Structure-property relations in mesoscopic BaTiO₃ and PbTiO₃

Structure-property relations in mesoscopic BaTiO₃ and PbTiO₃ are reviewed from the standpoint of effects of crystallite size on intrinsic behavior using the Landau-Ginzburg-Devonshire formalism. Experimental results based on x-ray diffractometry and quantitative calorimetry indicate that the critical crystallite sizes (CCS) for the stabilization of the cubic paraelectric phase in BaTiO₃ and PbTiO₃ are in the vicinity of 67 and 15 nm, respectively. The CCS scales inversely with the cubic-tetragonal transition temperature (Ttr). The depression in Ttr in PbTiO₃ is ∼15 (C with decreasing crystallite size (CS). A decrease in Ttr for BaTiO₃ was not observed. Both systems preserve their first order phase transformation characteristics with reduced CS. Electrostrictive coefficients were determined as a function of CS and were found to exhibit a pronounced increase with decreasing CS. The increase in the electrostrictive coefficients offsets the decrease in spontaneous polarization and results in an increase in piezoelectric moduli suggesting that strong piezoelectric activity could indeed be observed in the mesoscopic size range.