Tip Radius Research Articles

Prediction of the Secondary Arms Spacing Based on Dendrite Tip Kinetics and Cooling Rate.

Secondary dendrite arm spacing (SDAS) is one of the most important factors affecting macrosegregation and mechanical properties in solidification processes. Predicting SDAS is one of the major parameters in foundry technology. In order to predict the evolution of microstructures during the solidification process, we proposed a simple model which predicted the secondary dendrite arm spacing based solely on the tip velocity (related to the tip supersaturation) and cooling rate. The model consisted of a growing cylinder inside a liquid cylindrical envelope. Two important hypotheses were made: (1) Initially the cylinder radius was assumed to equal the dendrite tip radius and (2) the cylindrical envelope had a fixed radius in the order of the dendrite tip diffusion length. The numerical model was tested against experiments using various Pb-Sn alloys for a fixed temperature gradient. The results were found to be in excellent agreement with experimental measurements in terms of SDAS and dendrite tip velocity prediction. This simple model is naturally destined to be implemented as a sub-grid model in volume-averaging models to predict the local microstructure, which in turn directly controls the mushy zone permeability and macrosegregation phenomena.

Compensation Method for Correcting the Topography Convolution of the 3D AFM Profile Image of a Diffraction Grating

Any 3D AFM image is a convolution of the geometry of the AFM tip and the profile of the scanned sample, especially when the dimensions of the scanned sample are comparable to those of the AFM tip shape. The precise profile of the scanned sample can be extracted from the 3D AFM image if the geometry of the AFM tip is known. Therefore, in order to separate the geometry of the AFM probe tip from the 3D AFM image of a diffraction grating with a rectangular profile and to correct for the topographic convolutions induced by the AFM probe tip, a method is used to quantitatively evaluate the geometry of the AFM probe tip, including the tip radius and the included angle. A model for reconstructing the measured AFM image is proposed to correct topography convolutions caused by the AFM tip shape when scanning a diffraction grating with rectangular profiles. A series of experiments were performed to verify the effectiveness of the proposed AFM tip geometry evaluation method, and comparison experiments were conducted to demonstrate the feasibility and reliability of the proposed reconstruction model.

Fabrication of oscillating metal probe for dynamic scanning microwave microscopy

Abstract A microwave probe plays a critical role in near-field imaging, and there is a continuous effort to develop them through straightforward methods. This study designed and fabricated an oscillating metal probe and used it for scanning microwave imaging of micro-nano structures. The surface smoothness of the cantilever is approximately 19.3 nm after polishing with diamond abrasive paper, and the tip radius is less than 20 nm using electrochemical etching. The impact of metal electrode materials on microwave signals was assessed in the frequency range of 1–20 GHz. The microwave imaging capability of the devised probe was explored through the imaging of a micro-nano structure. The spatial resolution of microwave imaging reached 0.5 μm over a scanning area of 50 μm × 50 μm. This study has far-reaching significance for developing higher-performance microwave probes and advancing scanning microwave microscopy.

Temperature evolution characteristics of stem root during dark period in positive long spark discharge

Gas temperature plays an important role in the characterization of plasma parameters. The temperature evolution of stem roots during the dark period is at the heart of our understanding of the physical mechanism of streamer to the leader transition process in a long spark discharge. The quantitative schlieren system with high spatiotemporal resolution was designed to conduct positive leader discharge experiments with a 1.0 m rod-plate gap at atmospheric pressure, and the amplitude and rise time of positive impulse voltage waveforms were 380 kV and 200 μs, respectively. The time-resolved quantitative schlieren images of the discharge channel near the electrode tip can be captured to gather the temperature data of stem roots for case study. Further statistical tests revealed that due to the dispersion of the first streamer discharge, there were three evolutionary trends of gas temperature at the axis of the stem root in the early dark period. Interestingly, the gas temperature at the axis of the stem root was maintained at 1000–1200 K in regardless of the evolutionary trend in the early dark period. In addition, the statistical results indicate that there is a significant positive correlation between the curvature radius of the discharge electrode tip and the critical charge value Qcrit of the first streamer discharge, which leads to a transition in evolutionary trends of gas temperature at the axis of the stem root. This research has important guiding significance for understanding the physical mechanism of leader inception and the whole process modeling of long air gap discharge.

High performance field emission cathode based on the diamond nanowires prepared by nanocrystalline diamond films annealed in air

This paper reports the field emission (FE) characteristics of a diamond nanowires (DNWs) array. The nanocrystalline diamond (NCD) film was deposited on silicon by microwave plasma chemical vapor deposition (MPCVD) and then annealed in air forming DNWs and hydrogenated at last. A high-field flat-plate emission test structure with a 1.03 μm gap between anode and cathode was prepared and the electrical properties proved it feasible. The FE performance of DNWs array was measured in a vacuum test system and that of NCDs film as a comparison. Finally, their FE parameters were analyzed and extracted based on the Fowler–Nordheim (F-N) theory. The results show that transforming NCDs film into DNWs array can improve the FE characteristics greatly. The turn-on field is as low as 1.36 V μm−1 dropping by one order of magnitude, while the field enhancement factor and FE current density are up to 156.68 and 484.75 mA cm−2 respectively rising both by two orders of magnitude. This excellent FE performance stems from the characteristics of large aspect ratio, very small tip radius and high density of DNWs.

Influences of tool tip geometry on surface/subsurface damage formation in nanoscratching of single-crystal 4H-SiC

Creating a smooth surface finish with nanometer-scale roughness on SiC is extremely difficult due to its hard, brittle properties and crystal anisotropy. In this study, nanoscratching tests were performed on single-crystal 4H-SiC along various crystal directions by using a sharp Berkovich tip (radius ~150 nm) and a blunt spherical tip (radius ~1 μm), respectively, to reveal the effects of tool geometry on its surface integrity. Results indicate that, under the same load conditions, the Berkovich face-forward tip produced the greatest penetration depth, followed by the Berkovich edge-forward tip and the spherical tip. The extent of surface and subsurface damage caused by the three tips follows the same trend as the penetration depth. Phase transformation did not occur in the scratched surface with the three tips, while it was occurred in the chips generated with Berkovich face-forward tip. The critical load for surface crack formation was larger when scratching along <01−10> directions compared to scratching along <11−20> directions, independent of tool geometry. Microcrack-like defects may form in the subsurface even the surface is free of damage. The microcracks were caused by {01−11} pyramidal <a> and <a+c> slip and by {11−22} pyramidal <c+a> slip when scratching along <11−20> and <01−10> directions, respectively.

Quantifying both viscoelasticity and surface tension: why sharp tips overestimate cell stiffness

Quantifying the mechanical properties of cells is important to better understand how mechanics constrain cellular processes. Furthermore, because pathologies are usually paralleled by altered cell mechanical properties, mechanical parameters can be used as a novel way to characterize the pathological state of cells. Key features used in models are cell tension, cell viscoelasticity (representing the average of the cell bulk), or a combination of both. It is unclear which of these features is the most relevant or if both should be included. To clarify this, we performed microindentation experiments on cells with microindenters of various tip radii, including micron-sized microneedles. We obtained different cell-indenter contact radii and measured the corresponding contact stiffness. We derived a model predicting that this contact stiffness should be an affine function of the contact radius and that at vanishing contact radius, the cell stiffness should be equal to the cell tension multiplied by a constant. When microindenting leukocytes and both adherent and trypsinized adherent cells, the contact stiffness was indeed an affine function of the contact radius. For leukocytes, the deduced surface tension was consistent with that measured using micropipette aspiration. For detached endothelial cells, agreement between microindentation and micropipette aspiration was better when considering these as only viscoelastic when analyzing micropipette aspiration experiments. This work suggests that indenting cells with sharp tips while neglecting the presence of surface tension leads to an effective elastic modulus whose origin is in fact surface tension. Accordingly, using sharp tips when microindenting a cell is a good way to directly measure its surface tension without the need to let the viscoelastic modulus relax.

Unveiling unique scaling behavior in miscible, volatile Marangoni spreading.

We present a novel observation of the expansion of the outer tip radius of a fast-spreading ethanol-water film spreading over a deep substrate of water. The experimentally measured radius of the outer tip of the film (ro) and its velocity (Uo) display a complex scaling with time and drop properties. The variation showed by ro differed from the commonly observed scalings of t3/4 and t1/4. We propose novel scaling laws for ro and Uo by expressing ro as the sum of the radius of the stable part of the film rf and the length of the unstable part lp at the periphery of the stable part of the film, that had azimuthally uniformly spaced plumes. The radius of the stable part of the film scales as rf ∼ t1/4 since, while the film expands, the Marangoni stresses are balanced by viscous stresses within the film thickness. At the same time, lp ∼ t3/4 since the plumes grow at the periphery of the stable part of the film, with the driving surface tension stresses balanced by the viscous stresses in a shear layer below the plumes. Combining these two scaling laws yielded a novel, two-term scaling law for ro, which is close to a single power-law scaling ro ∼ t1/2. We obtain an expression for the dimensionless mean outer tip radius as , where t* = t/tξ, tξ = (rd4ρwμw/Δσ2)1/3 being the time scale. Similarly, we show that the dimensionless velocity scales as with the variables λ1 and λ2 being functions of t* and drop properties. These proposed scaling laws are shown to match our measurements, thereby validating the phenomenology of such miscible, volatile spreading.

Fatigue strength assessment of aluminium welded joints under variable amplitude loading using the Peak Stress Method

One of the simplest and most efficient ways to design lightweight structural components is the combination of welding and aluminum alloys. However, welded joints are extremely sensitive to fatigue failure and making accurate lifetime predictions is still challenging when Variable Amplitude (VA) loading conditions are involved. Among all design criteria available in the literature, the present investigation focuses on the Peak Stress Method (PSM), an engineering finite element (FE)-based approach to rapidly assess the fatigue strength of welded joints. In more detail, the PSM suggests modelling both weld toe and weld root as sharp V-notches having null tip radius and correlates their fatigue strength using the intensity of the local linear elastic asymptotic stress distributions described by the Notch Stress Intensity Factors (NSIFs). The theoretical formulation of the PSM for the fatigue strength assessment of welded joints subjected to VA loadings has been recently proposed by combining its Constant Amplitude (CA) formulation with the Palmgren-Miner's cumulative linear damage rule. Such VA formulation has been successfully validated against a large bulk of experimental fatigue results generated by testing welded joints made of structural steels under uniaxial as well as multiaxial loadings. In the present investigation, the VA formulation of the PSM has been further validated against experimental data relevant to welded joints made of aluminium alloy under VA loadings.

Improved ionic current rectification utilizing cylindrical nanochannels coated with polyelectrolyte layers of non-uniform thickness.

Conical nanochannels employed to create ionic current rectification (ICR) in nanofluidic devices are prone to clogging due to the contraction at one end. As an alternative approach for creating ICR, a cylindrical nanochannel covered with a polyelectrolyte layer (PEL) of variable thickness is proposed in the present study. The efficacy of the proposed design is studied by numerically solving the governing equations including the Poisson, Nernst-Planck, and Stokes-Brinkman equations. Furthermore, the fundamental mechanism behind ICR is explained using a simplified one-dimensional model. The effects of the nanochannel radius, concentration of PEL fixed charges, and bulk ionic concentration on the rectification factor are then investigated in detail. It is shown that the proposed nanochannel provides larger rectification factors as compared to conical nanochannels over wide ranges of the fixed charge concentration and bulk ionic concentration. Such a performance can be achieved even at channel radii much larger than the tip radius of conical nanochannels, indicating not only the better performance of the proposed nanochannel but also its likely longer service life, because of reducing the probability of total ionic current blockage. This means that the proposed nanochannel could find widespread use in fluidic devices, as a replacement for conical nanofluidic diodes.

A new pore-strength model for the quantitative strength prediction of ceramics under mode-I loading

Strength prediction under the action of pores is crucial for the safety of ceramics. Here, a quantitative prediction model of pore-strength response under mode-I loading was developed based on the new mapping relationship between stress intensity factor and tip radius. The new model was proved to have great application after comparison and analysis of the pore-strength test data of three typical ceramics as well as the pertinent data as-reported in the literature. Results indicated that when the tip radius of pore (ρ) exceeds the critical value (ρc = KIc2/(πσ02)), the stress intensity factor increases as a power function with increasing ρ, at which point the strength decay is significantly weakened, and when the ρ is lower than the ρc, the pore can be equated to a crack problem. This work can not only forecast and assess the failure strength of ceramics containing pores, but also provide guidance for the design of extremely dependable ceramics.

Asymptotic stress field for the blunt and sharp notches in bi-material media under mode III loading

Abstract This study introduces a novel approach to analyze the stress and displacement fields around blunt notches in bi-material media, focusing on mode III loading conditions. The eigenfunction expansion method is used to derive a simplified yet accurate solution, satisfying the boundary conditions for bi-material blunt V-notches. The robustness of the proposed asymptotic solution is validated through several finite element analyses, encompassing a range of notched geometries such as blunt V-notches, VO-notches, and circular holes. Notably, it is demonstrated that when the notch tip radius approaches zero, the solution coincides with the existing sharp V-notch model, illustrating the robustness of the methodology.

Determination of the radii of coated and uncoated silicon AFM sharp tips using a height calibration standard grating and a nonlinear regression function.

AFM sharp tips are used to characterize nanostructures and quantify the mechanical properties of the materials in several areas of research. The analytical results can show unpredicted errors if we do not know the exact values of the AFM tip radius. There are many techniques of in situ measurements for determining the actual AFM tip radius, but they are limited to uncoated tips. This paper presents an alternative and simple method to determine the radii of coated tips and an uncoated tip. Pt-coated, Cr/Au-coated, and uncoated Si tips were used to scan a calibration standard grating in AFM contact mode with sub-nanonewton load to obtain the curved scan profile of the edge corner of the grating structure. The data points of the curved profile of each tip were fitted with a nonlinear regression function to estimate the curvature radius of the tip. The results show that the estimated radius of the coated tips is in the range of nominal values provided by the tip manufacturer, while the estimated radius of the uncoated Si tip is bigger than the nominal radius because of tip blunting during the scan. However, this method yields an accurate estimate of the tip radius with a low root mean squared error of the curve fitting results.

Energy-saving discharge needle shape for electrohydrodynamic airflow generation

Electrohydrodynamics (EHD) is a way to produce low energy-consuming airflow without moving components. The basis of airflow by EHD is corona discharge. A way to generate corona discharge is done, among others, via needle-type emitter electrodes whose shape and arrangement play a crucial role in the effectiveness of the discharge. Until now, the needle shape was chosen somewhat arbitrarily, although it impacts the energy consumption of the EHD process. We lack systematic studies on the impact of needle shape on the EHD discharge process and associated airflow to help engineers and scientists choose the best shape. This in-silico study screens the impact of the needle shape parameters on EHD performance in terms of electrical power consumption and airflow generation. The study aims to find the ideal EHD needle shape for unrestricted and confined flow. For this purpose, we test three different geometrical configurations. The first configuration is a free-flow single-needle configuration. The second configuration adds a dielectric nearby, which represents a needle enclosure. Lastly, a configuration including a dielectric and a converging nozzle is examined. All studies use a 2D-axisymmetric, fully automatized EHD physics-based model. The first set of parametric studies explores the inherent geometrical properties of the needle shape, like tip radii (10–250 μm), needle cone angle (10–70°), and needle diameters (0.5–2 mm). The second set of parametric studies investigates the operation conditions, such as the emitter-collector distance (10–40 mm), the nozzle contraction ratio (0.04–1), and the operating voltage (6–32 kV). The results of the free-flow configuration show qualitative agreement with experiments on existing needle products. The ideal energy-saving needle shape for free flow configuration features a short conical tip length (i.e., a large angle ≥30°), a diameter of 2 mm, and a needle rip radius of 100 μm. The situation changes when a dielectric is present, and a sharp angle of 10° is favorable to reduce energy consumption. Since a dielectric inverts the optimal needle shape, it makes sense to customize it for a particular application in EHD airflow generation. We provide performance maps that can be used as design charts. This study is a guideline to optimize EHD devices further to reduce energy consumption and increase airflow speed.

Prediction of Nanoscale Water Meniscus Shape between Deliquescent KDP Crystal Optics and AFM Probe for Water-Dissolution Repairing.

KDP (KH2PO4) crystal optics are the key elements for megajoule laser facilities. Nanoscale surface defects would cause laser-induced damage when the optics are irradiated by a high-fluence laser (over 10 J/cm2). Dip-pen nanolithography (DPN) could be used to repair the nanoscale surface defects in the KDP optics by the water meniscus. The high humidity required for high-efficiency and soft KDP surfaces penetrated by the AFM probe brings challenges for accurately predicting the water meniscus shape to evaluate the effectiveness of the DPN water-dissolution repairing. The multisolutions of the Young-Laplace and Kelvin equations also lead to the wrong water meniscus shape. A theoretical model that takes the high humidity and the penetration of the AFM probes into account is developed. The parametrization Young-Laplace equations are adopted for the zero contact angle of the water films, and the AFM probe is treated as the combination of the cone and sphere for the water meniscus whose size is larger than the AFM tip radius under high humidity. The penetration of the AFM probe is modeled by Hertz theory. Both the water films (3.3 nm thickness at 99% relative humidity) and indentations (1.46 nm depth at 300 nN contact force) are non-negligible for the nanoscale water meniscus between the KDP surface and the AFM probe. Moreover, the rough-fine two-step method is proposed to lock the correct solution of the Young-Laplace and Kelvin equations. The effectiveness of the proposed model is verified by comparison with reported ESEM images and pull-off forces. In addition, the overgrowth dots on the KDP surface are compared with the water meniscus. The linear growth of the water meniscus would cause the linear growth of the overgrowth dot, which proves the proposed model could be used to guide the DPN water-dissolution repairing for the nanoscale surface defects in the KDP optics.

A unified thermal-field emission theory for metallic nanotips

The role of curvature effects, in the thermal-field (TF) emission of electrons from nanotips, has been investigated. It is found that for field emitter tips having tip radius of curvature Ra&amp;lt;50 nm, the error on using the planar tunneling potential to evaluate the current density is significant compared to the curvature-corrected potential. Furthermore, the error is found to be strongly temperature dependent at low apex fields, whereas at high fields, it is only moderate. For emitter tips having tip radius Ra≥5 nm, a unified expression for current density applicable for field, thermal-field, and thermionic emission is obtained. In the analysis, a single linearization point corresponding to the peak of the normal energy distribution of electrons is chosen, about which the Gamow exponent is expanded. The temperature-dependent curvature-corrected current density equation is numerically validated against a benchmark that performs the current density integral with the Kemble form of the Wentzel–Kramers–Brillouin transmission coefficient up to the peak of the tunneling potential, while above the barrier, the Morse transmission coefficient is used. The agreement is found to be good. It is inferred that the curvature plays a significant role in field and thermal-field emission, whereas in thermionic emission, it is not as important. In the limit where the apex radius of curvature Ra→∞, it is able to retrieve the Murphy–Good equation as well as the Richardson–Laue–Dushman equation in their respective limits.

Equiaxed colony growth in the small undercooled Y2O3-doped Al2O3–ZrO2 eutectic ceramic melt

Al2O3/ZrO2 eutectic bulks (20 mm in diameter) with different Y2O3 contents (0–4.5 mol %) were grown using the conventional casting method. Variations in the microstructural characteristics and colony tip growth behavior caused by Y2O3 addition in the central equiaxed grain zone were investigated. As Y2O3 was added to the Al2O3/ZrO2 binary eutectic, except for a decrease in colony size, the colony tip radius reduced drastically and then increased slightly. Colony growth behavior can be well predicted using the Lipton–Glicksman–Kurz (LGK) model. A critical Y2O3 content (0.5–1.1 mol%) exists below which the eutectic colony growth is accelerated owing to the Y2O3 addition, but slowed down otherwise. However, the average interphase spacing and ZrO2 rod diameter inside the colonies varied with Y2O3 content, converse to the growth rate.

Flow Confinement Effects on sUAS Rotor Noise

The goal of this paper is to investigate the effects of flow confinement on the noise generated by a small unmanned aerial system rotor measured and simulated in a partially closed test room. More specifically, the influence of the flow recirculation in the test room and the consequent blade turbulence interaction on both the tonal unsteady loading noise and the broadband laminar separation noise components are scrutinized. The study also aims at improving our prediction capabilities of drone rotor noise, and deepening our fundamental knowledge of rotor aeroacoustics in transitional boundary layer regimes. Numerical simulations are conducted by means of a scale-resolving wall-modelled lattice Boltzmann solver to calculate the unsteady flow and the noise generated by the same reference configuration used in our previous works, which consists in a rotor operated at a chord-based Reynolds number of about 70000 at 75% of the tip radius, both in hover and axial flow conditions. Results for a rotor in pristine flow conditions are compared to results obtained by simulating the rotor in a confined environment that reproduces the A-Tunnel test chamber of Delft University of Technology. One one hand, our study reveals that previously observed discrepancies between measured and predicted noise spectra in hover conditions are not due to the influence of the flow confinement on the laminar separation mechanisms, as hypothesized in our previous study, rather to a lack of numerical resolution. On the other hand, the new results reveal that, in hover conditions, the dominant effect of the flow recirculation is to increase the unsteady loading tonal noise components, whereas, in axial flow conditions, no significant effect due to the test environment is observed. Some of our conclusive observations are supported by results obtained using a source identification technique herein presented for the first time.

Data-driven based fracture prediction of notched components.

A data-driven approach is developed to predict the fracture load of a notched component. To do so, more than 1500 fracture tests (507 unique experimental data points) on mixed-mode I/II loading of notched brittle samples were collected from the literature. After pre-processing the raw data, six features of maximum tangential stress [Formula: see text], maximum tangential stress angle [Formula: see text], ultimate tensile strength [Formula: see text], fracture toughness [Formula: see text], notch opening angle [Formula: see text] and notch tip radius [Formula: see text] were selected by using the neighbourhood component analysis (NCA) technique. To predict the fracture load of various types of notched samples, several machine learning (ML) models were trained using the methods of Gaussian process regression (GPR), decision tree ensemble and artificial neural network (ANN). Then, the Bayesian optimization algorithm was applied to find the optimum hyperparameters for each model. Lastly, the performance of the models in predicting fracture load was evaluated against 124 unseen data points. The results revealed the high potential of data-driven methods for assessing the fracture load of notched brittle components with acceptable precisions of 92%, 89% and 88% accuracy, respectively, for GPR, decision tree ensemble and ANN models. The superior performance of the GPR method can be attributed to its ability to capture complex nonlinear relationships in the data while providing reliable uncertainty estimates. Furthermore, thanks to its interpolation capabilities, GPR is able to seamlessly fill the gaps between data points, resulting in more comprehensive and precise predictions across the entire range of input data. Additionally, the presented models were capable of predicting the fracture load of VO-shaped notched samples with acceptable accuracy, though this type of notch was not used in the model training process. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 2)'.

Multicone Diamond Waveguides for Nanoscale Quantum Sensing.

The long-lived electronic spin of the nitrogen-vacancy (NV) center in diamonds is a promising quantum sensor for detecting nanoscopic magnetic and electric fields in various environments. However, the poor signal-to-noise ratio (SNR) of prevalent optical spin-readout techniques presents a critical challenge in improving measurement sensitivity. Here, we address this limitation by coupling individual NVs to optimized diamond nanopillars, thereby enhancing the collection efficiency of fluorescence. Guided by near-field optical simulations, we predict improved performance for tall (≥5 μm) pillars with tapered sidewalls. This is subsequently verified by fabricating and characterizing a representative set of structures using a newly developed nanofabrication process. We observe increased SNR for optimized devices, owing to improved emission collimation and directionality. Promisingly, these devices are compatible with low-numerical-aperture collection optics and a reduced tip radius, reducing experimental overhead and facilitating improved spatial resolution for scanning applications.