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Title: The Conundrum of Relaxation Volumes in First-Principles Calculations of Charged Defects in UO2

Abstract

The defect relaxation volumes obtained from density-functional theory (DFT) calculations of charged vacancies and interstitials are much larger than their neutral counterparts, seemingly unphysically large. We focus on UO2 as our primary material of interest, but also consider Si and GaAs to reveal the generality of our results. In this work, we investigate the possible reasons for this and revisit the methods that address the calculation of charged defects in periodic DFT. We probe the dependence of the proposed energy corrections to charged defect formation energies on relaxation volumes and find that corrections such as potential alignment remain ambiguous with regards to its contribution to the charged defect relaxation volume. We also investigate the volume for the net neutral defect reactions comprising individual charged defects, and find that the aggregate formation volumes have reasonable magnitudes. This work highlights the issue that, as is well-known for defect formation energies, the defect formation volumes depend on the choice of reservoir. We show that considering the change in volume of the electron reservoir in the formation reaction of the charged defects, analogous to how volumes of atoms are accounted for in defect formation volumes, can renormalize the formation volumes of charged defects suchmore » that they are comparable to neutral defects. This approach enables the description of the elastic properties of isolated charged defects within an overall neutral material.« less

Authors:
; ; ; ; ; ORCiD logo; ; ;
Publication Date:
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1577208
Grant/Contract Number:  
10-2258; Nuclear Energy Advanced Modeling and Simulations
Resource Type:
Published Article
Journal Name:
Applied Sciences
Additional Journal Information:
Journal Name: Applied Sciences Journal Volume: 9 Journal Issue: 24; Journal ID: ISSN 2076-3417
Publisher:
MDPI AG
Country of Publication:
Switzerland
Language:
English

Citation Formats

Goyal, Anuj, Mathew, Kiran, Hennig, Richard G., Chernatynskiy, Aleksandr, Stanek, Christopher R., Murphy, Samuel T., Andersson, David A., Phillpot, Simon R., and Uberuaga, Blas P. The Conundrum of Relaxation Volumes in First-Principles Calculations of Charged Defects in UO2. Switzerland: N. p., 2019. Web. doi:10.3390/app9245276.
Goyal, Anuj, Mathew, Kiran, Hennig, Richard G., Chernatynskiy, Aleksandr, Stanek, Christopher R., Murphy, Samuel T., Andersson, David A., Phillpot, Simon R., & Uberuaga, Blas P. The Conundrum of Relaxation Volumes in First-Principles Calculations of Charged Defects in UO2. Switzerland. doi:10.3390/app9245276.
Goyal, Anuj, Mathew, Kiran, Hennig, Richard G., Chernatynskiy, Aleksandr, Stanek, Christopher R., Murphy, Samuel T., Andersson, David A., Phillpot, Simon R., and Uberuaga, Blas P. Wed . "The Conundrum of Relaxation Volumes in First-Principles Calculations of Charged Defects in UO2". Switzerland. doi:10.3390/app9245276.
@article{osti_1577208,
title = {The Conundrum of Relaxation Volumes in First-Principles Calculations of Charged Defects in UO2},
author = {Goyal, Anuj and Mathew, Kiran and Hennig, Richard G. and Chernatynskiy, Aleksandr and Stanek, Christopher R. and Murphy, Samuel T. and Andersson, David A. and Phillpot, Simon R. and Uberuaga, Blas P.},
abstractNote = {The defect relaxation volumes obtained from density-functional theory (DFT) calculations of charged vacancies and interstitials are much larger than their neutral counterparts, seemingly unphysically large. We focus on UO2 as our primary material of interest, but also consider Si and GaAs to reveal the generality of our results. In this work, we investigate the possible reasons for this and revisit the methods that address the calculation of charged defects in periodic DFT. We probe the dependence of the proposed energy corrections to charged defect formation energies on relaxation volumes and find that corrections such as potential alignment remain ambiguous with regards to its contribution to the charged defect relaxation volume. We also investigate the volume for the net neutral defect reactions comprising individual charged defects, and find that the aggregate formation volumes have reasonable magnitudes. This work highlights the issue that, as is well-known for defect formation energies, the defect formation volumes depend on the choice of reservoir. We show that considering the change in volume of the electron reservoir in the formation reaction of the charged defects, analogous to how volumes of atoms are accounted for in defect formation volumes, can renormalize the formation volumes of charged defects such that they are comparable to neutral defects. This approach enables the description of the elastic properties of isolated charged defects within an overall neutral material.},
doi = {10.3390/app9245276},
journal = {Applied Sciences},
number = 24,
volume = 9,
place = {Switzerland},
year = {2019},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.3390/app9245276

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Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Entropies of defect formation in ceria from first principles
journal, January 2013

  • Grieshammer, Steffen; Zacherle, Tobias; Martin, Manfred
  • Physical Chemistry Chemical Physics, Vol. 15, Issue 38
  • DOI: 10.1039/c3cp51913a

Crystal Structure Variations in Alpha Uranium at Low Temperatures
journal, January 1963


Segregation of ruthenium to edge dislocations in uranium dioxide
journal, October 2013


Projector augmented-wave method
journal, December 1994


Ab initio formation volume of charged defects
journal, October 2012


The crystal structure of arsenic at 4.2, 78 and 299°K
journal, May 1969


Energetics of intrinsic point defects in uranium dioxide from electronic-structure calculations
journal, January 2009


Electrostatic interactions between charged defects in supercells
journal, December 2010

  • Freysoldt, Christoph; Neugebauer, Jörg; Van de Walle, Chris G.
  • physica status solidi (b), Vol. 248, Issue 5
  • DOI: 10.1002/pssb.201046289

Activation Volume Tensor for Oxygen-Vacancy Migration in Strained CeO 2 Electrolytes
journal, May 2013


Dislocation interaction with C in α-Fe: A comparison between atomic simulations and elasticity theory
journal, August 2008


Elastic effects of vacancies in strontium titanate: Short- and long-range strain fields, elastic dipole tensors, and chemical strain
journal, August 2009


Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations
journal, January 2009


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Crystal structure of gallium metal
journal, February 1968


Periodic boundary conditions in ab initio calculations
journal, February 1995


Trapping, self-trapping and the polaron family
journal, May 2007


Anisotropic charge screening and supercell size convergence of defect formation energies
journal, March 2013


Understanding and correcting the spurious interactions in charged supercells
journal, August 2011


Pressure, relaxation volume, and elastic interactions in charged simulation cells
journal, January 2015


Impact of homogeneous strain on uranium vacancy diffusion in uranium dioxide
journal, March 2015


Formation entropies of intrinsic point defects in cubic In2O3 from first-principles density functional theory calculations
journal, January 2009

  • Ágoston, Péter; Albe, Karsten
  • Physical Chemistry Chemical Physics, Vol. 11, Issue 17
  • DOI: 10.1039/b900280d

Accurate prediction of defect properties in density functional supercell calculations
journal, November 2009


Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators
journal, August 1995


A fast and robust algorithm for Bader decomposition of charge density
journal, June 2006


Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs
journal, December 2008


First-principles calculation of mechanical properties of Si⟨001⟩ nanowires and comparison to nanomechanical theory
journal, May 2007


Ab initiomolecular dynamics for liquid metals
journal, January 1993


Density Functional Theory Calculations of UO 2 Oxidation: Evolution of UO 2+ x , U 4 O 9– y , U 3 O 7 , and U 3 O 8
journal, February 2013

  • Andersson, D. A.; Baldinozzi, G.; Desgranges, L.
  • Inorganic Chemistry, Vol. 52, Issue 5
  • DOI: 10.1021/ic400118p

Lattice Compression from Conduction Electrons in Heavily Doped Si:As
journal, October 1988


Size and shape of oxygen vacancies and protons in acceptor-doped barium zirconate
journal, July 2015


First-principles calculation and experimental study of oxygen diffusion in uranium dioxide
journal, January 2011


Lattice constant in nonstoichiometric uranium dioxide from first principles
journal, February 2018


The elastic dipole tensor for point defects in ionic crystals
journal, March 1984


Elastic effects on relaxation volume tensor calculations
journal, May 2008


The continuum elastic and atomistic viewpoints on the formation volume and strain energy of a point defect
journal, September 2006

  • Garikipati, K.; Falk, M.; Bouville, M.
  • Journal of the Mechanics and Physics of Solids, Vol. 54, Issue 9
  • DOI: 10.1016/j.jmps.2006.02.007

The volume of formation of Schottky defects in ionic crystals
journal, February 1981


Charged point defects in semiconductors
journal, December 2006

  • Seebauer, Edmund G.; Kratzer, Meredith C.
  • Materials Science and Engineering: R: Reports, Vol. 55, Issue 3-6
  • DOI: 10.1016/j.mser.2006.01.002

Atomistic modeling of intrinsic and radiation-enhanced fission gas (Xe) diffusion in <mml:math altimg="si236.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">UO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>±</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>: Implications for nuclear fuel performance modeling
journal, August 2014


A mechanism for the UO2 to α-U3O8 phase transformation
journal, June 1995


Advances in first-principles modelling of point defects in UO 2 : f electron correlations and the issue of local energy minima
journal, July 2013


Effects of doping on the lattice parameter of SrTiO 3
journal, June 2012

  • Janotti, Anderson; Jalan, Bharat; Stemmer, Susanne
  • Applied Physics Letters, Vol. 100, Issue 26
  • DOI: 10.1063/1.4730998

Densification behaviour of UO2 in six different atmospheres
journal, October 2002


First-principles calculation of the elastic dipole tensor of a point defect: Application to hydrogen in α -zirconium
journal, December 2016


The energy and elastic dipole tensor of defects in ionic crystals calculated by the supercell method
journal, February 1985


Stability of oxygen point defects in UO 2 by first-principles DFT + U calculations: Occupation matrix control and Jahn-Teller distortion
journal, July 2010


Neutron Diffraction Study of the in Situ Oxidation of UO 2
journal, August 2009

  • Desgranges, Lionel; Baldinozzi, Gianguido; Rousseau, Gurvan
  • Inorganic Chemistry, Vol. 48, Issue 16
  • DOI: 10.1021/ic9000889

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


Ab initio calculation of the macroscopic dielectric constant in silicon
journal, May 1986


The volume of formation of defects in ionic crystals
journal, February 1981


First-principles calculations for point defects in solids
journal, March 2014

  • Freysoldt, Christoph; Grabowski, Blazej; Hickel, Tilmann
  • Reviews of Modern Physics, Vol. 86, Issue 1
  • DOI: 10.1103/RevModPhys.86.253

Linear optical properties in the projector-augmented wave methodology
journal, January 2006


First-principles calculations of uranium diffusion in uranium dioxide
journal, July 2012


Electrostatics-based finite-size corrections for first-principles point defect calculations
journal, May 2014


Elastic constants, phonon density of states, and thermal properties of UO 2
journal, July 2011


Finite-size supercell correction schemes for charged defect calculations
journal, July 2012


Low‐Temperature Elastic Constants of Gallium Arsenide
journal, February 1962

  • Garland, C. W.; Park, K. C.
  • Journal of Applied Physics, Vol. 33, Issue 2
  • DOI: 10.1063/1.1702519

First-principles calculation of intrinsic defect formation volumes in silicon
journal, November 2005


First principles methods using CASTEP
journal, January 2005

  • Clark, Stewart J.; Segall, Matthew D.; Pickard, Chris J.
  • Zeitschrift für Kristallographie - Crystalline Materials, Vol. 220, Issue 5/6
  • DOI: 10.1524/zkri.220.5.567.65075

Effects of impurities on the lattice parameters of GaN
journal, October 2003


First-principles study of intrinsic point defects in ZnO: Role of band structure, volume relaxation, and finite-size effects
journal, May 2006


U and Xe transport in UO 2 ± x : Density functional theory calculations
journal, August 2011


The dielectric constant of UO2 below the Ne´el point
journal, June 1987


Plane-wave pseudopotential study of point defects in uranium dioxide
journal, August 2001


Effect of charge on point defect size misfits from ab initio: Aliovalently doped SrTiO 3
journal, June 2016