Pinning forces

Fluxoids, 23 803, 813 pinning force on, 23 826 Fluxon lattice, 23 812-815 Fluxon-line lattice, 23 813-814 Fluxons, 23 803, 817, 823-824... 

Maximum pinning force, 23 826 Maximum reflux ratio, <5 806 Maximum residue levels (MRLs), 14 337 18 541... 

Type B gelatin, 12 440-441 Type II anion exchangers, 14 390 Type I/II zwitterionic SCK micelles, 20 490 Type II metallic superconductors, pinning force in, 23 826... 

Opposing surface tension force is the pinning force. Essentially, pinning forces promoted by surface features tend to fix the contact line of the droplet and drive the DNA toward the contact line (solvent perimeter). Solutes such as salts and probes spread to the perimeter by convection as the droplet evaporates (Figure 4.36). Uneven evaporation leads to differences in spot uniformity. 

The symmetry changes of the vortex lattice in borocarbide superconductors affect their pinning properties as was shown for YNi2B2C (Silhanek et al. 2001). For the field orientation // c, the reorientation transition of the vortex lattice mentioned above was found to be associated with a significant kink in the volume pinning force Fp, whereas in the basal plane (for H c) the signature of nonlocal effects is a fourfold periodicity of Fp. 

Fig. 11.23. Free-body diagram for the interaction of a dislocation and an obstacle characterized by a pinning force F.

The beauty of this result is that it requires no particular insight into the details of the pinning force, only requiring a bound on its net strength. We will see in our discussion of precipitate hardening that both bow-out scenarios are possible and result in different conclusions as to the way in which Ar scales with the particle size and distribution. 

An influence of finite dimensions of multilayered nanostmctures on superconducting phase nucleation and vortex mobility is studied both experimentally and theoretically. Resistive characteristics are observed to be sensitive to the geometrical symmetry of samples. For multilayers with the symmetry plane in the superconducting layer the resistive transitions are widely spread with respect to the samples with the symmetry plane in normal layers. This result is explained by the joint action of Lorentz and pinning forces on the nascent vortex lattice. 

The studied SMN s are hard type II superconductors. So, the vortex lattice is formed while Hq becomes slightly less than H 2 iX). We will focus on the dependence of the vortex lattice nascent process on the R T) curves. At low temperatures, when the degeneracy of Hq is Ayi, a rather stable vortex lattice is formed. The perturbation of the lattice due to feeble bias current is smaller with respect to the interface pinning force. The R T) curve is sharp both for S- and N-type samples. This scenario is relatively trivial. 

The joint action of pinning and Lorentz forces on vortex chain depends on the geometrical symmetry of the nanostructure. For the SMN of N-type the vortex chain is located in the center of N layer and the pinning force obstructs the vortex penetration inside the S layer. As bias current flows through the superconducting parts of the sample, dissipative processes are absent and the resistive transition is sharp (Fig. 1). For S-type nanostructures, vortex chain nucleates inside the central superconducting layer. Electromagnetic interaction between vortices and bias current leads to dissipation, it follows that in the central layer the sample resistance is not suppressed completely and the resistive transition becomes wider. 

Przyslupski et al. (1979) have prepared by dc sputtering thin films such as LaMoeSg. They are annealed in the range of temperatures from 290 up to 1320 K. The transition temperatures have been measured as 6.2 and 5.4 K (11.4K for bulk material). The sample properties have been studied in magnetic fields up to 8 T and in the temperature range 1.7-4.2 K. The curves of the critical current and of the pinning force density show a highest critical current density reached for B = 0 and T = 1.7 K, with L = 1.7 x 10 A m . 

Appropriate summation of these interactions to obtain a volume pinning force density Fp,... 

Fig. 1. Specific pinning force Fp/p (defect density) vs. elementary interaction force fp for defects in Nb. Data are for pinning by dislocation loops ( ), voids due to irradiation by neutrons (O) and Ni ), and Nb2N precipitates (A). (From Kramer [ ].)...

The summation problem, i.e., the proper way to sum Individual defect fluxoid interactions (primarily in elemental superconductors) in order to compare with the experimentally determined volume pinning force density. 

From measurements of pinning force densities on thin-film samples of NbaGe and NbsGa with known microstructure, results were obtained which are compared with existing pinning theories. 

For both types of samples, the field and temperature dependences of the pinning force density can be separated, as has been reported for many superconducting materials [ ]... 

A double logarithmic plot of the maximum pinning force density vs. the upper critical induction gives a straight line from which n can be determined. 

In a similar way, the agreement of the experimental and theoretical field dependence [ ] of the pinning force density. 

The results for one representative NbsGe film prepared by sputtering are presented in Fig. 1. For temperatures between 19 and 4 K, the maximum pinning force density is [BdiT)]. The reduced pinning force density follows... 

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