Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects
We present a density functional theory (DFT) framework taking into account the finite temperature effects to quantitatively understand and predict charged defect equilibria in a metal oxide. Demonstration of this approach was performed on the technologically important tetragonal zirconium oxide, T-Z...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/75857 https://orcid.org/0000-0001-8966-4169 https://orcid.org/0000-0002-2688-5666 |
| _version_ | 1826212058020970496 |
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| author | Yildiz, Bilge Youssef, Mostafa Youssef Mahmoud |
| author2 | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Yildiz, Bilge Youssef, Mostafa Youssef Mahmoud |
| author_sort | Yildiz, Bilge |
| collection | MIT |
| description | We present a density functional theory (DFT) framework taking into account the finite temperature effects to quantitatively understand and predict charged defect equilibria in a metal oxide. Demonstration of this approach was performed on the technologically important tetragonal zirconium oxide, T-ZrO[subscript 2]. We showed that phonon free energy and electronic entropy at finite temperatures add a nonnegligible contribution to the free energy of formation of the defects. Defect equilibria were conveniently cast in Kröger–Vink diagrams to facilitate realistic comparison with experiments. Consistent with experiments, our DFT-based results indicate the predominance of free electrons at low oxygen partial pressure (P[subscript O2]≤10[superscript −6] atm) and low temperature (T≤1500 K). In the same regime of P[subscript O2] but at higher temperatures, we discovered that the neutral oxygen vacancies (F-centers) predominate. The nature of the predominant defect at high oxygen partial pressure has been a long-standing controversy in the experimental literature. Our results revealed this range to be dominated by the doubly charged oxygen vacancies at low temperatures (T≤1500 K) and free electrons at high temperatures. T-ZrO[subscript 2] was found to be hypostoichiometric over all ranges of T and PO2, mainly because of the doubly charged oxygen vacancies, which are responsible for inducing n-type conductivity via a self-doping effect. A range of 1.3 eV in the band gap of T-ZrO[subscript 2] starting from the middle of the gap toward the conduction band is accessible to the chemical potential of electrons (Fermi level) by varying T and PO[subscript 2] without extrinsic doping. The approach presented here can be used to determine the thermodynamic conditions that extremize certain desirable or undesirable defects to attain the optimal catalytic and electronic performance of oxides. |
| first_indexed | 2024-09-23T15:15:48Z |
| format | Article |
| id | mit-1721.1/75857 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:15:48Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/758572023-02-26T03:34:26Z Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects Yildiz, Bilge Youssef, Mostafa Youssef Mahmoud Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Youssef, Mostafa Youssef Mahm Yildiz, Bilge We present a density functional theory (DFT) framework taking into account the finite temperature effects to quantitatively understand and predict charged defect equilibria in a metal oxide. Demonstration of this approach was performed on the technologically important tetragonal zirconium oxide, T-ZrO[subscript 2]. We showed that phonon free energy and electronic entropy at finite temperatures add a nonnegligible contribution to the free energy of formation of the defects. Defect equilibria were conveniently cast in Kröger–Vink diagrams to facilitate realistic comparison with experiments. Consistent with experiments, our DFT-based results indicate the predominance of free electrons at low oxygen partial pressure (P[subscript O2]≤10[superscript −6] atm) and low temperature (T≤1500 K). In the same regime of P[subscript O2] but at higher temperatures, we discovered that the neutral oxygen vacancies (F-centers) predominate. The nature of the predominant defect at high oxygen partial pressure has been a long-standing controversy in the experimental literature. Our results revealed this range to be dominated by the doubly charged oxygen vacancies at low temperatures (T≤1500 K) and free electrons at high temperatures. T-ZrO[subscript 2] was found to be hypostoichiometric over all ranges of T and PO2, mainly because of the doubly charged oxygen vacancies, which are responsible for inducing n-type conductivity via a self-doping effect. A range of 1.3 eV in the band gap of T-ZrO[subscript 2] starting from the middle of the gap toward the conduction band is accessible to the chemical potential of electrons (Fermi level) by varying T and PO[subscript 2] without extrinsic doping. The approach presented here can be used to determine the thermodynamic conditions that extremize certain desirable or undesirable defects to attain the optimal catalytic and electronic performance of oxides. United States. Dept. of Energy (Contract DE-AC05-00OR22725) 2013-01-07T20:00:58Z 2013-01-07T20:00:58Z 2012-10 2012-07 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/75857 Youssef, Mostafa, and Bilge Yildiz. “Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects.” Physical Review B 86.14 (2012). © 2012 American Physical Society https://orcid.org/0000-0001-8966-4169 https://orcid.org/0000-0002-2688-5666 en_US http://dx.doi.org/10.1103/PhysRevB.86.144109 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Yildiz, Bilge Youssef, Mostafa Youssef Mahmoud Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects |
| title | Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects |
| title_full | Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects |
| title_fullStr | Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects |
| title_full_unstemmed | Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects |
| title_short | Intrinsic point-defect equilibria in tetragonal ZrO[subscript 2]: Density functional theory analysis with finite-temperature effects |
| title_sort | intrinsic point defect equilibria in tetragonal zro subscript 2 density functional theory analysis with finite temperature effects |
| url | http://hdl.handle.net/1721.1/75857 https://orcid.org/0000-0001-8966-4169 https://orcid.org/0000-0002-2688-5666 |
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