Hysteresis in the flux flow characteristics of a type II superconductor associated with the presence of normal metal precipitates

Unusual history-dependent flux flow properties are observed in a Pb_0.871Sn_0.129 alloy as tin precipitates from solution at room temperature. We find that the critical currents and flux flow curves depend upon the field history, the current history, and the orientational history of the sample. Two volume pinning force curves are observed with different force magnitudes and field locations of the force peak, depending upon whether the field is cycled to high fields or zero field before the force is measured. Flux flow noise measurements in these samples yield very low noise, consistent with our recent model, which predicts low noise in samples with closely spaced pinning centers that interrupt the flux motion. The experimental results are explained in terms of the formation of a nonequilibrium flux line lattice in the presence of precipitates, and the response of such a lattice to current, field, and orientational changes.Research Supported by U.S. ERDA Grant No. EY-76-S-02-2890. Items of equipment used in this work were provided by a Research Corporation Grant.     

加热方位对流动沸腾临界热流密度影响

为了研究重力场对流动沸腾临界热流密度的影响,搭建了两相沸腾换热实验系统。以蒸馏水为工质,采用单侧加热的窄缝通道,通过改变质量流速、入口过冷度和重力场与加热方位的夹角,考察不同加热方位临界热流密度特性和实验段流阻特性。分析了质量流速、入口过冷度、加热方位对流动沸腾临界热流密度的影响,并将实验数据与Ivey-Morris模型、Sudo模型和Wojtan模型的计算值进行了验证对比。结果表明:加热面呈0°放置时的临界热流密度最大,呈180°放置时最小,质量流速和入口过冷度的增大会加大临界热流密度。Sudo模型对本实验条件不适用;Ivey-Morris模型和Wojtan模型在加热面呈0°放置时与实验值符合情况良好,相对误差约在30%以内,其他加热方位时,计算值均大于实验值。     

Neutron diffraction studies of the morphology of flux line crystals in type II superconductors

Neutron diffraction measurements on flux line single crystals in different type II materials are reported. It is shown that the type, the perfection, and the orientation of the vortex lattice with respect to the metal crystal mainly depend on the symmetry of the crystal axis which is parallel to the magnetic field. Results on samples with twofold, fourfold, and sixfold symmetry axes are represented and compared with theoretical predictions. We further studied the dependence of the widths of rocking curves on temperature and flux density and show that there is a close connection between the mosaic spread of the vortex lattice and its elastic properties.     

Properties of the flux line lattice in hysteretic type II superconductors. I. Neutron diffraction experiments

A detailed study of neutron rocking curves on flux line lattices was made in single-crystalline hysteretic type II superconductors with Ginzburg-Landau parameters between 1.0 and 2.5. Information was obtained about the symmetry and the quality of the flux line lattice as a function of crystal orientation, sample purity, and magnetic field. The flux line lattice is always observed to form a single crystal. The width of the rocking curves, which is a measure of the misorientation of flux line crystallites in the plane perpendicular to the external field, is found to decrease strongly with increasing field along the initial magnetization curve, and to be much smaller upon decreasing the field from aboveH _c2 . This width varied between 8 and 1.5°. The minimum size of a coherently scattering flux line crystallite was estimated to be about 2–3 µm. Along the initial magnetization nearH _c1 the flux is found to form flux line bundles of constant lattice spacing. Although large flux density gradients have been observed earlier with field probes nearH _c1 ^1,2 , the lattice parameter measured with neutrons remained constant in this field range.     

Pinning in type II superconductors

Large and randomly arranged pinning centers cause a strong deformation of a flux line lattice, so that each pinning center acts on the lattice with a maximum force. The average force for such single-particle pinning can be inferred from a simple summing procedure and has a domelike dependence on magnetic field. Pinning centers of average force, such as clusters of dislocations, strongly deform the flux line lattice only in weak fields and in fields close to the critical field, where there is a peak in the dependence of the critical current on magnetic field. In the range of intermediate fields there is a weak collective pinning. A large concentration of weak centers leads to collective pinning in all fields. In this case, near the critical field a critical current peak should be observed. To explain this peak and to define the boundaries between the regions of collective and single-particle pinning the possible break-off of the flux line lattice from the lines of magnetic force should be taken into consideration, which leads to extra softening of the lattice.     

Equilibrium magnetization properties of irreversible superconducting niobium with peak effect

Measurements of the equilibrium magnetization curve of type II superconductors have usually only been possible on reversible specimens. In this paper, a method to measure the equilibrium magnetization curve of irreversible type II superconductors is described. Results obtained by this method from a hysteretic Nb specimen exhibiting the peak effect are reported. They show an irregularity in the shape of the equilibrium magnetization curve in the neighborhood ofH _c2 which corresponds to a minimum of the compressional modulusK of the flux line lattice. The minimum ofK also corresponds with the maximum of the critical current densityj _c, which strongly suggests that in this case the peak effect is originated by a “soft point” of the flux line lattice. The observed anomaly ofK is discussed in terms of a possible first-order phase transition in the flux line lattice.     

Flux vortex dynamics and electric fields in matched pinning systems

The pinning of flux vortices in type II superconductors has been the subject of extensive research. Certain experiments have attempted to investigate this problem by the use of specially prepared pinning structures consisting of regular arrays of pinning centers. In this paper a theory relating to such experiments is described. This theory is based on the existence and properties of defects in an otherwise perfect vortex lattice which is commensurate with a pinning array consisting of a triangular lattice of holes in a superconducting thin film. A quantitative treatment predicts the existence and position of substructure on the critical current versus magnetic field curves in addition to the main peaks previously predicted to occur when the vortex and hole lattices are exactly matched. The theory also qualitatively describes the overall shape of these curves. An analysis of the temperature dependence of this substructure shows broad agreement with existing experimental results. The application of this theory to future experiments should allow a detailed investigation of vortex lattice elasticity and flux flow.     

Properties of the flux line lattice in hysteretic type II superconductors. II. Neutron depolarization experiments

Neutron depolarization experiments made on the same samples as investigated previously by neutron diffraction experiments (part I of this report) are presented. The correlations between crystal lattice and flux line lattice are shown to lead to a different field dependence of the average misalignment of the flux lines compared with polycrystalline materials. The average tilting angles are found to depend strongly on the magnetic field and to differ for increasing and decreasing fields in the same way as the mutual misorientations of singlecrystalline flux line blocks in the plane perpendicular to the field. For a known defect structure the tilting angles may be used to calculate the average displacement of the flux lines and the basic pinning forces.     

Studies on nucleate boiling crisis of Helium-I in channels of superconducting magnet systems

The experimental results of measuring the critical heat flux of Helium-I under natural circulation and forced flow are described in this paper. The direction of the experiments under natural circulation depends upon the real geometry of superconducting magnet cooling channels. The influence of the nonheated zones and local hydraulic resistances on the critical heat flux is discussed and some experimental results are given. The critical heat flux of saturated Helium-I under forced flow in vertical tube is measured in a wide range of pressure, quality, and mass velocities. The expressions have been obtained which describe the dependency of the critical heat flux upon the different conditions.     

Hydrogen transport and large strain elastoplasticity near a notch in alloy X-750

The finite element method is used to solve the coupled large strain elastoplasticity boundary value problem and transient hydrogen diffusion initial boundary value problem. As an example, solutions are obtained in the neighborhood of a rounded notch in a 4-point bend specimen of alloy X-750 at two temperatures under plane strain deformation conditions. The model accounts for the dilatational strain caused by the presence of hydrogen in the lattice and the hydrostatic stress induced drift of hydrogen. The hydrogen population profiles in both normal interstitial lattice sites (NILS) and trapping sites are calculated and conditions for the predominance of the total amount of hydrogen by either of the populations are studied. The competition between hydrostatic stress and plastic strain in the enhancement of local hydrogen concentrations is investigated. The effect of different types of traps on the relative level of trapped hydrogen as a portion of the total hydrogen is examined. The numerical analysis in conjunction with current experimental evidence suggests a specifically designed line of experiments that will isolate the parameters crucial to hydrogen induced material degradation in X-750.     

Vortex Matter in Highly Strained Nb$$_{}$$Zr$$_{25}$$25: Analogy with Viscous Flow of Disordered Solids

We present the results of magnetization and magneto-transport measurements in the superconducting state of an as-cast Nb\(_{75}\)Zr\(_{25}\) alloy. We also report the microstructure of our sample at various length scales by using optical, scanning electron and transmission electron microscopies. The information of microstructure is used to understand the flux pinning properties in the superconducting state within the framework of collective pinning. The magneto-transport measurements show a non-Arrhenius behaviour of the temperature- and field-dependent resistivity across the resistive transition and is understood in terms of a model for viscous flow of disordered solids which is popularly known as the ‘shoving model’. The activation energy for flux flow is assumed to be mainly the elastic energy stored in the flux-line lattice. The scaling of pinning force density indicates the presence of two pinning mechanisms of different origins. The elastic constants of the flux-line lattice are used to estimate the length scale of vortex lattice movement, or the volume displaced by the flux-line lattice. It appears that the vortex lattice displacement estimated from elastic energy considerations is of the same order of magnitude as that of the flux bundle hopping length during flux flow. Our results could provide possible directions for establishing a framework where vortex matter and glass-forming liquids or amorphous solids can be treated in a similar manner for understanding the phenomenon of viscous flow in disordered solids or more generally the pinning and depinning properties of elastic manifolds in random media. It is likely that the vortex molasses scenario is more suited to explain the vortex dynamics in conventional low-T\(_C\) superconductors.     

Quantification of partially recrystallized polycrystals using electron backscatter diffraction

A new experimental method of determining the volume fraction of recrystallized structure in a polycrystalline material has been developed. This method is based upon the comparison of electron backscatter diffraction patterns from adjacent locations in a polycrystal. Positions along a line are tested to determine whether adjacent points have the same crystal lattice orientation indicating that no dislocation structure exists between the two locations. If the distance between the two positions is relatively small, it is assured that the two points lie within a region of essentially defect-free lattice. Scanning through a region of material in this manner yields the lineal fraction of recrystallized material which directly correlates with the volume fraction. This automatic measurement eliminates the subjectivity and human error always associated with the quantitative determination of fraction recrystallized in a material.     

Investigation on the heat transfer characteristics during flow boiling of liquefied natural gas in a vertical micro-fin tube

This paper presents an experimental investigation on the heat transfer characteristics of liquefied natural gas flow boiling in a vertical micro-fin tube. The effect of heat flux, mass flux and inlet pressure on the flow boiling heat transfer coefficients was analyzed. The Kim, Koyama, and two kinds of Wellsandt correlations with different F_tp coefficients were used to predict the flow boiling heat transfer coefficients. The predicted results showed that the Koyama correlation was the most accurate over the range of experimental conditions.     

Order parameter and magnetic field of the distorted vortex lattice and their application to flux pinning in type II superconductors. I. Parallel flux lines

A program for the rigorous calculation of the volume pinning force exerted by-imperfections on the flux line lattice in type II superconductors is outlined. As one step of this program, the order parameter, local magnetic field, supervelocity, and elastic energy of the distorted lattice of still parallel flux lines are calculated from the Ginzburg-Landau theory. These general solutions provide a transformation of the Ginzburg-Landau free energy functional of an imperfect material into a mere function of the flux line positions, and thus allow a definition of elastic and pinning force densities which for the first time apply also to large inductions. First, exact solutions for small strains and for fields close toH _c2 are derived. Then, approximate solutions are presented applying to larger strains and to arbitrary inductions. The forces on each flux line exerted by a small needle-shaped inclusion parallel to the flux lines are calculated.     

Effect of External Nonuniform Magnetic Field on Flux Creep Process in Superconductor

The effect of an external nonuniform magnetic field on the flux creep rate in a high-temperature superconductor with trapped magnetic flux was studied. The magnetic relaxation was suppressed when the superconductor was put into a field of permanent magnets or when it approached a ferromagnet. The effect arises when the field sources (being magnetized, the ferromagnet produces its own field) are placed near the superconductor surface, where the flux line ends are located. For these cases, we carried out the calculations of vortex and current density distributions, which demonstrate that reverse currents flow in the near-surface regions of the sample. This verifies the hypothesis suggested earlier about the influence of counter Lorentz forces retarding the creep of the vortices. In the interpretation of the results, we also take into consideration the magnetic force acting on the vortex ends in the external nonuniform magnetic field that allows us to explain the experimental results, in which the current structure in the sample is unipolar.     

零质量射流及其在进气道流动控制中的应用研究

该文采用数值方法,模拟了零质量射流激励器工作流场,并对其在超声速进气道流动中的控制效果进行了仿真研究。运用有限体积法求解N-S方程,空间离散采用Roe格式,时间离散采用基于LU-SGS的双时间步长方法。针对激励器压电振子的运动过程,使用了基于广义无限插值方法的并行化动网格生成技术,并考虑几何守恒律。研究了零质量射流的非定常特性,获得了不同驱动频率下激励器出口附近的流动参数并与实验值进行对比,进一步分析了激励器驱动频率对进气道流动控制效果的影响。结果表明：数值方法能较为准确的描述零质量射流,将零质量射流激励器运用于进气道流动控制能有效改善进气道性能。     

Order parameter and magnetic field of the distorted vortex lattice and their application to flux pinning in type II superconductors. II. Curved flux lines

From the Ginzburg-Landau equations, the order parameter, local magnetic field, supervelocity, and elastic energy are derived for an arbitrarily distorted lattice of curved or straight flux lines. Exact solutions are given for small strains and for fields close to the upper critical fieldH _c2 . These solutions are generalized to large strains and arbitrary inductions. The general expressions approximately reproduce all previous results. They apply even to isolated and to crossed flux lines and to flux line loops. As a first application of the distorted-lattice solutions the pinning force density exerted by a small inclusion on the flux line elements is calculated. It turns out that the force may be concentrated on a flux line section of length smaller than even the coherence length. The response of the flux line lattice to such localized forces requires treatment by a nonlocal theory of elasticity and is much larger than expected so far.     

Influence of formwork surface on the orientation of steel fibres within self-compacting concrete and on the mechanical properties of cast structural elements

The influences of formwork surface on the final orientation of steel fibres immersed in self-compacting concrete and on the resulting mechanical response of the cast structural elements are investigated. Experimental observations of fibre orientation within cast slabs, obtained via computed tomography, indicate that fibres tend to orient according to the flow patterns during casting, but such tendencies are suppressed near rough formwork surfaces. Fibre orientation, in turn, affects the mechanical properties of the concrete as demonstrated by the load testing of beams extracted from the cast slabs. These processes and results are simulated using a computational fluid dynamics model of the casting process, in tandem with a lattice model of the fracture of the beam specimens. The computational fluid dynamics model determines the coordinates of each fibre within the concrete, which serve as input to the lattice model. Through comparisons with the experimental data, it is shown that these simulations correctly predict the phenomena of interest. We conclude the paper by highlighting a relationship between the number and orientation of the immersed steel fibres crossing the fracture plane and the mechanical response of the structural elements.     

Current-induced spin-orbit torques

The ability to reverse the magnetization of nanomagnets by current injection has attracted increased attention ever since the spin-transfer torque mechanism was predicted in 1996. In this paper, we review the basic theoretical and experimental arguments supporting a novel current-induced spin torque mechanism taking place in ferromagnetic (FM) materials. This effect, hereafter named spin-orbit (SO) torque, is produced by the flow of an electric current in a crystalline structure lacking inversion symmetry, which transfers orbital angular momentum from the lattice to the spin system owing to the combined action of SO and exchange coupling. SO torques are found to be prominent in both FM metal and semiconducting systems, allowing for great flexibility in adjusting their orientation and magnitude by proper material engineering. Further directions of research in this field are briefly outlined.     

Correlation studies on flux flow noise of polycrystalline niobium and vanadium foils

Using two movable contact pairs, cross-correlation functions of flux flow noise from polycrystalline niobium and vanadium foils have been measured. The results are compared with theoretical predictions derived from Clem's theory for the voltage associated with vortex motion across superconductors. Two cases are considered: (a) shot noise of randomly distributed flux entities moving with constant velocity and (b) noise due to locally generated random fluctuations of vortex velocity. There is strong evidence that the observed flux flow noise is produced by local flux flow fluctuations at pinning sites.Supported by Deutsche Forschungsgemeinschaft.