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The temperature and frequency dependence of capacitance versus voltage ( C- V) curves was investigated for ceramic CaCu3 Ti4 O12 samples sintered in atmospheres of vacuum, air and oxygen, respectively. A drastic capacitance rise at higher dc voltages and low ac frequencies was observed for all these CaCu3Ti4O12 CCTO samples, and it is especially strong for the sample sintered in vacuum, which has not been found previously. The shape as well as the asymmetry of the C- V curves suggest that the dielectric behavior is related to charged trap states. It also indicates that a slow relaxation process, which is strongly correlated with the re-positioning of oxygen vacancies related trap charges, takes place in CCTO. The main trap charge relaxation process is thought to occur between the boundaries perpendicular and parallel to the external electric field, and the anisotropy of the defect dipoles provide the possibilities for trap charge repositioning which maybe the reason of the huge dielectric constant. [ABSTRACT FROM AUTHOR]