Vaporization and caloric studies on lead titanate

Thermodynamic studies of a single crystal lead titanate (PbTiO3) under equilibrium conditions by the method of Knudsen effusion mass spectrometry (KEMS) were conducted in the temperature range 950–1210 K. The vaporization of pure PbO(c) was investigated at temperatures of 810–1040 K. Thermodynamic quantities of sublimation enthalpy, activity, and entropy were derived from the partial pressures of gaseous Pb, PbO, and O2 over the lead titanate and pure lead oxide reference samples. The sublimation enthalpy of Pb from PbTiO3(c) at T=1080 K was Δ sub H 1080 K 0 ( Pb ) = ( 340 ± 11 ) kJ mol − 1 and for PbO was Δ sub H 1080 K 0 = ( 251 ± 12 ) kJ mol − 1 . Heat capacity measurements under constant pressure ( C p ( T ) 0 ) by dynamic scanning calorimetry (DSC) in the temperature range 298–1273 K resulted in two polynomial equations. The C p ( T ) 0 values increased from 106 to 139±0.2J mol−1 K−1 below the ferroelectric–paraelectric phase transition at Tc=763 K, and C p ( T ) 0 ≅(112±0.3) J mol−1 K−1 was almost constant above Tc. The low values of entropy, ΔtrsS=(2.1±0.9) J mol−1 K−1 and enthalpy, ΔtrsH=(1.57±0.7) kJ mol−1, and the λ (lambda)-shape of the ferro-paraelectric phase change in the C p ( T ) 0 function suggest that the transition can be classified as a first order one with a tendency to a continuous one. The enthalpy and the entropy values were calculated from the C p ( T ) 0 polynomials and from the vaporization studies. Deduced from empirical and experimental approaches, the heat of reaction was Δ r H 298 0 ( PbTiO 3 ( c ) ) = − ( 26.4 ± 1.8 ) kJ mol − 1 and the heat of formation was Δ f H 298 0 ( PbTiO 3 ( c ) ) = − ( 1190.4 ± 3.9 ) kJ mol − 1 . The thermodynamic activity of Pb and PbO in lead titanate was temperature dependent and their values were a=(8.67±2.9)10−4, and (9.96±3.6)10−3, respectively, at a temperature of 1000 K. Near the ferroelectric–paraelectric phase change at 770 K, PbTiO3(c) has a long-term stability.