Extrinsic Size Effects Research Articles

P−n Junction Dynamics Induced in a Graphene Channel by Ferroelectric-Domain Motion in the Substrate

The p-n junctions dynamics in graphene channel induced by stripe domains nucleation, motion and reversal in a ferroelectric substrate is explored using self-consistent approach based on Landau-Ginzburg-Devonshire phenomenology combined with classical electrostatics. We revealed the extrinsic size effect in the dependence of the graphene channel conductivity on its length. For the case of perfect electric contact between the ferroelectric and graphene, relatively low gate voltages are required to induce the pronounced hysteresis of ferroelectric polarization and graphene charge in response to the periodic gate voltage. Pronounced nonlinear hysteresis of graphene conductance with a wide memory window corresponds to high amplitudes of gate voltage. We predict that the considered nano-structure "top gate/dielectric layer/graphene channel/ferroelectric substrate" can be a promising candidate for the fabrication of new generation of modulators and rectifiers based on the graphene p-n junctions.

Investigating the extrinsic size effect of palladium and gold spherical nanoparticles

In many optical applications, knowing the variations of the plasmonic resonance wavelengths of a special kind of nanoparticles in terms of their size before the experiment began, can assist the users in selection of an appropriate preparation method for the optimum functionality. In this work, in order to show the role of the preparation method on the mean size and the size distribution of nanoparticles, two different chemical bottom-up and physical top-down methods were used for the synthesis of palladium and gold nanoparticles. Chemical reduction of metal salt and laser ablation in liquid media methods were respectively used for preparation of palladium and gold nanoparticles. It is shown that the chemical bottom-up method results in the formation of smaller particles with narrower size distribution. Optical properties and plasmonic resonance absorption of the prepared nanoparticles were investigated by UV–vis spectroscopy and their size distribution were determined by transmission electron microscopy (TEM) images. Using the measured size distribution of nanoparticles, their optical extinctions are modelled using the Mie theory of scattering. A comprehensive study on the extrinsic size effect of palladium and gold nanoparticles is performed and the dipolar and the quadrupolar Mie resonances in these nanoparticles are investigated in details. The reported results can be used for selecting the preparation method of these nanoparticles and for choosing the appropriate laser wavelength to excite stronger or weaker Mie resonances for specific applications.

Extrinsic size effect of pyroelectric response of ferroelectric films

We have developed the theoretical model for calculation of the main characteristics of pyroelectric response of pyroactive multilayer structures, which are the basic elements of the modern pyroelectric detectors of radiation and other transducers. In the framework of the proposed model, the dependences of the pyroelectric response frequency spectra on the ferroelectric film thickness have been investigated. It was found that a pronounced extrinsic size effect is inherent to the pyroelectric response frequency spectra, such as the strong thickness dependence of the response maximal value and its frequency position. The thickness dependences of the frequency position of the maximum pyroelectric response and the optimal thickness of the pyroactive ferroelectric film have been calculated. The frequency spectra of the pyroelectric current and voltage calculated theoretically are in quantitative agreement with the experimental ones for the Al/P(VDF-TrFE)/Ti/Si pyroactive structure. The developed procedure is important for improving the sensitivity of pyroelectric devices. The obtained analytical expressions allow optimizing the performances of pyroactive elements using the existence of the size effect, which depends on the pyroactive ferroelectric film and substrate thicknesses, as well as on the conditions of heat transfer and exchange at the corresponding boundaries of the pyroactive structure.

Brittle-to-Ductile Transition in Metallic Glass Nanowires.

When reducing the size of metallic glass samples down to the nanoscale regime, experimental studies on the plasticity under uniaxial tension show a wide range of failure modes ranging from brittle to ductile ones. Simulations on the deformation behavior of nanoscaled metallic glasses report an unusual extended strain softening and are not able to reproduce the brittle-like fracture deformation as found in experiments. Using large-scale molecular dynamics simulations we provide an atomistic understanding of the deformation mechanisms of metallic glass nanowires and differentiate the extrinsic size effects and aspect ratio contribution to plasticity. A model for predicting the critical nanowire aspect ratio for the ductile-to-brittle transition is developed. Furthermore, the structure of brittle nanowires can be tuned to a softer phase characterized by a defective short-range order and an excess free volume upon systematic structural rejuvenation, leading to enhanced tensile ductility. The presented results shed light on the fundamental deformation mechanisms of nanoscaled metallic glasses and demarcate ductile and catastrophic failure.

Gradient plasticity used for modeling extrinsic and intrinsic size effects in the torsion of Au microwires

AbstractThe gradient plasticity theory proposed by Aifantis and coworkers has been successfully used to model size effect phenomena at the microscale and nanoscale, by introducing into the formulation an internal length scale associated with the phenomenological coefficients of the gradient plasticity model. In this paper, Aifantis’ gradient plasticity theory is applied to model the sample size-dependent torsion of thin wires, with a strain-dependent internal length scale as well as grain size dependence based on the Hall-Petch relationship. This study reveals that internal length scale is related with sample size and grain size, with such a connection determined by the ductility of the material.

Ductilisation of tungsten (W) through cold-rolling: R-curve behaviour

Here we show that cold-rolling of tungsten (W) decreases the stable crack growth onset temperature. Furthermore, we show that stable crack growth is accompanied by crack bridging, which in turn is triggered by dislocation activity. The entire stable crack growth regime shows ductile intergranular fracture.Our ductilisation approach is the modification of microstructure through cold-rolling. In this work, we assess two different microstructures obtained from (i) cold-rolled and (ii) severely cold-rolled tungsten plates. From these plates, single-edge cracked-plate tension (SECT) specimens were cut and tested in the L-T direction. Crack growth resistance (R) curves were obtained using the direct-current-potential-drop method (DCPM). The experiments show the following results: cold-rolled plates are brittle at room temperature (RT), but show stable crack growth at 250°C (523K) and a fracture toughness, KIQ, of about 100MPa(m)1/2 at a crack extension, Δa, of 0.6mm. Severely cold-rolled tungsten plates show stable crack growth at RT and a fracture toughness, KIQ, of 100MPa(m)1/2 at a crack extension, Δa, of 0.3mm. Scanning electron microscopy (SEM) analyses of the stable crack growth region show intergranular fracture with microductile character.The question of why cold-rolling causes the stable crack growth onset temperature to decrease (or in other words, why cold-rolling causes the brittle-to-ductile transition (BDT) temperature to decrease) is discussed against the background of (i) intrinsic and extrinsic size effects, (ii) crystallographic texture, (iii) impurities and (iv) the role of dislocations. Our results suggest that the spacing between the dislocation nucleation sites (high angle grain boundaries (HAGBs) act as dislocation source) is the most important parameter responsible for the decrease of the stable crack growth onset temperature.

Size-dependent plastic stability of Zr-based metallic glass

The size effect on the plastic stability of a Zr-based metallic glass was investigated. It was found that, by geometrically decreasing the sample size, the metallic glass displayed a transition of unstable–metastable–stable plastic deformation, indicating an obvious extrinsic size effect on the plastic stability of the metallic glass. The size effect was explained from the view point of plastic zone and elastic energy dissipation. This finding implies that the present Zr metallic glass is ductile in nature and its plastic deformation can be stabilized intrinsically or extrinsically in suitable conditions.

Deformation patterns in cross-sections of twisted bamboo-structured Au microwires

In order to investigate an almost pure extrinsic size effect we propose an experimental approach to investigate the deformation structure within single crystalline cross-sections of twisted bamboo-structured Au microwires. The cross-sections of individual 〈100〉 oriented grains of 25μm thick Au microwires have been characterized by Laue microdiffraction. The diffraction data were used to calculate the misorientation of each data point with respect to the neutral fiber in the center of the cross-section as well as the kernel average misorientation to map the global and local deformation structure as function of the imposed maximum plastic shear strain. The study is accompanied by crystal plasticity simulations which yield the equivalent plastic strain distributions in the cross-section of the wire. The global deformation structures are directly related to the activated slip systems, resulting from the real orientations of the investigated grains. When averaging the degree of deformation along ring segments, an almost continuous but non-linear increase of misorientation from the center toward the surface is observed, reflecting the overall strain gradient imposed by torsion. For the local deformation structure, pronounced and graded deformation traces are observed which often pass over the neutral fiber of the twisted wire and which are obviously reflecting domains of high geometrically necessary dislocations content.

Extrinsic mechanical size effects in thin ZrNi metallic glass films

Mechanical size effects in ZrxNi100−x thin metallic glass films are investigated for thicknesses from 200 to 900nm. Local order, elastic properties and rate sensitivity are shown to be thickness independent, while hardness and fracture resistance are not. The increase of hardness with decreasing thickness is related to the substrate constraint on shear banding. Fracture surfaces exhibit a corrugated morphology, except for thickness below 400nm exhibiting perfectly flat surfaces. The corrugations appear again on the thinnest films when adding a cap layer, indicating that the fracture mechanisms are primarily dominated by the loading configuration and geometry which constrain the plastic zone extension. Increasing the Ni content from 25% to 58% leads to an increase of elastic modulus, Poisson ratio, strength, activation volume, and fracture toughness. These changes can be understood based on the change in thermodynamic fragility and Zr–Ni bonds formation. Zr75Ni25 composition shows exceptionally large rate sensitivity exponent equal to 0.058. The fracture mechanisms are not modified by composition and the fracture toughness is systematically low due to the confinement of the plastic zone.

Effect of Vegard strains on the extrinsic size effects in ferroelectric nanoparticles

By changing the size and the shape of ferroelectric nanoparticles, one can govern their polar properties, including their improvement in comparison with the bulk material. The shift of the ferroelectric transition temperature can reach hundreds of degrees Kelvin. A phenomenological description of these effects was proposed in the framework of Landau-Ginsburg-Devonshire (LGD) theory using the concepts of surface tension and surface bond contraction. However, this description contains a series of poorly defined parameters, and the physical nature is ambiguous. It appears that the size and shape dependences of the phase transition temperature, along with all polar properties, are defined by the nature of the size effect. Existing LGD-type models do not take into account that defect concentration strongly increases near the particle surface. In order to develop an adequate phenomenological description of size effects in ferroelectric nanoparticles, one should consider Vegard strains (local lattice deformations) originating from defect accumulation near the surface. In this paper, we propose a theoretical model that takes into account Vegard strains and performs a detailed quantitative comparison of the theoretical results with experimental ones for quasispherical ${\mathrm{KTa}}_{1\text{\ensuremath{-}}x}{\mathrm{Nb}}_{x}{\mathrm{O}}_{3}$ nanoparticles (average radius 25 nm), which reveal the essential (about 100 K) increase of the transition temperature in spherical nanoparticles in comparison with bulk crystals. From the comparison between the theory and experiment, we established the leading contribution of Vegard strains to the extrinsic size effects in ferroelectric nanoparticles. We determined the dependence of Vegard strains on the content of Nb and reconstructed the Curie temperature dependence on the content of Nb using this dependence. The dependence of the Curie temperature on the Nb content becomes a nonmonotonic one for the small (20 nm) elongated ${\mathrm{KTa}}_{1\text{\ensuremath{-}}x}{\mathrm{Nb}}_{x}{\mathrm{O}}_{3}$ nanoparticles. We established that the accumulation of intrinsic and extrinsic defects near the surface can play a key role in the physical origin of extrinsic size effects in ferroelectric nanoparticles and govern its main features.

Intrinsic and extrinsic size effects in the deformation of amorphous CuZr/nanocrystalline Cu nanolaminates

Introducing a soft crystalline phase into an amorphous alloy can promote the compound’s ductility. Here we synthesized multilayered nanolaminates consisting of alternating amorphous Cu54Zr46 and nanocrystalline Cu layers. The Cu layer thickness was systematically varied in different samples. Mechanical loading was imposed by nanoindentation and micropillar compression. Increasing the Cu layer thickness from 10 to 100nm led to a transition from sharp, cross-phase shear banding to gradual bending and co-deformation of the two layer types (amorphous/nanocrystalline). Specimens with a sequence of 100nm amorphous Cu54Zr46 and 50nm Cu layers show a compressive flow stress of 2.57±0.21GPa, matching the strength of pure CuZr metallic glass, hence exceeding the linear rule of mixtures. In pillar compression, 40% strain without fracture was achieved by the suppression of percolative shear band propagation. The results show that inserting a ductile nanocrystalline phase into a metallic glass prevents catastrophic shear banding. The mechanical response of such nanolaminates can be tuned by adjusting the layer thickness.

Influence of coherent twin boundaries on three-point bending of gold nanowires

In the present work we elucidate the deformation mechanisms of twinned Au nanowires (NWs) under three-point bending by means of molecular dynamics simulations. We further investigate the effects of twin boundary orientation, NW diameter and twin boundary spacing on the mechanical properties and deformation behaviors of NWs. Our simulation results reveal that dislocation slip, twin boundary associated mechanisms and deformation twinning work in parallel in the heterogeneous localized plastic deformation of twinned Au NWs under bending. The dislocation–twin boundary interactions can be significantly altered by changing the twin boundary orientation as well as the bending direction. Furthermore, the NW diameter and twin boundary spacing strongly influence the competition between individual deformation mechanisms, which in turn leads to extrinsic and intrinsic size effects on the strength and the bending ductility of the NWs.

Extended Maxwell-Garnett-Mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix.

The optical properties of metallic spherical nanoparticles embedded in host liquid matrix are studied. Extended Maxwell-Garnett-Mie formulation which accounts for size dispersion, the intrinsic confinement, and extrinsic size effect, is proposed for the calculation of the effective dielectric function and absorption coefficient of size dispersion of colloidal solution of Au and Ag nanoparticles in water. We demonstrate that the size distribution induces an inhomogeneous broadening and an increase of the amplitude of the plasmon band. A large redshift of the plasmon band is also observed for silver nanoparticles. Compared to the conventional Maxwell Garnett theory, we demonstrated that this model gives better description of the measured absorption spectra of colloidal gold solutions.

Emergence of localized plasticity and failure through shear banding during microcompression of a nanocrystalline alloy

Microcompression testing is used to probe the uniaxial stress–strain response of a nanocrystalline alloy, with an emphasis on exploring how grain size and grain boundary relaxation state impact the complete flow curve and failure behavior. The yield strength, strain hardening, strain-to-failure and failure mode of nanocrystalline Ni–W films with mean grain sizes of 5, 15 and 90nm are studied using taper-free micropillars that are large enough to avoid extrinsic size effects. Strengthening is observed with grain refinement, but catastrophic failure through strain localization is found as well. Shear banding is found to cause failure, resembling the deformation of metallic glasses. Finally, we study the influence of grain boundary state by employing heat treatments that relax nonequilibrium boundary structure but leave grain size unchanged. A pronounced strengthening effect and increased strain localization are observed after relaxation in the finer grained samples.

Extrinsic size effect in microcompression of polycrystalline Cu/Fe multilayers

Microcompression tests of Cu/Fe multilayers with diameters ranging from 0.6 to 2.0 μm show that the flow stress increases with increasing pillar diameter, which implies that “larger is stronger”. Finite element analysis results explain the stress and strain distributions in the pillars, and suggest that the dimensional constraint is responsible for the strengthening. This work reveals a new mechanism of extrinsic size effect in polycrystalline multilayer pillars, which is opposite to the extrinsic size effect in single-crystal pillars.

Atypical dielectric behavior in sol–gel derived fine grain PZT/CeO2 nanocomposites

We present here dielectric and electrical modulus studies of sol–gel derived fine grain (100−x)PZT/xCeO2 nanocomposites. Dielectric response shows superimposed local maxima(s) in high frequency regimes, which, in low frequency regions seems to be overshadowed by high conductivity. Observed local maxima(s) were found to be in concurrence with the nadir(s) observed in the imaginary part of electrical modulus plotted on the temperature plane. In addition to this, calculated bulk and grain boundary capacitance exhibit maxima(s) in the measured temperature range displaying the existence of both bulk and grain boundary transition in nanocomposite formation. Therefore, a collective effect of these two processes has been thought to be a plausible mechanism for observed dielectric behavior of nanocomposites. Anomalous increase in bulk transition temperature of 2wt% ceria substituted nanocomposite was also observed. Possibilities of increase in transition temperature have also been discussed taking in to account the extrinsic size effect.

On strain-rate sensitivity and size effect of brittle solids: transition from cooperative phenomena to microcrack nucleation

An idealized brittle microscale system is subjected to dynamic uniaxial tension in the medium-to-high strain-rate range $$(\dot \varepsilon \in \;[100\;s^{-1},\;1 \times 10^{7} \;s^{-1}])$$ to investigate its mechanical response under constrained spatial and temporal scales. The setup of dynamic simulations is designed to ensure practically identical in-plane stress conditions on a system of continuum particles forming a two-dimensional, geometrically and structurally disordered, lattice. The rate sensitivity of size effects is observed as well as the ordering effect of kinetic energy. A simple phenomenological expression is developed to account for the tensile strength sensitivity of the small-sized brittle systems to the strain-rate and extrinsic size effects, which may serve as a guideline for formulation of constitutive relations in the MEMS design. The representative sample is defined as a square lattice size for which the tensile strength becomes rate-insensitive and an expression is proposed to model its evolution between two asymptotes corresponding to the limiting loading rates. The dynamics of damage accumulation is analyzed as a function of sample size and loading rate.

Transition from homogeneous-like to shear-band deformation in nanolayered crystalline Cu/amorphous Cu–Zr micropillars: Intrinsic vs. extrinsic size effect

The microcompression method was used to investigate the compressive plastic flow behavior of nanolayered crystalline/amorphous (C/A) Cu/Cu–Zr micropillars within wide ranges of intrinsic layer thicknesses (h∼5–150nm) and extrinsic sample sizes (350–1425nm) with the goal of revealing the intrinsic size effect, extrinsic size effect and their interplay on the plastic deformation behavior. The nanolayered C/A micropillars exhibited deformation behaviors of strain-hardening followed by strain-softening that were dependent on the thickness of the layers. At h⩽10nm, the strain-softening is related to shear deformation that is caused by fractures in the amorphous layers. At h>10nm, however, the strain-softening is related to the reduction in dislocation density caused by dislocation absorption. Correspondingly, the deformation mode of the C/A micropillars transitioned from homogeneous-like to shear band type as h decreased to the critical value of ∼10nm, which is indicative of a significant intrinsic size effect. The extrinsic size effect on the plastic deformation also became remarkable when h was less than ∼10nm, and the interplay between the intrinsic and extrinsic size effects leads to an ultrahigh strength of ∼4.8GPa in the C/A micropillars, which is close to the ideal strength of Cu and considerably greater than the ideal strength of the amorphous phase. The underlying strengthening mechanism was discussed, and the transition in deformation mode was quantitatively described by considering the strength discrepancy between the two constituent crystalline and amorphous layers at different length scales.

In situ deformation of micro-objects as a tool to uncover the micro-mechanisms of the brittle-to-ductile transition in semiconductors: the case of indium antimonide

At ambient temperature and pressure, most of the semiconductor materials are brittle: this is the case of the III–V compound semiconductor indium antimonide, InSb. To study the role of dislocation nucleation at the onset of brittle-to-ductile transition, InSb micro-pillars have been fabricated by focused ion beam and in situ compressed at room temperature in a scanning electron microscope, in order to correlate the observation of slip traces at the pillar surface and features of the stress–strain curve. Transmission electron microscopy (TEM) thin foils have been cut out of the pillars to study the deformation microstructure. The TEM study of dislocations and the observation of slip traces at surfaces show that increasing the surface-to-volume ratio of the pillars modifies the dislocation nucleation conditions and favors plasticity even at room temperature. The role of dislocation nucleation from free surfaces is thus discussed within the larger context of the micro-pillar compression technique and extrinsic size effects.

Intrinsic and extrinsic size effects on deformation in nanolayered Cu/Zr micropillars: From bulk-like to small-volume materials behavior

By using microcompression methodology, deformation of nanolayered Cu/Zr micropillars was systematically investigated within wide ranges of intrinsic layer thickness (5–100nm) and extrinsic sample size (300–1200nm). The intrinsic size effect, extrinsic size effect and their interplay were respectively revealed. Competition between the intrinsic and extrinsic size effects leads to experimental observation of a critical layer thickness of ∼20nm, above which the deformation is predominantly intrinsic-size-related and insensitive to sample size, while below which the two size effects are comparable. The underlying deformation mechanisms were proposed to transform from bulk-like to small-volume materials behavior. Deformation mode is correspondingly transited from homogeneous extrusion/barreling to inhomogeneous shear banding, but the two competing modes coexist in the layer thickness range from ∼50 to 20nm. In the regime of shear deformation, the extrinsic size dependence is displayed in that the deformation was controlled by shear bands nucleation in larger pillars while controlled by shear bands propagation in smaller pillars. A deformation mode map is developed to clearly elucidate the coupling intrinsic and extrinsic size effects on the deformation mode of nanolayered pillars.