Anomalous atomic displacement parameters and local dynamics in the Curie range of a Pb-free relaxor ferroelectric system (Bi1-xBax)(Fe1-xTix)O3(0.36 ≤ x ≤ 0.50)

We report here the relaxor ferroelectric (RFE) behaviour in a multiferroic solid solution system, (Bi_1-xBa_x)(Fe_1-xTi_x)O₃, at a critical disorder level of x_C ∼ 0.35 in BiFeO₃ and 0.65 (i.e., 1-x_C = 0.35) in BaTiO₃ similar to the 1:2 ratio of Mg²⁺ and Nb⁵⁺ in the canonical RFE Pb(Mg_1/3Nb_2/3)O₃. This Pb-free system, like canonical Pb-based RFEs, does not exhibit macroscopic symmetry breaking and shows only the signatures of ergodicity breaking at Vogel-Fulcher freezing temperature (T_VF). The atomic displacement parameters (ADPs) of Fe³⁺/Ti⁴⁺ and O^2-, obtained using high wave vector (Q) and high-resolution synchrotron x-ray diffraction data as a function of temperature, show anomalous diffuse peaks in the Curie range. It is shown that the diffuse peak in ADPs is due to softening of the vibrational frequencies of the B-O chain (B = Fe³⁺/Ti⁴⁺ and O = O^2-) below the Burns temperature (T_B) followed by hardening below the characteristic temperature (T'_m), which corresponds to a peak in the dielectric permittivity (ɛ').