Solid friction from stick–slip down to pinning and aging

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between macroscopic hard rough solids, whose main dynamical features are well described by the Rice–Ruina rate and state-dependent constitutive law. We show that it results from two combined effects: (i) the threshold rheology of nanometer-thick junctions jammed under confinement into a soft glassy structure and (ii) the geometric aging, i.e. slow growth of the real area of contact via asperity creep interrupted by sliding. Closer analysis leads to identifying a second aging-rejuvenation process, at work within the junctions themselves. We compare the effects of structural aging at such multicontact, very highly confined, interfaces with those met under different confinement levels, namely boundary lubricated contacts and extended adhesive interfaces involving soft materials (hydrogels, elastomers). This leads us to propose a classification of frictional junctions in terms of the relative importance of jamming and adsorption-induced metastability.

Solid friction from stick–slip down to pinning and aging

All authors

Tristan Baumberger &; Christiane Caroli

https://doi.org/10.1080/00018730600732186

Published online:

28 November 2010

Table     

Fermi level pinning effects at gate–dielectric interfaces influenced by interface state densities

The dependences of Fermi-level pinning on interface state densities for the metal–dielectric, ploycrystalline silicon–dielectric, and metal silicide–dielectric interfaces are investigated by calculating their effective work functions and their pinning factors. The Fermi-level pinning factors and effective work functions of the metal–dielectric interface are observed to be more susceptible to the increasing interface state densities, differing significantly from that of the ploycrystalline silicon–dielectric interface and the metal silicide–dielectric interface. The calculation results indicate that metal silicide gates with high-temperature resistance and low resistivity are a more promising choice for the design of gate materials in metal-oxide semiconductor(MOS) technology.     

Alumina nano-inclusions as effective flux pinning centers in Y–Ba–Cu–O superconductor fabricated by seeded infiltration and growth

The YBa₂Cu₃O_7?x (Y123) textured bulk superconductors with various amounts of nanometer alumina particles were fabricated by a seeded infiltration and growth process. The addition of nanometer alumina was found to be effective for an improvement of the superconducting properties. The critical current density (J_c) values were increased twice in self field with a slight addition amount of nanometer alumina particles (maximum J_c at 0.01 wt.% alumina addition). The present work suggests that the use of insulating inclusions in the nanometer sub-scale can stabilize the flux-line lattice and greatly enhance the pinning capabilities of the infiltrated samples. No refinement of Y211 particles was observed with alumina addition. The J_c improvement by nanometer alumina inclusions is likely rendered to the insulating nano-pinning centers that have been successfully embedded into superconducting Y123 matrix. On the other hand, we examined the effect of the pinning centers size on the superconducting properties of infiltrated YBCO bulk samples. To this effect insulating nano-pinning centers with two different size distributions has been successfully incorporated within YBCO matrix of bulk superconductor by slightly doping with nano-particle alumina dispersions. Two alumina nano-particle dispersions with mean size diameters of about 20 nm and 130 nm were used. It was shown that the size of the pinning centers can affect considerably the J_c performances and the pinning mechanism.     

Strongly enhanced pinning force density in YBCO–BaTiO3 nanocomposite superconductor

YBa₂Cu₃O_7−δ–BaTiO₃ (4 wt.%) (YBCO–BTO (4%)) composite bulk polycrystalline sample has been synthesized by solid state reaction method. The structure of composite sample has been investigated by X-ray diffraction and magnetization measurements were carried out using MPMS SQUID VSM. The superconducting transition temperature of the YBCO–BTO (4%) sample was similar to that of pure YBCO. The critical current density (J_c) for YBCO–BTO (4%) sample increases significantly as compared to pure YBCO sample. The enhancement of the critical current density in the YBCO–BTO (4%) sample has been attributed to the presence of BaTiO₃ nanoparticles acting as artificial pinning centres. The introduction of BaTiO₃ particles in YBCO increases pinning force density from 0.71 GN/m² to 1.41 GN/m² at 4 K and 0.33 MN/m² to 0.97 MN/m² at 77 K.     

Do columnar defects produce bulk pinning?

From magneto-optical imaging performed on heavy-ion-irradiated YBa(2)Cu(3)O(7-delta) single crystals, it is found that at fields and temperatures where strong single vortex pinning by individual irradiation-induced amorphous columnar defects is to be expected, vortex motion is limited by the nucleation of vortex kinks at the specimen surface. In the material bulk, vortex motion occurs through (easy) kink sliding. Depinning in the bulk determines the screening current only at fields comparable to or larger than the matching field, at which the majority of vortices is not trapped by an ion track.     

Enhancement of pinning and the peak effect in Y1–xFexBa2Cu3Oy high-temperature superconductors

Complex structural and magnetic studies of polycrystalline samples of the Y_{1 – x}Fe_xBa₂Cu₃O_y high-T_c superconductor (x = 0, 0.02, 0.05) have been carried out in order to determine the effect of weak doping with a magnetic 3d ion on structural changes and the critical current density J_c. An increase in the Fe content results in a significant change in J_c and its field dependence. The dependences J_c(H) become nonmonotonic and demonstrate a pronounced peak (peak effect); as a result, the J_c increases strongly in wide temperature and magnetic field regions. The analysis of the field dependences of the pinning force reveals a scaling behavior. The parameters of the scaling function correspond to the point magnetic defects under strong effects of a thermally activated flux flow. Thus, the weak Fe doping (several molar percent) is a promising way to significant improvement of transport properties of high-T_c superconducting materials based on 123-type compounds.     

Higher borides and oxygen-enriched Mg–B–O inclusions as possible pinning centers in nanostructural magnesium diboride and the influence of additives on their formation

The study of high pressure (2 GPa) synthesized MgB₂-based materials allows us to conclude that higher borides (with near MgB₁₂ stoichiometry) and oxygen-enriched Mg–B–O inclusions can be pinning centers in nanostructural magnesium diboride matrix (with average grain sizes of 15–37 nm). It has been established that additions of Ti or SiC as well as manufacturing temperature can affect the size, amount and distribution of these inclusions in the material structure and thus, influence critical current density. The superconducting behavior of materials with near MgB₁₂ stoichiometry of matrix is discussed.     

Is there nuclear pinning of vortices in superfluid pulsars?

We develop a fully consistent semianalytical model in order to study the vortex-nucleus interaction in the inner crust of neutron stars. In the framework of the local-density approximation and assuming a constant pairing gap and a square-well nuclear potential, the model takes into account all energy contributions and determines unambiguously the structure of the vortex core. The results show that, irrespective of the value of the pairing gap, only interstitial pinning takes place all along the inner crust. This is in contrast with all existing calculations, which predict nuclear pinning in the deeper layers of the crust. Should further studies confirm this surprising result, the explanation of pulsar glitches in terms of depinning of vortices will have to be carefully revisited.     

Depinning dynamics of driven colloids with random pinning： a numerical study

Using Langevin simulations, we have investigated numerically the depinning dynamics of driven two-dimensional colloids subject to the randomly distributed point-like pinning centres. With increasing strength of pinning, we find a crossover from elastic to plastic depinnings, accompanied by an order to disorder transition of state and a substantial increase in the depinning force. In the elastic regime, no peaks are found in the differential curves of the velocity－force dependence (VFD) and the transverse motion is almost none. In addition, the scaling relationship between velocity and force is found to be valid above depinning. However, when one enters the plastic regime, a peak appears in the differential curves of VFD and transverse diffusion occurs above depinning. Furthermore, history dependence is found in the plastic regime.     

Anisotropic vortex pinning in the β-pyrochlore oxide superconductor KOs2O6

Vortex pinning in the β-pyrochlore oxide superconductor KOs₂O₆ with T_c = 9.6 K is investigated by measuring magnetic torque. A large anisotropy of magnetic torque is observed in the superconducting state below T_p = 7.6 K, where a first-order structural transition takes place, in spite of the inherent isotropic nature of the structural and electronic properties. Magnetic torque is enhanced at external magnetic fields parallel to the [1 1 1] and [0 0 1] directions. Moreover, a pronounced peak effect is also observed in the magnetic field dependence of the torque in these two directions. We consider that the observed anisotropy is related to a microstructure associated with the structural transition.     

Disturbance rejection and H∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances.A dynamical network is said to be robust to disturbance,if the H ∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small.It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H ∞ control problem of a set of independent systems whose dimensions are equal to that of a single node.A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node.To improve this,local feedback injections are applied to a small fraction of the nodes in the network.Some criteria for possible performance improvement are derived in terms of linear matrix inequalities.It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.     

Can the effective pinning potential of MgB2 behave logarithmically in the high temperature range?

The pinning potential barrier U_o(T,H) is the main parameter describing the flux pinning of MgB₂. Comparing the experimental results published recently by Thompson et al. and Bygoslavsky et al., one can prove theoretically that in the high temperature range, U_o(T,H) is of logarithmic form similar to that suggested for high T_c superconductors by Zeldov et al.. Meanwhile, the major pinning centers of MgB₂ employ the planar pinning mechanism. Furthermore, it is found that U_o(T,H) depends on the temperature linearly and also on the magnetic field with the form H^−1∼−2 at high temperature range.     

ICEMS study of isothermal oxidation of Fe–Mn–Al–C–Cr–Si–Mo, Fe–Mn–Al–C–Cr–Si and Fe–9Cr–1Mo alloys

The purpose of this paper is to investigate the isothermal behavior of Fe–27.3Mn–7.6Al–C–6.5Cr–0.25Si–0.88Mo (Mo(0)) and Fe–27.3Mn–7.6Al–1.0C–6.5Cr–0.25Si (Mo(1)) alloys and compare it against Fe–9Cr–1Mo (FCR) commercial alloy. The experiments were carried out at 600°C, 700°C, 750°C and 850°C, each one during 72 h in static air. The oxidation kinetics was measured as a function of time using a Thermogravimetry analyzer (TGA). The structure and composition of the oxide scale were characterized by X-ray diffraction (XRD) and Integral Conversion Electron Mössbauer Spectroscopy (CEMS). The TGA results show that at all oxidation temperatures the sample FCR exhibit the lowest kinetic corrosion and the lowest weight gain, whereas Mo(0) the highest. By CEMS technique it were found a broad magnetic sextet, which has been fit by one hyperfine field distribution with mean hyperfine field characteristic to ferritic/martensite phase, one Fe^3?+? doublet and one singlet for the Mo(0) and Mo(1) alloys. Samples oxidized at highest temperatures exhibit a strong paramagnetic line, probably due that the Cr or Mn oxides may be enriched on the surface. Then, the magnetic phase can be converted partially into austenite phase at highest temperatures.     

Commensurability effects in the critical forces of a superconducting film with Kagomé pinning array at submatching fields

Using molecular dynamics simulations, we find the commensurability force peaks in a two-dimensional superconducting thin-film with a Kagomé pinning array. A transport force is applied in two mutually perpendicular directions, and the magnetic field is increased up to the first matching field. Usually the condition to have pronounced force peaks in systems with periodic pinning is associated to the rate between the applied magnetic field and the first matching field, it must be an integer or a rational fraction. Here, we show that another condition must be satisfied, the vortex ground state must be ordered. Our calculations show that the pinning size and strength may dramatically change the vortex ground state. Small pinning radius and high values of pinning strength may lead to disordered vortex configurations, which fade the critical force peaks. The critical forces show anisotropic behavior, but the same dependence on pinning strength and radius is observed for both driven force directions. Different to cases where the applied magnetic field is higher than the first matching field, here the depinning process begins with vortices weakly trapped on top of a pinning site and not with interstitial vortices. Our results are in good agreement with recent experimental results.     

Electro-optic metal–insulator–semiconductor–insulator–metal Mach-Zehnder plasmonic modulator

The performance of a CMOS-compatible electro-optic Mach-Zehnder plasmonic modulator is investigated using electromagnetic and carrier transport simulations. Each arm of the Mach-Zehnder device comprises a metal–insulator–semiconductor–insulator–metal (MISIM) structure on a buried oxide substrate. Quantum mechanical effects at the oxide/semiconductor interfaces were considered in the calculation of electron density profiles across the structure, in order to determine the refractive index distribution and its dependence on applied bias. This information was used in finite element simulations of the electromagnetic modes within the MISIM structure in order to determine the Mach-Zehnder arm lengths required to achieve destructive interference and the corresponding propagation loss incurred by the device. Both inversion and accumulation mode devices were investigated, and the layer thicknesses and height were adjusted to optimise the device performance. A device loss of <8 dB is predicted for a MISIM structure with a 25 nm thick silicon layer, for which the device length is <3 μm, and <5 dB loss is predicted for the limiting case of a 5 nm thick silicon layer in a 1.2 μm long device: in both cases, the maximum operating voltage is 7.5 V.     

Characterization of bismuth–tin–lead and bismuth–tin–lead–cadmium fusible alloys

Microstructure, electrical, mechanical and thermal properties of quenched bismuth–tin eutectic, Rose (Bi₅₀Sn_22.9Pb_27.1) and Wood’s (Bi₅₀Sn_12.5Pb₂₅Cd_12.5) alloys have been investigated using scanning electron microscopy, X-ray diffraction analysis, the double bridge method, the dynamic resonance method, Vickers hardness measurement and thermal analysis. Wood’s alloy (Bi–Pb–Sn–Cd) has low electrical resistivity and melting point but a high elastic modulus and internal friction when compared with the Rose (Bi–Pb–Sn) alloy. The presence of cadmium in Wood’s alloy decreases its melting point and electrical resistivity with an increase in its elastic modulus, which improves the mechanical properties. Wood’s alloy (Bi–Pb–Sn–Cd) has better properties, which make it useful in various applications such as in protection shields for radiotherapy, locking of mechanical devices and welding at low temperature.     

Study of magnetic flux pinning in granular YBa2Cu3O7 − y /nanoZrO2 composites

In this work, the effect of ZrO₂ nanoparticles prepared in a low-pressure arc discharge plasma on magnetic flux pinning of granular YBa₂Cu₃O_{7 ? y} /nanoZrO₂ composites has been studied. It has been shown that the ZrO₂ nanoparticles do not change the superconducting transition and the microstructure of superconductors. At a temperature of 5 K, the addition of 0.5 and 1 wt % of ZrO₂ nanoparticles may lead to the additional effect of magnetic flux pinning and the increase in the critical current density J _c. The J _c value for composites with 1 wt % is two times larger than that for the reference sample. The fishtail effect is observed for YBa₂Cu₃O_{7 ? y} /nanoZrO₂ composites at the temperatures of 20 and 50 K. The problems associated with the additional effect of magnetic flux pinning of granular YBa₂Cu₃O_{7 ? y} /nanoZrO₂ composites and the appearance of the fishtail effect have been discussed.     

Chern–Simons–Rozansky–Witten topological field theory

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern–Simons and Rozansky–Witten theory and can be regarded as a topologically-twisted version of the N=4$N=4$d=3$d=3$ supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kähler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern–Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.     

The effect of pinning centers in Zn-doped CuBa2Ca3Cu4O12−y high-temperature superconductors

CuBa₂Ca₃Cu₄O_12−y (Cu:1234) high-temperature superconductors (HTS) doped with up to 2% Zn were grown using the high-pressure synthesis technique. Magnetization loops of the samples were measured at various temperatures between 5 and 77.3 K and magnetic fields up to 14 T. Critical current densities J_c of the samples were estimated using the critical state model. The results show that Zn-induced pinning centers increase J_c of Cu:1234 several times, depending on field and temperature. From the experimentally determined field-temperature region in which a higher Zn concentration lead to a higher J_c, we suggest the existence of a cross-over from quite efficient, extended (in the c-axes direction) pinning centers to point-like (inefficient) pinning centers at a certain temperature, depending on field. This effect can be attributed to the fact that, unlike other HTS, in Cu:1234 there is a second critical temperature T_c2 of about 70–80 K (in zero field, and 50–60 K in 15 T), related to the over-doping of pyramidal basal plane (outer CuO₂ plane).