The meaning of $\chi_{1}$, $\chi_{2}$, and $E_{b}$ are the same as discussed in Sec. \[sec:lead-free-relaxor\].

![Fitting the relative permittivity of PZN-0.13PT at $f=1,10,100$ kHz using Eq. (\[eq:PZN\]). Note the abnormal decrease in the range below $\sim250$ K. The second panel is $w_{2}\left(T\right)$. \[fig:PZN-relaxor\]](Fig5_v2){width="6cm"}

To verify that Eq. (\[eq:PZN\]) indeed works, we experimentally obtained the permittivity of Pb(Zn$_{1/3}$Nb$_{2/3}$)$_{0.87}$Ti$_{0.13}$O$_{3}$ (PZN-0.13PT) versus temperature at frequencies $f=1,10,100$ kHz. As Fig. \[fig:PZN-relaxor\](a) shows, all three fittings are satisfactory. With Eq. (\[eq:PZN\]) and the fittings, we are able to single out $w_{2}\left(T\right)$, which shows a slight increase of the peak temperature ($T_{o}$, around $220$ K) with frequency [\[]{}Fig. \[fig:PZN-relaxor\](b)[\]]{}. We note that in this fitting there is no need to have two $\gamma$ values above and below $T_{o}$ [@Uchino2014]. The asymmetric peak shown in Fig. \[fig:PZN-relaxor\](a) is naturally caused by the Maxwell-Boltzmann distribution function.

                     1 kHz    10 kHz   100 kHz
  ----------------- -------- -------- ---------
      $\gamma$        2.02     1.82     1.63
     $T_{O}$ (K)     219.6    229.0     240.6
     $E_{b}$ (K)      22.3     22.9     23.5
   $\chi_{1}$ [^1]   56601    55781     53529
     $\chi_{2}$      1320.9   1284.2   1238.0
    $\theta$ (K)     102.4    103.1     104.5

  : Fitting parameters of PZN-0.13PT’s permittivity measured at different frequencies. As the table demonstrates, $\gamma$ and $T_{C}$ are the most important variable that changes 