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

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

Current theoretical approaches to collective behavior of dislocations

Enhancement of superconducting and mechanical properties in BSCCO with Pb additions

Publisher Summary This chapter discusses the collective dislocation behavior in cyclic deformation. During plastic flow, the spatial arrangement of the dislocation structure essentially derives from a competition between two factors. When it exists, the interaction of dislocations with strong and dense localized obstacles other than dislocations (small clusters and precipitates, lattice friction and Peierls forces) tends to induce rather uniform dislocation distributions. In such conditions, the plastic flow properties of the bulk material may simply reflect the behavior of isolated mobile dislocations. In contrast, the mutual interactions of dislocations, both local and long ranged, become all the more important as dislocations multiply. Thus, the contribution of dislocation interactions to the flow stress increases during plastic flow. At a certain stage that is characterized by a critical stress, strain, or dislocation density, the collective dislocation behavior sets in which is characterized by the emergence of dislocation-rich and dislocation-poor regions. This is usually referred to as dislocation patterning.

Chapter 57 Collective behaviour of dislocations in plasticity

First experimental data on the plasticity, strength and microhardness of C60 fullerite crystals are reported. It is concluded that the mechanical properties of the crystals studied are isotropic, and the values of their breaking point are low. The obtained results are compared with those for other materials (graphite, indium etc.).

On the mechanical properties of C60 fullerite crystals

Mechanical tests of C60/C70 single crystals allow one to assign them to the category of soft and fragile materials. Their mechanical properties are comparable with those of graphite but, in contrast, they are isotropic. The dependence of C60/C70 microhardness on the temperature in the range 77–570 K and on the influence of solvent residues has been examined. Preliminary data on microhardness of pure C60 and C70 have been obtained.

Mechanical properties and deformation of fullerites

The data for the microhardness and fracture toughness of Y–Ba–Cu–O and Bi-based single crystals and ceramics in the temperature range 77–293 K are presented and analyzed. Our study reveals that the microhardness of high temperature superconductors is very sensitive to the oxygen stoichiometry, the phase composition, the temperature, and to the microstructural defects such as impurities, intergranular boundaries, and voids. Attention is drawn to the anisotropy of the micromechanical properties and to the features of the fracture in the vicinity of the indentation. The data available on the plasticity of Y–Ba–Cu–O and Bi–Sr–Ca–Cu–O from micro- and macrotests are compared.

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Influence of oxygen content and structural defects on low-temperature mechanical properties of high-temperature superconducting single crystals and ceramics

Data are reported on the deformation and structure of YBa 2 Cu 3 O 7− x ceramics and single crystals, and other high- T c metal-oxides at T≌77–1200 K , and the data on the microhardness of single crystals of various compositions are compared. The activation parameters of the deformation processes are estimated under crystal indentation. The effect of oxygen content on the mechanical properties of ceramics and single crystals is commented on and the role of dislocations in the deformation of ceramic crystallites and single crystals is discussed. A conclusion is drawn about the determinant role played by the processes of grain boundary glide and crack formation at the deformation of ceramic samples. Finally, the first results from studies of the mechanical properties of a new class of materials-fullerites C 60 -are reported.

Deformation, structure and properties of ceramics and crystals of high-Tc superconductors

To summarize we point out the following. 1. (i) There is an analogy in macroscopic stress behaviour of discontinuous flow associated with thermomechanical instability or Portevin-Le Chatelier effect. It may be suggested that statistics of these types of plastic instability do not depend on the particular mechanism but are governed by common laws. 2. (ii) The manifestation of a power law in distribution densities, being a sign of self-organization in the dislocation dynamics, depends on the material and on deformation conditions. 3. (iii) In order to draw definite conclusions about the nature of common features of the phenomenon of plastic instability it would be interesting to study simultaneously the macroscopic parameters of deformation curves and “mesoscopic” ones, namely the electric responses to the defect motion. Investigations of the size effect on statistics might also shed light on the problem.

V.S. Bobrov

Papers

On the mechanical properties of C60 fullerite crystals

Mechanical properties and deformation of fullerites

Influence of oxygen content and structural defects on low-temperature mechanical properties of high-temperature superconducting single crystals and ceramics

Deformation, structure and properties of ceramics and crystals of high-Tc superconductors

Statistical aspects of low temperature discontinuous deformation