a lot with frequency. \[tab:Fitting-parameters-of-PZN\]

Table \[tab:Fitting-parameters-of-PZN\] summarizes fitting parameters of the permittivity measured at various frequencies. Among all the parameters, the critical component $\gamma$ changes most (19.3% from 1 kHz to 100 kHz), and decreases with increasing frequency; similarly, $T_{O}$ also changes by 9.5%. On the other hand, $E_{b}$, $\chi_{1}$, $\chi_{2}$, $\theta$ are relatively constant, which are independent of the frequency, and may be taken as material parameters. Such results hints towards the following formula that describes the dependence of PZN-0.13PT on both temperature and the probing frequency $$\begin{aligned}
\chi\left(T,\nu\right)= & \frac{\chi_{1}}{1+\left|\frac{T-T_{O}\left(\nu\right)}{\theta}\right|^{\gamma\left(\nu\right)}}P\left(E_{b},T\right)+\chi_{2}\left[1-P\left(E_{b},T\right)\right],\label{eq:PZN-1}\end{aligned}$$ where the two functions $T_{O}\left(\nu\right)$ and $\gamma\left(\nu\right)$ are frequency dependent while other parameters are constants for a given material. It is also worth noting that for PZN-0.13PT $\chi_{2}\ll\chi_{1}$, which indicates that dipoles with kinetic energy above the potential well play a more important role, in contrast to the case of BZT (see Tab. \[tab:Fitting-parameters-of-BZT\]).

![Fitting the relative permittivity of Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-0.05Pb(Zr$_{0.53}$Ti$_{0.47}$)O$_{3}$ measured at $800$ Hz using Eq. (\[eq:PZN\]). The second panel is $w_{2}\left(T\right)$. \[fig:PMN-PZT\]](Fig6_new_v3){width="6cm"}

To further verify the proposed formula, we also fit the permittivity versus temperature of another lead-based relaxor, Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-0.05Pb(Zr$_{0.53}$Ti$_{0.47}$)O$_{3}$ [@Gridnev2004]. It can be seen from Fig. \[fig:PMN-PZT\](a) that the overall fitting is satisfactory. Figure \[fig:PMN-PZT\](b) 