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We report temperature and magnetic-field dependence of flux pinning force in bulk MgB 2 with variable grain size. The samples are prepared by advanced methods, allowing minimizing effects of porosity, impurities, and inclusions of secondary phases. The effects of grain connectivity, flux-creep phenomena, and grain size on critical current density and flux pinning curves are analyzed. We have compared the field dependence of the pinning force for a range of samples with the predictions of theoretical models accounting for the effect of the grain size. There is qualitative agreement between grain-boundary pinning mechanism proposed by Hampshire and Jones ͓J. Phys. C 21, 419 ͑1987͔͒ and the experimentally observed grain-size dependence of pinning force in bulk MgB 2 .

Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically. We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modeled and analyzed. The formalism is based on the Maxwell equations and a material current-voltage characteristics, linear for normal metals and nonlinear for superconductors, plus a careful account of the boundary conditions. For Ohmic films, we consider the response to a delta function sourcefield turned on instantly. As one of few problems in nonlocal electrodynamics, this has an analytical solution, which we obtain in both Fourier and real space. Next, the dynamical behavior of a square superconductor film during ramping up of the field, and subsequently returning to zero, is treated numerically. Then, this remanent state is used as initial condition for triggering thermomagnetic nonlocality implies that induced currents flow in the entire sample [3,4]. Thus, the film behavior is qualitatively different from that of bulks, and magneto-optical imaging (MOI) of thin superconductors has revealed strong piling up of the magnetic field around the sample edges, where values far above H a are reached [5]. At internal boundaries, such as the inner edge of a planar ring, the field can, due to the nonlocal electrodynamics, be in the opposite direction of the applied field [6,7]. Strongly modified behavior is found also in films patterned with regular arrays of small holes (antidots), which tend to guide the flux into the superconductor [8][9][10][11].The response of Ohmic films exposed to varying transverse magnetic fields is also described by nonlocal electrodynamics, but here the material responds linearly. Numerical solutions for strip and disc geometries have shown that the combination of nonlocality and dissipation causes a rapid penetration of a suddenly applied magnetic field [12,13]. Different from superconductors, even regions deep inside an Ohmic film are quickly penetrated by the magnetic field.A phenomenon that involves both the critical-state and Ohmic properties is the occurrence of flux avalanches or flux jumps. These are commonly observed in type-II superconductors at low temperatures, and are caused by a thermomagnetic instability which drives the superconductor from the critical-state to a high resistivity state [14]. The instability is triggered, e.g. by a small temperature fluctuation which reduces the flux pinning locally, and some quantized flux lines, or vortices, will start moving. This creates local heat dissipation and the temperature will increase even further, thus forming a positive feedback loop. The result can be an exponential growth in the temperature and a large-scale runaway of magnetic flux. In superconducting films the thermomagnetic instability is seen by MOI to manifest as abrupt avalanches of mag...

We report the grain size dependence of critical current and grain boundary pinning in bulk MgB2. By combining polarized optical microscopy and electron backscatter diffraction, we obtain evidence of special grain boundaries with a high density of dislocations that are able to provide high critical current in MgB2 polycrystals. We argue that reduction of grain size to the nanoscale level is sufficient to provide the critical current densities required for large-scale applications at the boiling temperature of liquid hydrogen.

It is well known that a substantial increase in critical current density can be achieved by the heat-treatment of ex situ magnesium diboride powderin-tube wires. However, it is not clear whether this is due to a true sintering process involving the significant transport of material and densification, or due for instance to the removal of volatile impurities from particle interfaces, limited chemical reactions at particle boundaries, or simply contact formation between particles by thermally activated direct adhesion. We believe that the term sintering in the magnesium diboride literature may often be used loosely when neither neck formation nor densification occurs during heat-treatment, and have designed experiments to understand what is happening during this processing step. We have studied the effect of a range of heat-treatments on the microstructure of pellets produced from commercial MgB 2 powder using X-ray diffraction, scanning electron microscopy, Vickers hardness tests and by density measurements using Archimedes' principle. The results are compared to those from a dense sample produced from the same powder by resistive sintering. No significant densification is observed in pellets produced by conventional pressure-less heat-treatment up to 1100 • C. However, a clear correlation between density and hardness is established by comparison with results for bulk MgB 2 produced by resistive sintering, which confirms that a classical sintering process has been induced in the latter samples.