Thermodynamics of formation of solid solutions between BaZrO3 and BaPrO3

Abstract

A linear relationship between the standard enthalpy of formation from binary oxides, ΔfHox, 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 ΔfHox of Pr-substituted barium zirconates BaZr1–xPrxO3. A dependence of the relative change of the standard entropies, S298, 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 S298 was proposed, and S298 of BaPrO3 was calculated as (162.8 ± 2.8) J·mol-1·K-1. Knowing S298 of BaPrO3 and using the literature data for S298 of BaZrO3, the values of S298 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 ΔfHox. The values of standard entropy changes, ΔfSox, and Gibbs energy changes, ΔfGox, 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 ΔfHox and ΔfGox becoming more positive, indicating the decrease of the relative stability with respect to the corresponding binary oxides. Expanded uncertainties of the estimated values of ΔfHox and ΔfGox are equal to 14 kJ∙mol-1, and those of S298 and ΔfSox – 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).