Microstructure-critical current density model for MgB2 wires and tapes

MgB2 wires and tapes were prepared by the powder in tube method using different processing technologies and thoroughly characterized for their superconducting properties. Either prereacted MgB2 (ex situ) or a mixture of Mg+2B (in situ) was used as the precursor powder. In some wires the precursor powder was mixed with SiC. The critical current density (J(c)) of these wires was found to differ by orders of magnitude, the highest J(c) being 10(4) A cm(-2) at 10.5 T and 4.2 K. The microstructure of these wires was investigated using quantitative electron microscopy and spectroscopy methods [B. Birajdar, N. Peranio, and O. Eibl, Supercond. Sci. Technol. 21, 073001 (2008)]: combined scanning electron microscopy, electron probe microanalysis, and transmission electron microscopy analysis with artifact-free sample preparation, elemental mapping, and advanced chemical quantification. Wires with prereacted MgB2 (ex situ) show oxygen-poor MgB2 colonies (a colony is a dense arrangement of several MgB2 grains) embedded in a porous oxygen-rich matrix introducing structural granularity. Wires with elemental precursors (in situ) are generally more dense but show inhibited MgB2 phase formation with significantly higher fraction of B-rich secondary phases in comparison to the ex situ wires. SiC in the in situ wires results in the formation of Mg2Si secondary phases. In situ and mechanically alloyed samples show smaller (20-100 nm) MgB2 grains, the grain size being slightly larger than the coherence length. All samples show Mg oxide. SiC added samples annealed beyond 950 degrees C yield formation of Si oxide compounds, whereas Mg2Si is found for annealing temperatures of less than 650 degrees C. The critical current is limited due to the anisotropy but also due to structural granularity. A microstructure-critical current density model is given to explain the large, orders of magnitude, differences in the J(c) of MgB2 wires and tapes. The model contains the following microstructure parameters: (1) MgB2 grain size, (2) colony size, (3) volume fraction of B-rich secondary phases, and (4) oxygen mole fraction. The logarithmic critical current densities as a function of magnetic field were parametrized and the decay field and the critical current density at zero field (J(c0)) was quantitatively correlated with the parameters of the microstructure. The MgB2 grain size is negatively correlated with the decay field and the three other microstructure parameters show correlation with J(c0). Sample preparation influencing the microstructure parameters is discussed. A detailed analysis is given to correlate the microstructural data with respect to fundamental parameters of a flux-line pinning model established for anisotropic superconductors.