{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T08:43:53Z","timestamp":1763023433480,"version":"3.45.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T00:00:00Z","timestamp":1720137600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T00:00:00Z","timestamp":1720137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Instituto Polit\u00e9cnico de Viana do Castelo"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Solid State Electrochem"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Materials of the system Pr\n                    <jats:sub>2<\/jats:sub>\n                    O\n                    <jats:sub>3<\/jats:sub>\n                    -ZrO\n                    <jats:sub>2<\/jats:sub>\n                    , namely the Pr\n                    <jats:sub>2<\/jats:sub>\n                    Zr\n                    <jats:sub>2<\/jats:sub>\n                    O\n                    <jats:sub>7<\/jats:sub>\n                    -based pyrochlores, have received considerable attention in the last decade, being a very interesting structure for defect chemistry because of its high solubility for various dopants, anti-site behaviour between A and B, and the multitude of possible combinations of A and B that are compatible in this type of structure. The compositions (Pr\n                    <jats:sub>2-x<\/jats:sub>\n                    Zr\n                    <jats:sub>x<\/jats:sub>\n                    )Zr\n                    <jats:sub>2<\/jats:sub>\n                    O\n                    <jats:sub>7+x\/2<\/jats:sub>\n                    (x = 0.15), Pr\n                    <jats:sub>2<\/jats:sub>\n                    Zr\n                    <jats:sub>2<\/jats:sub>\n                    O\n                    <jats:sub>7<\/jats:sub>\n                    , and Pr\n                    <jats:sub>2<\/jats:sub>\n                    (Zr\n                    <jats:sub>2-x<\/jats:sub>\n                    Pr\n                    <jats:sub>x<\/jats:sub>\n                    )O\n                    <jats:sub>7-x\/2<\/jats:sub>\n                    (x = 0.1), were prepared in previous works through the coprecipitation method and were characterised by impedance spectroscopy as a function of the oxygen partial pressure. In the present work, a defect chemistry model is proposed, and, based on the previously obtained experimental conductivity data, the relevant thermodynamic parameters were obtained by fitting, using a non-linear optimisation numerical method. The mobility of oxygen vacancies and interstitials oxygen were accurately determined, as well as the equilibrium constant of the formation of anti-Frenkel defects. It was observed that deviations from the stoichiometry promote an increase in ionic conductivity, respectively, 1.3x10\n                    <jats:sup>-4<\/jats:sup>\n                    , 1.4x10\n                    <jats:sup>-3<\/jats:sup>\n                    and 1.7x10\n                    <jats:sup>-2<\/jats:sup>\n                    S\/cm, for the stoichiometric, excess of Pr and excess of Zr composition. The higher value obtained for the composition with an excess of Zr\n                    <jats:sup>4+<\/jats:sup>\n                    , suggests a higher interstitial oxygen mobility when compared with the oxygen vacancy mobility. It is also demonstrated that the novel applied methodology of fitting conductivity experimental data with an optimisation numerical method is suitable for determining the thermodynamically relevant parameters of defect chemistry models, allowing the prediction of material properties.\n                  <\/jats:p>","DOI":"10.1007\/s10008-024-05995-3","type":"journal-article","created":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T08:01:54Z","timestamp":1720166514000},"page":"4965-4972","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Defect chemistry of pyrochlore Pr2O3-ZrO2 system: the relevant thermodynamic parameters"],"prefix":"10.1007","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4595-3641","authenticated-orcid":false,"given":"J. C. C.","family":"Abrantes","sequence":"first","affiliation":[]},{"given":"E.","family":"Gomes","sequence":"additional","affiliation":[]},{"given":"A. V.","family":"Shlyakhtina","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,5]]},"reference":[{"key":"5995_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ssi.2019.115138","volume":"344","author":"J Zhang","year":"2020","unstructured":"Zhang J, Lenser C, Menzler NH, Guillon O (2020) Comparison of solid oxide fuel cell (SOFC) electrolyte materials for operation at 500 \u00b0C. Solid State Ion 344:115138. https:\/\/doi.org\/10.1016\/j.ssi.2019.115138","journal-title":"Solid State Ion"},{"key":"5995_CR2","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1051\/jp4:2005128032","volume":"128","author":"T-H Yeh","year":"2005","unstructured":"Yeh T-H, Hsu W-C, Chou C-C (2005) Mechanical and electrical properties of ZrO 2 (3Y) doped with RENbO 4 (RE = Yb, Er, Y, Dy, YNd, Sm, Nd). Journal de Physique IV (Proceedings) 128:213\u2013219. https:\/\/doi.org\/10.1051\/jp4:2005128032","journal-title":"Journal de Physique IV (Proceedings)"},{"key":"5995_CR3","doi-asserted-by":"publisher","first-page":"9247","DOI":"10.1016\/j.ceramint.2013.05.032","volume":"39","author":"S Yoon","year":"2013","unstructured":"Yoon S, Noh T, Kim W et al (2013) Structural parameters and oxygen ion conductivity of Y2O3\u2013ZrO2 and MgO\u2013ZrO2 at high temperature. Ceram Int 39:9247\u20139251. https:\/\/doi.org\/10.1016\/j.ceramint.2013.05.032","journal-title":"Ceram Int"},{"key":"5995_CR4","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/S0167-2738(02)00381-8","volume":"152\u2013153","author":"C Xia","year":"2002","unstructured":"Xia C (2002) Microstructures, conductivities, and electrochemical properties of Ce0.9Gd0.1O2 and GDC\u2013Ni anodes for low-temperature SOFCs. Solid State Ion 152\u2013153:423\u2013430. https:\/\/doi.org\/10.1016\/S0167-2738(02)00381-8","journal-title":"Solid State Ion"},{"key":"5995_CR5","doi-asserted-by":"publisher","first-page":"3018","DOI":"10.1016\/j.ijhydene.2009.07.002","volume":"35","author":"B Li","year":"2010","unstructured":"Li B, Wei X, Pan W (2010) Improved electrical conductivity of Ce0.9Gd0.1O1.95 and Ce0.9Sm0.1O1.95 by co-doping. Int J Hydrogen Energy 35:3018\u20133022. https:\/\/doi.org\/10.1016\/j.ijhydene.2009.07.002","journal-title":"Int J Hydrogen Energy"},{"key":"5995_CR6","doi-asserted-by":"publisher","first-page":"1602","DOI":"10.1039\/C5EE03858H","volume":"9","author":"Z Gao","year":"2016","unstructured":"Gao Z, Mogni LV, Miller EC et al (2016) A perspective on low-temperature solid oxide fuel cells. Energy Environ Sci 9:1602\u20131644. https:\/\/doi.org\/10.1039\/C5EE03858H","journal-title":"Energy Environ Sci"},{"key":"5995_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.ssi.2004.07.013","volume":"176","author":"D Lee","year":"2005","unstructured":"Lee D, Kim W, Chol S et al (2005) Characterization of ZrO co-doped with ScO and CeO electrolyte for the application of intermediate temperature SOFCs. Solid State Ion 176:33\u201339. https:\/\/doi.org\/10.1016\/j.ssi.2004.07.013","journal-title":"Solid State Ion"},{"key":"5995_CR8","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/S0167-2738(02)00874-3","volume":"158","author":"H Yamamura","year":"2003","unstructured":"Yamamura H, Nishino H, Kakinuma K, Nomura K (2003) Electrical conductivity anomaly around fluorite\u2013pyrochlore phase boundary. Solid State Ion 158:359\u2013365. https:\/\/doi.org\/10.1016\/S0167-2738(02)00874-3","journal-title":"Solid State Ion"},{"key":"5995_CR9","doi-asserted-by":"publisher","first-page":"541","DOI":"10.2109\/jcersj.112.541","volume":"112","author":"H Nishino","year":"2004","unstructured":"Nishino H, Yamamura H, Arai T et al (2004) Effect of cation radius ratio and unit cell free volume on oxide-ion conductivity in oxide systems with pyrochlore-type composition. J Ceram Soc Jpn 112:541\u2013546. https:\/\/doi.org\/10.2109\/jcersj.112.541","journal-title":"J Ceram Soc Jpn"},{"key":"5995_CR10","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.materresbull.2019.04.021","volume":"116","author":"AV Shlyakhtina","year":"2019","unstructured":"Shlyakhtina AV, Pigalskiy KS (2019) Tolerance factor as the basic criterion in searching for promising oxygen-ion and proton conductors among Ln2-xDxM2O7-\u03b4 (Ln = La-Lu; M= Sn, Ti, Zr, Hf; D= Sr, Ca, Mg; x = 0, 0.1) 3+\/4+ pyrochlores. Mater Res Bull 116:72\u201378. https:\/\/doi.org\/10.1016\/j.materresbull.2019.04.021","journal-title":"Mater Res Bull"},{"key":"5995_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.electacta.2021.139632","volume":"403","author":"NV Lyskov","year":"2022","unstructured":"Lyskov NV, Shchegolikhin AN, Stolbov DN et al (2022) Study of oxygen-ion conductivity and luminescence in the ZrO2 \u2013 Nd2O3 system: impact of local heterogeneity. Electrochim Acta 403:139632. https:\/\/doi.org\/10.1016\/j.electacta.2021.139632","journal-title":"Electrochim Acta"},{"key":"5995_CR12","doi-asserted-by":"publisher","first-page":"9982","DOI":"10.1016\/j.ijhydene.2016.02.152","volume":"41","author":"AV Shlyakhtina","year":"2016","unstructured":"Shlyakhtina AV, Abrantes JCC, Gomes E et al (2016) Effect of Pr3+\/Pr4+ ratio on the oxygen ion transport and thermomechanical properties of the pyrochlore and fluorite phases in the ZrO2\u2013Pr2O3 system. Int J Hydrogen Energy 41:9982\u20139992. https:\/\/doi.org\/10.1016\/j.ijhydene.2016.02.152","journal-title":"Int J Hydrogen Energy"},{"key":"5995_CR13","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.ssi.2014.09.035","volume":"271","author":"DAA Belov","year":"2015","unstructured":"Belov DAA, Shlyakhtina AVV, Abrantes JCC et al (2015) Electrochemical behavior of the pyrochlore- and fluorite-like solid solutions in the Pr2O3\u2013ZrO2 system. Part I Solid State Ion 271:79\u201385. https:\/\/doi.org\/10.1016\/j.ssi.2014.09.035","journal-title":"Part I Solid State Ion"},{"key":"5995_CR14","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.actamat.2017.10.044","volume":"144","author":"J Shamblin","year":"2018","unstructured":"Shamblin J, Tracy CL, Palomares RI et al (2018) Similar local order in disordered fluorite and aperiodic pyrochlore structures. Acta Mater 144:60\u201367. https:\/\/doi.org\/10.1016\/j.actamat.2017.10.044","journal-title":"Acta Mater"},{"key":"5995_CR15","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.jcrysgro.2014.06.037","volume":"402","author":"SM Koohpayeh","year":"2014","unstructured":"Koohpayeh SM, Wen J-J, Trump BA et al (2014) Synthesis, floating zone crystal growth and characterization of the quantum spin ice Pr2Zr2O7 pyrochlore. J Cryst Growth 402:291\u2013298. https:\/\/doi.org\/10.1016\/j.jcrysgro.2014.06.037","journal-title":"J Cryst Growth"},{"key":"5995_CR16","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/j.jmmm.2016.05.030","volume":"416","author":"J Alam","year":"2016","unstructured":"Alam J, Jana YM, Biswas AA (2016) Crystal-field study of magnetization and specific heat properties of frustrated pyrochlore Pr2Zr2O7. J Magn Magn Mater 416:391\u2013400. https:\/\/doi.org\/10.1016\/j.jmmm.2016.05.030","journal-title":"J Magn Magn Mater"},{"key":"5995_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.94.134428","volume":"94","author":"P Bonville","year":"2016","unstructured":"Bonville P, Guitteny S, Gukasov A et al (2016) Magnetic properties and crystal field in Pr2Zr2O7. Phys Rev B 94:134428. https:\/\/doi.org\/10.1103\/PhysRevB.94.134428","journal-title":"Phys Rev B"},{"key":"5995_CR18","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.snb.2018.04.178","volume":"270","author":"F Zhong","year":"2018","unstructured":"Zhong F, Shi L, Zhao J et al (2018) Pyrochlore Pr2Zr2-xMxO7+\u03b4 (M = Al, Ga, In) solid-state electrolytes: defect-mediated oxygen hopping pathways and enhanced NO2 sensing properties. Sens Actuators B Chem 270:130\u2013139. https:\/\/doi.org\/10.1016\/j.snb.2018.04.178","journal-title":"Sens Actuators B Chem"},{"key":"5995_CR19","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/j.electacta.2018.09.152","volume":"293","author":"F Zhong","year":"2019","unstructured":"Zhong F, Zhao J, Shi L et al (2019) Pyrochlore Pr2Zr1.95In0.05O7+\u03b4 oxygen conductors: defect-induced electron transport and enhanced NO2 sensing performances. Electrochim Acta 293:338\u2013347. https:\/\/doi.org\/10.1016\/j.electacta.2018.09.152","journal-title":"Electrochim Acta"},{"key":"5995_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jallcom.2020.155841","volume":"845","author":"M Fortu\u00f1o-Morte","year":"2020","unstructured":"Fortu\u00f1o-Morte M, Beltr\u00e1n-Mir H, Cordoncillo E (2020) Study of the role of praseodymium and iron in an environment-friendly reddish orange pigment based on Fe doped Pr2Zr2O7: a multifunctional material. J Alloys Compd 845:155841. https:\/\/doi.org\/10.1016\/j.jallcom.2020.155841","journal-title":"J Alloys Compd"},{"key":"5995_CR21","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1111\/jace.18846","volume":"106","author":"EL Santos Veiga","year":"2023","unstructured":"Santos Veiga EL, Villafruela XV, Llorca J et al (2023) The catalytic activity of the Pr2Zr2\u2212x FexO7\u00b1\u03b4 system for the CO oxidation reaction. J Am Ceram Soc 106:1369\u20131380. https:\/\/doi.org\/10.1111\/jace.18846","journal-title":"J Am Ceram Soc"},{"key":"5995_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpowsour.2021.230847","volume":"520","author":"F Zhong","year":"2022","unstructured":"Zhong F, Yang S, Chen C et al (2022) Defect-induced pyrochlore Pr2Zr2O7 cathode rich in oxygen vacancies for direct ammonia solid oxide fuel cells. J Power Sources 520:230847. https:\/\/doi.org\/10.1016\/j.jpowsour.2021.230847","journal-title":"J Power Sources"},{"key":"5995_CR23","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1002\/andp.19354160705","volume":"416","author":"DAG Bruggeman","year":"1935","unstructured":"Bruggeman DAG (1935) Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizit\u00e4tskonstanten und Leitf\u00e4higkeiten der Mischk\u00f6rper aus isotropen Substanzen. Ann Phys 416:636\u2013664. https:\/\/doi.org\/10.1002\/andp.19354160705","journal-title":"Ann Phys"},{"key":"5995_CR24","doi-asserted-by":"publisher","first-page":"1984","DOI":"10.1111\/j.1551-2916.2010.03684.x","volume":"93","author":"A Yang","year":"2010","unstructured":"Yang A, Wang C, Guo R, Huang Y (2010) Microstructure and electrical properties of porous PZT ceramics fabricated by different methods. J Am Ceram Soc 93:1984\u20131990. https:\/\/doi.org\/10.1111\/j.1551-2916.2010.03684.x","journal-title":"J Am Ceram Soc"},{"key":"5995_CR25","doi-asserted-by":"publisher","unstructured":"Abrantes JCC (2023) DefChem - Defect Chemistry Toolbox. https:\/\/doi.org\/10.57910\/ipvc-prometheus-defchem2023","DOI":"10.57910\/ipvc-prometheus-defchem2023"},{"key":"5995_CR26","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/S0167-2738(00)00417-3","volume":"135","author":"F Poulsen","year":"2000","unstructured":"Poulsen F (2000) Structure, Raman spectra and defect chemistry modelling of conductive pyrochlore oxides. Solid State Ion 135:595\u2013602. https:\/\/doi.org\/10.1016\/S0167-2738(00)00417-3","journal-title":"Solid State Ionics"},{"key":"5995_CR27","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0167-2738(00)00715-3","volume":"134","author":"H Takamura","year":"2000","unstructured":"Takamura H, Tuller HL (2000) Ionic conductivity of Gd2GaSbO7 \u2013 Gd2Zr2O7 solid solutions with structural disorder. Solid State Ion 134:67\u201373","journal-title":"Solid State Ionics"},{"key":"5995_CR28","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/0167-2738(96)00118-X","volume":"86\u201388","author":"TH Yu","year":"1996","unstructured":"Yu TH, Tuller HL (1996) Ionic conduction and disorder in the Gd2Sn2O7 pyrochlore system. Solid State Ion 86\u201388:177\u2013182. https:\/\/doi.org\/10.1016\/0167-2738(96)00118-X","journal-title":"Solid State Ionics"},{"key":"5995_CR29","first-page":"307","volume-title":"Solid State Physics","author":"FA Kr\u00f6ger","year":"1956","unstructured":"Kr\u00f6ger FA, Vink HJ (1956) Relations between concentrations of imperfections in crystalline solids. In: Seitz F, Turnbull D (eds) Solid State Physics. Academic Press, New York, pp 307\u2013435"}],"container-title":["Journal of Solid State Electrochemistry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10008-024-05995-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10008-024-05995-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10008-024-05995-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T08:35:32Z","timestamp":1763022932000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10008-024-05995-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,5]]},"references-count":29,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["5995"],"URL":"https:\/\/doi.org\/10.1007\/s10008-024-05995-3","relation":{},"ISSN":["1432-8488","1433-0768"],"issn-type":[{"type":"print","value":"1432-8488"},{"type":"electronic","value":"1433-0768"}],"subject":[],"published":{"date-parts":[[2024,7,5]]},"assertion":[{"value":"28 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 May 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 June 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}