Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Large-grain high-temperature superconductors of the form RE-Ba-Cu-O (where RE is a rare-earth element) can trap magnetic fields of several tesla at low temperatures, and so can be used for permanent magnet applications. The magnitude of the trapped field is proportional to the critical current density and the volume of the superconductor. Various potential engineering applications for such magnets have emerged, and some have already been commercialized. However, the range of applications is limited by poor mechanical stability and low thermal conductivity of the bulk superconductors; RE-Ba-Cu-O magnets have been found to fracture during high-field activation, owing to magnetic pressure. Here we present a post-fabrication treatment that improves the mechanical properties as well as thermal conductivity of a bulk Y-Ba-Cu-O magnet, thereby increasing its field-trapping capacity. First, resin impregnation and wrapping the materials in carbon fibre improves the mechanical properties. Second, a small hole drilled into the centre of the magnet allows impregnation of Bi-Pb-Sn-Cd alloy into the superconductor and inclusion of an aluminium wire support, which results in a significant enhancement of thermal stability and internal mechanical strength. As a result, 17.24 T could be trapped, without fracturing, in a bulk Y-Ba-Cu-O sample of 2.65 cm diameter at 29 K.

High-temperature superconductor bulk magnets that can trap magnetic fields of over 17 tesla at 29 K

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

Since the first days of high-Tc superconductivity, the materials science and the physics of grain boundaries in superconducting compounds have developed into fascinating fields of research. Unique electronic properties, different from those of the grain boundaries in conventional metallic superconductors, have made grain boundaries formed by high-Tc cuprates important tools for basic science. They are moreover a key issue for electronic and large-scale applications of high-Tc superconductivity. The aim of this review is to give a summary of this broad and dynamic field. Starting with an introduction to grain boundaries and a discussion of the techniques established to prepare them individually and in a well-defined manner, the authors present their structure and transport properties. These provide the basis for a survey of the theoretical models developed to describe grain-boundary behavior. Following these discussions, the enormous impact of grain boundaries on fundamental studies is reviewed, as well as high-power and electronic device applications.

/pdf/grain-boundaries-in-high-t-c-superconductors-2widq11ljn.pdf

Grain boundaries in high- T c superconductors

On fretting maps

Thin film growth by a non-vacuum deposition technique, namely, the chemical solution deposition (CSD) method, is reviewed with emphasis on the growth of various oxide films and their properties. Various aspects of the solution chemistries for the different routes are discussed, and the effects of solution precursor properties on the conversion of the as-deposited film to the desired phase are also discussed. Crystal structures and functional properties common to many oxide materials are briefly reviewed.

https://iopscience.iop.org/article/10.1088/0953-2048/19/2/R01/pdf

Solution-derived textured oxide thin films—a review

Transport critical current density anisotropy measurements have been conducted on liquid-phase processed YBa 2 Cu 3 O x superconductors (123) with differing Y 2 BaCuO 5 (211) content and particle size. It is found that for specimens with micron-size 211 inclusions and low 211 content, the critical current density, J c , increases with 211. In contrast, J c is determined to decrease with 211 content when the specimens contain large 211 particles and high volume fraction of 211. Moreover, the ability of 211 to act as pinning sites appears to diminish at moderate magnetic fields, whereas the crystal defects that are associated with the 123–211 interfaces appear to be effective pinning centers at high fields. It is proposed that the variation in J c with 211 content is not unique, but depends on the 211 content and the particle size, as well as the strength of the applied magnetic field.

Influences of Y2BaCuO5 particle size and content on the transport critical current density of YBa2Cu3Ox superconductor

We have grown epitaxial CeO2 buffer layers on biaxially textured Ni–W substrates for YBCO coated conductors using a newly developed metal organic decomposition (MOD) approach. Precursor solution of 0.25 M concentration was spin coated on short samples of Ni–3 at%W (Ni–W) substrates and heat-treated at 1100 °C in a gas mixture of Ar–4%H2 for 15 min. Detailed x-ray studies indicate that CeO2 films have good out-of-plane and in-plane textures with full-width-half-maximum values of 5.8° and 7.5°, respectively. High temperature in situ XRD studies show that the nucleation of CeO2 films starts at 600 °C and the growth completes within 5 min when heated at 1100 °C. SEM and AFM investigations of CeO2 films reveal a fairly dense microstructure without cracks and porosity. Highly textured YSZ barrier layers and CeO2 cap layers were deposited on MOD CeO2-buffered Ni–W substrates using rf-magnetron sputtering. Pulsed laser deposition (PLD) was used to grow YBCO films on these substrates. A critical current, Jc, of about 1.5 MA cm−2 at 77 K and self-field was obtained on YBCO (PLD)/CeO2 (sputtered)/YSZ (sputtered)/CeO2 (spin-coated)/Ni–W.

http://iopscience.iop.org/article/10.1088/0953-2048/16/11/009/pdf

MOD approach for the growth of epitaxial CeO2 buffer layers on biaxially textured Ni–W substrates for YBCO coated conductors

The adiabatic elastic constants of aluminum have been measured with an ultrasonic pulse technique at liquid‐heluim, liquid‐nitrogen, and room temperatures The values of the elastic constants at 4°K are c11=1163, c12=648, and c44=309 in units of 1010 N/m2 The Debye characteristic temperature calculated from these figures is θ=425°K in good agreement with the value obtained from speciffic heat dataThe shear elastic constants ½(c11−c12) and c44 are discussed with reference to the theory given by Leigh

Elastic Constants of Aluminum

The six third-order elastic constants of copper were determined at 295, 77, and 4.2\ifmmode^\circ\else\textdegree\fi{}K from measurements of the change in the velocity of sound accompanying the application of a uniaxial stress. Irradiation with neutrons or $\ensuremath{\gamma}$ rays as well as dilute alloy additions was used in an attempt to pin the dislocations so that their effects could be eliminated. It was found that dislocation still contributed to the measurements even though the experimental data were linear and reproducible and showed no changes in ultrasonic attenuation with stress. The ultimate criterion for determining when the dislocation effects had been eliminated was the comparison of the pressure derivatives of the second-order elastic constants calculated from the uniaxial stress measurements with the pressure derivatives obtained by direct measurement. Only the neutron-irradiated sample passed this test, and all the results presented were obtained on this sample. At room temperature the third-order elastic constants agree with those obtained by Hiki and Granato. At 4.2\ifmmode^\circ\else\textdegree\fi{}K, the results are ${C}_{111}=\ensuremath{-}20\ifmmode\pm\else\textpm\fi{}2$, ${C}_{112}=\ensuremath{-}12\ifmmode\pm\else\textpm\fi{}1.5$, ${C}_{123}=\ensuremath{-}5\ifmmode\pm\else\textpm\fi{}1.5$, ${C}_{144}=\ensuremath{-}1.3\ifmmode\pm\else\textpm\fi{}0.2$, ${C}_{166}=\ensuremath{-}7.1\ifmmode\pm\else\textpm\fi{}0.25$, and ${C}_{456}=+0.25\ifmmode\pm\else\textpm\fi{}0.08{10}^{12}$ dyn/${\mathrm{cm}}^{2}$. It should be noted that these results do not satisfy the Cauchy relations ${C}_{112}={C}_{166}$ and ${C}_{123}={C}_{144}={C}_{456}$. A value of the Gr\"uneisen $\ensuremath{\gamma}$ in the limit of low temperatures was calculated and found to be within the experimental error of the value obtained from thermal-expansion measurements.

Kamel Salama

Papers

Solution-derived textured oxide thin films—a review

Influences of Y2BaCuO5 particle size and content on the transport critical current density of YBa2Cu3Ox superconductor

MOD approach for the growth of epitaxial CeO2 buffer layers on biaxially textured Ni–W substrates for YBCO coated conductors

Elastic Constants of Aluminum

Third-Order Elastic Constants of Copper at Low Temperature