Magnetic Flux Penetration and Motion in Antiferromagnetic Superconductors

The paper reviews a concept of induced spin-flop domain inside vortices in an antiferromagnetic superconductor. Such phenomenon may occur when an external magnetic field is strong enough to flip over magnetic moments in the core of the vortex from their ground state configuration. The formation of the domain structure inside vortices modifies the surface energy barrier of the superconductor. During this process the entrance of the flux is stopped and a newly created state exhibits perfect shielding. Such behavior should be visible as a plateau on the dependence of flux density as a function of the external magnetic field. The end of the plateau determines the critical field, which has been called the second critical field for flux penetration. Moreover, it is predicted and described how this phenomenon modifies flux creep in layered superconductors. The various scenarios of changing the creep regime from thermal to quantum and vice versa at constant temperature are discussed.     

Effect of Critical Current Density and Critical Temperature on ac Susceptibility

Based on the flux creep equation, the effect of critical current density and critical temperature on ac susceptibility is investigated numerically in a superconducting slab immersed in an ac magnetic field. The current density dependence of the flux creep activation barrier is employed as the logarithmic law. The fundamental ac susceptibilities of the slab as a function of temperature for the same ac field have been derived in a unified picture. The results show that ac susceptibility in flux creep regime is affected by critical current density and critical temperature.     

Time resolved nanosecond vortex dynamics in high Tc superconducting films

Flux dynamics in a high T_c superconducting thin film is investigated in the ns time scale. The initial metastable state is determined by applying a pulsed magnetic field to a sample previous cooled below the irreversibility line. Selective local heating of the film with a pulsed laser spot lowers the vortex pinning force suddenly. The magnetic flux rearrangements that follow generate a voltage pulse between two contacts on the zero current biased sample. Detail simulations were performed in the framework of a phenomenological model based on Maxwell Equations with constitutive relations for creep and flux flow that fully describe the observed voltage signals.     

Thermal peculiarities of the electric mode formation of high temperature superconductors with the temperature-decreasing n-value

Formation peculiarities of the static thermo-electric modes that may be observed in high temperature superconductors at the DC current are studied taking into consideration the temperature-decreasing dependence of the power exponent (n-value) of the voltage-current characteristic of a superconductor. The used models are based on the steady zero-dimensional models. The study is made for the conduction-cooling and liquid coolant conditions at different operating temperatures. It allows us to investigate the non-isothermal voltage-current characteristic of Bi2223 and YBCO that rooted the development of their stable and unstable thermo-electric regimes. It is shown that the temperature dependence of an n-value may lead, first, to usually observed static voltage-current and temperature-current characteristics having one stable and unstable parts and, second, to unexpected thermo-electric states in the temperature range that is closed to its transition into the normal state. It is a result of the formal temperature variation of the differential resistivity of a superconductor depending on its temperature-decreasing critical current density and n-value. As a result, to describe correctly thermal stability conditions and analyze theoretically the quench processes in high temperature superconductors, the temperature dependences of their critical current density and n-value must be restored before the transition of a superconductor into the normal state as carefully as possible.     

Heat transfer and wave characteristics of a binary freon film flowing over a three-dimensional textured surface

The results of the study of heat transfer, crisis phenomena, and wave characteristics of laminar-wavy liquid films falling over a vertical three-dimensional texture surface have been considered. The R21/R114 freon mixture is served as a working fluid. Some peculiarities of heat transfer, hydrodynamics, and development of crisis phenomena in a binary liquid film falling over heat-releasing surfaces of different geometry have been revealed. The dependence of the heat-transfer coefficient on the flow rate for a three-dimensional texture surface in the regime of evaporation is shown to be similar to the dependence for a smooth surface with slightly intensified heat transfer in the region of inlet film Reynolds numbers of 100–500. The heat transfer coefficients of nucleate boiling on the studied types of structured surfaces are much lower than for a smooth tube. In the regime of undeveloped nucleate boiling, the critical heat flux for all surface types is deter-mined by the dependence obtained by considering the appearance of the heat transfer crisis in an evaporating wave liquid film.     

Current–Voltage Measurements on a Bi2Sr2CaCu2O x Whisker and Investigation of Its Vortex Dynamics in Self Field

We report current–voltage measurements carried out on a high quality Bi₂Sr₂CaCu₂O _x whisker in a large temperature range below the critical temperature. When a perpendicular field is applied, the current–voltage curves are typical of the flux flow regime at low fields and resemble flux creep characteristics at high fields. This change, related to what is described as the critical current peak effect is associated to a transition between different vortex phases. In this contribution, we focus on the dynamics of the vortices in self field. We show that the critical current in the flux flow regime can be calculated straightforwardly taking into account inter-vortex forces only, supposing that free vortices run between pinned vortices.     

Low-temperature deformation behaviour of polycrystalline copper

Low-temperature plastic flow in copper was investigated by studying its tensile and creep deformation characteristics. The dependence of the flow stress on temperature and strain rate was used to evaluate the thermal activation energy while the activation area was derived from the change-in-stress creep experiments. A value of 0.6 eV was obtained for the total obstacle energy both in electrolytic and commerical copper. The activation areas in copper of three selected purities fell in the range 1200 to 100 b². A forest intersection mechanism seems to control the temperature dependent part of the flow stress. The increase in the athermal component of the flow stress with impurity content in copper is attributed to a change in the dislocation density. The investigation also revealed that thermal activation of some attractive junctions also takes place during low-temperature creep. The model of attractive junction formation on a stress decrement during creep, yields a value of 45±10 ergs cm⁻² for the stacking fault energy in copper.     

The Numerical Study of Influence of Flux Creep on AC Losses in Superconductors

Numerical simulation of AC losses in superconductors with gaint flux creep was carried out based on the collective creep model of the vortex glass. Influence of physical parameters, including frequency (f) and the amplitude (B _ac) of AC field, current density distribution (j), DC field (B _d), and temperature (T) on AC losses was studied based on a unified method and the Maxwell equations. The frequency-dependent AC losses is the most important among the results which differ from the static models. Also, AC losses derived in the flux creep state are larger than those in the critical-state when the sample is only partly penetrated by the field, which is the second difference between the flux creep model and the static models. Moreover, the dependence of AC losses on B _ac are derived and compared with that based on the Bean model. Preliminary comparison with experiments showed that the procedure could give qualitative understanding and estimation of AC losses in superconductors with giant flux creep.     

Evidence for quantum tunneling of vortices in superconductors

Flux creep in disordered superconductors may be governed by quantum tunneling of Abrikosov vortices rather than by thermal activation processes. The expectation is that in the quantum tunneling regime the creep rate would be temperature independent. This assumes that the parameters describing the pinning potential and other aspects of the superconducting films are temperature independent. In the case of extremely thin superconducting films the coherence length retains its temperature dependence well into the quantum tunneling regime, leading to an unusual temperature dependence of the electrical resistance in this regime. This has been observed in ultrathin superconducting films of Pb, Al, and Bi. In low magnetic fields, at low temperatures, sheet resistances vary with temperature as RR₀ exp(T/T₀), where T₀ and R₀ are constants.     

Creep crack growth in fiber reinforced composites with rate-dependent bridging - Role of a viscous fiber matrix interface

A model is developed for creep crack growth in continuous fiber reinforced composites wherein a growing matrix crack is subjected to rate-dependent bridging by unbroken fibers. The rate-dependence in this model arises as a result of the presence of a viscous fiber/matrix interfacial layer. Under load this layer undergoes shear flow causing time-dependent pull-out of bridging fibers from the crack surfaces. The mechanics of time-dependent bridging is combined with a failure criterion based on secondary failure in a crack-tip creep process zone. The dependence of the matrix creep crack growth rates on flaw size and crack wake parameters as well as on composite microstructure is derived. It is shown that the crack wake plays a predominant role in influencing not only the magnitude of creep crack growth rates but also the relationship of growth rates to the crack sizes. A closed form expression is derived for the dependence of crack growth rates on loading, creep and bridging parameters in the regime wherein crack growth rates are independent of crack size.     

The high-temperature creep behaviour of an Al-1 wt% Cu solid-solution alloy

The creep behaviour of an Al-1 wt% Cu solid-solution alloy is investigated at a temperature of 813 K under stress range of 0.5–5 MPa. The creep characteristics of the alloy including the stress dependence of the steady-state creep rate (n=4.4), the shape of creep curve (normal primary stage), the transient creep after stress increase, and the value of the true activation energy for creep, suggest that some form of dislocation climb is the rate-controlling process at higher stresses above 1 MPa. However, at low stresses (< 1 MPa), the creep curves show no distinguished steady state, and the stress dependence of the minimum creep rate is as high as ～ 8. The creep behaviour of the alloy is discussed based on recent theories available for describing creep in solid-solution alloys.     

The Effect of Three-Dimensional Deformations on Local Heat Transfer to a Nonuniformly Heated Falling Film of Liquid

An experimental investigation is performed of heat transfer under conditions of flow of a water film on a vertical surface with a heater 150×150 mm in size in the range of the Reynolds number values from 1 to 45. A map of modes of flow of the liquid film is plotted, and regions of heat transfer are identified. Data are obtained on the longitudinal coordinate dependence of the heater wall temperature and of the local heat flux on the symmetry axis of the heater. Local coefficients of heat transfer are measured. The experimental data are compared with the results of numerical calculations for a smooth film. The effect of the forming of jet flows on heat transfer to the liquid film is analyzed.     

Heat transfer through a porous plate at cooling gas supply in an asymptotic suction regime

The analytical solution is carried out for the one- and two-dimensional problem of the thermal state of a porous plate surrounded by the flow of high-temperature and homogenous cooling gases in a permeable cooling system. Cooling gas flow in a laminar regime of asymptotic suction is considered, which provides effective heat shielding with minimum dependence on the parameters of the permeable wall. Heat exchange from the high-temperature gas is accepted for both laminar and turbulent boundary layers.     

Current–Voltage Measurements and Vortex Dynamics in a Bi2Sr2CaCu2O x Whisker: Observation of the Peak Effect and Calculation of the Critical Current in the Flux Flow Regime with and Without Applied Field

In this article, we report current–voltage measurements carried out on a Bi₂Sr₂CaCu₂O _x whisker in a large temperature range below the critical temperature with and without applied magnetic field. We examine the critical current peak effect and the vortex dynamics at low field. The critical current peak effect consists of the initial increase of the critical current that subsequently decreases as the applied field is increased. For current–voltage measurements, this effect is associated with a change in the current–voltage curves that are typical of the flux flow regime at low fields and resemble flux creep characteristics for higher fields. As a general rule, our observations are consistent with the models that link the peak effect to vortex phase transitions. We calculate the critical current in self-field in the flux flow regime taking into account intervortex forces. We suppose that most vortices are pinned by defects while mobile vortices move through plastic channels between the strongly pinned vortex regions. When an external field is applied, we suggest that the increase in the critical current that is observed is linked to oscillations of the pinned vortices.     

Boundary element solution of thermal creep flow in microfluidic devices

Flow in rarefied gases can be caused by a tangential temperature gradient along the contour boundaries (tangential heat flux), without the presence of any other external driven force, inducing a fluid motion from colder to hotter regions. This phenomenon is known as thermal creep and has gained importance in recent years in connection with micro-scale gas flow systems. Prediction of the flow field in micro-systems can be obtained by using continuum based models under appropriate boundary conditions accounting for the slip velocity due to tangential shear rate and heat flux. In this work a boundary integral equation formulation for Stokes slip flow, based on the normal and tangential projection of the Green's integral representational formulae for the velocity field is presented. The tangential heat flux is evaluated in terms of the tangential gradient of the temperature integral representational formulae presenting singularities of the Cauchy type, which are removed by the use of an auxiliary potential field. These formulations are used to evaluate the performance of different microfluidic devices.     

Effect of Dissipation on Quantum Tunneling of Vortices in Tl2Ba2Ca2Cu3O10+δSuperconductors

The temperature and magnetic field dependence of the magnetic relaxation rate has been investigated at low temperatures (1.8 < T < 10 K) on two Tl₂Ba₂Ca₂Cu₃O_10+δ samples (epitaxial thin film and sintered pellet). The temperature dependence gives evidence of a crossover in the mechanism of vortex motion, from classical thermal activation to quantum tunneling as temperature decreases. The field dependence of the relaxation rate indicates a crossover in the dimensionality of vortices, from three-dimensional flux lines to two-dimensional pancake vortices as field increases. For the thin film, the temperature dependence of the rate has been fitted to the theoretically predicted expressions for finite-temperature enhancement of the quantum rate in different regimes of dissipation. In spite of the similarity of the fits, the estimate of the ratio of Hall to viscous drag terms in the equation of motion indicates that quantum tunneling in this system occurs in an intermediate dissipative regime, where both terms contribute to the motion of vortices.     

Heat transfer in YBaCuO thin film/sapphire substrate system

The thermal boundary resistance at the YBaCuO thin film/Al₂O₃ substrate interface was investigated. The transparency for thermal phonons incident on the interface as well as for phonons moving from the substrate was determined. We have measured a transient voltage response of current-biased films to continuously modulated radiation. The observed knee in the modulation frequency dependence of the response reflects the crossover from the diffusion regime to the contact resistance regime of the heat transfer across the interface. The values of transparency were independently deduced both from the phonon escape time and from the time of phonon return to the film which were identified with peculiarities in the frequency dependence. The results are much more consistent with the acoustic mismatch theory than the diffuse mismatch model.We are grateful to A. Elantev for helpful discussion. We acknowledge the financial support of the Russian Scientific Council on the HTS problem (Project No. 90462).     

Effect of Dissipation on Quantum Tunneling of Vortices in Tl2Ba2Ca2Cu3O10+δSuperconductors

The temperature and magnetic field dependence of the magnetic relaxation rate has been investigated at low temperatures (1.8 < T < 10 K) on two Tl₂Ba₂Ca₂Cu₃O₁₀₊ samples (epitaxial thin film and sintered pellet). The temperature dependence gives evidence of a crossover in the mechanism of vortex motion, from classical thermal activation to quantum tunneling as temperature decreases. The field dependence of the relaxation rate indicates a crossover in the dimensionality of vortices, from three-dimensional flux lines to two-dimensional pancake vortices as field increases. For the thin film, the temperature dependence of the rate has been fitted to the theoretically predicted expressions for finite-temperature enhancement of the quantum rate in different regimes of dissipation. In spite of the similarity of the fits, the estimate of the ratio of Hall to viscous drag terms in the equation of motion indicates that quantum tunneling in this system occurs in an intermediate dissipative regime, where both terms contribute to the motion of vortices.     

The state of vortex glass induced by creep of vortices in percolation superconductors

The influence of magnetic flux creep on the dynamics of vortices in percolation superconductors containing fractal clusters of the normal phase has been considered. Dependences of the resistance of these superconductors on the transport current are obtained for different fractal dimensions of cluster boundaries. It is established that the vortex-glass state is implemented in percolation superconductors with a fractal cluster structure under collective creep of vortices.