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We have studied flux-pinning effects of MgB$_2$ superconductor by doping (Fe,Ti) particles of which radius is 163 nm on average. 5 wt.\% (Fe, Ti) dopedMgB$_2$ among the specimens showed the best field dependence of magnetizationand 25 wt.\% one did the worst at 5 K . The difference of field dependence ofmagnetization of the two increased as temperature increased. Here we showexperimental results of (Fe, Ti) particle-doped MgB$_2$ according to dopantlevel and the causes of the behaviors. Flux-pinning effect of volumedefects-doped superconductor was modeled in ideal state. During the study, wehad to divide M-H curve of volume defect-dominating superconductor as threediscreet regions for analyzing flux pinning effects, which are diamagneticincrease region, $\Delta$H=$\Delta$B region, and diamagnetic decrease region.As a result, flux-pinning effects of volume defects decreased as dopant levelincreased over the optimal dopant level, which was caused by decrease offlux-pinning limit of a volume defect. And similar behaviors are obtained asdopant level decreased below the optimal dopant level, which was caused by thedecreased number of volume defects. Comparing the theory with experimentalresults, deviations increased as dopant level increased over the optimal dopantlevel, whereas the two was well matched on less dopant level than the optimaldopant level. The behavior is considered to be caused by segregation of volumedefects. On the other hand, the property of over-doped specimens dramaticallydecrease as temperature increases, which is caused by double decreases offlux-pinning limit of a volume defect and segregation effect.

Flux-Pinning Behaviors and Mechanism According to Dopant Level in (Fe, Ti) Paticle-Doped MgB$_2$ Superconductor