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Whereas there are two critical fields that are H$_{c1}$ and H$_{c2}$ in theideal type II superconductor, there is another critical field H$_{c1}'$ definedas the field showing the maximum diamagnetic property in the real type IIsuperconductor. We would present that H$_{c1}'$ is able to be provedtheoretically and experimentally. We have derived an equation based onflux-pinning effect of volume defects. MgB$_2$ bulks which were synthesized byMg and B are similar to this model. The number of quantum fluxes pinned at adefect of radius r, a pinning penetration depth, magnetic flux penetrationmethod, and a magnetization at H$_{c1}'$ in the static state are suggestedthrough the equation of the model. It was speculated that pinned fluxes at avolume defect in the superconductor have to be pick-out depinned from thedefect and move an inside of the superconductor when pick-out forces of pinnedfluxes is larger than pinning force of the defect (F$_{pickout}$ $>$F$_{pinning}$) or when the shortest distance between pinned fluxes at a volumedefect is the same as that of H$_{c2}$. In reality, $\Delta$G$_{dynamic}$ whichis sum of fluxes movement energy and fluxes vibration energy is involved inmovement of pinned fluxes. When volume defects are small and many, the numberof pinned fluxes at a volume defect calculated by experimental results wascloser to that of ideally calculated ones because of a small$\Delta$G$_{dynamic}$. However, when volume defects are large and a few, thenumber of pinned fluxes at a volume defect calculated by experimental resultswere much fewer than that of ideally calculated ones because of a large$\Delta$G$_{dynamic}$.

Increases of a Diamagnetic Property by Flux-Pinning in Volume Defect-Dominating Superconductors