Diffuse ferroelectric transition and relaxational dipolar freezing in (Ba,Sr)TiO3 .3. Role of order parameter fluctuations

Results of a high-temperature x-ray powder diffraction study of the phase transition between cubic and tetragonal phases of (Ba1-xSrx)TiO3 are 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 approximate to 75 degrees C which is nearly 25 degrees C lower than T'(m)(= 102 +/- 1 degrees C). It is shown that the spontaneous polarization also increases gradually below T'(m) and levels off at T-p approximate to 75 degrees C. 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 relaxer ferroelectric transitions for which T'(m) should be frequency dependent.