Diffuse ferroelectric transition and relaxational dipolar freezing in (Ba,Sr)TiO₃: III. Role of order parameter fluctuations

Abstract

Results of a high-temperature x-ray powder diffraction study of the phase transition between cubic and tetragonal phases of (Ba_1-xSr_x)TiO₃are presented for x = 0.08 and 0.12 which exhibit sharp and diffuse dielectric anomalies, respectively. Experimental evidence and arguments are advanced to show that the cubic and tetragonal phases coexist over a wide range of temperatures and that this coexistence is due to the fluctuation of the order parameter which is coupled electrostrictively to strains. For x = 0.08, the phase coexistence disappears below the dielectric anomaly temperature T'_m, indicating the critical nature of the fluctuations. For x = 0.12, these fluctuations are non-critical since the phase coexistence persists even below T'_m. The complete conversion to the tetragonal phase occurs at T_s ≈ 75° which is nearly 25° lower than T'_m (=102 ± 1° ). It is shown that the spontaneous polarization also increases gradually below T'_m and levels off at T_p ≈ 75°. The existence of structural and polarization anomalies well below the frequency-independent dielectric anomaly temperature T'_m cannot be rationalized either in terms of the Landau-like theories for ferroelectric transitions which predict T_s=T_p=T'_m or in terms of dipole glass transitions and/or relaxor ferroelectric transitions for which T'_m should be frequency dependent.