Pinning centers

The two asperities in relative sliding are separated from each other at a nominal distance p. One of the asperities is assumed rigid while the other one deforms elastically with a deflection u. The total energy of the pinning center can be written as... 

Following the approach similar to that of the atomic-scale model, the evolution of the system state and the lateral force on the asperity can be determined in terms of AUldrj = 0. If we chose V rj)= VQ cos ir rj) as the potential function for the repulsive and attractive pinning center, respectively, the lateral force F=-dy/d7 can be plotted as a function of the traveling distance p, as shown in Fig. 17. 

The changes of lateral force F in forward and backward motions follow the curve 1 and 2, respectively. It can be observed that there is one saddle-node bifurcation for the repulsive pinning center, but two bifurcations for the attractive piiming center. This suggests that the interfacial instability results from different mechanisms. On one hand, the asperity suddenly looses contact as it slides over a repulsive pinning center, but in the attractive case, on the other hand, the... 

Fig. 16—A pair of asperities in relative sliding and interacting with each other via a pinning center.

Fig. 17 —Lateral force acting on the asperity versus the traveling distance r, (a) for repulsive pinning center, the dotted area corresponds to the net work done by the force, (b) for attractive pinning center.

The friction from the repulsive pinning center is of particular interest because it is contrary to the common belief that friction must result from attractive interactions between sliding surfaces. The results presented in Fig. 17(a) demonstrate that friction can be created by purely repulsive interactions. What really matters is the instability of the sliding body and energy dissipation, rather than the attractive or repulsive nature of interactions. This may also shed a light on the efforts to explore the correlation between friction and adhesion. 

At a pin-to-pin center distance of 4.5 mm and with 250-p tip pins, it was possible to array 4800 samples onto 25- x 75-mm filter strips. Developed spots appeared sharp and uniform (Figure 6.11). The reported threshold sensitivity was calculated as approximately 10 nM for purified G3PDH protein (10 pg/25nL) spotted at several dilutions. The drawback to this approach is the extensive washing required to remove nonspecific proteins and reagents from the membrane. 

Other deposition techniques have been used (35) and a promising technique of chemical vapor deposition has been reported and substantial critical current densities obtained by Berry et al. (39) and by Watanabe et al. (40). Values of Jc at 77 K and at 2 T and 27 T were 4 x 105 and 6.5 x 104 A/cm2 respectively (40). The surface of the film shows significant growth of c axis material in the plane as well as the desired normal to the plane growth. On the other hand this mixed phase growth may supply additional pinning centers for the improved critical current. 

We discussed the role of heterogeneities in connection with scattering experiments in Sect. 4.4. They should be still more important in phase separation because they can serve as seeds of nucleation or pinning centers of domains. There is no theory on this aspect at present. 

For large values of u our flow equations break down. Qualitatively the flow is towards large u and small K. We can, however, find the asymptotic behavior in this phase by solving the initial model in the strong pinning limit exactly. To find this solution we will assume strong pinning centers and weak thermal fluctuations ... 

They assumed that the flux lines may be pinned by weak superconducting layers (intrinsic pinning centers) or extrinsic pinning such as twin planes. They supposed that weak superconducting layers and twin planes work as pinning centers most effectively when 6 = 90° and 0 = 0, respectively. 

The derivative over (p is denoted by a dot above the relevant quantity—for example, -3 = dti/dtp. Below we introduce the effective potential w 3,l). Then the Hamiltonian of a rotating dipole with a pinned center of mass could be represented in terms (41) as follows ... 

The origin of the nonlinearity and hysteresis in the films is most likely due to displacement of domain walls [4], If domain walls move in a medium with a random distribution of pinning center, the response of the material can be described, in the first approximation by Rayleigh relations. We next demostrate how optical interferometry can be sued to verify whether this particular model applies to the investigated pzt thin film. In the case of the converse piezoelectric effect, when the driving field E is varied between — Eo and Eo, the piezoelectric strain x is hysteretic and can be expressed by the following Rayleigh relations ... 

In contrast to H c, no significant increase in pinning was found at T < Tn for the field direction H Lc (James et al., 2001) where the vortices are aligned perpendicular to the c-axis. Because the planar domain boundaries are directed along [110] and [110] with the ferromagnetic moment parallel to the domain plane direction (c-axis), these planar pinning centers are expected to become ineffective when the vortices are tilted away from the c-axis (see also Section 4.10). 

Figure 11. Pinning and nucleation. Pinning means that coercivity is created by trapping the domain wall at pronounced inhomogenities (pinning centers). In the absence of pinning centers, the coercivity is determined by the reversal field at which the original magnetization configuration becomes unstable (nucleation).

The temperature dependence of B 2 is shown in Fig. 2.29 by open circles [183]. The data reveal a positive curvature which has been observed for many other organic superconductors by ac-susceptibility and resistivity measurements. The solid line is a one-parameter fit using (2.17) for fixed / which describes the data down to the lowest temperature. The exact temperature dependence of B 2 depends on the detailed nature of the pinning centers which... 

Nb thin films have been deposited on porous silicon (PS) substrates. The PS templates consists of a short-range order matrix of pores with mean diameter of 10 nm and mean interpore distance of 40 nm, which act as an array of artificial pinning centers. Commensurability effects between the Abrikosov vortex lattice and the artificial one were investigated by transport measurements. 

Furthermore, EEL spectra of small Ag (n < 13) and Cu (n < 7) clusters show clear evidence for a size effect in their electronic structure [214]. The clusters were generated by sputtering with an UHV-compatible Xe-ion gun [45]. After size-selection with a quadrupole mass spectrometer, they have been deposited in situ in submonolayer quantities on a magnesium oxide film. Figure 1.44 displays EEL spectra taken at T = 45K for 0.04 ML of Ag (n < 13) clusters, deposited at low kinetic energy (Ek = 3-6eV) to prevent their fragmentation [215]. Each deposition was made on a freshly prepared film to avoid creation of defects, which are known to act as pinning centers for deposited clusters [216,217]. 

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