Cover Image

Thermodynamics of formation of solid solutions between BaZrO3 and BaPrO3

Dmitry S. Tsvetkov, Vladimir V. Sereda, Dmitry A. Malyshkin, Anton L. Sednev-Lugovets, Andrey Yu. Zuev, Ivan L. Ivanov


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).


doped barium zirconate; thermodynamics; thermodynamic properties prediction

Full Text:



Kreuer KD. Proton-Conducting Oxides. Annu Rev Mater Res. 2003;33(1):333–59. doi:10.1146/annurev.matsci.33.022802.091825

Norby T. Proton Conductivity in Perovskite Oxides. Boston, MA: Springer US; 2009. 217 p. (Ishihara T, editor. Perovskite Oxide for Solid Oxide Fuel Cells). doi:10.1007/978-0-387-77708-5_11

Sažinas R, Einarsrud M-A, Grande T. Toughening of Y-doped BaZrO3 proton conducting electrolytes by hydration. J Mater Chem A. 2017;5(12):5846–57. doi:10.1039/C6TA11022C

Iguchi F, Tsurui T, Sata N, Nagao Y, Yugami H. The relationship between chemical composition distributions and specific grain boundary conductivity in Y-doped BaZrO3 proton conductors. Solid State Ion. 2009;6–8(180):563–8. doi:10.1016/j.ssi.2008.12.006

Babilo P, Uda T, Haile SM. Processing of yttrium-doped barium zirconate for high proton conductivity. J Mater Res. 2007;22(5):1322–30. doi:10.1557/jmr.2007.0163

Ryu KH, Haile SM. Chemical stability and proton conductivity of doped BaCeO3–BaZrO3 solid solutions. Solid State Ion. 1999;125(1):355–67. doi:10.1016/S0167-2738(99)00196-4

Duval SBC, Holtappels P, Vogt UF, Pomjakushina E, Conder K, Stimming U, Graule T. Electrical conductivity of the proton conductor BaZr0.9Y0.1O3−δ obtained by high temperature annealing. Solid State Ion. 2007;178(25):1437–41. doi:10.1016/j.ssi.2007.08.006

Kjølseth C, Fjeld H, Prytz Ø, Dahl P, Estournès C, Haugsrud R, Norby T. Space–charge theory applied to the grain boundary impedance of proton conducting BaZr0.9Y0.1O3−δ. Solid State Ion. 2010;181. doi:10.1016/j.ssi.2010.01.014

Magrasó A, Frontera C, Gunnæs AE, Tarancón A, Marrero-López D, Norby T, Haugsrud R. Structure, chemical stability and mixed proton–electron conductivity in BaZr0.9−xPrxGd0.1O3−δ. J Power Sources. 2011;196(22):9141–7. doi:10.1016/j.jpowsour.2011.06.076

Fabbri E, Markus I, Bi L, Pergolesi D, Traversa E. Tailoring mixed proton-electronic conductivity of BaZrO3 by Y and Pr co-doping for cathode application in protonic SOFCs. Solid State Ion. 2011;202(1):30–5. doi:10.1016/j.ssi.2011.08.019

Fabbri E, Bi L, Tanaka H, Pergolesi D, Traversa E. Chemically Stable Pr and Y Co-Doped Barium Zirconate Electrolytes with High Proton Conductivity for Intermediate-Temperature Solid Oxide Fuel Cells. Adv Funct Mater. 2011;21(1):158–66. doi:10.1002/adfm.201001540

Tsvetkov D, Sednev-Lugovets A, Malyshkin D, Sereda V, Zuev A, Ivanov I. Crystal structure and high-temperature thermodynamic properties of Pr-doped barium zirconates, BaZr1-xPrxO3 (x = 0.1, 0.5). J Phys Chem Solids. Forthcoming 2020.

Huntelaar ME, Booij AS, Cordfunke EHP. The standard molar enthalpies of formation of BaZrO3(s) and SrZrO3(s). J Chem Thermodyn. 1994;26(10):1095–101. doi:10.1006/jcht.1994.1127

Gonçalves MD, Maram PS, Muccillo R, Navrotsky A. Enthalpy of formation and thermodynamic insights into yttrium doped BaZrO3. J Mater Chem A. 2014;2(42):17840–7. doi:10.1039/C4TA03487B

Katsura T, Kitayama K, Sugihara T, Kimizuka N. Thermochemical Properties of Lanthanoid-Iron-Perovskite at High Temperatures. Bull Chem Soc Jpn. 1975;48(6):1809–11. doi:10.1246/bcsj.48.1809

Katsura T, Sekine T, Kitayama K, Sugihara T, Kimizuka N. Thermodynamic properties of Fe-lathanoid-O compounds at high temperatures. J Solid State Chem. 1978;23(1):43–57. doi:10.1016/0022-4596(78)90052-X

Petrov AN, Kropanev AY, Zhukovskij BM. Thermodynamic properties of rare earth cobaltites, RCoO3. Zhurnal Fizicheskoj Khimii. 1984;58(1):50–3.

Navrotsky A. Energetics of Phase Transition in AX, ABO3 and AB2O4 Compounds. New York: Academic Press; 1981. 71 p. (O’Keefe M., Navrotsky A., Editors. Structure and Bonding in Crystals).

Shannon RD. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr Sect A. 1976;32(5):751–67. doi:10.1107/S0567739476001551

Ushakov SV, Cheng J, Navrotsky A, Wu JR, Haile SM. Formation Enthalpies of Tetravalent Lanthanide Perovskites by High Temperature Oxide Melt Solution Calorimetry. MRS Online Proceedings Library Archive. 2002;718. doi:10.1557/PROC-718-D7.17

Morss LR, Mensi N. Enthalpy of Formation of Barium Lanthanide(IV) Oxides: BaCeO3, BaPrO3, and BaTbO3. Boston, MA: Springer; 1982. 279 p. (G.J. McCarthy, H.B. Silber, J.J. Rhyne, Editors. The Rare Earths in Modern Science and Technology). doi:10.1007/978-1-4613-3406-4_56

NIST Standard Reference Database Number 69 [Internet]. Washington: National Institute of Standards and Technology; 2018 [modified October 2018; cited 2020 April 26]. Available from:

Todd SS, Lorenson RE. Heat Capacities at Low Temperatures and Entropies at 298.16°K. of Metatitanates of Barium and Strontium. J Am Chem Soc. 1952;74(8):2043–5. doi:10.1021/ja01128a054

Navrotsky A. Thermochemistry of crystalline and amorphous phases related to radioactive waste. Netherlands: Kluwer Academic Publishers; 1998. 267 p. (P.A. Sterne, A. Gonis, A.A. Borovoi, Editors. Actinides and the environment)

SpringerMaterials [Internet]. New York; 2020 [modified 2020 April 28; cited 2020 April 28]. Available from:

Termicheskie konstanty veshestv [Internet]. Moscow: Moscow State University; 2020 [modified 2020 April 28; cited 2020 April 28]. Available from:

Goudiakas J, Haire RG, Fuger J. Thermodynamics of lanthanide and actinide perovskite-type oxides IV. Molar enthalpies of formation of MM′O3 (M = Ba or Sr, M′ = Ce, Tb, or Am) compounds. J Chem Thermodyn. 1990;22(6):577–87. doi:10.1016/0021-9614(90)90150-O

Antunes I, Amador U, Alves A, Correia MR, Ritter C, Frade JR, Pérez-Coll D, Mather GC, Fagg DP. Structure and Electrical-Transport Relations in Ba(Zr,Pr)O3−δ Perovskites. Inorg Chem. 2017;56(15):9120–31. doi:10.1021/acs.inorgchem.7b01128

Jacobson AJ, Tofield BC, Fender BEF. The structures of BaCeO3, BaPrO3 and BaTbO3 by neutron diffraction: lattice parameter relations and ionic radii in O-perovskites. Acta Cryst B. 1972;28(3):956–61. doi:10.1107/S0567740872003462

Glasser L, Jenkins HDB. Predictive thermodynamics for condensed phases. Chem Soc Rev. 2005;34(10):866–74. doi:10.1039/B501741F

Kurosaki K, Konings RJM, Wastin F, Yamanaka S. The low-temperature heat capacity and entropy of SrZrO3 and BaZrO3. J Alloys Compd. 2006;424(1):1–3. doi:10.1016/j.jallcom.2005.09.096

Ahrens M, Maier J. Thermodynamic properties of BaCeO3 and BaZrO3 at low temperatures. Thermochim Acta. 2006;443(2):189–96. doi:10.1016/j.tca.2006.01.020

Cordfunke EHP, van der Laan RR, van Miltenburg JC. Thermophysical and thermochemical properties of BaO and SrO from 5 to 1000 K. J Phys Chem of Solids. 1994;55(1):77–84. doi:10.1016/0022-3697(94)90186-4

Konings RJM, Beneš O, Kovács A, Manara D, Sedmidubský D, Gorokhov L, et al. The Thermodynamic Properties of the f-Elements and their Compounds. Part 2. The Lanthanide and Actinide Oxides. J Phys Chem Ref Data. 2014;43(1):013101. doi:10.1063/1.4825256


Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Copyright (c) 2020 Dmitry Tsvetkov, Vladimir Sereda, Dmitry Malyshkin, Anton Sednev-Lugovets, Andrey Zuev, Ivan Ivanov

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Scopus logo WorldCat logo DOAJ logo CAS logo BASE logo eLibrary logo

Chimica Techno Acta, 2014-2023
ISSN 2411-1414 (Online)
Copyright Notice