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 .
The lattice parameters of MgB 2 up to a pressure of 8 GPa were determined using high-resolution x-ray powder diffraction in a diamond anvil cell. The bulk modulus, B 0 , was determined to be 151Ϯ5 GPa. Both experimental and first-principles calculations indicate nearly isotropic mechanical behavior under pressure. This small anisotropy is in contrast to the two-dimensional nature of the boron p states. The pressure dependence of the density of states at the Fermi level and a reasonable value for the average phonon frequency ͗͘ account within the context of BCS theory for the reduction of T c under pressure.
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.
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