Ferroelectric-paraelectric phase transitions in the lead(x) calcium(1-x) titanium trioxide and the lead(x) barium(y) strontium(1-x-y) titanium oxide perovskite systems

The paraelectric-ferroelectric phase transformations in the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ca{dollar}sb{lcub}1-rm x{rcub}{dollar}TiO{dollar}sb3{dollar} and the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}rm y{rcub}{dollar}Sr{dollar}sb{lcub}1-rm x-rm y{rcub}{dollar}TiO{dollar}sb3{dollar} systems are analyzed. Studies on the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}rm y{rcub}{dollar}Sr{dollar}sb{lcub}1-rm x-rm y{rcub}{dollar}TiO{dollar}sb3{dollar} system were focussed on the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}0.5-rm x{rcub}{dollar}Sr{dollar}sb{lcub}0.5{rcub}{dollar}TiO{dollar}sb3{dollar} and the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Sr{dollar}sb{lcub}0.5-rm x{rcub}{dollar}Ba{dollar}sb{lcub}0.5{rcub}{dollar}TiO{dollar}sb3{dollar} compositions. X-ray studies indicate that both Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ca{dollar}sb{lcub}1-rm x{rcub}{dollar}TiO{dollar}sb3{dollar} and Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}rm y{rcub}{dollar}Sr{dollar}sb{lcub}1-rm x-rm y{rcub}{dollar}TiO{dollar}sb3{dollar} form a solid solution in the entire composition range studied. Transmission electron microscopy studies combined with dielectric measurements reveal that lead and calcium atoms order on alternate {dollar}{lcub}111{rcub}{dollar} planes for the x {dollar}>{dollar} 0.2 compositions, in the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ca{dollar}sb{lcub}1-rm x{rcub}{dollar}TiO{dollar}sb3{dollar} system, but, the ordering is less than perfect. No structural ordering was observed in the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}rm y{rcub}{dollar}Sr{dollar}sb{lcub}1-rm x-rm y{rcub}{dollar}TiO{dollar}sb3{dollar} system for the compositions studied. Dielectric constant as function of temperature was measured to study the paraelectric-ferroelectric phase transitions in these systems. Addition of calcium titanate was found to broaden the width of the ferroelectric-paraelectric transition region in the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ca{dollar}sb{lcub}1-rm x{rcub}{dollar}TiO{dollar}sb3{dollar} system. Hysteresis measurements reveal that Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ca{dollar}sb{lcub}1-rm x{rcub}{dollar}TiO{dollar}sb3{dollar} is ferroelectric at room temperature for the x {dollar}ge{dollar} 0.5 compositions. A similar behavior was observed for the x {dollar}>{dollar} 0.2 compositions in Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}0.5-rm x{rcub}{dollar}Sr{dollar}sb{lcub}0.5{rcub}{dollar}TiO{dollar}sb3{dollar} and for the x {dollar}>{dollar} 0.1 compositions in the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Sr{dollar}sb{lcub}0.5-rm x{rcub}{dollar}Ba{dollar}sb{lcub}0.5{rcub}{dollar}TiO{dollar}sb3{dollar} system. Diffuse phase transitions in solid solutions are primarily attributed to statistical fluctuations in compositions on a microscopic scale. The size of the ferroelectric nucleus determines the fluctuations in compositions and is of paramount importance in determining the nature of the paraelectric-ferroelectric phase transformation in solid solutions. A mathematical model based on probability distribution functions was used in this study to quantitatively establish the size of such fluctuations in composition for the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ca{dollar}sb{lcub}1-rm x{rcub}{dollar}TiO{dollar}sb3{dollar} and the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}rm y{rcub}{dollar}Sr{dollar}sb{lcub}1-rm x-rm y{rcub}{dollar}TiO{dollar}sb3{dollar} systems. The size of the ferroelectric nucleus was determined to be 15A for the Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ca{dollar}sb{lcub}1-rm x{rcub}{dollar}TiO{dollar}sb3{dollar} system and for the ternary system it was determined to be between 15-30A for Pb{dollar}sb{lcub}rm x{rcub}{dollar}Ba{dollar}sb{lcub}0.5-rm x{rcub}{dollar}Sr{dollar}sb{lcub}0.5{rcub}{dollar}TiO{dollar}sb3{dollar} and between 10-20A for the Pb{do...