frequency is extracted

and shown in the inset of Figure 6. Strong frequency dispersion is observed for all of the samples. It is clear that the deteriorative degree of dielectric relaxation increases from 12.1 nm, reaches the peak at 22.5 nm, and then declines. A comparison between the samples of 12.1 and 25 nm is made. Uniformly, the sample with the grain size of 25 nm is shown to perform superior on dielectric relaxation. The dielectric constant frequency response of the PNZT samples shares exactly the same response for the CeO2 samples (one dielectric relaxation peak within the frequency range). A possible reason [19] to the cited observation could be the broadened dielectric peak and the transition temperature shift. The dielectric constant shows phase transition as expected for normal ferroelectrics. The region around the dielectric peak is broadened, which is one of the most important characteristics of disordered perovskite structure with the diffuse phase GSK2126458 transition. The transition temperature is found to shift forward to lower temperature with the grain size from 12.1 to 22.5 nm, while the transition RG-7388 cell line temperature remains at the same position with further increasing grain size. Concerning the strong frequency dispersion, it is mainly

attributed to the low-frequency space charge accumulation effect. Such strong frequency dispersion in dielectric constant appears to be a common feature in ferroelectrics associated with non-negligible ionic conductivity. Therefore, the reason for the

dielectric relaxation of the PNZT samples could be the possible mechanism behind the frequency dependence of the k value of the CeO2 samples. Many dielectric relaxation models (Cole-Davidson, Havriliak-Negami, and Kohlrausch-Williams-Watts) were proposed to interpret the dielectric relaxation, which is also termed as the frequency dependence of the k value. The Havriliak-Negami (HN) model is suitable Dynein for almost all of the high-k materials as it has three parameters for fitting (α, β, and τ). In contrast, the Cole-Davidson (CD) model only has two parameters for fitting (β and τ). Thus, if the CD model is able to fit the cerium oxides, it will be more significant for the specified physical mechanism compared to the HN model. Concerning the Kohlrausch-Williams-Watts (KWW) model, it has also two adjusting parameters for fitting (β and τ). The CD and KWW models have certain links in both high frequency and low frequency approximations. Besides, the CD model is widely used in glass-forming materials to explain the frequency dependence of the dielectric constants [20]. Here, dielectric relaxation can be described by the CD law for all of the CeO2 samples. CD fittings are denoted by solid lines in Figure 6. In 1951, D. W. Davidson and R. H. Cole [21] proposed the CD equation to interpret data observed on propylene glycol and glycerol based on the Debye expression. The CD equation can be represented by ϵ*(ω).