Using Cohen’s Effect Size to Identify Distinguishing Statements in Q-Methodology

Q-methodology was introduced more than 80 years ago to study subjective topics such as attitudes, perceptions, preferences, and feelings and there has not been much change in its statistical components since then. In Q-methodology, subjective topics are studied using a combination of qualitative and quantitative techniques. It involves development of a sample of statements and rank-ordering these statements by study participants using a grid known as Q-sort table. After completion of Q-sort tables by the participants, a by-person factor analysis (i.e., the factor analysis is performed on persons, not variables or traits) is used to analyze the data. Therefore, each factor represents a group of individuals with similar views, feelings, or preferences about the topic of the study. Then, each group (factor) is usually described by a set of statements, called distinguishing statements, or statements with high or low factor scores. In this article, we review one important statistical issue, i.e. the criteria for identifying distinguishing statements and provide a review of its mathematical calculation and statistical background. We show that the current approach for identifying distinguishing statements has no sound basis, which may result in erroneous findings and seems to be appropriate only when there are repeated evaluations of Q-sample from the same subjects. However, most Q-studies include independent subjects with no repeated evaluation. Finally, a new approach is suggested for identifying distinguishing statements based on Cohen’s effect size. We demonstrate the application of this new formula by applying the current and the suggested methods on a Q-dataset and explain the differences.

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.

Kinetics insights into size effects of carbon nanotubes'growth and their supported platinum catalysts for 4,6-dinitroresorcinol hydrogenation

Size effects are a well-documented phenomenon in heterogeneous catalysis,typically attributed to alterations in geometric and electronic properties.In this study,we investigate the influence of catalyst size in the preparation of carbon nanotube(CNT)and the hydrogenation of 4,6-dinitroresorcinol(DNR)using Fe_(2)O_(3)and Pt catalysts,respectively.Various Fe_(2)O_(3)/Al_(2)O_(3)catalysts were synthesized for CNT growth through catalytic chemical vapor deposition.Our findings reveal a significant influence of Fe_(2)O_(3)nanoparticle size on the structure and yield of CNT.Specifically,CNT produced with Fe_(2)O_(3)/Al_(2)O_(3)containing 28%(mass)Fe loading exhibits abundant surface defects,an increased area for metal-particle immobilization,and a high carbon yield.This makes it a promising candidate for DNR hydrogenation.Utilizing this catalyst support,we further investigate the size effects of Pt nanoparticles on DNR hydrogenation.Larger Pt catalysts demonstrate a preference for 4,6-diaminoresorcinol generation at(100)sites,whereas smaller Pt catalysts are more susceptible to electronic properties.The kinetics insights obtained from this study have the potential to pave the way for the development of more efficient catalysts for both CNT synthesis and DNR hydrogenation.

Enhanced soft magnetic properties of SiO_(2)-coated FeSiCr magnetic powder cores by particle size effect

It has been known that metal FeSiCr powders with large average particle sizes have been typically employed to prepare magnetic powder cores(SMCs),with few studies reported on the influence of magnetic properties for original powders with various average particle sizes less than 10m.In this work,SiO_(2)-coated FeSiCr SMCs with different small particle sizes were synthesized using the sol-gel process.The contribution of SiO_(2)coating amount and voids to the soft magnetic properties was elaborated.The mechanism was revealed such that smaller particle sizes with less voids could be beneficial for reducing core loss in the SMCs.By optimizing the core structure,permeability and magnetic loss of 26 and 262 kW/cm^(3)at 100 kHz and 50 mT were achieved at a particle size of 4.8m and ethyl orthosilicate addition of 0.1 mL/g.The best DC stacking performance,reaching 87%,was observed at an ethyl orthosilicate addition rate of 0.25 mL/g under 100 Oe.Compared to other soft magnetic composites(SMCs),the FeSiCr/SiO_(2)SMCs exhibit significantly reduced magnetic loss.It further reduces the magnetic loss of the powder core,providing a new strategy for applications of SMCs at high frequencies.

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.

Strength criterion for crystalline rocks considering grain size effect and tensile-compressive strength ratio

The macroscopic mechanical properties of rocks are significantly influenced by their microstructure.As a material bonded by mineral grains,the grain morphology of crystalline rock is the primary factor influencing the strength.However,most strength criteria neglect the strength variations caused by different grain characteristics in rocks.Furthermore,the traditional linear criteria tend to overestimate tensile strength and exhibit apex singularity.To address these shortcomings,a piecewise strength criterion that considers the grain size effect has been proposed.A part of an ellipse was employed to construct the envelope of the tensive-shear region on the meridian plane,to accurately reproduce the low tensile-compressive strength ratio.Based on the analysis of experimental data,both linear and exponential modification functions that account for grain size effects were integrated into the proposed criterion.The corresponding finite element algorithm has been implemented.The accuracy and applicability of the proposed criterion were validated by comparing with the experimental data.

The Role of the Size Effect on the Drying of Refractory Castables—How Its Under-standing Could Narrow the Gap between Laboratory Studies and Industrial Reality

Refractories have unique capabilities such as sustaining their shape and properties at extreme conditions such as the combination of high temperatures and thermal shock,contact with molten metals and slags and in some circumstances resistance to erosion from abrasive particles.Given the large processing output of the heavy industries such as the cement and steel ones which both require high temperature processes,the refractories structures span various meters and weight of several tons.As the water removal stage of hydraulic bonded castables in industrial sites takes hours(10-60 h)due to the risk of explosive spalling,efforts to mitigate it are commonly studied.This has provided theoretical understanding of the general aspects of drying and important tools,such as the thermogravimetry analysis(TGA),for the design of refractory compositions with higher explosive spalling resistance.However,the optimization of this process is still far from the industrial reality especially because the actual linings that require the drying are orders of magnitude larger than the samples considered in the laboratory tests.Therefore,this study proposed the analysis of the sample volume effect on the water removal dynamics through TGA of high alumina castables with calcium aluminate cement.Conventionalφ5 cm×5 cm cylindrical samples were assessed in a laboratory scale equipment whereas macro TGA were carried out considering 20 cm×20 cm×20 cm and 30 cm×30 cm×30 cm cubic samples.Additionally,the effect of polymeric fibers was also considered.It was found out that the different thermal gradients within the macro TGA samples resulted in an inflection on the sample’s heating rate and that the mass loss was affected by the volume considered,especially for the composition without additives.These findings highlight the requirement of carefully taking into consideration the different dimensional sizes and thermal gradients in the samples when analyzing and interpreting the laboratory studies,and especially when trying to extrapolate such results to the industrial reality.

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.

Gold/Mg-Al mixed oxides catalysts for oxidative esterification of methacrolein:Effects of support size and composition on gold loading

Gold catalysts supported on Mg-Al mixed oxides for oxidative esterification of methacrolein are prepared by impregnation.Effects of the support particle size,concentration of HAuCl4 solution and Mg/Al ratio on gold loading and catalytic properties are investigated.The catalysts are characterized by CO_(2)-TPD,EDS,XPS,STEM and XRD techniques.Catalysts with smaller support particle size show more uniform gold distribution and higher gold dispersion,resulting in a higher catalytic performance,and the uniformity of gold and the activity of the catalysts with larger support particle size can be improved by decreasing the concentration of HAuCl4 solution.The Mg/Al molar ratio has significant effect on the uniformity of gold and the activity of the catalyst,and the optimum Mg/Al molar ratio is 0.1–0.2.This study underlines the importance of engineering support particle size,concentration of HAuCl4 solution and density of adsorption sites for efficient gold loading on support by impregnation.

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.

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.

Styrene epoxidation catalyzed by polyoxometalate/quaternary ammonium phase transfer catalysts: The effect of cation size and catalyst deactivation mechanism

Catalytic epoxidation of alkenes is an important type of organic reaction in chemical industry,and the deep insight into catalyst deactivation will help to develop new epoxidation process.In this work,series of quaternary ammoniums bearing different cationic sizes,i.e.MTOA+(methyltrioctylammonium,[(C_(8)H_(17))_(3)CH_(3)N]+),HTMA+(hexadecyltrimethylammonium,[(C_(16)H_(33))(CH_(3))_(3)N]+) and DMDOA+(dimethyldioctadecylammonium,[(C_(18)H_(37))_(2)(CH_(3))_(2)N]+) were incorporated with polyoxometalate (POM) anions to prepare phase transfer catalysts (PTCs),which were used in the styrene epoxidations.Among them,(MTOA)_(3)PW_(4)O_(24)exhibits the best catalytic performance judged from the highest styrene conversion rate(52%) and styrene oxide selectivity (93%),during which the styrene epoxidation conditions were optimized.Meanwhile,the deactivation mechanism of this kind of PTCs was proposed firstly,i.e.in the case of low H_(2)O_(2) content,the oxidant can only be used in the styrene epoxidation,in which the catalyst can transform into stable Keggin-type POM.But when the content of H_(2)O_(2) is higher,the excess H_(2)O_(2) can reactivate the Keggin-type POM into active (PW_(4)O_(24))_(3)-anions,which can trigger the ring-opening polymerization of styrene oxide.Consequently,the catalyst is deactivated by adhered poly(styrene oxide)irreversibly,which was determined by NMR spectra.In this situation,the active moiety{PO_(4)[WO(O_(2))_(2)]_(4)}_(3)-in phase-transfer catalytic system can break into some unidentified species with low W/P ratio with the presence of epoxides.This work will be beneficial for the design of new PTCs in alkene epoxidation in fine chemical industry.

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.

Determination method of mesh size for numerical simulation of blast load in near-ground detonation

In order to improve the overall resilience of the urban infrastructures, it is required to conduct blast resistant design for important building structures in the city. For complex terrain in the city, it is recommended to determine the blast load on the structures via numerical simulation. Since the mesh size of the numerical model highly depends on the explosion scenario, there is no generally applicable approach for the mesh size selection. An efficient method to determine the mesh size of the numerical model of near-ground detonation based on explosion scenarios is proposed in this study. The effect of mesh size on the propagation of blast wave under different explosive weights was studied, and the correlations between the mesh size effect and the charge weight or the scaled distance was described. Based on the principle of the finite element method and Hopkinson-Cranz scaling law, a mesh size measurement unit related to the explosive weight was proposed as the criterion for determining the mesh size in the numerical simulation. Finally, the applicability of the method proposed in this paper was verified by comparing the results from numerical simulation and the explosion tests and was verified in AUTODYN.

Numerical simulation on size effect of copper with nano-scale twins

To understand the tensile deformation of electro-deposited Cu with nano-scale twins, a numerical study was carried out based on a conventional theory of mechanism-based strain gradient plasticity （CMSG）. The concept of twin lamella strengthening zone was used in terms of the cohesive interface model to simulate grain-boundary sliding and separation. The model included a number of material parameters, such as grain size, elastic modulus, plastic strain hardening exponent, initial yield stress, as well as twin lamellar distribution, which may contribute to size effects of twin layers in Cu polycrystalline. The results provide information to understand the mechanical behaviors of Cu with nano-scale growth twins.

Ligand Size Effect on PdLn Oxidative Addition with Aryl Bromide： A DFT Study

The process and mechanism of the ligand volume controlled Pd（PR3）2 （PR3=PH3, PMe3, and PtBu3） oxidative addition with aryl bromide were investigated, using density functional theory method with the conductor-like screening model. Association pathway and dissocia-tion pathway were investigated by the comparison of several energies. The cleavage energy of Pd（PR3）2 complex was calculated, as well as the oxidative addition reaction barrier energy of Pd（PR3）n （n=1,2） with aryl bromide in N,N-dimethylformamide solvent. This study proved that the ligands volume possessed a great impact on the mechanism of oxidative addition： less bulky ligand palladium associated with aryl bromide via two donor ligands,but larger bulky ligand palladium coordinated via monoligand.

Size effects on plastic deformation behavior in micro radial compression of pure copper

Micro radial compression tests were carried out on cylindrical specimens of pure copper polycrystals with different grain sizes. Experimental results indicated that phenomena of decreasing forming force, increasing scatter of forming force and more irregular surface topography occurred with the increase of grain size. A modified surface model based on dislocations pile-up in surface layer grains, and a flow stress scattering formulation based on standard deviation and grain size distribution were proposed to analyze size effects on forming force in micro compression. The inhomogeneous deformation of surface layer grains was discussed by the main deformation manner of rotation. A good agreement with the experimental results was achieved.

Size effects on deformation behavior of C5210 phosphor bronze thin sheet

To investigate the effects of thickness and grain size on mechanical and deformation properties of C5210 phosphor bronze thin sheets, samples with different grain sizes were obtained through annealing heat treatment at different temperatures; and then tensile tests of samples with different thicknesses and grain sizes were conducted at room temperature. The results show that yield strength increases with decreasing thickness from 800 to 50 μm, but work hardening exponent and total elongation decrease, and a modified model was proposed to describe the relation between yield strength and thickness; yield strength decreases as the grain size increases, but work hardening exponent shows an increasing trend, total elongation increases to a peak and then decreases. Fracture morphology of tensile specimens was observed by SEM, which indicates that all tensile specimens are ductile fracture. The dimple intensity increases as the specimen thickness increases but reduces with the specimen grain size increasing.