240 nm AlGaN-based deep ultraviolet micro-LEDs:size effect versus edge effect

240 nm AlGaN-based micro-LEDs with different sizes are designed and fabricated.Then,the external quantum efficiency(EQE)and light extraction efficiency(LEE)are systematically investigated by comparing size and edge effects.Here,it is revealed that the peak optical output power increases by 81.83%with the size shrinking from 50.0 to 25.0μm.Thereinto,the LEE increases by 26.21%and the LEE enhancement mainly comes from the sidewall light extraction.Most notably,transversemagnetic(TM)mode light intensifies faster as the size shrinks due to the tilted mesa side-wall and Al reflector design.However,when it turns to 12.5μm sized micro-LEDs,the output power is lower than 25.0μm sized ones.The underlying mechanism is that even though protected by SiO2 passivation,the edge effect which leads to current leakage and Shockley-Read-Hall(SRH)recombination deteriorates rapidly with the size further shrinking.Moreover,the ratio of the p-contact area to mesa area is much lower,which deteriorates the p-type current spreading at the mesa edge.These findings show a role of thumb for the design of high efficiency micro-LEDs with wavelength below 250 nm,which will pave the way for wide applications of deep ultraviolet(DUV)micro-LEDs.

Experimental study on the size effect on the equation of state of concretes under shock loading

Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.

Size effect of fracture characteristics for anisotropic quasi-brittle geomaterials

Understanding the size effect exhibited by the fracture mechanism of anisotropic geomaterials is important for engineering practice. In this study, the anisotropic features of the nominal strength, apparent fracture toughness, effective fracture energy and fracture process zone(FPZ) size of geomaterials were first analyzed by systematic size effect fracture experiments. The results showed that the nominal strength and the apparent fracture toughness decreased with increasing bedding plane inclination angle.The larger the specimen size was, the smaller the nominal strength and the larger the apparent fracture toughness was. When the bedding inclination angle increased from 0° to 90°, the effective fracture energy and the effective FPZ size both first decreased and then increased within two complex variation stages that were bounded by the 45° bedding angle. Regardless of the inherent anisotropy of geomaterials,the nominal strength and apparent fracture toughness can be predicted by the energy-based size effect law, which demonstrates that geomaterials have obvious quasi-brittle characteristics. Theoretical analysis indicated that the true fracture toughness and energy dissipation can be calculated by linear elastic fracture mechanics only when the brittleness number is higher than 10;otherwise, size effect tests should be adopted to determine the fracture parameters.

Size effects on the tensile strength and fracture toughness of granitic rock in different tests

This study investigates the tensile failure mechanisms in granitic rock samples at different scales by means of different types of tests.To do that,we have selected a granitic rock type and obtained samples of different sizes with the diameter ranging from 30 mm to 84 mm.The samples have been subjected to direct tensile strength(DTS)tests,indirect Brazilian tensile strength(BTS)tests and to two fracture toughness testing approaches.Whereas DTS and fracture toughness were found to consistently grow with sample size,this trend was not clearly identified for BTS,where after an initial grow,a plateau of results was observed.This is a rather complete database of tensile related properties of a single rock type.Even if similar databases are rare,the obtained trends are generally consistent with previous scatter and partial experimental programs.However,different observations apply to different types of rocks and experimental approaches.The differences in variability and mean values of the measured parameters at different scales are critically analysed based on the heterogeneity,granular structure and fracture mechanics approaches.Some potential relations between parameters are revised and an indication is given on potential sample sizes for obtaining reliable results.Extending this database with different types of rocks is thought to be convenient to advance towards a better understanding of the tensile strength of rock materials.

Size effect on transverse free vibrations of ultrafine nanothreads

Due to their unique properties and appealing applications,low dimensional sp^(3)carbon nanostructures have attracted increasing attention recently.Based on the beam theory and atomistic studies,this work carries out a comprehensive investigation on the vibrational properties of the ultrathin carbon nanothreads(NTH).Size effect is observed in transverse free vibrations of NTHs.To quantify such effects,the modified couple stress theory(MCST)is utilized to modify the Timoshenko beam theory.According to the first four order frequencies of NTHs from atomistic simulations,the critical length scale parameter of MCST is calibrated as 0.1 nm.It is shown that MCST has minor effect on the first four order modal shapes,except for the clamped boundary.MCST makes the modal shapes at the clamped boundary closer to those observed in atomistic simulations.This study suggests that to some extent the MCST-based Timoshenko beam theory can well describe the transverse vibration characteristics of the ultrafine NTHs,which are helpful for designing and fabricating the NTH-based nanoscale mechanical resonators.

Multi-dimensional size effects and representative elements for nonpersistent fractured rock masses: A perspective of geometric parameter distribution

This study takes a fractured rock mass in the Datengxia Hydropower Station,China as an example to analyze the size effects and determine the representative elementary sizes.A novel method considering geometric parameter distributions is proposed in this work.The proposed method can quickly and simply determine the size effects and representative elementary sizes.Specifically,geometric parameter distributions,including fracture frequency,size and orientation,are generated on the basis of the Bernoulli trial and Monte Carlo simulation.The distributions are assessed using the coefficient of variation(CV),and the acceptable variations for CV(5%,10%and 20%)are used to determine representative elementary sizes.Generally,the representative element of rock masses is the representative elementary volume(REV).The present study extends the representative element to other dimensions,i.e.representative elementary length(REL)and representative elementary area(REA)for one and two dimensions,respectively.REL and REA are useful in studying the size effects of one-(1D)and twodimensional(2D)characteristics of rock masses.The relationships among multi-dimensional representative elementary sizes are established.The representative elementary sizes reduce with the increase in the dimensions,and REA and REV can be deduced by REL.Therefore,the proposed method can quickly and simply determine REL and further estimate REA and REV,which considerably improves the efficiency of rock mass analysis.

Size effects on the mixed modes and defect modes for a nano-scale phononic crystal slab

The size-dependent band structure of an Si phononic crystal(PnC)slab with an air hole is studied by utilizing the non-classic wave equations of the nonlocal strain gradient theory(NSGT).The three-dimensional(3D)non-classic wave equations for the anisotropic material are derived according to the differential form of the NSGT.Based on the the general form of partial differential equation modules in COMSOL,a method is proposed to solve the non-classic wave equations.The bands of the in-plane modes and mixed modes are identified.The in-plane size effect and thickness effect on the band structure of the PnC slab are compared.It is found that the thickness effect only acts on the mixed modes.The relative width of the band gap is widened by the thickness effect.The effects of the geometric parameters on the thickness effect of the mixed modes are further studied,and a defect is introduced to the PnC supercell to reveal the influence of the size effects with stiffness-softening and stiffness-hardening on the defect modes.This study paves the way for studying and designing PnC slabs at nano-scale.

Insights into the size effect of ZnCr_(2)O_(4)spinel oxide in composite catalysts for conversion of syngas to aromatics

Direct conversion of syngas to aromatics(STA)over oxide-zeolite composite catalysts is promising as an alternative method for aromatics production.However,the structural effect of the oxide component in composite catalysts is still ambiguous.Herein,we investigate the size effect by selecting ZnCr_(2)O_(4)spinel,as a probe oxide,mixing with H-ZSM-5 zeolite as a composite catalyst for STA reaction.The CO conversion,aromatics selectivity and space-time yield(STY)of aromatics are all significantly improved with the crystal size of ZnCr_(2)O_(4)oxide decreases,which can mainly attribute to the higher oxygen vacancy concentration and thus the rapid generation of more C1oxygenated intermediate species.Based on the understanding of the size-performance relationship,ZnCr_(2)O_(4)-400 with a smaller size mixing with H-ZSM-5 can achieve32.6%CO conversion with 76%aromatics selectivity.The STY of aromatics reaches as high as 4.79 mmol g_(cat)^(-1)h^(-1),which outperforms the previously reported some typical catalysts.This study elucidates the importance of regulating the size of oxide to design more efficient oxidezeolite composite catalysts for conversion of syngas to value-added chemicals.

Characterization of size effect of natural convection in melting process of phase change material in square cavity

The accelerating effect of natural convection on the melting of phase change material(PCM)has been extensively demonstrated.However,such an influence is directly dependent on the size and shape of domain in which phase change happens,and how to quantitatively describe such an influence is still challenging.On the other hand,the simulation of natural convection process is considerably difficult,involving complex fluid flow in a region changing with time,and is typically not operable in practice.To overcome these obstacles,the present study aims to quantitatively investigate the size effect of natural convection in the melting process of PCM paraffin filled in a square latent heat storage system through experiment and simulation,and ultimately a correlation equation to represent its contribution is proposed.Firstly,the paraffin melting experiment is conducted to validate the two-dimensional finite element model based on the enthalpy method.Subsequently,a comprehensive investigation is performed numerically for various domain sizes.The results show that the melting behavior of paraffin is dominated by the thermal convection.When the melting time exceeds 50 s,a whirlpoor flow caused by natural convection appears in the upper liquid phase region close to the heating wall,and then its influencing range gradually increases to accelerate the melting of paraffin.However,its intensity gradually decreases as the distance between the melting front and the heating wall increases.Besides,it is found that the correlation between the total melting time and the domain size approximately exhibits a power law.When the domain size is less than 2 mm,the accelerating effect of natural convection becomes very weak and can be ignored in practice.Moreover,in order to simplify the complex calculation of natural convection,the equivalent thermal conductivity concept is proposed to include the contribution of natural convection to the total melting time,and an empirical correlation is given for engineering applications.

Oxidative dehydrogenation of ethane with carbon dioxide over silica molecular sieves supported chromium oxides:Pore size effect

SBA-15 with varied pore size from 4 to 8 nm were synthesized by tuning the temperature of hydrothermal treatment,the supports were then used to load the active phase Cr Oxthrough a conventional impregnation method.The resulting catalysts were characterized by small/wide angle XRD,N_(2) adsorption/desorption,FT-IR,TEM-EDX,XPS,TPR and CO_(2)-TPD to study the feature of structure,surface chemical state,redox and basicity.It was found from these results that the metal species could be well dispersed on catalysts with larger pore size.Cr^(6+)species could enter into the framework by substituting the Si atoms of SBA-15,and Cr^(3+)mainly exist on extra framework.Pore size had profound effects on reducibility,surface composition and basicity.Cr^(6+)species were necessary to activate the C-H bonds of alkanes,while the basicity played an important role in activating C-O bonds of CO_(2).The best performances were achieved over the sample Cr supported on SBA-15 with a pore diameter of 7 nm in oxidative dehydrogenation of ethane in the presence of CO_(2).

Numerical simulation on borehole breakout and borehole size effect using discrete element method

Estimation of horizontal stress magnitudes from borehole breakouts has been an attractive topic in the petroleum and mining industries,although there are critical research gaps that remain unfilled.In this paper,numerical simulation is conducted on Gosford sandstone to investigate the borehole breakout and its associated borehole size effect,including temperature influence.The discrete element method(DEM)model shows that the borehole breakout angular span is constant after the initial formation,whereas its depth propagates along the minimum horizontal stress direction.This indicates that the breakout angular span is a reliable parameter for horizontal stress estimation.The borehole size effect simulations illustrated the importance of borehole size on breakout geometries in which smaller borehole size leads to higher breakout initiation stress as well as the stress re-distribution from borehole wall outwards through micro-cracking.This implies that the stress may be averaged over a distance around the borehole and breakout initiation occurs at the borehole wall rather than some distance into the rock.In addition,the numerical simulation incorporated the thermal effect which is widely encountered in deep geothermal wells.Based on the results,the higher temperature led to lower breakout initiation stress with same borehole size,and more proportion of shear cracks was generated under higher temperature.This indicates that the temperature might contribute to the micro-fracturing mode and hence influences the horizontal stress estimation results from borehole breakout geometries.Numerical simulation showed that breakout shape and dimensions changed considerably under high stress and high temperature conditions,suggesting that the temperature may need to be considered for breakout stress analysis in deep locations.

Size effect of sandstone after high temperature under uniaxial compression

Uniaxial compression tests on sandstone samples with five different sizes after high temperature processes were performed in order to investigate the size effect and its evolution. The test results show that the density, longitudinal wave velocity, peak strength, average modulus and secant modulus of sandstone decrease with the increase of temperature, however, peak strain increases gradually. With the increase of ratio of height to diameter, peak strength of sandstone decreases, which has an obvious size effect. A new theoretical model of size effect of sandstone material considering the influence of temperature is put forward, and with the increase of temperature, the size effect is more apparent. The threshold decreases gradually with the increase of temperature, and the deviations of the experimental values and the theoretical values are between 0.44% and 6.06%, which shows quite a credibility of the theoretical model.

Tailoring mechanical properties of PμSL 3D-printed structures via size effect

Projection micro stereolithography(PμSL)has emerged as a powerful three-dimensional(3D)printing technique for manufacturing polymer structures with micron-scale high resolution at high printing speed,which enables the production of customized 3D microlattices with feature sizes down to several microns.However,the mechanical properties of as-printed polymers were not systemically studied at the relevant length scales,especially when the feature sizes step into micron/sub-micron level,limiting its reliable performance prediction in micro/nanolattice and other metamaterial applications.In this work,we demonstrate that PμSL-printed microfibers could become stronger and significantly more ductile with reduced size ranging from 20μm to 60μm,showing an obvious size-dependent mechanical behavior,in which the size decreases to 20μm with a fracture strain up to~100%and fracture strength up to~100 MPa.Such size effect enables the tailoring of the material strength and stiffness of PμSL-printed microlattices over a broad range,allowing to fabricate the microlattice metamaterials with desired/tunable mechanical properties for various structural and functional applications.

Size effects in the uniaxial compressive properties of 3D printed models of rocks:an experimental investigation

Transparent physical models of real rocks fabricated using three-dimensional(3D)printing technology are used in photoelas-tic experiments to quantify the evolution of the internal stress and deformation fields of rocks.Therefore,they are rendered as an emerging powerful technique to quantitatively reveal the intrinsic mechanisms of rock failure.The mechanical behav-ior of natural rocks exhibits a significant size effect;however,limited research has been conducted on whether transparent physical models observe similar size effects.In this study,to make the transparent printed models accurately demonstrate the mechanical behavior of natural rocks and reveal the internal mechanism of the size effect in rock mechanical behavior,the size effect in 3D printed models of fractured and porous rocks under uniaxial compressive loading was investigated.Transparent cylindrical models with different sizes that contained different fractured and porous structures were printed using the fracture and porous characteristics extracted from natural coal and sandstone.The variation in uniaxial compres-sive strength and elastic modulus of fractured and porous models for increasing model sizes were obtained through uniaxial compression experiments.Finally,the influence of internal discontinuous structural features,such as fractures and pores,on the size effect pertaining to the mechanical behavior of the model was analyzed and elaborated by comparing it with the mechanical properties of the continuous homogeneous model without fractures and pores.The findings provided support and reference to analyze the size effect of rock mechanical behavior and the effect of the internal discontinuous structure using 3D printed transparent models.

Flow stress and tribology size effects in scaled down cylinder compression

Microforming is an effective method to manufacture small metal parts.However,macro forming can not be transferred to microforming directly because of size effects.Flow stress and tribology size effects were studied.Scaled down copper T2 cylinder compression was carried out with the lubrication of castor oil and without lubrication.The results show that the flow stress decreases with decreasing the initial specimen diameter in both lubrication conditions,and the flow stress decreases by 30 MPa with the initial specimen diameter decreasing from 8 mm to 1 mm.The friction factor increases obviously with decreasing the initial specimen diameter in the case of lubricating with castor oil,and the friction factor increases by 0.11 with the initial specimen diameter decreasing from 8 mm to 1 mm.However,the tribology size effect is not found in the case without lubrication.The reasons of the flow stress and tribology size effects were also discussed.

Size Effects of the Critical Temperature in Ferroelectric Thin Films

The size effects of the critical behaviors for the systems of interacting spins are discussed extensively inliterature.In this paper,the finite-size dependence of the critical temperature and susceptibility of the ferroelectric thinfilm are investigated numerically based on the four-state Potts model with the nearest-neighbor interactions between thedipole moments.The four orientations of the domains exist in the ferroelectric film and the movement of the domainwalls determines the polarization switching process besides the boundary conditions of the film.The critical exponentsare obtained and our investigations show that the boundary conditions play the important roles for the ferroelectricproperties of the thin films and the critical behavior of the thin films strongly depends on the feature of the surface.

The size effect and high activity of nanosized platinum supported catalysts for low temperature oxidation of volatile organic compounds

Pt/Al_(2)O_(3) catalysts with smaller size of Pt nanoparticles were prepared by ethylene glycol reduction method in two different way and their oxidation activities for three typical VOCs(volatile organic compounds)were evaluated.The catalyst prepared by first adsorption and then reduction procedure is denoted as L-Pt/Al_(2)O_(3) while the catalyst prepared by first reduction and then loading procedure is defined as R-Pt/Al_(2)O_(3).The results show that L-Pt/Al_(2)O_(3) with the stronger interaction between Pt species and Al_(2)O_(3) exhibit smaller size of Pt nanoparticles and favorable thermal stability compared with R-Pt/Al_(2)O_(3).L-Pt/Al_(2)O_(3) is favor of the formation of more adsorbed oxygen species and more Pt^(2+)species,resulting in high catalytic activity for benzene and ethyl acetate oxidation.However,R-Pt/Al_(2)O_(3) catalysts with higher proportion of Pt^(0)/Pt^(2+)and bigger size of Pt particles exhibits higher catalytic activity for n-hexane oxidation.Pt particles in R-Pt/Al_(2)O_(3) were aggregated much more serious than that in L-Pt/Al_(2)O_(3) at the same calcination temperature.The Pt particles supported on Al_(2)O_(3) with~10 nm show the best catalytic activity for n-hexane oxidation.

Alloying Behaviour and Atomic Size Effect in Palladium-rich Pd-RE Systems

The alloying behaviour, including solid solubilities of rare-earths as well as the formation and stability of various intermediate phases in palladium-rich Pd-RE systems were studied by means of the atomic size factor and the reduced transition temperatures. A strong analogy is observed in the plots of the reduced transition temperatures of various intermediate phases against the atomic numbers of rare-earths, and the law proposed by Hume-Rothery and Raynor for dependence of liquidus temperature on atomic radius in simple alloy systems has been extended to more complicated alloy systems.

Collective excitations and quantum size effects on the surfaces of Pb(111)films:An experimental study

Pb(111)film is a special system that exhibits strong quantum size effects in many electronic properties.The collective excitations,i.e.,plasmons,in Pb(111)films are also expected to show signatures of the quantum size effect.Here,using high-resolution electron energy loss spectroscopy,we measured the plasmons on the surface of Pb(111)films with different film thicknesses and analyzed the plasmon dispersions.One surface plasmon branch exhibits prominent damping in the small momentum range,which can be attributed to the interaction between the top and bottom interfaces of the Pb(111)films.With the film thickness increasing,the critical momentum characterizing the damping in Pb(111)films decays not only much slower in Pb(111)films than in other metal films,and even in films with the thickness up to 40 monolayers the damping still exists.The slow decay of the surface plasmon damping,manifesting the strong quantum size effect in Pb(111)films,might be related to the strong nesting of the Fermi surface along the(111)direction.

Application of fractal theory to size effect of disordered materials

For disordered materials it is impossible to measure constant material properties using the Euclidian geometrical dimension of the test specimens. Based on the theory of fractal geometry, the fractal dimension of the damaged microstructure is applied to measure the strength and fracture toughness of imitation marbles, which turn out to be scale invariant material constants. In this paper, the experimental data are treated and interpreted by the theory of fractal geometry. Reasonable results are obtained and the size effects on strength and fracture energy are observed.