Non-linear permittivity study of the crossover from ferroelectric to relaxor and cluster glass in BaTi1−xSnxO3 (x = 0.175–0.30)

The electric susceptibilities χ1, χ2, and χ3 of BaTi1−xSnxO3 ceramics with 0.175 ≤ x ≤ 0.30 are measured at 90 ≤ T ≤ 350 K and 37 ≤ f ≤ 106 Hz. Crossover from ferroelectric (x = 0.175) to relaxor behavior (x = 0.30) via coexistence of both (x = 0.25) is indicated by increasing polydispersivity and suppression of χ2 intensity. The relaxor properties are due to weak random fields acting on dipolar Ti4+ clusters in non-polar Sn4+ environment. Upon cooling frustrated interaction between the blocked polar nanoregions yields a cluster glass ground state for x = 0.30 as verified by the dynamic criticality of χ1, χ3, and the scaled non-linear susceptibility a3.