Thermodynamics of Formation of Solid Solutions between BaZrO3 and BaPrO3

Abstract

A linear relationship between the standard enthalpy of formation from binary oxides, ΔfH°ox, and the Goldschmidt tolerance factor, t, for some AIIBIVO3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf, Ce, Pr, Tb, U, Pu, Am) perovskite oxides was used for estimation of ΔfH°ox of Pr-substituted barium zirconates BaZr1–xPrxO3. A dependence of the relative change of the standard entropies, S°298, on the relative change of the molar volumes in the reactions of formation of AIIBIVO3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf, Ce) from binary oxides was also found to be linear. Using this dependence, a relatively precise method of estimating S°298 was proposed, and S°298 of BaPrO3 was calculated as (162.8 ± 2.8) J·mol–1·K–1. Knowing S°298 of BaPrO3 and using the literature data for S°298 of BaZrO3, the values of S°298 of BaZr1–xPrxO3 were predicted on the assumption that BaZr1–xPrxO3 is a regular or ideal solution of BaPrO3 in BaZrO3 as evidenced by the very small enthalpy of mixing calculated based on the estimated ΔfH°ox. The values of standard entropy changes, ΔfS°ox, and Gibbs energy changes, ΔfG°ox, for the reactions of formation of BaZr1–xPrxO3 from BaO, ZrO2 and PrO2 were also estimated. Substituting Pr for Zr in BaZr1–xPrxO3 results in ΔfH°ox and ΔfG°ox becoming more positive, indicating the decrease of the relative stability with respect to the corresponding binary oxides. Expanded uncertainties of the estimated values of ΔfH°ox and ΔfG°ox are equal to 14 kJ · mol–1, and those of S°298 and ΔfS°ox — less than 2.8 J · mol–1·K–1 and 3.5 J · mol–1·K–1, respectively, for BaZr1–xPrxO3 (x = 0.0–1.0).