the number of dipoles above potential wells increases with $T$ as governed by the function $P\left(E_{b},T\right)$ (see Fig. \[fig:components\]). The combined effects of the two factors give rise to the susceptibility peak at $T_{m}$. However, the situation for lead-based relaxors is different. The function $\chi_{1}/\left(1+\left|\frac{T-T_{O}}{\theta}\right|^{\gamma}\right)$ [\[]{}see Eq. (\[eq:PZN\])[\]]{}, which largely determines the value of $T_{m}$, manifests the vestige of a true phase transition in normal ferroelectrics, which is torn down by random electric fields and/or PNRs in relaxors.

Rationale for Eq. (\[eq:h1T\])
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![The energy well for dipoles is shifted and lowered when an electric field is applied .\[fig:falling\]](Fig7){width="8cm"}

For lead-free BZT, we propose Eq. \[eq:h1T\] to describe the susceptibility of dipoles with kinetic energy higher than $E_{b}$. This choice follows the Debye relaxation, i.e., $\chi\sim1/\left(1+\omega^{2}\tau^{2}\right)$ [@Kasap2006], where $\omega$ is a constant (the probing frequency), and $\tau$ is temperature-dependent relaxation time. For a thermally activated process, the relation between $\tau$ and $T$ is often specified by the Arrhenius law, i.e., $1/\tau=A\exp\left(-E_{a}/T\right)$, where $E_{a}>0$ is the activation energy [@PinnedPhonon; @negativeActivation; @Pirc2007]. In this case, the susceptibility will be $\chi\sim1/\left[1+A^{2}\omega^{2}\exp\left(\frac{2E_{a}}{T}\right)\right]$, which is discussed by Jonscher [@Jonscher1981]. However, the dynamic process considered here describes dipoles falling to a state of lower energy, which 