Direct evidence for Vögel–Fulcher freezing in relaxor ferroelectrics

Direct evidence for freezing in two relaxor ferroelectrics, ${\mathrm{PbMg}}_{\mathrm{1/3}}{\mathrm{Nb}}_{\mathrm{2/3}}{\mathrm{O}}_{\mathrm{3}}$ and ${\mathrm{PbSc}}_{\mathrm{1/2}}{\mathrm{Ta}}_{\mathrm{1/2}}{\mathrm{O}}_{\mathrm{3}},$ at a certain temperature $T_f\text{≠0\hspace{0.17em}}\mathrm{K}$ was obtained from the temperature dependence of the maximum relaxation time, ${\tau }_{\max }.$ It was shown that ${\tau }_{\max }\mathrm{(T)}$ follows the Vögel–Fulcher (VF) law, and tends toward infinity as temperature approaches $T_f.$ The freezing temperature $T_f$ derived from ${\tau }_{\max }\mathrm{(T)}$ coincides with the value of $T_f$ obtained from the fit of frequency, ω, dependence of the temperature, $T_{\max },$ of the dielectric permittivity maximum to the same VF law. Thus, this result solves the controversy that the VF law for ${\mathrm{\omega (T}}_{\max })$ may not correspond to the freezing of the spectrum.