Importance of elastic finite-size effects: Neutral defects in ionic compounds

Burr, P. A.; Cooper, M. W.  D.

doi:10.1103/PhysRevB.96.094107

Title: Importance of elastic finite-size effects: Neutral defects in ionic compounds

Journal Article · Fri Sep 15 00:00:00 EDT 2017 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.96.094107· OSTI ID:1396125

Burr, P. A. ^[1]; Cooper, M. W. D. ^[2]

Univ. of New South Wales, Sydney, NSW (Australia)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Small system sizes are a well known source of error in DFT calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite size effects have been well characterised, but self-interaction of charge neutral defects is often discounted or assumed to follow an asymptotic behaviour and thus easily corrected with linear elastic theory. Here we show that elastic effect are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequatly small supercells are used; moreover, the spurious self-interaction does not follow the behaviour predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground state structure of (charge neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768 and 1500 atoms), and careful analysis determines that elastic effects, not electrostatic, are responsible. The spurious self-interaction was also observed in non-oxide ionic compounds and irrespective of the computational method used, thereby resolving long standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects are a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g. hybrid functionals) or when modelling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studies oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells | greater than 96 atoms.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Nuclear Energy (NE); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-06NA25396; AC52- 06NA25396

OSTI ID:: 1396125

Alternate ID(s):: OSTI ID: 1390645

Report Number(s):: LA-UR-17-22161; PRBMDO; TRN: US1702843

Journal Information:: Physical Review B, Vol. 96, Issue 9; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 16 works

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References (83)

Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Point defect interactions in harmonic cubic lattices Hardy, J. R.; Bullough, R. Philosophical Magazine, Vol. 15, Issue 134 https://doi.org/10.1080/14786436708227696	journal	February 1967
Nonlocal theory of elastic interaction between point defects Gairola, B. K. D. Physica Status Solidi (b), Vol. 85, Issue 2 https://doi.org/10.1002/pssb.2220850221	journal	February 1978
Influence of charge states on energies of point defects and clusters in uranium dioxide Crocombette, Jean-Paul Physical Review B, Vol. 85, Issue 14 https://doi.org/10.1103/PhysRevB.85.144101	journal	April 2012
Superiority of DFT+U with non-linear core correction for open-shell binary rare-earth metal oxides: a case study of native point defects in cerium oxides Huang, Bolong Philosophical Magazine, Vol. 94, Issue 26 https://doi.org/10.1080/14786435.2014.933908	journal	August 2014
First-principles DFT $+ U$ modeling of actinide-based alloys: Application to paramagnetic phases of UO $_{2}$ and (U,Pu) mixed oxides Dorado, Boris; Garcia, Philippe Physical Review B, Vol. 87, Issue 19 https://doi.org/10.1103/PhysRevB.87.195139	journal	May 2013
Vacancies in SiC: Influence of Jahn-Teller distortions, spin effects, and crystal structure Zywietz, A.; Furthmüller, J.; Bechstedt, F. Physical Review B, Vol. 59, Issue 23 https://doi.org/10.1103/PhysRevB.59.15166	journal	June 1999
Vacancy–Vacancy Interaction Induced Oxygen Diffusivity Enhancement in Undoped Nonstoichiometric Ceria Yuan, Fenglin; Zhang, Yanwen; Weber, William J. The Journal of Physical Chemistry C, Vol. 119, Issue 23 https://doi.org/10.1021/acs.jpcc.5b01317	journal	May 2015
Modelling of oxygen vacancy aggregates in monoclinic HfO ₂ : can they contribute to conductive filament formation? Bradley, Samuel R.; Bersuker, Gennadi; Shluger, Alexander L. Journal of Physics: Condensed Matter, Vol. 27, Issue 41 https://doi.org/10.1088/0953-8984/27/41/415401	journal	September 2015
Ab initio study of solution energy and diffusion of caesium in uranium dioxide Gupta, F.; Pasturel, A.; Brillant, G. Journal of Nuclear Materials, Vol. 385, Issue 2 https://doi.org/10.1016/j.jnucmat.2008.12.009	journal	March 2009
Vacancy mediated cation migration in uranium dioxide: The influence of cluster configuration Cooper, M. W. D.; Middleburgh, S. C.; Grimes, R. W. Solid State Ionics, Vol. 266 https://doi.org/10.1016/j.ssi.2014.08.010	journal	November 2014
Convergence of supercell calculations for point defects in semiconductors: Vacancy in silicon Puska, M. J.; Pöykkö, S.; Pesola, M. Physical Review B, Vol. 58, Issue 3 https://doi.org/10.1103/PhysRevB.58.1318	journal	July 1998
Supercell size scaling of density functional theory formation energies of charged defects Hine, N. D. M.; Frensch, K.; Foulkes, W. M. C. Physical Review B, Vol. 79, Issue 2 https://doi.org/10.1103/PhysRevB.79.024112	journal	January 2009
Electrostatic interactions between charged defects in supercells Freysoldt, Christoph; Neugebauer, Jörg; Van de Walle, Chris G. physica status solidi (b), Vol. 248, Issue 5 https://doi.org/10.1002/pssb.201046289	journal	December 2010
Computational testing of trivalent dopants in CeO ₂ for improved high-κ dielectric behaviour Keating, Patrick R. L.; Scanlon, David O.; Watson, Graeme W. J. Mater. Chem. C, Vol. 1, Issue 6 https://doi.org/10.1039/C2TC00385F	journal	January 2013
Point defects and non-stoichiometry in thoria Murphy, S. T.; Cooper, M. W. D.; Grimes, R. W. Solid State Ionics, Vol. 267 https://doi.org/10.1016/j.ssi.2014.09.017	journal	December 2014
Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations Freysoldt, Christoph; Neugebauer, Jörg; Van de Walle, Chris G. Physical Review Letters, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevLett.102.016402	journal	January 2009
Connecting point defect parameters with bulk properties to describe diffusion in solids Chroneos, A. Applied Physics Reviews, Vol. 3, Issue 4 https://doi.org/10.1063/1.4968514	journal	December 2016
Melting behavior of (Th,U)O2 and (Th,Pu)O2 mixed oxides Ghosh, P. S.; Kuganathan, N.; Galvin, C. O. T. Journal of Nuclear Materials, Vol. 479 https://doi.org/10.1016/j.jnucmat.2016.06.037	journal	October 2016
From ultrasoft pseudopotentials to the projector augmented-wave method Kresse, G.; Joubert, D. Physical Review B, Vol. 59, Issue 3, p. 1758-1775 https://doi.org/10.1103/PhysRevB.59.1758	journal	January 1999
Boundaries determine the formation energies of lattice defects in two-dimensional buckled materials Jain, Sandeep K.; Juričić, Vladimir; Barkema, Gerard T. Physical Review B, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevB.94.020102	journal	July 2016
Fast Parallel Algorithms for Short-Range Molecular Dynamics Plimpton, Steve Journal of Computational Physics, Vol. 117, Issue 1 https://doi.org/10.1006/jcph.1995.1039	journal	March 1995
Periodic boundary conditions in ab initio calculations Makov, G.; Payne, M. C. Physical Review B, Vol. 51, Issue 7 https://doi.org/10.1103/PhysRevB.51.4014	journal	February 1995
Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y. Physical Review B, Vol. 57, Issue 3, p. 1505-1509 https://doi.org/10.1103/PhysRevB.57.1505	journal	January 1998
Anisotropic charge screening and supercell size convergence of defect formation energies Murphy, Samuel T.; Hine, Nicholas D. M. Physical Review B, Vol. 87, Issue 9 https://doi.org/10.1103/PhysRevB.87.094111	journal	March 2013
Understanding and correcting the spurious interactions in charged supercells Taylor, Samuel E.; Bruneval, Fabien Physical Review B, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevB.84.075155	journal	August 2011
Accurate prediction of defect properties in density functional supercell calculations Lany, Stephan; Zunger, Alex Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 8 https://doi.org/10.1088/0965-0393/17/8/084002	journal	November 2009
Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Physical Review B, Vol. 52, Issue 8 https://doi.org/10.1103/PhysRevB.52.R5467	journal	August 1995
First-principles DFT modeling of nuclear fuel materials Liu, X. -Y.; Andersson, D. A.; Uberuaga, B. P. Journal of Materials Science, Vol. 47, Issue 21 https://doi.org/10.1007/s10853-012-6471-6	journal	April 2012
Ab initio calculations of the energetics of the neutral Si vacancy defect Mercer, J. L.; Nelson, J. S.; Wright, A. F. Modelling and Simulation in Materials Science and Engineering, Vol. 6, Issue 1 https://doi.org/10.1088/0965-0393/6/1/001	journal	January 1998
Charge states of point defects in uranium oxide calculated with a local hybrid functional for correlated electrons Crocombette, Jean-Paul; Torumba, Doru; Chartier, Alain Physical Review B, Vol. 83, Issue 18 https://doi.org/10.1103/PhysRevB.83.184107	journal	May 2011
Conduction in polar crystals. I. Electrolytic conduction in solid salts Mott, N. F.; Littleton, M. J. Transactions of the Faraday Society, Vol. 34 https://doi.org/10.1039/tf9383400485	journal	January 1938
First-Principles Calculation of Point Defects in Uranium Dioxide Iwasawa, Misako; Chen, Ying; Kaneta, Yasunori MATERIALS TRANSACTIONS, Vol. 47, Issue 11 https://doi.org/10.2320/matertrans.47.2651	journal	January 2006
Calculation of strain effects on vacancy-mediated diffusion of impurities in fcc structures: General approach and application to ${Ni}_{1 - x} {Si}_{x}$ Garnier, Thomas; Li, Zebo; Nastar, Maylise Physical Review B, Vol. 90, Issue 18 https://doi.org/10.1103/PhysRevB.90.184301	journal	November 2014
Vacancy clustering in zirconium: An atomic-scale study Varvenne, Céline; Mackain, Olivier; Clouet, Emmanuel Acta Materialia, Vol. 78 https://doi.org/10.1016/j.actamat.2014.06.012	journal	October 2014
First-principles study of defects and phase transition in UO ₂ Yu, Jianguo; Devanathan, Ram; Weber, William J. Journal of Physics: Condensed Matter, Vol. 21, Issue 43 https://doi.org/10.1088/0953-8984/21/43/435401	journal	October 2009
Fission gas in thoria Kuganathan, Navaratnarajah; Ghosh, Partha S.; Galvin, Conor O. T. Journal of Nuclear Materials, Vol. 485 https://doi.org/10.1016/j.jnucmat.2016.12.011	journal	March 2017
Understanding Oxygen-Vacancy Migration in the Fluorite Oxide CeO ₂ : An Ab Initio Study of Impurity-Anion Migration Genreith-Schriever, Annalena R.; Hebbeker, Pascal; Hinterberg, Judith The Journal of Physical Chemistry C, Vol. 119, Issue 51 https://doi.org/10.1021/acs.jpcc.5b07813	journal	December 2015
From solid solution to cluster formation of Fe and Cr in α -Zr Burr, P. A.; Wenman, M. R.; Gault, B. Journal of Nuclear Materials, Vol. 467 https://doi.org/10.1016/j.jnucmat.2015.10.001	journal	December 2015
Light-element diffusion in Mg using first-principles calculations: Anisotropy and elastodiffusion Agarwal, Ravi; Trinkle, Dallas R. Physical Review B, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevB.94.054106	journal	August 2016
Modeling of $Ce O_{2}$ , ${Ce}_{2} O_{3}$ , and $Ce O_{2 - x}$ in the $LDA + U$ formalism Andersson, D. A.; Simak, S. I.; Johansson, B. Physical Review B, Vol. 75, Issue 3 https://doi.org/10.1103/PhysRevB.75.035109	journal	January 2007
Point defect modeling in materials: Coupling ab initio and elasticity approaches Varvenne, Céline; Bruneval, Fabien; Marinica, Mihai-Cosmin Physical Review B, Vol. 88, Issue 13 https://doi.org/10.1103/PhysRevB.88.134102	journal	October 2013
Method for locating low-energy solutions within $DFT + U$ Meredig, B.; Thompson, A.; Hansen, H. A. Physical Review B, Vol. 82, Issue 19 https://doi.org/10.1103/PhysRevB.82.195128	journal	November 2010
Temperature accelerated dynamics study of migration process of oxygen defects in UO2 Ichinomiya, Takashi; Uberuaga, Blas P.; Sickafus, Kurt E. Journal of Nuclear Materials, Vol. 384, Issue 3 https://doi.org/10.1016/j.jnucmat.2008.12.040	journal	February 2009
Structural phase transformation through defect cluster growth in Gd-doped ceria Li, Zhi-Peng; Mori, Toshiyuki; Ye, Fei Physical Review B, Vol. 84, Issue 18 https://doi.org/10.1103/PhysRevB.84.180201	journal	November 2011
First-principles study on defect chemistry and migration of oxide ions in ceria doped with rare-earth cations Nakayama, Masanobu; Martin, Manfred Physical Chemistry Chemical Physics, Vol. 11, Issue 17 https://doi.org/10.1039/b900162j	journal	January 2009
Chemical Strain and Point Defect Configurations in Reduced Ceria Wang, Bu; Xi, Xiaoning; Cormack, Alastair N. Chemistry of Materials, Vol. 26, Issue 12 https://doi.org/10.1021/cm500946s	journal	June 2014
The elastic dipole tensor for point defects in ionic crystals Gillan, M. J. Journal of Physics C: Solid State Physics, Vol. 17, Issue 9 https://doi.org/10.1088/0022-3719/17/9/006	journal	March 1984
Linking atomic and mesoscopic scales for the modelling of the transport properties of uranium dioxide under irradiation Bertolus, Marjorie; Freyss, Michel; Dorado, Boris Journal of Nuclear Materials, Vol. 462 https://doi.org/10.1016/j.jnucmat.2015.02.026	journal	July 2015
Occupation matrix control of d- and f-electron localisations using DFT + U Allen, Jeremy P.; Watson, Graeme W. Phys. Chem. Chem. Phys., Vol. 16, Issue 39 https://doi.org/10.1039/C4CP01083C	journal	January 2014
Association of defects in doped non-stoichiometric ceria from first principles Grieshammer, Steffen; Nakayama, Masanobu; Martin, Manfred Physical Chemistry Chemical Physics, Vol. 18, Issue 5 https://doi.org/10.1039/C5CP07537H	journal	January 2016
Lanthanum energetics in cubic ZrO2 and UO2 from DFT and DFT+U studies Liu, Xiang-Yang; Sickafus, Kurt E. Journal of Nuclear Materials, Vol. 414, Issue 2 https://doi.org/10.1016/j.jnucmat.2011.03.042	journal	July 2011
A combined DFT + U and Monte Carlo study on rare earth doped ceria Grieshammer, Steffen; Grope, Benjamin O. H.; Koettgen, Julius Physical Chemistry Chemical Physics, Vol. 16, Issue 21 https://doi.org/10.1039/c3cp54811b	journal	January 2014
Advances in first-principles modelling of point defects in UO ₂ : f electron correlations and the issue of local energy minima Dorado, B.; Freyss, M.; Amadon, B. Journal of Physics: Condensed Matter, Vol. 25, Issue 33 https://doi.org/10.1088/0953-8984/25/33/333201	journal	July 2013
A many-body potential approach to modelling the thermomechanical properties of actinide oxides Cooper, M. W. D.; Rushton, M. J. D.; Grimes, R. W. Journal of Physics: Condensed Matter, Vol. 26, Issue 10 https://doi.org/10.1088/0953-8984/26/10/105401	journal	February 2014
Kinetically evolving irradiation-induced point defect clusters in ${UO}_{2}$ by molecular dynamics simulation Aidhy, Dilpuneet S.; Millett, Paul C.; Desai, Tapan Physical Review B, Vol. 80, Issue 10 https://doi.org/10.1103/PhysRevB.80.104107	journal	September 2009
Impact of uniaxial strain and doping on oxygen diffusion in CeO2 Rushton, M. J. D.; Chroneos, A. Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06068	journal	August 2014
The energy and elastic dipole tensor of defects in ionic crystals calculated by the supercell method Leslie, M.; Gillan, N. J. Journal of Physics C: Solid State Physics, Vol. 18, Issue 5 https://doi.org/10.1088/0022-3719/18/5/005	journal	February 1985
First-principles calculation of the elastic dipole tensor of a point defect: Application to hydrogen in $α$ -zirconium Nazarov, R.; Majevadia, J. S.; Patel, M. Physical Review B, Vol. 94, Issue 24 https://doi.org/10.1103/PhysRevB.94.241112	journal	December 2016
Stability of oxygen point defects in ${UO}_{2}$ by first-principles $DFT + U$ calculations: Occupation matrix control and Jahn-Teller distortion Dorado, Boris; Jomard, Gérald; Freyss, Michel Physical Review B, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevB.82.035114	journal	July 2010
Comparison of interatomic potentials for UO2. Part I: Static calculations Govers, K.; Lemehov, S.; Hou, M. Journal of Nuclear Materials, Vol. 366, Issue 1-2 https://doi.org/10.1016/j.jnucmat.2006.12.070	journal	June 2007
On the ionicity of carbon in Be ₂ C. A theoretical investigation of its electronic structure Herzig, P.; Redinger, J. The Journal of Chemical Physics, Vol. 82, Issue 1 https://doi.org/10.1063/1.448755	journal	January 1985
First-principles study of noble gas impurities and defects in UO $_{2}$ Thompson, Alexander E.; Wolverton, C. Physical Review B, Vol. 84, Issue 13 https://doi.org/10.1103/PhysRevB.84.134111	journal	October 2011
First-principles calculations for point defects in solids Freysoldt, Christoph; Grabowski, Blazej; Hickel, Tilmann Reviews of Modern Physics, Vol. 86, Issue 1 https://doi.org/10.1103/RevModPhys.86.253	journal	March 2014
Defect cluster formation in M2O3-doped cubic ZrO2 Zacate, M. Solid State Ionics, Vol. 128, Issue 1-4 https://doi.org/10.1016/S0167-2738(99)00348-3	journal	February 2000
Analysis of Intrinsic Defects in CeO ₂ Using a Koopmans-Like GGA+ U Approach Keating, Patrick R. L.; Scanlon, David O.; Morgan, Benjamin J. The Journal of Physical Chemistry C, Vol. 116, Issue 3 https://doi.org/10.1021/jp2080034	journal	November 2011
Orbital Ordering, Jahn-Teller Distortion, and Anomalous X-Ray Scattering in Manganates Elfimov, I. S.; Anisimov, V. I.; Sawatzky, G. A. Physical Review Letters, Vol. 82, Issue 21 https://doi.org/10.1103/PhysRevLett.82.4264	journal	May 1999
Development of Xe and Kr empirical potentials for CeO ₂ , ThO ₂ , UO ₂ and PuO ₂ , combining DFT with high temperature MD Cooper, M. W. D.; Kuganathan, N.; Burr, P. A. Journal of Physics: Condensed Matter, Vol. 28, Issue 40 https://doi.org/10.1088/0953-8984/28/40/405401	journal	August 2016
Stability of polyatomic molecules in degenerate electronic states - I—Orbital degeneracy Jahn, H. A.; Teller, E. Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 161, Issue 905, p. 220-235 https://doi.org/10.1098/rspa.1937.0142	journal	July 1937
Systematic Analysis of Core Photoemission Spectra for Actinide Di-Oxides and Rare-Earth Sesqui-Oxides Kotani, Akio; Yamazaki, Takao Progress of Theoretical Physics Supplement, Vol. 108 https://doi.org/10.1143/PTPS.108.117	journal	January 1992
DFT + U investigation of charged point defects and clusters in UO ₂ Vathonne, Emerson; Wiktor, Julia; Freyss, Michel Journal of Physics: Condensed Matter, Vol. 26, Issue 32 https://doi.org/10.1088/0953-8984/26/32/325501	journal	July 2014
Electrostatics-based finite-size corrections for first-principles point defect calculations Kumagai, Yu; Oba, Fumiyasu Physical Review B, Vol. 89, Issue 19 https://doi.org/10.1103/PhysRevB.89.195205	journal	May 2014
The elastic interaction of point defects Eshelby, J. D. Acta Metallurgica, Vol. 3, Issue 5 https://doi.org/10.1016/0001-6160(55)90140-1	journal	September 1955
The elastic strengths of point defects Hardy, J. R. Journal of Physics and Chemistry of Solids, Vol. 29, Issue 11 https://doi.org/10.1016/0022-3697(68)90051-6	journal	November 1968
Experimental electronic structure of ${Be}_{2} C$ Tzeng, C. -T.; Tsuei, K. -D.; Lo, W. -S. Physical Review B, Vol. 58, Issue 11 https://doi.org/10.1103/PhysRevB.58.6837	journal	September 1998
Ab initio analysis of the defect structure of ceria Zacherle, T.; Schriever, A.; De Souza, R. A. Physical Review B, Vol. 87, Issue 13 https://doi.org/10.1103/PhysRevB.87.134104	journal	April 2013
Trapping and diffusion of fission products in ThO2 and CeO2 Xiao, H. Y.; Zhang, Y.; Weber, W. J. Journal of Nuclear Materials, Vol. 414, Issue 3 https://doi.org/10.1016/j.jnucmat.2011.05.037	journal	July 2011
What Is the Actual Local Crystalline Structure of Uranium Dioxide, UO ₂ ? A New Perspective for the Most Used Nuclear Fuel Desgranges, L.; Ma, Y.; Garcia, Ph. Inorganic Chemistry, Vol. 56, Issue 1 https://doi.org/10.1021/acs.inorgchem.6b02111	journal	December 2016
First-principles calculation of intrinsic defect formation volumes in silicon Centoni, Scott A.; Sadigh, Babak; Gilmer, George H. Physical Review B, Vol. 72, Issue 19 https://doi.org/10.1103/PhysRevB.72.195206	journal	November 2005
Ordering of oxygen vacancies and excess charge localization in bulk ceria: A $DFT + U$ study Murgida, G. E.; Ferrari, V.; Ganduglia-Pirovano, M. Verónica Physical Review B, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevB.90.115120	journal	September 2014
First-principles study of noble gas stability in ThO 2 Shao, Kuan; Han, Han; Zhang, Wei Journal of Nuclear Materials, Vol. 490 https://doi.org/10.1016/j.jnucmat.2017.04.031	journal	July 2017
First-order phase transition in ${UO}_{2} :$ $^{235} U$ and $^{17} O$ NMR study Ikushima, K.; Tsutsui, S.; Haga, Y. Physical Review B, Vol. 63, Issue 10 https://doi.org/10.1103/PhysRevB.63.104404	journal	February 2001
Probing oxygen vacancy concentration and homogeneity in solid-oxide fuel-cell cathode materials on the subunit-cell level Kim, Young-Min; He, Jun; Biegalski, Michael D. Nature Materials, Vol. 11, Issue 10 https://doi.org/10.1038/nmat3393	journal	August 2012

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