Size-scale Effects Research Articles

Size-dependent pyroelectric properties of gallium nitride nanowires

The size scale effect on the pyroelectric properties is studied for gallium nitride (GaN) nanowires (NWs) based on molecular dynamics simulations and the theoretical analysis. Due to the significant influence of the surface thermoelasticity and piezoelectricity at the nanoscale, the pyroelectric coefficient of GaN NWs is found to depend on the cross-sectional size. This size-dependent pyroelectric coefficient of GaN NWs together with the size-dependent dielectric constant reported in our previous study is employed to study the pyroelectric potential of GaN NWs subjected to heating. The results show that the size scale effect is significant for thin NWs (cross-sectional size in nanometers) and may raise the pyroelectric potential of GaN NWs by over 10 times. Such a size scale effect on the pyroelectric properties of NWs originates from the influence of thermoelasticity, piezoelectricity, and dielectricity at the nanoscale and decreases with increasing cross-section of GaN NWs. It is expected that the present study may have strong implication in the field of energy harvesting at the nanoscale, as pyroelectricity offers a new avenue to the design of novel nanogenerators.

The dynamic strength of concrete and macroscopic temporal parameter characterized in fracture process

The structural-temporal approach based on the notion of incubation time is used for interpretation of strength behaviour of concrete in the fracture process. Temporal dependences of concrete under influence of steel spiral fiber, water, a scale level of fracture are evaluated by the incubation time criterion. Effect of more significant increase of strength in dynamic condition than static at growth percentage of fiber is explained by behaviour of the incubation time related with presence of defect in specimen. Numerical simulation of dynamic strength with different percentage of spiral fibers is given. Both size effect and scale effect for concrete samples subjected to impact loading are considered. Statistical nature of a size effect contrasts to a scale effect that is related to the definition of a spatio-temporal representative volume determining the fracture event on the given scale level.

Thin Flexible Thermal Ground Planes: Fabrication and Scaling Characterization

Thermal ground planes (TGPs) are passive thermal management devices that utilize the latent heat associated with phase change to achieve high effective thermal conductance, similar to heat pipes. In this paper, we develop flexible TGPs with an ultra-thin thickness of 0.5 mm using copper-cladded polyimide as the encasing material, woven copper mesh as a wick, and electroplated copper pillars to support a vapor core. The lowest thermal resistance of one TGP is characterized to be only 1/3 that of an equivalently sized copper heat spreader. The effects of size scaling of evaporator and condenser, and overall TGP sizes on the thermal resistances of TGPs are experimentally characterized. A simple series thermal resistance model, which accounts for vapor core thermal resistance, is developed to predict the measured results. This experimentally validated model can be used for the design of TGPs with varying sizes of evaporator and condenser, and overall size. [2015-0032]

Scaling approach toward nano electro-discharge machining: Nanoscale patterning of carbon nanotube forests

Micro-electro-discharge machining (μEDM) is a versatile technique for micromachining of electrically conductive materials with resolutions limited within the micrometer scale. This paper reports an approach to pushing the resolution limit of μEDM down to the nanometer scale. EDM with different electrode tip sizes is performed on carbon nanotube forests and the results reveal a favorable scaling effect of the tip size on the working voltage required for the breakdown of the dielectric between the electrode and workpiece, suggesting that downsizing of the electrode tip assists in the reduction of the discharge pulse energy. Based on this finding, controlled patterning of grating-like structures with ~200nm height is demonstrated on carbon nanotube forests with an estimated pulse energy of 1nJ, achieved using a tungsten electrode with a tip radius of 3μm. Theoretical analysis of this process setting shows a close match with the experimental results, further supporting the scaling effect. These results suggest the feasibility of the approach toward “nano-EDM” for an extensive range of potential applications in micro/nanodevice and nanotechnology areas.

Scale-size effects analysis of optimal periodic material microstructures designed by the inverse homogenization method

Periodic homogenization models are often used to compute the elastic properties of periodic composite materials based on the shape/periodicity of a given material unit-cell. Conversely, in material design, the unit-cell is not known a priori, and the goal is to design it to attain specific properties values – inverse homogenization problem. This problem is often solved by formulating it as an optimization problem. In this approach, the unit-cell is assumed infinitely small and with periodic boundary conditions. However, in practice, the composite material comprises a finite number of measurable unit-cells and the stress/strain fields are not periodic near the structure boundary. It is thus critical to investigate whether the obtained topologies are affected when applied in the context of real composites. This is done here by scaling the unit-cell an increasing number of times and accessing the apparent properties of the resulting composite by means of standard numerical experiments.

A borehole stability study by newly designed laboratory tests on thick-walled hollow cylinders

At several mineral exploration drilling sites in Australia, weakly consolidated formations mainly consist of sand particles that are poorly bonded by cementing agents such as clay, iron oxide cement or calcite. These formations are being encountered when drilling boreholes to the depth of up to 200 m. To study the behaviour of these materials, thick-walled hollow cylinder (TWHC) and solid cylindrical synthetic specimens were designed and prepared by adding Portland cement and water to sand grains. The effects of different parameters such as water and cement contents, grain size distribution and mixture curing time on the characteristics of the samples were studied to identify the mixture closely resembling the formation at the drilling site. The Hoek triaxial cell was modified to allow the visual monitoring of grain debonding and borehole breakout processes during the laboratory tests. The results showed the significance of real-time visual monitoring in determining the initiation of the borehole breakout. The size-scale effect study on TWHC specimens revealed that with the increasing borehole size, the ductility of the specimen decreases, however, the axial and lateral stiffnesses of the TWHC specimen remain unchanged. Under different confining pressures the lateral strain at the initiation point of borehole breakout is considerably lower in a larger size borehole (20 mm) compared to that in a smaller one (10 mm). Also, it was observed that the level of peak strength increment in TWHC specimens decreases with the increasing confining pressure.

Role of Grain Size in Redox Induced Thin Film Stress in Ceria Systems

Transitioning from the micro to nano morphology scale can result in dramatic changes in electrical and optical properties of films. Space charge effects and creation of a significantly greater fraction of interfaces/grain boundaries are believed to give rise to such size scale effects. While electrical properties have generally dominated research in this area, mechanical properties, such as film stress and strain, also exhibit scaling effects. In-situ wafer curvature measurements are employed to measure these stresses on pure and 10% Praseodymium doped ceria (PCO) thin films during oxidation-reduction cycling and over a range of temperatures and oxygen partial pressures. These measured stress values are compared to the values reported for the bulk PCO and also to the thin film defect equillibria model developed by some of the co-authors and was found to fit well with the predicted values. In both the pure ceria and PCO thin films, the compositional stresses increased with decreasing grain sizes thus corroborating the idea that the space charge effects near surfaces and interfaces has a significant impact on the compositional stresses.

Bioresorbable scaffolds for bone tissue engineering: Optimal design, fabrication, mechanical testing and scale-size effects analysis

Bone scaffolds for tissue regeneration require an optimal trade-off between biological and mechanical criteria. Optimal designs may be obtained using topology optimization (homogenization approach) and prototypes produced using additive manufacturing techniques. However, the process from design to manufacture remains a research challenge and will be a requirement of FDA design controls to engineering scaffolds. This work investigates how the design to manufacture chain affects the reproducibility of complex optimized design characteristics in the manufactured product. The design and prototypes are analyzed taking into account the computational assumptions and the final mechanical properties determined through mechanical tests. The scaffold is an assembly of unit-cells, and thus scale size effects on the mechanical response considering finite periodicity are investigated and compared with the predictions from the homogenization method which assumes in the limit infinitely repeated unit cells. Results show that a limited number of unit-cells (3–5 repeated on a side) introduce some scale-effects but the discrepancies are below 10%. Higher discrepancies are found when comparing the experimental data to numerical simulations due to differences between the manufactured and designed scaffold feature shapes and sizes as well as micro-porosities introduced by the manufacturing process. However good regression correlations (R2 > 0.85) were found between numerical and experimental values, with slopes close to 1 for 2 out of 3 designs.

Unravelling the physics of size-dependent dislocation-mediated plasticity.

Size-affected dislocation-mediated plasticity is important in a wide range of materials and technologies. Here we develop a generalized size-dependent dislocation-based model that predicts strength as a function of crystal/grain size and the dislocation density. Three-dimensional (3D) discrete dislocation dynamics (DDD) simulations reveal the existence of a well-defined relationship between strength and dislocation microstructure at all length scales for both single crystals and polycrystalline materials. The results predict a transition from dislocation-source strengthening to forest-dominated strengthening at a size-dependent critical dislocation density. It is also shown that the Hall–Petch relationship can be physically interpreted by coupling with an appropriate kinetic equation of the evolution of the dislocation density in polycrystals. The model is shown to be in remarkable agreement with experiments. This work presents a micro-mechanistic framework to predict and interpret strength size-scale effects, and provides an avenue towards performing multiscale simulations without ad hoc assumptions.

Scale and size effects in dynamic fracture of concretes and rocks

Structural-temporal approach based on the notion of incubation time is used for interpretation of strain-rate effects in the fracture process of concretes and rocks. It is established that temporal dependences of concretes and rocks are calculated by the incubation time criterion. Experimentally observed different relations between ultimate stresses of concrete and mortar in static and dynamic conditions are explained. It is obtained that compressive strength of mortar at a low strain rate is greater than that of concrete, but at a high strain rate the opposite is true. Influence of confinement pressure on the mechanism of dynamic strength for concretes and rocks is discussed. Both size effect and scale effect for concrete and rocks samples subjected to impact loading are analyzed. Statistical nature of a size effect contrasts to a scale effect that is related to the definition of a spatio-temporal representative volume determining the fracture event on the given scale level.

Kinetic simulation of direct-current driven microdischarges in argon at atmospheric pressure

A one-dimensional, implicit particle-in-cell Monte Carlo collision model is used to simulate the plasma kinetic properties at a steady state in a parallel-plate direct current argon glow microdischarge under various operating conditions, such as driving voltage (30–1000 V) and gap size (10–1000 µm) at atmospheric pressure. First, a comparison between rf and dc modes is shown for the same pressure, driving voltage and gap spacing. Furthermore, the effect of gap size scaling (in the range of 10–1000 µm) on the breakdown voltage, peak electron density and peak electron current density at the breakdown voltage is examined. The breakdown voltage is lower than 150 V in all gaps considered. The microdischarge is found to have a neutral bulk plasma region and a cathode sheath region with size varying with the applied voltage and the discharge gap. In our calculations, the electron and ion densities are of the order of 1018–1023 m−3, which is in the glow discharge limit, as the ionization degree is lower than 1% . The electron energy distribution function shows a two-energy group distribution at a gap of 10 µm and a three-energy group distribution at larger gaps such as 200 µm and 1000 µm, emphasizing the importance of the gap spacing in dc microdischarges.

A Multi-Scale Numerical Method for the Study of Size-Scale Effects in Ductile Fracture

The use of a stress-strain constitutive relation for the undamaged material and a traction-separation cohesive crack model with softening for cracking has been demonstrated to be an effective strategy to predict and explain the size-scale effects on the mechanical response of quasi-brittle materials. In metals, where ductile fracture takes place, the situation is more complex due to the interplay between plasticity and fracture. In the present study, we propose a multi-scale numerical method where the shape of a global constitutive relation used at the macro-scale, the so-called hardening cohesive zone model, can be deduced from meso-scale numerical simulations of polycrystalline metals in tension. The shape of this constitutive relation, characterized by an almost linear initial branch followed by a plastic plateau with hardening and finally by softening, is in fact the result of the interplay between two basic forms of nonlinearities: elasto-plasticity inside the grains and classic cohesive cracking for the grain boundaries.

Size-dependent magnetic properties in Cu0.25Co0.25Zn0.5Fe2O4

Cu0.25Co0.25Zn0.5Fe2O4 nanoparticles were prepared by a co-precipitation method and the size was varied by varying annealing temperatures. The cation distribution, estimated using Mössbauer spectroscopy, shows that it is the same for all samples, irrespective of the size. The variation of Curie temperature and saturation magnetization as a function of particle size, studied using d.c. magnetization, clearly indicates that these are a result of finite size scaling effects. The superparamagnetic size limit is estimated to be 8 nm.

Flaw-tolerance of nonlocal discrete systems and interpretation according to network theory

Discrete systems are modeled as a network of nodes (particles, molecules, or atoms) linked by nonlinear springs to simulate the action of van der Waals forces. Such systems are nonlocal if links connecting non-adjacent nodes are introduced. For their topological characterization, a nonlocality index (NLI) inspired by network theory is proposed. The mechanical response of 1D and 2D nonlocal discrete systems is predicted according to finite element (FE) simulations based on a nonlinear spring element for large displacements implemented in the FE programme FEAP. Uniaxial force-displacement responses of intact and defective systems (with links or nodes removed) are numerically simulated. Strain localization phenomena, size-scale effects and the ability to tolerate defects are investigated by varying the degree of nonlocality.

Scaling Properties of Step-Etch Perpendicular Magnetic Tunnel Junction With Dual-CoFeB/MgO Interfaces

We built and studied the size scaling effect of perpendicular magnetic tunnel junctions (p-MTJs) with stepetch structure and dual-MgO/CoFeB interfaces. The step-etch structure yields symmetrical R-H loop, while dual-MgO/CoFeB interfaces raises cell anisotropy, thus the data retention time. The p-MTJ of 45-nm diameter shows spin-transfer torque switching voltage Vsw with tight temporal sigma (σ(V sw ) c0 ) reduces with MTJ area, its density (J c0 ) increases. One plausible explanation of this observation is that the magnetization reversal of small MTJ follows the single-domain macrospin model, while that of the larger MTJ may be affected by the nucleation of domain during the magnetization reversal, and the wall motion leads to Jc0 lowering; the other may be due to process-induced film damage. Fortunately, the switching efficiency (E b /|I c0 |) is higher for smaller p-MTJ.

Experimental and Numerical Analysis of Rock Block Stability Using a Remotely Positioned Laser Doppler Vibrometer

This paper examines a new method of evaluating the stability of a rock slope using a remotely positioned LDV (laser Doppler vibrometer). We conducted an experiment using physical models and performed a numerical analysis to evaluate the new method. The physical model included: (1) concrete blocks on an artificial soil slope with two block sizes and three slopes; (2) concrete blocks bonded to the concrete base with different contact area. The LDV measurements agreed with conventional seismometer measurements. The dominant frequency of the blocks varied with the stability and dominant frequency and the amplitude varied with the block size. The numerical model was used to examine a concrete block adhered to a concrete base with different contact areas. The dominant frequency of the blocks determined using the numerical model agreed with those obtained from the physical experiments. We analyzed different sized blocks to examine the scaling effects. The dominant frequency of the blocks was inversely related to the block size. These results demonstrated the effectiveness of LDV for evaluating the stability of rock slopes and cleared the block size scaling effects.

Relationship between urbanization, direct and indirect greenhouse gas emissions, and expenditures: A multivariate analysis

In this paper, we analyze the relationships between Finnish household types and their consumption-based carbon footprints. We calculate footprints by combining expenditure data with life-cycle greenhouse gas emission intensities derived from an environmentally extended input–output model. By applying regression analysis, we explore the effects of expenditure, urbanity, and household size on total, direct, and indirect emissions. The separate analyses for direct and indirect GHGs provide insights, not previously found in the literature, on the relationship between urbanity and carbon footprints. Holding expenditure constant, a rural lifestyle seems to be related to the highest GHG emissions. However, keeping in mind that the absolute amount of indirect emissions is major to direct emissions from home energy and private driving, the less prominent or even reversed relationship between indirect emissions and urbanity is also worth noting. The existence of household size scale effects depends whether direct or indirect GHGs are explained. We demonstrate that in order to gain a comprehensive understanding of mitigation policies and their effects, not only the averages but the various patterns of direct and direct emissions must be kept in mind. This paper complements the earlier carbon footprint assessments from the same authors by providing a comprehensive statistical analysis.

Computational study of plasma sustainability in radio frequency micro-discharges

We apply an implicit particle-in-cell Monte-Carlo (PIC-MC) method to study a radio-frequency argon microdischarge at steady state in the glow discharge limit, in which the microdischarge is sustained by secondary electron emission from the electrodes. The plasma density, electron energy distribution function (EEDF), and electron temperature are calculated in a wide range of operating conditions, including driving voltage, microdischarge gap, and pressure. Also, the effect of gap size scaling (in the range of 50-1000 μm) on the plasma sustaining voltage and peak electron density at atmospheric pressure is examined, which has not been explored before. In our simulations, three different EEDFs, i.e., a so-called three temperature hybrid mode, a two temperature α mode, and a two temperature γ mode distribution, are identified at different gaps and voltages. The maximum sustaining voltage to avoid a transition from the glow mode to an arc is predicted, as well as the minimum sustaining voltage for a steady glow discharge. Our calculations elucidate that secondary electrons play an essential role in sustaining the discharge, and as a result the relationship between breakdown voltage and gap spacing is far away from the Paschen law at atmospheric pressure.

Time-Dependent Crack Growth Thresholds of Ni-Base Superalloys

A micromechanical model has been developed for predicting the time-dependent crack growth threshold and its variability by considering oxide formation or cavity formation ahead of an elastic crack subjected to a sustained load at a stress intensity factor, K, at elevated temperatures in air. It is demonstrated that stress relaxation associated with a volume-expansion process such as the formation of creep cavities or oxides with a positive transformation strain can induce residual stresses at the tip of the elastic crack. The near-tip residual stresses must be overcome by the external load, thereby instigating a growth threshold, K th, for the onset of time-dependent crack growth. This micromechanical framework provides the basis for developing appropriate predictive models for the time-dependent crack growth thresholds associated with several damage processes, including (1) oxidation-assisted intergranular crack growth, (2) K-controlled creep crack growth along an intergranular path, and (3) stress corrosion cracking. The micromechanical threshold models have been utilized to predict the time-dependent crack growth thresholds of a variety of Ni-base superalloys. The material parameters that contribute to the variability of the time-dependent crack growth thresholds have been identified and related to variations of mixed oxides or creep cavities formed near the crack tip. A size scale effect is also predicted for the transformation toughening phenomenon, which is largest at or below K th but diminishes at increasing K levels above the threshold. Finally, the micromechanical models are utilized to identify means for suppressing time-dependent crack growth in Ni-base alloys.

Scaling of the mean and variance of population dynamics under fluctuating regimes

Theoretical ecologists have long sought to understand how the persistence of populations depends on the interactions between exogenous (biotic and abiotic) and endogenous (e.g., demographic and genetic) drivers of population dynamics. Recent work focuses on the autocorrelation structure of environmental perturbations and its effects on the persistence of populations. Accurate estimation of extinction times and especially determination of the mechanisms affecting extinction times is important for biodiversity conservation. Here we examine the interaction between environmental fluctuations and the scaling effect of the mean population size with its variance. We investigate how interactions between environmental and demographic stochasticity can affect the mean time to extinction, change optimal patch size dynamics, and how it can alter the often-assumed linear relationship between the census size and the effective population size. The importance of the correlation between environmental and demographic variation depends on the relative importance of the two types of variation. We found the correlation to be important when the two types of variation were approximately equal; however, the importance of the correlation diminishes as one source of variation dominates. The implications of these findings are discussed from a conservation and eco-evolutionary point of view.