Tip Radius Of Curvature Research Articles

A Two-Parameter Function for Nanoscale Indentation Measurement of Near Surface Properties

A two-parameter function for estimation of projected area in instrumented indentation measurement is obtained to account for indenter tip imperfection. Imperfection near indenter tip is modeled using a spherical function and combined with a linear function describing the edge boundary of the indenter. Through an analytical fusion technique, the spherical and linear functions are combined into a single function with two unknown geometric parameters of tip radius of curvature and edge slope. Data from indentation measurement of force and displacement, using a Berkovich tip and single crystal alumina and silica samples, are implemented in the proposed area function yielding estimated values of Young’s modulus. Results were compared with that obtained from Oliver and Pharr technique for deep as well as shallow indentation regimes. The estimates for Young’s modulus were found to agree quite favorably. More importantly, in contrast to the Oliver–Pharr technique, the use of the two-parameter function resulted in a significantly more accurate estimation of Young’s modulus for shallow indentation depth of 0–50nm. The error in estimation of Young’s modulus was found to be within 10% for indentation depths of 25–50nm and within 20% for indentation depths of 0–25nm.

A method to quantitatively evaluate the Hamaker constant using the jump-into-contacteffect in atomic force microscopy

We find that the ‘jump-into-contact’ of the cantilever in the atomic force microscope(AFM) is caused by an inherent instability in the motion of the AFM cantilever. Theanalysis is based on a simple model of the cantilever moving in a nonlinear force field. Weshow that the ‘jump-into-contact’ distance can be used to find the interaction of thecantilever tip with the surface. In the specific context of the attractive van der Waalsinteraction, this method can be realized as a new method of measuring the Hamakerconstant for materials. The Hamaker constant is determined from the deflection of thecantilever at the ‘jump-into-contact’ using the force constant of the cantilever and the tipradius of curvature, all of which can be obtained by measurements. The results have beenverified experimentally on a sample of cleaved mica, a sample of Si wafer with natural oxideand a silver film, using a number of cantilevers with different spring constants. Weemphasize that the method described here is applicable only to surfaces that have vander Waals interaction as the tip–sample interaction. We also find that the tip tosample separation at the ‘jump-into-contact’ is simply related to the cantileverdeflection at this point, and this provides a method to exactly locate the surface.

Phase-Field Simulation of Free Dendrite Growth of Aluminum-4.5 mass% Copper Alloy

The free dendrite growth of aluminum-4.5 mass%copper alloy has been investigated using a three-dimensional phase-field model with thin-interface-limit parameters. The dendrite growth velocity and the tip radius of curvature are measured for a given value of anisotropy intensity of the interface energy, and the stability parameters are determined at different degrees of undercooling. The dendrite growth velocities are compared with those obtained by LKT (Lipton, Kurz and Trivedi) model, and the role of the stability parameter is quantitatively discussed.

Free Dendrite Growth of Fe–0.5mass%C Alloy– Three-dimensional Phase-field Simulation and LKT Model –

The free dendrite growth of iron–0.5mass% carbon alloy has been investigated using a three-dimensional phase-field model with thin-interface-limit parameters. The dendrite growth velocity and the tip radius of curvature are determined at different degrees of undercooling, and then the stability parameter for the alloy is estimated. The dendrite growth velocities obtained by phase-field simulations are compared with those obtained using the LKT model with the stability parameter of 0.05. The two are in good agreement and the validity of the LKT model is discussed with regard to practical applications.

Microstructure of the current channel of an atmospheric-pressure diffuse discharge in a rod-plane air gap

The multichannel structure of the current channel of an atmospheric-pressure diffuse discharge excited in a 10-cm rod-plane air gap was investigated using the imprint technique. A voltage pulse with an amplitude of 240 kV, a duration of 180 ns, and a rise time of 14 ns was applied to a 1-cm-diameter bullet-shaped cathode with a tip curvature radius of 0.2 mm; the discharge current reached 350 A. It is found that the diameter of the discharge channel in the anode plane varies in the range 2.5–9.7 mm from shot to shot. The overall imprint of the current channel is formed of 170–9500 imprints of microchannels with an average diameter of 5–20 μm. The parameters of the observed microstructure do not correlate with variations in the main electric characteristics of the discharge and the parameters of the generated X-ray pulse. It is shown that the formation of the microstructure is related to the onset of cathode-directed plasma structures developing from the anode. It is suggested that the same mechanism is responsible for both the formation of the current channels structure and the anode microstructure of diffuse nanosecond discharges developing in atmospheric-pressure air gaps with a highly nonuniform electric field.

Nanoprocessing on Silicon (100) Surface by Using SPM and the Study of the Structural Change

The fabricating methods of nanoscale shapes on Si (100) surface by using atomic force microscope (AFM) and scanning tunneling microscope (STM) were investigated. As a result, nanoscale grooves and faces were fabricated by the scratching methods using AFM. The scratching loads had a major influence on these shapes. Nanoscale pits, grooves and faces were fabricated by STM as a result of controlling the sample bias voltage and the tip curvature radius of tungsten probes. Cross-sectional TEM observations of the nanoscale grooves and faces fabricated by AFM and STM were carried out to study the microstructural changes of Si single crystals. As a result of the TEM observations, it was found that many dislocations and an amorphous phase appeared in the surface of the grooves and faces fabricated by AFM. On the other hand, the single crystalline structure without a dislocation was preserved in the surface of the grooves and faces fabricated by STM. Based on these results, it is considered that the fabricating mechanisms of AFM and STM are a mechanical processing and an electric field evaporation, respectively.

Reactive interdiffusion in the binary system Ni-Si: Morphology of the Ni3Si2 phase

In binary multiphase diffusion, it is generally admitted that interfaces between phases are necessarily plane. However, a few cases exist, as the binary diffusion couples Ni-Si, Mo-Si, and Fe-Al, for which an intermediate phase of each system grows with an irregular needlelike morphology. To characterize the nonplanar growth of Ni3Si2 in bulk samples, the authors studied the behavior of intermetallic compound formation by optical microscopy and x-ray microtomography, for different annealing times. They show that both the average height and the tip radius of curvature grow as the square root of time with two diffusion coefficients separated by orders of magnitude. Moreover, x-ray diffraction indicates that the needles are aligned along the crystallographicc-axis. These results could be consistently explained by an anisotropic diffusion model.

Domain nucleation and hysteresis loop shape in piezoresponse force spectroscopy

Electromechanical hysteresis loop measurements in piezoresponse force microscopy (PFM) [piezoresponse force spectroscopy (PFS)] have emerged as a powerful technique for probing ferroelectric switching behavior on the nanoscale. Interpretation of PFS data requires the relationship between the domain parameters and PFM signal to be established. Here, the authors analyze the switching process using modified point charge model. The charge parameters are selected to reproduce tip-induced surface potential and tip radius of curvature. The relationship between geometric parameters of semiellipsoidal domain and PFM signal is derived using linear Green’s function theory. The role of domain nucleation on hysteresis loop is established.

Electroless Nickel Plating under Continuous Ultrasonic Irradiation to Fabricate a Near-Field Probe Whose Metal Coat Decreases in Thickness toward the Tip

This paper describes a size-dependent electroless plating method to fabricate a new type of probe with a locally decreasing thickness of metal and a tiny tip size for a combined high resolution shear-force and near-field optical microscope. In this method, the tip size and decreasing thickness profile, which affect the resolution capabilities of the microscopes, are controlled by adding a continuous ultrasonic wave with a frequency of 1 MHz to a nickel plating bath. The probe with a tip radius of curvature of 25 nm was successfully fabricated at an ultrasonic power density of 1.6 W cm−2, its metal thickness gradually decreased from 850 to 20 nm toward the distal tip.

Volume of a Nanoscale Water Bridge

Water bridges formed through capillary condensation at nanoscale contacts first stretch and then break during contact rupture. Atomic force microscopy (AFM) pull-off experiments performed in air with hydrophilic tips and samples show that stretched nanoscopic water bridges are in mechanical equilibrium with the external pull-off force acting at the contact but not in thermodynamic equilibrium with the water vapor in air. The experimental findings are explained by a theoretical model that considers constant water volume and decrease of water meniscus curvature during meniscus stretching. The model predicts that the water bridge breakup distance will be roughly equal to the cubic root of the water bridge volume. A thermodynamic instability was noticed for large water bridges formed at the contact of a blunt AFM tip (curvature radius of 400 nm) with a flat sample. In this case, experiments showed rise and stabilization of the volume of the water at the contact in about 1 s. For sharp AFM tips (curvature radius below 50 nm), the experiments indicated that formation of stable water bridges occurs in a much shorter time (below 5 ms).

Self-aligned fabrication of single crystal diamond gated field emitter array

This paper describes a self-aligned fabrication process for diamond gated field emitter array (FEA). Utilizing the non-conformal coverage sputtering conditions of silicon oxide, an interesting “sphere on cone” structure is formed on diamond nano tip array, which is the key point of gate hole opening process. This structure causes shadowing at certain regions of side-wall during Ti / Au gate metal deposition. Removal of “sphere” by wet etching leads to the successful fabrication of a single crystalline diamond gated FEA. Scanning electron microscope observations reveal the fabrication of a uniform emitter array with tip radius of curvature (20 nm) and gate hole (1.4 μm). We also confirmed that no noticeable physical damage exists on tip. In field emission characteristics of the fabricated single crystal diamond gated FEA, gate voltage control of field emission current is realized.

Observations of the advancing δ -ferrite/γ -austenite/liquid interface during the peritectic reaction

The peritectic transition, where δ -ferrite and liquid transform into γ -austenite, is an important aspect of product quality and process control in many ferrous and non-ferrous alloys. Due to the high temperatures at which the transition takes place, relatively little experimental work has been carried out to quantify the underlying phenomena. This paper presents recent work in visualizing the peritectic reaction stage of the transition. The visualization was carried out on the surface of hyperperitectic Fe-4.7 wt% Ni samples using a Confocal Scanning Laser Microscope (CSLM) equipped with a gold-image furnace. The focus of the research is to quantify the rate and shape evolution of the γ -austenite phase as it envelopes the δ -ferrite grains. Tip radii of 8 and 5 μ m were witnessed and it was found that, as these tips approached one-another their shape was altered and their growth rates decreased due to soft impingement of their respective diffusion fields. Comparing the separation distance at the point of soft impingement with the tip radius suggested a proportionality constant between tip radius of curvature and diffusion field size of between 1.1 and 1.3.

Nanoelectromechanics of polarization switching in piezoresponse force microscopy

Nanoscale polarization switching in ferroelectric materials by piezoresponse force microscopy in weak and strong indentation limits is analyzed using exact solutions for coupled electroelastic fields under the tip. Tip-induced domain switching is mapped on the Landau theory of phase transitions, with domain size as an order parameter. For a point charge interacting with a ferroelectric surface, switching by both first and the second order processes is possible, depending on the charge–surface separation. For a realistic tip, the domain nucleation process is first order in charge magnitude and polarization switching occurs only above a certain critical tip bias. In pure ferroelectric or ferroelastic switching, the late stages of the switching process can be described using a point charge model and arbitrarily large domains can be created. However, description of domain nucleation and the early stages of growth process when the domain size is comparable with the tip curvature radius (weak indentation) or the contact radius (strong indentation) requires the exact field structure. For higher order ferroic switching (e.g., ferroelectroelastic), the domain size is limited by the tip–sample contact area, thus allowing precise control of domain size.

Fabrication of Free-Standing Metallic Pyramidal Shells

This paper describes a technique for fabricating three-dimensional, metallic, pyramidal microstructures with base dimensions of 1−2 μm, wall thicknesses of ∼100−200 nm, and tip-curvature radius of ∼50 nm. The procedure begins with the fabrication of pyramidal pits in the surface of an n-doped silicon substrate. An electrically insulating surface layer of SiO2 covers the regions outside the pits. These pits are patterned using either conventional photolithography or soft lithography and formed by selective anisotropic etching. The resulting topographically patterned silicon serves as the cathode for the selective electrodeposition of metal in the pyramidal pits. Removing the silicon template by etching generates free-standing, pyramidal, metallic microstructures.

Characterization of cell tip curvature in directional solidification

We experimentally characterize the geometry of cell tips in directional solidification by determining their curvature radius. Observations are made on a dilute alloy of a plastic crystal (SCN) confined in a thin sample. They go from the cellular regime to the weakly dendritic regime. Attention is drawn on providing an objective measure, insensitive to the irrelevant features of the measurement procedure and capable of characterizing the overall cell tip region. This is achieved by fitting tip shapes to suitably selected parabolas. We obtain this way accurate and coherent measures that give sense to the evolution of tip curvature radius with control parameters. A scan over large ranges of velocity V, cell spacing Λ and thermal gradient G reveals no significant change at the cell to dendrite transition but some scaling laws which differ from those expected at low or large Péclet numbers. They thus provide definite information for understanding cell tip geometry over the cell to dendrite transition regime.

Electrical and optical characterization of field emitter tips with integrated vertically stacked focus

A revised version of the authors' BPM that includes quantitatively accurate closed-form expressions for the Fowler-Nordheim coefficients is summarized. For field emitter arrays with integrated focus with the gate and focus biased at the same potential (V/sub G/, = V/sub F/) the emission current was 100 nA/tip at 42 V, with about 50% intercepted by the focus. It was deduced that the tip radius of curvature is 2.4-3.6 nm. Analytical model, numerical simulation, and transmission electron microscopy micrographs all gave tip ROC values in this range. We studied electron beam collimation with lowering the focus voltage VF at different values of the gate voltage V/sub G/, and observed that the optimal VF is about 0.25 V/sub G/, confirming earlier predictions by the authors. From the measurements of beam collimation as a function of cathode-anode separation, we deduced the horizontal velocity of electrons. Under optimal collimation the estimated horizontal velocity was practically zero, and diameter of the spot size produced by a 5 /spl times/ 5 array with a 40 /spl times/ 40 /spl mu/m footprint on the phosphor screen biased at 5 kV and located 15 mm away was at most 50 /spl mu/m.

Giant field amplification in tungsten nanowires

The original RF-sputtering-assisted technique to produce metal wires with tip-curvature radii at the nanometer scale was developed and applied to tungsten. The wire tips were characterized by scanning electron microscopy. Field-emission tests of those wires exhibit excellent performance and reliable processability. Very high field-amplification factors of 18000 were demonstrated.

Length and speed selection in dendritic growth of electrohydrodynamic convection in a nematic liquid crystal

We present results on dendritic growth of electrohydrodynamic convection in a nematic liquid crystal subject to parallel magnetic and electric fields. Previous work found that these dendrites have many properties in common with crystalline dendrites. Nevertheless, crystalline dendrites are significantly different from the system studied here. Specifically, the length selection mechanism for these dendrites is substantially richer than that which controls crystalline dendritic growth. In contrast with the sharp selection mechanism operating in the case of crystalline dendrites, these dendrites show only partial selection. As the separation between electrodes and the magnetic field becomes larger, the selection becomes even less sharp. We quantify the selection by measuring two important characteristics of these dendrites, their length scale, as reflected by the tip radius of curvature, and their growth speed. We measure these quantities as functions of the most important control parameters: the spacing of the liquid crystal cell, the magnetic field, and the applied voltage. A nontrivial scaling relationship is found for the tip radius of curvature. These dendrites occur in a system containing only one state of matter, and they are defined not by an abrupt boundary but by a diffuse interface. We find that the width of that interface is determined solely by the applied magnetic field.

A possible interpretation of enhanced raman scattering in the vicinity of a nanotip

Theoretical and experimental studies on Raman scattering in a space with small bodies are briefly reviewed. Probabilities of radiative transitions for atoms (molecules) in the vicinity of bodies with dimensions much smaller than a wavelength are calculated. It is shown that in the vicinity of a nanosphere with |e|≫1, the probability of a single-photon electric dipole transition increases by a factor of 9, and the probability of a two-photon transition—by a factor of 81. In the vicinity of a conical needle resting on a plane (the needle and plane have |e|≫1), the radiative transition probability increases by a factor (λ/R in)2 and (λ/R in)4 for single-and two-photon transitions, respectively (R in is the radius of the needle tip curvature). This theoretical result is offered to interpret the enhancement of radiative processes experimentally observed in the referenced studies.

Contrast Mechanism Maps for Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) is one of the most established techniques for the observation and local modification of ferroelectric domain structures on the submicron level. Both electrostatic and electromechanical interactions contribute at the tip-surface junction in a complex manner, which has resulted in multiple controversies in the interpretation of PFM. Here we analyze the influence of experimental conditions such as tip radius of curvature, indentation force, and cantilever stiffness on PFM image contrast. These results are used to construct contrast mechanism maps, which correlate the imaging conditions with the dominant contrast mechanisms. Conditions under which materials properties can be determined quantitatively are elucidated.