Intrinsic Size Effects Research Articles

Two-Dimensional Au Nanocrystals: Shape/Size Controlling Synthesis, Morphologies, and Applications

The fascinating roles of two-dimensional (2D) nanomaterials in natural super-strong bio-composites (i.e. aragonite platelets in nacre and apatite platelets in bone) have aroused great interest in scientific communities to synthesize their artificial counterparts with controllable geometric and physical properties. The quantum 2D confinement of electrons recently revealed in graphene nanosheets further inspires to explore 2D metal nanocrystals with intrinsic anisotropic properties and quantum size effect. Among them, 2D Au nanocrystals stand out not only due to their unique structure- and environmental-dependent properties, but also due to their rapid development in synthesis approaches and emerging applications in electronics, optics, sensing and biomedicines. In this Review the aim is to rationalize numerous newly published studies on 2D Au nanocrystals and to gain insight into their shape/size controlling synthesis, diverse morphologies, properties, and applications, potentially serving a handy guide to achieve on-demand 2D Au nanocrystals.

A mechanistic cutting force model with consideration of the intrinsic and geometric size effects decoupled

In machining processes, the specific cutting energy increases nonlinearly as the uncut chip thickness decreases. This phenomenon is called the size effect and can be classified into two types by its cause—geometric and intrinsic. The geometric size effect is caused by the decrease of the effective rake angle with the decrease of the uncut chip thickness when the tool has a finite radius of the cutting edge. The intrinsic size effect results from the nature of the material, in which the resistance against plastic deformation (flow stress) increases as the length scale of the material deformed decreases. In order to improve the prediction accuracy of a cutting force model in micro-machining, it is important to understand each of these size effects and reflect them into the cutting force model accurately. In this regard, this study develops an experimental method to decouple the geometric and intrinsic size effects and models them individually. Based on this, a mechanistic cutting force model including the geometric and intrinsic size effects in separate terms is constructed and compared to the existing models which do not consider them separately.

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.

Unconventional route to encapsulated ultrasmall gold nanoparticles for high-temperature catalysis.

Ultrasmall gold nanoparticles (us-AuNPs, <3 nm) have been recently recognized as surprisingly active and extraordinarily effective green catalysts. Their stability against sintering during reactions, however, remains a serious issue for practical applications. Encapsulating such small nanoparticles in a layer of porous silica can dramatically enhance the stability, but it has been extremely difficult to achieve using conventional sol-gel coating methods due to the weak metal/oxide affinity. In this work, we address this challenge by developing an effective protocol for the synthesis of us-AuNP@SiO2 single-core/shell nanospheres. More specifically, we take an alternative route by starting with ultrasmall gold hydroxide nanoparticles, which have excellent affinity to silica, then carrying out controllable silica coating in reverse micelles, and finally converting gold hydroxide particles into well-protected us-AuNPs. With a single-core/shell configuration that prevents sintering of nearby us-AuNPs and amino group modification of the Au/SiO2 interface that provides additional coordinating interactions, the resulting us-AuNP@SiO2 nanospheres are highly stable at high temperatures and show high activity in catalytic CO oxidation reactions. A dramatic and continuous increase in the catalytic activity has been observed when the size of the us-AuNPs decreases from 2.3 to 1.5 nm, which reflects the intrinsic size effect of the Au nanoparticles on an inert support. The synthesis scheme described in this work is believed to be extendable to many other ultrasmall metal@oxide nanostructures for much broader catalytic applications.

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.

Computational modeling of intrinsically induced strain gradients during compression of c-axis-oriented magnesium single crystal

A finite-deformation strain gradient crystal plasticity model is implemented in a three-dimensional finite-element framework in order to analyze the deformation behavior and the stress–strain response of magnesium single crystals under c-axis orientation. The potential-based and thermodynamically consistent material model is formulated in a non-local and non-linear inelastic context in which dislocation densities are introduced via plastic strain gradients. Experiments have shown that the internal length scale of the microstructure starts to affect the overall stress–strain response when the sample size decreases to the micron scale. As a consequence, strain gradients develop, leading to an additional energetic-like hardening effect which results in an increase of the macroscopic strength with decreasing crystal size. In the case of uniaxial compression of c-axis-oriented single-crystal micropillars, the model is able to predict the discrete dislocation glide in terms of a band-shaped slip zone. Two different pillar sample sizes are taken into account in order to investigate the intrinsic size effect during plastic deformation where the crystallographic orientation leads to the activation of pyramidal {112¯2}〈112¯3〉 slip systems as reported in various experimental studies. The interaction of those slip systems is expressed in terms of latent hardening and excess dislocation development. A comparison between numerical results and corresponding experimental data is presented.

On the homogenization of metal matrix composites using strain gradient plasticity

The homogenized response of metal matrix composites (MMC) is studied using strain gradient plasticity. The material model employed is a rate independent formulation of energetic strain gradient plasticity at the micro scale and conventional rate independent plasticity at the macro scale. Free energy inside the micro structure is included due to the elastic strains and plastic strain gradients. A unit cell containing a circular elastic fiber is analyzed under macroscopic simple shear in addition to transverse and longitudinal loading. The analyses are carried out under generalized plane strain condition. Micro-macro homogenization is performed observing the Hill-Mandel energy condition, and overall loading is considered such that the homogenized higher order terms vanish. The results highlight the intrinsic size-effects as well as the effect of fiber volume fraction on the overall response curves, plastic strain distributions and homogenized yield surfaces under different loading conditions. It is concluded that composites with smaller reinforcement size have larger initial yield surfaces and furthermore, they exhibit more kinematic hardening.

Particle Size and Support Effects in Electrocatalysis

Researchers increasingly recognize that, as with standard supported heterogeneous catalysts, the activity and selectivity of supported metal electrocatalysts are influenced by particle size, particle structure, and catalyst support. Studies using model supported heterogeneous catalysts have provided information about these effects. Similarly, model electrochemical studies on supported metal electrocatalysts can provide insight into the factors determining catalytic activity. High-throughput methods for catalyst synthesis and screening can determine systematic trends in activity as a function of support and particle size with excellent statistical certainty. In this Account, we describe several such studies investigating methods for dispersing precious metals on both carbon and oxide supports, with particular emphasis on the prospects for the development of low-temperature fuel-cell electrocatalysts. One key finding is a decrease in catalytic activity with decreasing particle size independent of the support for both oxygen reduction and CO oxidation on supported gold and platinum. For these reactions, there appears to be an intrinsic particle size effect that results in a loss of activity at particle sizes below 2-3 nm. A titania support, however, also increases activity of gold particles in the electrooxidation of CO and in the reduction of oxygen, with an optimum at 3 nm particle size. This optimum may represent the superposition of competing effects: a titania-induced enhanced activity versus deactivation at small particle sizes. The titania support shows catalytic activity at potentials where carbon-supported and bulk-gold surfaces are normally oxidized and CO electrooxidation is poisoned. On the other hand, platinum on amorphous titania shows a different effect: the oxidation reduction reaction is strongly poisoned in the same particle size range. We correlated the influence of the titania support with titania-induced changes in the surface redox behavior of the platinum particles. For both supported gold and platinum particles in electrocatalysis, we observe parallels to the effects of particle size and support in the equivalent heterogeneous catalysts. Studies of model supported-metal electrocatalysts, performs efficiently using high throughput synthetic and screening methodologies, will lead to a better understanding of the mechanisms responsible for support and particle size effects in electrocatalysis, and will drive the development of more effective and robust catalysts in the future.

On the dynamics of vortex structure in ferroelectric nanoparticles

The dynamics of vortex structure for polarizations in free-standing ferroelectric nanoparticles has been numerically investigated based on a thermodynamics-based continuum phase field approach under open-circuit boundary conditions. Both size effect and surface effect have been considered in this work: different assumptions for the extrapolation length have been made for the electric boundary condition and therefore accounting for the intrinsic size effect; the surface effect is studied by introducing the intrinsic surface stress, which causes volume mechanical balancing stress in the nanoparticles below free surfaces. The computed results are summarized in this article for square-shaped nanodots. It has been noticed that the particle size and intrinsic surface stress together play significant roles in the dynamics of vortex structure for polarizations. They affect both polarization configuration and existence conditions in ferroelectric nanoparticles.

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.

Grain Size‐Dependent Properties of Dense Nanocrystalline Barium Titanate Ceramics

The grain size influence on the dielectric relaxation and nonlinear dielectric properties of BaTiO3 ceramics with grain size in the range of (92÷936) nm densified by Spark Plasma Sintering (SPS) from ultrafine powders were investigated. The progressive reduction of the Curie temperature and of the effective permittivity results from a combination of intrinsic size effects and low‐permittivity grain boundary layer. A model of dielectric cylindrical cavities was employed in order to calculate intrinsic effective permittivity values in GHz range. An interesting feature is the presence of a thermally activated Debye‐like relaxation in the ferroelectric state of ceramics with grain size above 300 nm, with activation energies of 0.45–0.49 eV, which seems to be related to the domain walls forced motion under the applied field. By diminishing grain size, a progressive reduction of the ferroelectric nonlinear character was obtained, reaching a macroscopic non‐switching character and a linear permittivity versus field dependence for the finest ceramics (grain size of 90–100 nm) until very high values of the applied field. The observed behavior supports the idea of frozen polarization induced by pinning centers as due to a large number of grain boundaries and charged defects in the fine structures.

Size-Dependent Hamaker Constant for Silver Nanoparticles

The nonretarded size-dependent Hamaker constant for spherical silver nanoparticles was calculated by using the Lifshitz theory. The size dependence of the Hamaker constant was taken into account based on the size effect of the dielectric permittivity of silver nanoparticles. The experimental data for bulk silver dielectric permittivity was modified to include the intrinsic size effect of the scattering of the conduction electrons by the surface of the nanoparticles. The intrinsic size effect leads to a substantial increase of the Hamaker constant for nanoparticles with radii of the order 1 nm, when the mean free path of conducting electrons in the nanoparticles is limited by the particles’ boundaries.

Size Dependence of Ferroelectric Polarization in PbTiO3 Nanoislands

We report a size dependence of switchable polarization in PbTiO3 nanoislands with heights of 2–7 nm and widths of 40–80 nm. An atomic force microscopy (AFM) system that was capable of probing a switching charge from a single PbTiO3 nanoisland using a conductive AFM tip as a top electrode has been developed. Using the AFM system, the switching charge as small as 10 fC was detected within a tolerance of ±4 fC. The switchable polarization (ΔP) over 150 µC/cm2 was observed for the nanoislands as small as 5 nm in height, and ΔP rapidly decreased with the height below 5 nm. Comparing the height or thickness dependence of ΔP and stable domain states between the nanoislands and ultrathin films, it was found that the polarization in the nanoislands can be switched by external fields more easily than that in the ultrathin films. The decrease in ΔP of the nanoislands with the height below 5 nm can be attributed to the intrinsic size effects.

Linear optical absorption and photoluminescence emission properties of gold nanoparticles prepared by laser ablation technique

Gold nanoparticles of average size varying between 1.1 and 3.3 nm are prepared by 1064 nm Nd:YAG laser ablation of solid gold target kept in ethylene glycol medium. The measured UV-Visible absorption spectra showed the presence of sharp absorption peaks in the UV and in the visible regions due to the interband transition and surface plasmon resonance (SPR) oscillations in Au nanoparticles, respectively. The increase in linewidth of the SPR peaks with the reduction in particle sizes is observed due to intrinsic size effects. The prepared samples exhibit photoluminescence (PL) emissions in the UV-Visible region peaked at ∼354 nm due to the recombination of electrons with holes from sp conduction band to d-band of Au. The peak PL intensity in the sample prepared with 60 minutes of laser ablation time is enhanced by a factor of ∼2.5 compared to that obtained in the sample prepared with a laser-ablation time duration of 15 minutes.

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.

Tensile response of passivated films with climb-assisted dislocation glide

The tensile response of single crystal films passivated on two sides is analysed using climb enabled discrete dislocation plasticity. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with a lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The dislocation motion in the films is by glide-only or by climb-assisted glide whereas in the surface passivation layers dislocation motion occurs by glide-only and penalized by a friction stress. For realistic values of the friction stress, the size dependence of the flow strength of the oxidised films was mainly a geometrical effect resulting from the fact that the ratio of the oxide layer thickness to film thickness increases with decreasing film thickness. However, if the passivation layer was modelled as impenetrable, i.e. an infinite friction stress, the plastic hardening rate of the films increases with decreasing film thickness even for geometrically self-similar specimens. This size dependence is an intrinsic material size effect that occurs because the dislocation pile-up lengths become on the order of the film thickness. Counter-intuitively, the films have a higher flow strength when dislocation motion is driven by climb-assisted glide compared to the case when dislocation motion is glide-only. This occurs because dislocation climb breaks up the dislocation pile-ups that aid dislocations to penetrate the passivation layers. The results also show that the Bauschinger effect in passivated thin films is stronger when dislocation motion is climb-assisted compared to films wherein dislocation motion is by glide-only.

Effect of ablation time and laser fluence on the optical properties of copper nano colloids prepared by laser ablation technique

Copper (Cu) nanoparticles of average sizes (radius in nm) varying between 1.7 and 6 nm have been prepared by 1,064 nm Nd:YAG laser ablation of solid copper target in water medium. The nanostructures of the samples have been characterized using high-resolution transmission electron microscopes (HRTEM). The UV–visible absorption spectra obtained with a UV–visible spectrophotometer show sharp absorptions in the ultraviolet region and visible region due to the interband transition and surface plasmon resonance (SPR) oscillations in Cu nanoparticles, respectively. The increase in the linewidth of the SPR absorption peaks with the reduction in particle sizes are observed due to the intrinsic size effects. The behaviour of the UV–visible spectra associated with the Cu nanoparticles is studied as a function of laser fluence and laser ablation time.

Length scale-dependent deformation behavior of nanolayered Cu/Zr micropillars

The mechanical behavior of incoherent Cu/Zr multilayers was studied in uniaxial compression experiments using micropillars with individual layer thicknesses (h) ranging from 5 to 100nm. The deformation behavior of these micropillars are size dependent, transiting from dislocation dominated symmetrical slip at large h to shear localization induced by asymmetric slip and grain boundary mediated deformation at small h. During compression studies the multilayer micropillars exhibit a transition from strain hardening to shear softening at small h, and work softening at greater h. A maximum strain hardening rate is observed at a critical h of 20nm, which was explained in terms of a transition from dislocation interactions to cross-slip of dislocations. The mechanical strength of the micropillars is also dependent on h, which was quantitatively analyzed using the confined layer slip model. In addition, the influence of pillar diameter on the mechanical behavior is also investigated. The effect of extrinsic size on the deformation mechanisms is discussed with respect to the intrinsic size effect with variation in h.

Intrinsic and extrinsic size effects in the deformation of metallic glass nanopillars

Nanosized pillars with diameters ranging from 90 to 600nm of four amorphous alloys, Cu47Ti33Zr11Ni6Sn2Si1, Zr50Ti16.5Cu15Ni18.5, Zr61.8Cu18Ni10.2Al10 and Al86Ni9Y5, were fabricated and tested in situ in a transmission electron microscope. The major consideration when varying the composition was the change in bulk modulus and Poisson’s ratio, which may affect the deformation mode and ductility of metallic glasses (MGs) at the nanoscale. Differences between the deformation behavior of tapered (1.5–3°) and taper-free systems were also investigated. The yield stress of all the MGs measured through the in situ experiments is found to be essentially size independent, irrespective of tapering. With increasing size, all the MGs examined show a ductile-to-brittle transition under compression; the transition point, however, depends on the chemical composition of the specific MG investigated. The lower the μ/B ratio, the larger the pillar diameter above which more brittle behavior occurs. Al86Ni9Y5 taper-free MG showed a transition threshold to brittle behavior at the largest pillar diameter of 300nm. A micromechanical model is presented to explain the various dependencies.

Effect of Thickness on the Thermo-Mechanical Response of Free-Standing Thermoset Nanofilms from Molecular Dynamics

We characterize how film thickness affects the thermo-mechanical response of free-standing nanofilms composed of a thermoset polymer, diglycidyl ether of Bisphenol A (DGEBA) with 3,3′-diaminodiphenyl sulfone (33DDS), via molecular dynamics. We find that the glass transition temperature, Young’s modulus, and yield stress of the films decrease with decreasing thickness with the later two properties deviating from their bulk values at slightly larger thicknesses. The relative role of (i) intrinsic size effects, (ii) changes in quench depth (T – Tg), and (iii) variability in curing degree, on the depression of mechanical response of ultrathin films, are quantified. We find that intrinsic size effects contribute over 60% of the total change in mechanical response for the entire range of thicknesses studied.