Thermodynamics of formation of solid solutions between BaZrO3 and BaPrO3

Abstract

A linear relationship between the standard enthalpy of formation from binary oxides, Δ_fH_ox, and the Goldschmidt tolerance factor, t, for some A^IIB^IVO₃ (A = Ca, Sr, Ba; B = Ti, Zr, Hf, Ce, Pr, Tb, U, Pu, Am) perovskite oxides was used for estimation of Δ_fH_ox of Pr-substituted barium zirconates BaZr_1–xPr_xO₃. 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 A^IIB^IVO₃ (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 BaZr_1–xPr_xO₃ were predicted on the assumption that BaZr_1–xPr_xO₃ is a regular or ideal solution of BaPrO₃ in BaZrO₃ as evidenced by the very small enthalpy of mixing calculated based on the estimated Δ_fH_ox. The values of standard entropy changes, Δ_fS_ox, and Gibbs energy changes, Δ_fG_ox, for the reactions of formation of BaZr_1–xPr_xO₃ from BaO, ZrO₂ and PrO₂ were also estimated. Substituting Pr for Zr in BaZr_1–xPr_xO₃ results in Δ_fH_ox and Δ_fG_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 Δ_fH_ox and Δ_fG_ox are equal to 14 kJ∙mol^-1, and those of S₂₉₈ and Δ_fS_ox – less than 2.8 J∙mol^-1·K^-1 and 3.5 J∙mol^-1·K^-1, respectively, for BaZr_1–xPr_xO₃ (x = 0.0–1.0).