Wire Of Rectangular Cross Section Research Articles

Fatigue tests of superelastic NiTi wires: an analysis using factorial design in single cantilever bending

This paper investigates the fatigue behavior of superelastic NiTi shape memory alloy thin wires with circular and rectangular cross-sections under single cantilever bending mode. A dynamic mechanical analyzer operating in single cantilever mode is employed as a testing machine. The fatigue life of the wires was analyzed at different strain amplitudes and loading frequencies. The simultaneous influence of these parameters was assessed through a factorial design with replication. Circular wires have higher fatigue life compared to rectangular wires. Higher strain amplitudes decrease the fatigue life of both circular and rectangular cross-section wires. On the other hand, the loading frequency strongly affected the rectangular cross-section wire, while having a significantly weaker effect on the circular wire. The NiTi wires showed fatigue lives between 103 and 105 cycles in the evaluated range of strain amplitude, which falls within the fatigue life observed for shape memory alloy (SMA) wires under similar loading conditions. Furthermore, the factorial design proved to be a valuable tool in the study of fatigue life of NiTi SMA, especially for the visualization and interpretation of the effect of the chosen variables.

Calculating the magnetic force of solenoid inductor wound by rectangular cross‐section wire

A new semi-analytical expression is presented based on two integrations for calculating the magnetic force of a solenoid inductor wound by rectangular cross-section wire. The authors simplified the solenoid inductor coil to a collection of circular coils, and the current density of the coils in the radial direction which was inversely proportional to its radius is considered. The obtained expressions can be implemented by adaptive Gaussian quadrature integration with MATLAB programming. In addition, they used the filament method and the finite element method to calculate the magnetic force on the solenoid inductor coil. The correctness of the semi-analytical expressions was verified by comparing the results of the semi-analytical numerical method with those of the filament method and the finite element method, respectively. The derived semi-analytical expressions of magnetic force allow a low computational time compared with the filament method and the finite element method to a specific accuracy. The calculation results show that: the solenoid inductor coil tends to compress in the axial direction, and the axial magnetic force on the outermost coils is the largest; the solenoid inductor coil tends to expand outward in the radial direction, and the radial magnetic force on the intermediate coil is the largest.

Joule Heating in Rectangular Conductors

Abstract Analytic solution for nonuniform internal Joule heating in a wire of rectangular cross section is obtained. The eigenvalues for convective or weak radiative boundary conditions are accurately estimated by asymptotic expansions. The problem is governed by the aspect ratio, the convection parameter β, and a nonuniform parameter α which relates to the slope of the electric resistivity. There exists a maximum α above which the conductor would fail due to high temperature.

The effect of surface roughness and grain-boundary scattering on the electrical conductivity of thin metallic wires

We report a new formula for the electrical conductivity of a thin wire of rectangular cross-section, obtained from an exact solution of the Boltzmann equation by assuming perfectly diffuse surface scattering and absence of grain boundaries. Also, we calculate the electrical conductivity of polycrystalline metallic wires, both for the case of rectangular and circular cross-sections and for arbitrary values of Fuchs’ specularity parameter, by means of a seminumerical procedure that solves the Boltzmann equation by summing over classical trajectories in accordance with Chambers’ method. Following Szczyrbowski and Schmalzbauer, the scattering by grain boundaries is represented by a peculiar specularity parameter and a boundary transmittance. The difference between one and the sum of these two probabilities measures the probability of diffuse scattering. We examine the dependence of the conductivity on the values of these parameters and the effects of disorder on the diameters of the grains.

Coupling of gap plasmons in multi-wire waveguides

We investigate the coupling of gap plasmons in various configurations of neighboring metallic nanowires. Starting with the basic element defining a gap plasmon, consisting of two neighboring silver wires, we study the energy splitting and symmetry properties of hybridized plasmons resulting from the interaction of two wire pairs. The system is shown to display non-avoided crossings of hybridized modes, and it evolves at short distances towards a degenerate system consisting of four wires arranged in a square, where two new gap plasmons emerge from redshifted higher-energy modes. The gap modes of three neighboring wires are also described in a continuous transition from a coplanar configuration to an equilateral triangle arrangement. The interaction between wire pairs is shown to be weak enough to prevent efficient transfer of plasmon signal from a pair to the other one, which is beneficial to avoid crosstalking, but not to produce waveguide couplers. The coupling is significantly increased by placing a wire of rectangular cross section in between the wire pairs, thus allowing us to achieve large plasmon-signal transfers within propagation distances below the attenuation length. Our results can find application in the design of signal-processing devices based upon gap plasmons.

A fluctuation-based characterization of athermal phase transitions: Application to shape memory alloys

We employ a fluctuation-based technique to investigate the athermal component associated with martensite phase transition, which is a prototype of temperature-driven structural transformation. Statistically, when the phase transition is purely athermal, we find that the temporal sequence of avalanches under constant drive is insensitive to the drive rate. We have used fluctuations in electrical resistivity or “noise” in nickel titanium shape memory alloys in three different forms: a thin film exhibiting well-defined transition temperatures, a highly disordered film, and a bulk wire of rectangular cross-section. Noise is studied in the realm of dynamic transition, viz., while the temperature is being ramped, which probes into the kinetics of the transformation at real time scales, and could probably stand out as a promising tool for material testing in various other systems, including nanoscale devices.

High-frequency conductance of a thin rectangular metal wire

The high-frequency conductance of a straight metal wire of rectangular cross section is calculated. The case when the transverse dimensions of the wire are several times smaller than its length is considered. The condition of diffuse reflection of electrons from the internal surfaces of the wire are taken as the boundary conditions for the problem. The limiting cases are considered, and the results are discussed.

The polaron effect on the binding energy of a shallow donor impurity in quantum-well wires in an electric field

Using a variational technique, the effect of electron-longitudinal optical (LO) phonon interaction on the ground and the first few excited states of a hydrogenic impurity in a semiconductor quantum wire of rectangular cross section under an external electric field is studied theoretically for the impurity atom doped at various positions. The results for the binding energy as well as polaronic correction are obtained as a function of the size of the wire, the applied uniform electric field and the position of the impurity. It is found that the presence of optical phonons changes significantly the values of the impurity binding energies of the system. Taking into account the electron–LO phonon interaction the 1 s → 2 p y and 1 s → 2 p z transition energies are calculated as a function of applied electric field for different impurity positions.

On universality in metallic nanocohesion

A semiclassical trace formula for the mesoscopic oscillations of the cohesive force in a metallic nanowire of constant cross section is derived. It is shown that the force oscillations are universal, in the sense that their r.m.s. amplitude is independent of the area of the cross section, only for cross sections with a continuous one-dimensional symmetry. For a wire of rectangular cross section, the r.m.s. amplitude of the force oscillations is shown to be proportional to the aspect ratio of the cross section.

Collective excitation inGaAs−AlxGa1−xAs quantum wires: Multisubband model

The effects of the potential barrier height on the collective excitations of an electron gas confined in a GaAs-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As quantum wire of rectangular cross section are investigated theoretically by using the self-consistent field approximation theory proposed by Singwi, Tosi, Land, and Sj\"olander (STLS) [Phys. Rev. 176, 589 (1968)]. For several potential barrier heights, we calculated the effective potential, plasmon energy, structure factor, and pair-correlation function, considering a three-subband model with only the lowest subband populated by electrons. We verified that the intersubband plasmon is more sensitive to the potential barrier height variation than the intrasubband plasmon. We also observed that the confining potential effect decreases with the increasing of the wire width. The random-phase approximation results are also presented by comparison with the STLS results and significant differences were found.

Polarizability of a donor impurity in a GaAsAlGaAs quantum wire

The polarizability and the ground state binding energy of a donor impurity located in a semiconductor quantum well wire of rectangular cross-section with finite barrier potential is calculated through the variational method. We assume that the donor is located at the center of the wire and that the electric field is applied in the direction perpendicular to the wire length ( z-direction), making an angle θ with the x-axis. We present our results for the ground state binding energy as a function of the size of the wire for several values of the electric field strength and of the angle θ. It is found that the polarizabilities decrease as the wire dimensions ( L x and L y ) decrease, until they reach a minimum at a certain value of L x ( L y fixed) and then increase as the width becomes smaller. The binding energies and the polarizabilities, as expected, have a strong dependence on the geometrical form of the wire and on the angle θ.

Potential Barrier Height Effects on the Intrasubband and Intersubband Quasi-One-Dimensional Plasmons

The effects of the potential barrier height on the collective excitations of a electron gas confined in a GaAs-AlxGa1-xAs quantum wire of rectangular cross-section are investigated theoretically. For several potential barrier heights, we calculated the plasmon energy, structure factor and pair-correlation function, within the Random-Phase Approximation regime, considering a three-subband model with only the lowest subband populated by electrons. We verified that the intersubband plasmon is more sensitive to the potential barrier height variation than the intrasubband plasmon. We also observed that the confining potential effect decreases with the increasing of the wire-width.

Rapid computation of static fields produced by thick circular solenoids

A straightforward method is proposed for computing the magnetic field produced by a circular coil that contains a large number of turns wound onto a solenoid of rectangular cross section. The coil is thus approximated by a circular ring containing a continuous constant current density, which is very close to the real situation when wire of rectangular cross section is used. All that is required is to evaluate two functions, which are defined as integrals of periodic quantities; this is done accurately and efficiently using trapezoidal-rule quadrature. The solution can be obtained so rapidly that this procedure is ideally suited for use in stochastic optimization. An example is given, in which this approach is combined with a simulated annealing routine to optimize shielded profile coils for NMR.

Non‐markovian behavior of quantum confined electronic systems

AbstractThe holomorphic memory function method is modified to include geometrical confinement. A ‘ballistic memory function’ is identified, showing that energy quantization due to lateral confinement is associated with a retardation in the system. Consequently, the ballistic conductance quantization of waveguides is shown to be caused by long‐lived correlations between values of the applied field at different points in the device. A renormalized force correlation function shows the mutual influence of geometrical confinement and scattering mechanisms: confinement‐induced memory effects modify the elastic scattering white‐relaxation spectrum and transform it into a scattering mechanism with enhanced retardation properties. Evidence of these phenomena is given through the numerical evaluation of the ac conductance and time‐dependent current for a rectangular crosssection wire of finite length.

Stress distribution and hydride orientation in ZrNbCu garter spring under complex loading

A garter spring of the tight fit design in a PHWR experience three type of loads: an axial load due to spring tension, a compressive load due to coolant tube resting on it and a torus moment due to bending. The influence of these, on the hydride orientation in Zr2.5Nb0.5Cu garter springs has been studied by stress analysis and out-of-pile simulation experiments. The stress analysis showed that the magnitude of the stress is maximum at the surface and it decreases rapidly towards the core of the spring wire of rectangular cross section. This trend has also been observed in the experimental results. The preferred orientation of hydrides was found to be confined to the surface up to a depth of 300 μm. A random distribution of hydrides was observed at the central region where the stress was evidently below the threshold value for reorientation. Further a map of the planes of maximum principal stresses at the surface layer of the spring helix, constructed by stress analysis was found to be consistent with the observed hydride distribution. The diametrical compressive load did not show much influence on the hydride morphology in the range of 0–4 kg/turn under the axial load of 1 kg. It was also seen that the axial load of 1 kg imposed by the tight fit design did not significantly alter the hydride distribution which is primarily governed by torus bending.

Evaluation of structural integrity of superconducting magnet coils

Three types of coil have been devised and constructed, using superconductive wire of rectangular cross-section, from which specimens were taken for mechanical testing. Short beam shear and transverse tension characteristics have been measured, in both interturn and interlayer directions, in an attempt to assess the merits of the short beam shear test. The prime objective of this first phase of the programme is to establish a test method from which engineering design data may be generated on the various bonding techniques used in coil construction. To establish confidence in the value and meaning of the results from the shear tests, specimens were analysed using finite element methods and a comparison made with measured values.

Electron-phonon effects on the ground impurity level in quasi-one-dimensional semiconductor heterostructures

We calculate the effects of the electron-phonon interaction on the binding energies of an impurity placed in a quantum-well wire of rectangular cross section and finite barrier potential to the confined electrons. The calculations are performed as a function of the size of the wire for different positions of the impurity and for several values of the heights of the barrier potential. The results show that the energies are almost the same in wires with comparable cross-sectional area.

Quantum size effect in thin-wire transport

A quantum transport theory for electric conductivity is presented for the condition that the de Broglie wavelength of a thermal electron becomes comparable to the transverse dimensions of a thin wire of rectangular cross section. The theoretical results, which include the effect of size quantization, are analyzed in the ultrathin limit (UTL). In the UTL the ratio of longitudinal resistivity to bulk resistivity is shown to be proportional to $\frac{{\ensuremath{\lambda}}_{D}^{2}}{A}$, where ${\ensuremath{\lambda}}_{D}$ is the de Broglie wavelength and $A$ is the area of cross section. The results for transverse resistivity are also given and discussed.