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

Nonadiabatic effects in optical phonon self-energy

The authors demonstrated the mechanics of materials for crystalline whiskers composed of C60 molecules; compressive deformation of the whiskers was observed by in situ transmission electron microscopy with simultaneous force measurement by means of an optical cantilever method, as used in atomic force microscopy. In response to compression along the long axis, the whiskers bent first elastically, then buckled. A whisker with 160nm diameter fractured brittlely at a strain of 0.08. According to Euler’s formula, Young’s modulus of the whisker was estimated to be 32–54GPa, which is 160%–650% of that of C60 bulk crystals.

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Buckling of C60 whiskers

In previous studies, sublimed C60-rich fullerene films on silicon, when slid against a 52100 steel ball under dry conditions, have exhibited low coefficient of friction (∼0.12). Films with different purities can be produced by sublimation at different substrate temperatures. In this paper, effects of purity of fullerene films and ion implantation of the films with Ar ions on the friction and wear properties of sublimed fullerene films are reported. C60-rich films (called here films with high purity) exhibit low macroscale friction. An increased amount of C70 and impurities in the fullerene film determined using Raman and Fourier transform infrared (FTIR), increases its coefficient of friction. Microscale friction measurements using friction force microscopy also exhibited similar trends. Low coefficient of friction of sublimed C60-rich films on silicon is probably due to the formation of a tenacious transfer film of C60 molecules on the mating 52100 steel ball surface. Based on scanning tunneling microscopy (STM), transmission electron microscopy (TEM), and high resolution TEM (HRTEM), we found that fullerene films primarily consisted of C60 molecules in a fcc lattice structure. Nanoindenter was used to measure hardness and elastic modulus of the as-deposited films. Ion-implantation with 1 × 1016 Ar+ cm−2 reduced macroscale friction down to about 0.10 from 0.12 with an increase in wear life by a factor of 4; however, doses of 5 × 1016 ions cm−2 gave three times higher friction and poorer wear life; higher doses disintegrated the C60 molecules. Based on STM, TEM, Raman, FTIR, and laser desorption Fourier-transform ion cyclotron resonance mass spectrometer (LD/FT/ICR) studies, we found that the ion implantation with a dose of 1 × 1016 Ar+ cm−2 resulted in smoothening of the fullerene film surface probably by compacting clusters, but without disintegrating the C60 molecules. However, a high dose of 5 × 1016 Ar+ cm−2 damaged the C60 molecules, converting it to an amorphous carbon. Nanoindentation studies show that ion implantation with a dose of 1 × 1016 Ar+ cm−2 resulted in an increase in the hardness from about 1.2 to 4.0 GPa and in elastic modulus from about 70 to 75 GPa and modified the elastic-plastic deformation behavior.

Materials characterization and effect of purity and ion implantation on the friction and wear of sublimed fullerene films

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

On the Mechanical Properties of C60 Fullerite Crystals

This work is devoted to the growing and characterization of perfect C
 60
 single crystals with the aim of further understanding of the physical properties of this material related to the low energy excited states which determine in a considerable degree its electronic properties, which, in turn, are important for its possible application Here we present several characterization techniques based on optical properties of C
 60
 crystals and the first results of the investigation of the C
 60
 samples grown at the orbital space station “MIR”

R. A. Dilanyan

Papers

On the mechanical properties of C60 fullerite crystals

Mechanical properties and deformation of fullerites

On the Mechanical Properties of C60 Fullerite Crystals

Optical Characteristics of C60 Single Crystals Grown in Microgravity Conditions