Insights into the dielectric response of ferroelectric relaxors from statistical modeling

Ferroelectric relaxors are complex materials with distinct properties. The\nunderstanding of their dielectric susceptibility, which strongly depends on\nboth temperature and probing frequency, have interested researchers for many\nyears. Here we report a macroscopic and phenomenological approach based on\nstatistical modeling to investigate and better understand how the dielectric\nresponse of a relaxor depends on temperature. Employing the Maxwell-Boltzmann\ndistribution and considering temperature dependent dipolar orientational\npolarizability, we propose a minimum statistical model and specific equations\nto understand and fit numerical and experimental dielectric responses versus\ntemperature. We show that the proposed formula can successfully fit the\ndielectric response of typical relaxors, including Ba(Zr,Ti)O$_{3}$,\nPb(Zn$_{1/3}$Nb$_{2/3}$)$_{0.87}$Ti$_{0.13}$O$_{3}$, and\nPb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-0.05Pb(Zr$_{0.53}$Ti$_{0.47}$)O$_{3}$, which\ndemonstrates the general applicability of this approach.\n