a normal-superdiffusive transition. Our analysis indicates that these intriguing observations stem from the transport of one-dimensional phonons excited as a result of elastic stiffening with a fivefold enhancement of Young's modulus. The persistent divergent trend of the observed thermal conductivity with sample length reveals a real possibility of creating novel van der Waals crystal-based thermal superconductors with κ values higher than those of any known materials.

Температурная зависимость проводимости нитевидных кристаллов теллура

In the temperature range 77−273K, a comparative analysis of the electrical conductivity of a whisker, an epitaxial film, and a single crystal of tellurium was undertaken. The electrical conductivity of the film and the single crystal increased monotonically up to 200K, then began to rise steeply, corresponding to thermal excitation of intrinsic carriers. The electrical conductivity of whiskers decreased with increasing temperature to 230K, after which it began to increase more gradually. It is assumed that in the case of tellurium whiskers, the classical size effect took place: the decrease in electrical conductivity was due to diffuse scattering of carriers by the lateral surface of the tellurium crystal and was intensified with increasing temperature. The uneven, tightly-convoluted surface of the samples was shown in images produced in a scanning electron microscope in the nanometer range.

Manifestations of classical size effect and electronic viscosity in the magnetoresistance of narrow two-dimensional conductors: Theory and experiment

We develop a classical kinetic theory of magnetotransport of 2D electrons in narrow channels with partly diffusive boundary scattering and apply it to description of magnetoresistance measured in the temperature interval 4.2-30 K in long mesoscopic bars fabricated from high-purity GaAs quantum well structures. Both experiment and theory demonstrate a number of characteristic features in the longitudinal and Hall resistances caused by the size effect in two dimensions owing to the high ballisticity of the transport. In addition to the features described previously, we also reveal a change in the slope of the first derivative of magnetoresistance when the cyclotron orbit diameter equals to half of the channel width. These features are suppressed with increasing temperature as a result of the electronic viscosity due to electron-electron interaction. By comparing theory and experiment, we determine the characteristic time of relaxation of angular distribution of electrons caused by electron-electron scattering.

Level excursion analysis of probabilistic quasibrittle fracture

It has widely been acknowledged that no structures can be designed to be risk free, and therefore reliability analysis plays an essential role in the design of engineering structures. The recent focus has been placed on structures made of brittle heterogenous (a.k.a. quasibrittle) materials, such as ceramics, composites, concrete, rock, cold asphalt mixture, and many more at the microscale. This paper presents a level excursion model for the analysis of probabilistic failure of quasibrittle structures, in which the failure statistics is calculated as a first passage probability. The model captures both the spatial randomness of local material resistance and the random stress field induced by microstructures (e.g. randomly distributed flaws). The model represents a generalization of the classical weakest-link model at the continuum limit and it recovers the classical Weibull distribution as an asymptotic distribution function. The paper discusses two applications of the model. The model is first applied to the strength distribution of polycrystalline silicon (poly-Si) MEMS specimens. It is shown that the model agrees well with the experimentally measured strength distributions of poly-Si MEMS specimens of different sizes. The model predicts a complete size effect curve of the mean structural strength transitioning from a vanishing size effect at the small-size limit to the classical Weibull size effect at the large-size limit. The second application is concerned with the left tail of strength distribution of quasibrittle structures. By taking into account both random stress and strength fields, the model is used to investigate the origin of the power-law tail distribution of structural strength.

Thermal transport exceeding bulk heat conduction due to nonthermal micro/nanoscale phonon populations

While classical size effects usually lead to a reduced effective thermal conductivity, we report here that nonthermal phonon populations produced by a micro/nanoscale heat source can lead to enhanced heat conduction, exceeding the prediction from Fourier's law. We study nondiffusive thermal transport by phonons at small distances within the framework of the Boltzmann transport equation (BTE) and demonstrate that the transport is significantly affected by the distribution of phonons emitted by the source. We discuss analytical solutions of the steady-state BTE for a source with a sinusoidal spatial profile, as well as for a three-dimensional Gaussian “hot spot,” and provide numerical results for single crystal silicon at room temperature. If a micro/nanoscale heat source produces a thermal phonon distribution, it gets hotter than that predicted by the heat diffusion equation; however, if the source predominantly produces low-frequency acoustic phonons with long mean free paths, it may get significantly cooler than that predicted by the heat equation, yielding an enhanced heat transport beyond bulk heat conduction.

Size Effect on Nominal Strength of Circular Stirrup-Confined RC Columns under Axial Compression: Mesoscale Study

AbstractMost previous studies have made great progress in the size effect of concrete materials and several classic size effect laws (SELs) have been proposed. However, there is a lack of size effe...

Numerical study on shear failure and the corresponding size effect of interior RC beam-column joints

The shear failure of the core zone of reinforced concrete (RC) beam-column joint has brittle characteristics, so the size effect of shear strength can be caused. Based on the existing experimental research results, the numerical test method is used to analyze the structural size, axial compression ratio, and stirrup ratio on the effect of failure mechanism and failure mode of the RC beam-column joint, and reveal their influence on the size effect of shear strength. The maximum cross-sectional dimension of the joint is 900 mm × 900 mm. The results show that: (1) under the monotonic loading, the beam-column nodes exhibit brittle shear failure in the core region, and the nominal shear strength has a significant size effect; (2) the increase in the axial compression ratio can enhance the shear capacity of the middle joint and also strengthen the size effect of shear strength; (3) an increase in the stirrup ratio can increase the shear capacity of the joint, but it can also weaken the size effect of the shear strength. Lastly, the classical size effect law proposed by Bažant can reflect the size effect of shear failure of the middle node, but it cannot describe the quantitative influence of the axial compression ratio and stirrup ratio.

Thermosize voltage induced in a ballistic graphene nanoribbon junction

A thermoelectric voltage is induced in a junction, constituted of two dissimilar materials under a temperature gradient. Similarly, a thermosize voltage is expected to be induced in a junction made by the same material but having different sizes, so-called thermosize junction. This is a consequence of dissimilarity in Seebeck coefficients due to differences in classical and/or quantum size effects in the same materials with different sizes. The studies on thermosize effects in the literature are mainly based on semiclassical models under relaxation time approximation or even simpler local equilibrium ones where only very general ideas and results have been discussed without considering quantum transport approaches and specific materials. To make more realistic predictions for a possible experimental verification, here we consider ballistic thermosize junctions made by narrow and wide (n−w) pristine graphene nanoribbons with perfect armchair edges and calculate the electronic contribution to the thermosize voltage, at room temperature, by using the Landauer formalism. The results show that the maximum thermosize voltage can be achieved for semiconducting nanoribbons and it is about an order of magnitude larger than that of metallic nanoribbons. In the semiconducting case, the thermosize voltage forms a characteristic plateau for a finite range of gating conditions. We demonstrate, through numerical calculations, that the induced thermosize voltage per temperature difference can be in the scale of mV/K, which is high enough for experimental measurements. Owing to their high and persistent thermosize voltage values, graphene nanoribbons are expected to be good candidates for device applications of thermosize effects.

(Invited) Phonon Transport in Nanoporous Si Films — from Periodic Nanopores to Nanoslots

Thermal transport within periodic nanoporous thin films has been widely studied for their potential applications in thermoelectrics and other phonon-related applications (1-4). A good thermoelectric material should have a high electrical conductivity σ, a high Seebeck coefficient S, and a low thermal conductivity k. The combination of these properties leads to a high dimensionless thermoelectric figure of merit (ZT), defined as ZT=S2σT/k, where T represents the absolute temperature. In nanoporous Si thin films, phonons can be diffusively scattered by nanopore edges to reduce the lattice part of the thermal conductivity (kL ), as the classical phonon size effects. On the other hand, electrons with usually much shorter mean free paths (MFPs) are slightly affected, leading to maintained S2σ and improved ZTs. With ultrafine periodic porous features, the phonon dispersion can also be modified due to coherent phonon transport within a periodic structure. This phenomenon involves the wave nature of lattice vibrations and is known as phononic effects. In this situation, kL can be largely reduced to enhance ZTs. Among existing studies on periodic nanoporous Si films, inconsistency can often be found among experimental and theoretical studies of the reduced lattice thermal conductivity for varied nanoporous patterns. Such divergence can be partially attributed to measurement errors and pore-edge damage introduced by varied nanofabrication techniques, namely reactive ion etching (RIE), deep RIE (DRIE), and a focused ion beam (FIB). To evaluate the impact of phononic effects, the thermal conductivities of periodic and aperiodic nanoporous Si films are compared in previous studies (5, 6). Along another line, the specific heat C, solely depending on the phonon dispersion, can also be measured to justify the phonon dispersion variation (7). In this work, the thermal conductivity of the same Si thin film is continuously measured with added rows of nanopores drilled by a FIB. When phononic effects exist, it is anticipated that the thermal resistance can be largely increased from single to multiple rows of nanopores. Without phononic effects, the thermal resistance of a patterned Si film should linearly increase with the number of nanopore rows. Beyond Si films with periodic nanopores, other nanoporous patterns are also investigated for their impact on the thermal transport, e.g., equally spaced nanoslots patterned on a Si thin film. When the neck width between adjacent nanoslots is smaller than the dominant phonon MFPs but longer than the electron MFPs, largely improved thermoelectric performance is anticipated (8). An analytical model has been developed to compute the transport properties of such structures, which yields identical results as complicated phonon and electron MC simulations. To compare with theoretical predictions, thermal measurements are also carried out on a Si thin film with nanofabricated neck region in its middle.