Correlations between volume defects and grain boundaries in flux-pinning of MgB2 superconductor

In order to enhance flux-pinning effect of grain boundaries, we quenched 5 wt% (Fe, Ti) doped MgB2 superconductor in water. During the study, we discovered that there was a correlation between pinned fluxes at volume defects and pinned fluxes at grain boundaries. We present mechanisms of the correlation and details of relative calculations. Pinned fluxes at a volume defect are leak-out-depinned through grain boundaries because grain boundaries are connected to the volume defect. Several equations were derived, which are push-out-depinned force of flux quanta from a volume defect, flux-pinning force of flux quanta at grain boundaries, and the number of leak-out-depinned fluxes from a volume defect. TEM images proved that many grain boundaries would exist on MgB2 grains which are contact on (Fe, Ti) particles. A result was obtained by comparing M-H curve of air-cooled 5 wt% (Fe, Ti) doped MgB2 with that of water-quenched one on the base of the equations, which shows approximately 34% of the number of flux quanta pinned at the volume defect was leak-out-depinned from the volume defect and pinned at the grain boundaries. The study suggested that amount of pinned fluxes at grain boundaries could be calculated by M-H curve of superconductor.