Origin Of Size Effect Research Articles

Size effects and the existence of scalable materials and systems

Size effects are particular types of scale effect, where the response of a material is dependent to some extent on its size. These types of behaviour manifest to a greater or lesser extent in all materials, and pose a problem for constitutive models, where material parameters determined through experimentation at one size are inapplicable at different sizes. The origin of size effects is microstructural, through defects and structures ranging from cracks, fibres, grains, porosity, dislocations, precipitates, etc., and which has led to the creation of a plethora of microscale and mesoscale models in an attempt to represent the phenomena. In this paper an entirely different approach is taken where metamaterial constitutive models are created that eliminate entirely particular types of size effect. Such an approach has only recently been made possible with the arrival of a new scaling theory called finite similitude, which from a material-model standpoint starts from the unlikely position that it is founded on transport equations defined on a trial-spacetime manifold (where the scaled experiment resides). The approach however features a countably infinite number of similitude rules that in principle can capture any scale effect. It is this feature that enables metamaterials and metasystems to be defined on a projection of the trial spacetime manifold to the scaling-space manifold, where all physical quantities are dependent on a single dimensional scaling parameter. Metasystem and metamaterial models are shown to exist on the scaling space that feature the extraordinary ability to represent behaviours over a range of length scales. Although the models created are idealised they nevertheless provide a practical approach through testing at different sizes and it is demonstrated in the paper how real-world size effects can be captured efficiently.

Modeling the indentation size effects of polymers, based on couple stress elasticity and shear transformation plasticity

This work attempts to construct models which can describe the size effects in modulus and hardness of polymers measured by indentation tests. Firstly, the origin of size effects in the procedure of nanoindentation is analyzed. The finding of the literature that the indentation size effects of polymers are of significant elastic nature is further discussed and confirmed. The elastic size effects are described by a model, through introducing a model of elastic unloading load with consideration of couple stress elasticity into the Oliver-Pharr indentation approach. The accordingly proposed modulus model and hardness model agree excellently with a large amount of experimental data obtained from literatures. The models show that the elastic size effects of polymers and their experimental observations are mainly determined by the molecular structures. The fitting results verify that the size effects in indentation hardness of polymers with complex molecular structures are significantly elastic. It is postulated that the plastic size effects in indentation hardness of polymers are only derived from their glassy components. A shear transformation plasticity formula of glassy polymers recently proposed by literature is slightly extended to characterize the size dependent deformations in indentation tests. A hardness model with consideration of size effects is accordingly obtained and agrees well with related experimental data.

Origins of size effects in initially dislocation-free single-crystal silver micro- and nanocubes

We report phenomenal yield strengths—up to one-fourth of the theoretical strength of silver—recorded in microcompression testing of initially dislocation-free silver micro- and nanocubes synthesized from a multistep seed-growth process. These high strengths and the massive strain bursts that occur upon yield are results of the initially dislocation-free single-crystal structure of the pristine samples that yield through spontaneous nucleation of dislocations. When the pristine samples are exposed to a focused ion-beam to fabricate pillars and then compressed, the dramatic strain burst does not occur, and they yield at a quarter of the strength compared to the pristine counterparts. Regardless of the defect-state of the samples prior to testing, a size effect is apparent—where the yield strength increases as the sample size decreases. Since dislocation starvation and the single-arm-source mechanisms cannot explain a size effect on yield strength in dislocation-free samples, we investigate the dislocation nucleation mechanisms controlling the size effect through careful experimental observations and molecular statics simulations. We find that intrinsic or extrinsic symmetry breakers such as surface defects, edge roundness, external sample shape, or a high vacancy concentration can influence dislocation nucleation, and thus contribute to the size effect on yield strength in initially dislocation-free samples.

A strong basis for friction as the origin of size effect in cutting of metals

A study has been made of the phenomenon of size effect in cutting of metals, namely increase in the specific energy with decreasing chip thickness, in the absence of edge radius effects and under ideal two-dimensional cutting conditions. Freshly cleaved glass knives are used to achieve cutting edges that are sharp on an atomic level. An instrumented ultramicrotomy apparatus is described in which it is possible to achieve two-dimensional orthogonal cutting at small cutting depths in the range of 100 nm to 3 micrometers. Based on observations with three metals (aluminum, copper and zinc), new evidence is presented in support of tool-chip friction as the primary source of the size effect. It is shown that size effect arises as a result of non-proportional decrease of the friction component with the underlying length scale. Calculation of the shear flow stress during cutting showed that this was approximately constant for a given material, independent of the depth of cut. Size dependence of tool-chip friction and contact size is interpreted in terms of the junction growth and adhesion models. Cutting experiments are also carried out with tools covered with solid and liquid contaminants. These results show that contaminant films effectively diminish adhesion and lead to a drastic reduction in the size effect, suggesting practical benefits for industrial manufacturing processes.

Fast Polarization Reversal in Polycrystalline Ferroelectric Thin Films: The Origin of Size Effects

The origin of size effects in polycrystalline ferroelectric films of Pb(Zr1-xTix)O3 having the frequency dependence of coercive field in the form ln(ν/ν0)∼1/Ec2 is investigated. A model of a surface source emitting thin ferroelectric domains with reversed polarization is employed to explain this unusual frequency dependence of polarization switching in polycrystalline films in a wide range of frequencies. The model also predicts that the activation energy for domain nucleation increases with the source size, indicating an increase in the coercive field as minimum size sources deteriorate. The proposed mechanism for the domain nucleation in polycrystalline PZT films can explain the electrode size dependence of the limiting frequency. This dependence is related with increasing role of the athermal domain growth in strongly inhomogeneous electric field near electrode edges.

On the origin of indentation size effects and depth dependent mechanical properties of elastic polymers

Abstract Indentation size effects have been observed in both polymers and metals but, unlike in metals, the origin of size effects in polymers is not well understood. To clarify the role of second order gradients of displacements, a model polymer is examined with spherical and Berkovich tips at probing depths between 5 and 25 μm. Applying different theories to determine the elastic modulus, it is found that with a pyramidal tip, the elastic modulus increases with decreasing indentation depth, while tests with the spherical tip yielded essentially constant values for the elastic modulus independent of indentation depth. The differences between these tips are attributed to second order displacement gradients, as they remain essentially constant with a spherical tip while they increase in magnitude with decreasing indentation depth applying a Berkovich tip.

Origin of size effect on efficiency of organic photovoltaics

It is widely accepted that efficiency of organic solar cells could be limited by their size. However, the published data on this effect are very limited and none of them includes analysis of light intensity dependence of the key cell parameters. We report such analysis for bulk heterojunction solar cells of various sizes and suggest that the origin of both the size and the light intensity effects should include underlying physical mechanisms other than conventional series resistance dissipation. In particular, we conclude that the distributed nature of the ITO resistance and its influence on the voltage dependence of photocurrent and dark current is the key to understanding size limitation of the organic photovoltaics (OPV) efficiency. Practical methods to overcome this limitation as well as the possibility of producing concentrator OPV cells operating under sunlight concentrations higher than 10 suns are discussed.

Size Dependence of Optical Properties in Semiconductor Nanocrystals

An extension of the classic thermodynamic theory to nanometer scale has generated a new interdisciplinary theory - nanothermodynamics. It is the critical tool for the investigation of the size-dependent physicochemical properties in nanocrystals. A simple and unified nanothermodynamic model for the melting temperature of nanocrystals has been established based on Lindemann’s criterion for the melting, Mott’s expression for the vibrational melting entropy, and Shi’s model for the size dependence of the melting point. The developed model has been extensively verified in calculating a variety of size- and dimensionality-dependent phase transition functions of nanocrystals. In this work, such a model was extended to explain the underlying mechanism behind the bandgap energy enhancement and Raman red shifts in semiconductor nanocrystals by (1) investigating the crystal size r, dimensionality d, and constituent stoichiometry x dependences of bandgap energies Eg in semiconductor quantum dots (QDs) and quantum wires (QWs); and (2) revealing the origin of size effect on the Raman red shifts in low dimensional semiconductors by considering the thermal vibration of atoms. For Eg, it is found that: (1) Eg increases with a decreasing r for groups IV, III-V and II-VI semiconductors and the quantum confinement effect is pronounced when r becomes comparable to the exciton radius; (2) the ratio of Eg(r, d)QWs/Eg(r, d)QDs is size-dependent, where Eg(r, d) denotes the change in bandgap energy; (3) the crystallographic structure (i.e. zinc-blende and wurtzite) effect on Eg of III-V and II-VI semiconductor nanocrystals is limited; and (4) for both bulk and nanosized III-V and II-VI semiconductor alloys, the composition effects on Eg are substantial, having a common nonlinear (bowing) relationship. For the Raman red shifts, the lower limit of vibrational frequency was obtained by matching the calculation results of the shifts with the experimental data of Si, InP, CdSe, CdS0.65Se0.35, ZnO, CeO2, as well as SnO2 nanocrystals. It shows that: (1) the Raman frequency (r) decreases as r decreases in both narrow and wide bandgap semiconductors; (2) with the same r, the sequence of size effects on (r) from strong to weak is nanoparticles, nanowires, and thin films; and (3) the Raman red shift is caused by the size-induced phonon confinement effect and surface relaxation. These results are consistent with experimental findings and may provide new insights into the size, dimensionality, and composition effects on the optical properties of semiconductors as well as fundamental understanding of high-performance nanostructural semiconductors towards their applications in optoelectronic devices.

Determinants of Thermal Conductivity and Diffusivity in Nanostructural Semiconductors

The origin of size effects in the thermal conductivity and diffusivity of nanostructural semiconductors was investigated through the establishment of a unified nanothermodynamic model. The contributions of size-dependent heat capacity and cohesive energy as well as the interface scattering effects were considered during the modeling. The results indicate the following: (1) both the thermal conductivity and diffusivity decrease with decreasing nanocrystal sizes (x) of Si and Si/SiGe nanowires, Si thin films and Si/Ge(SiGe) superlattices, and GaAs/AlAs superlattices when x > 20 nm; (2) the heat transport in semiconductor nanocrystals is determined largely by the increase of the surface (interface)/volume ratio; (3) the interface scattering effect predominates in the reduction of thermal conductivity and diffusivity while the intrinsic size effects on average phonon velocity and phonon mean free path are also critical; (4) the quantum size effect plays a crucial role in the enhancement of the thermal conductivity with a decreasing x (<20 nm). These findings provide new insights into the fundamental understanding of high-performance nanostructural semiconductors toward application in optoelectronic and thermoelectric devices.

Origin of size effect on superconductivity in (R 0.8Pr 0.2)Ba 2Cu 3O 7 studied by soft X-ray absorption spectroscopy

O K-edge X-ray absorption near-edge structure (XANES) spectroscopy of (R 0.8Pr 0.2)Ba 2Cu 3O 7 (R=Y, Tm, Dy, Gd, Eu and Sm) has been performed to investigate the dependence of hole distribution on ionic size of the R 3+ ions. Near the O 1s absorption edge, pre-peaks at ∼527.8 and ∼528.5 eV are assigned to transitions into O 2p hole states located in the CuO 3 ribbons and CuO 2 planes, respectively. As deduced from O K-edge X-ray absorption spectra, the hole concentrations in the CuO 2 planes decrease monotonically with increasing ionic size of the rare-earth elements. The present XANES results clearly demonstrate that the suppression of superconductivity in (R 1− x Pr x )Ba 2Cu 3O 7 with ionic radius of the R 3+ ions results predominantly from the hole-depletion effect.

Molecular dynamics study of pbtio3using non-empirical potentials

Abstract Molecular dynamics simulations for finite clusters of PbTiO3 using non-empirical, many-body potentials were performed in order to better understand the origin of size effects in ferroelectrics. The interatomic potentials used are based on the ionic Potential Induced Breathing (PIB) model with correction terms fit to energy differences between PIB and linearized augmented plane wave (LAPW) total energies. Uncorrected PIB calculations give incorrectly a paraelectric cubic perovskite ground phase due to the neglect of covalency and polarizability. The new potentials, however, do give a correct ferroelectric tetragonal perovskite ground phase for a perfect lattice. Consistent with experiment, we find that a finite cluster of 1295 atoms is non-ferroelectric due to the presence of a large depolarization field. A metallic coating on the cluster was simulated in order to attempt to cancel out the depolarization field but no model was found that gave a realistic ferroelectric ground state. This may be due...