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Density Functional Theory Calculations Applied to Nuclear Fuels

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Handbook of Materials Modeling

Abstract

The goal of nuclear fuel performance modeling is to assess the margin to failure, and it is used by researchers, industry, and regulators to develop fuel designs, optimize reactor operation, and evaluate accident scenarios. Accurate models of material properties and the evolution of material properties as a function time in the reactor (burnup) are critical for accomplishing predictive fuel performance simulations. Historically, these models were fitted to reactor test data and they were empirical in nature, which limited their application to the range of conditions covered by the available test data. By developing mechanistic models that resolve the microstructure, its evolution, and impact on properties, predictive simulations can be achieved. This requires a multi-scale modeling framework that at the atomistic scale uses density functional theory (DFT) calculations to determine model parameters governing, for example, point defect and fission gas thermodynamics and kinetics as well as thermal conductivity. This chapter reviews DFT methods applicable to these problems and exemplifies results for primarily UO2, which is the most common fuel in light water reactors. Additionally, advanced fuels such as U3Si2, metallic uranium, and UN are briefly discussed. Challenges, opportunities, and limitations as well as the role of DFT calculations in the multi-scale modeling framework are also covered.

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References

  • Andersson DA, Lezama J, Uberuaga BP, Conradson SD (2009) Cooperativity among defect sites in AO2+x and A4O9 (A=U,Np,Pu): density functional calculations. Phys Rev B 79:024110

    Article  ADS  Google Scholar 

  • Andersson DA, Uberuaga BP, Nerikar PV, Unal C, Stanek CR (2011) U and Xe transport in UO2±x: density functional theory calculations. Phys Rev B 84:054105

    Article  ADS  Google Scholar 

  • Andersson DA, Espinosa-Faller FJ, Uberuaga BP, Conradson SD (2012) Stability and migration of large oxygen clusters in UO2+x: density functional theory calculations. J Chem Phys 136:234702

    Article  ADS  Google Scholar 

  • Andersson DA, Baldinozzi G, Desgranges L, Conradson DR, Conradson SD (2013) Density functional theory calculations of UO2 oxidation: evolution of UO2+x, U4O9-y, U3O7, and U3O8. Inorg Chem 52:2769–2778

    Article  Google Scholar 

  • Andersson DA et al (2014) Atomistic modeling of intrinsic and radiation-enhanced fission gas (Xe) diffusion in UO2±x: implications for nuclear fuel performance modelling. J Nucl Mater 451:225–242

    Article  ADS  Google Scholar 

  • Andersson DA, Tonks MR, Casillas L, Vyas S, Nerikar P, Uberuaga BP, Stanek CR (2015) Multiscale simulation of xenon diffusion and grain boundary segregation in UO2. J Nucl Mater 462:15–25

    Article  ADS  Google Scholar 

  • Anisimov VI, Aryasetiawan F, Lichtenstein AI (1997) First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+U method. J Phys Condens Matter 9:767–808

    Article  ADS  Google Scholar 

  • Ball RGJ, Grimes RW (1990) Diffusion of Xe in UO2. Chem Soc Faraday Trans 86:1257–1261

    Article  Google Scholar 

  • Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–3100

    Article  ADS  Google Scholar 

  • Beeler B, Good B, Rashkeev S, Deo C, Baskes M, Okuniewski M (2010) First principles calculations for defects in U. J Phys: Cond Matter 22:505703

    Google Scholar 

  • Beeler B, Deo C, Baskes M, Okuniewski M (2013) First principles calculations of the structure and elastic constants of α, β and γ uranium. J Nucl Mater 433:143–151

    Article  ADS  Google Scholar 

  • Berna GA, Beyer CE, Davis KL, Lanning DD (1997) FRAPCON–3: a computer code for the calculation of steady-state, thermal-mechanical behavior of oxide fuel rods for high burnup. Technical report NUREG/CR-6534, vol 2, PNNL–11513

    Google Scholar 

  • Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979

    Article  ADS  Google Scholar 

  • Brincat NA, Molinari M, Parkera SC, Allen GC, Storr MT (2015) Computer simulation of defect clusters in UO2 and their dependence on composition. J Nucl Mater 456:329–333

    Article  ADS  Google Scholar 

  • Bruneval F, Varvenne C, Crocombette JP, Clouet E (2015) Pressure, relaxation volume, and elastic interactions in charged simulation cells. Phys Rev B 91:024107

    Article  ADS  Google Scholar 

  • Claisse A, Schuler T, Lopes DA, Olsson P (2016a) Transport properties in dilute UN(X) solid solutions (X=Xe,Kr). Phys Rev B 94:174302

    Article  ADS  Google Scholar 

  • Claisse A, Klipfel M, Lindbom N, Freyss M, Olsson P (2016b) GGA+U study of uranium mononitride: a comparison of the U-ramping and occupation matrix schemes and incorporation energies of fission products. J Nucl Mater 478:119–124

    Article  ADS  Google Scholar 

  • Cooper MWD, Murphy ST, Andersson DA (2018) The defect chemistry of UO2±x from atomistic simulations. J Nucl Mater 504:251–260. https://doi.org/10.1016/j.jnucmat.2018.02.034

    Article  ADS  Google Scholar 

  • Crocombette JP (2012) Influence of charge states on energies of point defects and clusters in uranium dioxide. Phys Rev B 85:144101

    Article  ADS  Google Scholar 

  • Desgranges L, Baldinozzi G, Rousseau G, Nièpce JC, Calvarin G (2009) Neutron diffraction study of the in situ oxidation of UO2. Inorg Chem 48:7585–7592

    Article  Google Scholar 

  • Desgranges L, Baldinozzi G, Siméone D, Fischer HE (2011) Refinement of the α-U4O9 crystalline structure: new insight into the U4O9 → U3O8 transformation. Inorg Chem 50:6146–6151

    Article  Google Scholar 

  • Devanathan R et al (2010) Modeling and simulation of nuclear fuel materials. Energy Environ Sci 3:1406–1426

    Article  Google Scholar 

  • Dorado B, Amadon B, Freyss M, Bertolus M (2009) DFT+U calculations of the ground state and metastable states of uranium dioxide. Phys Rev B 79:235125

    Article  ADS  Google Scholar 

  • Dorado B et al (2011) First-principles calculation and experimental study of oxygen diffusion in uranium dioxide. Phys Rev B 83:035126

    Article  ADS  Google Scholar 

  • Dorado B, Andersson DA, Stanek CR, Bertolus M, Uberuaga BP, Martin G, Freyss M, Garcia P (2012) First-principles calculations of uranium diffusion in uranium dioxide. Phys Rev B 86:035110

    Article  ADS  Google Scholar 

  • Dorado B, Garcia P (2013) First-principles DFT + U modeling of actinide-based alloys: application to paramagnetic phases of UO2 and (U,Pu) mixed oxides. Phys Rev B 87:195139

    Article  ADS  Google Scholar 

  • Dudarev SL, Nguyen Manh D, Sutton AP (1997) Effect of Mott-Hubbard correlations on the electronic structure and structural stability of uranium dioxide. Phil Mag B 75:613–628

    Article  ADS  Google Scholar 

  • Freysoldt C, Neugebauer J, Van de Walle CG (2009) Fully ab initio finite-size corrections for charged-defect supercell calculations. Phys Rev Lett 102:016402

    Article  ADS  Google Scholar 

  • Freysoldt C, Grabowski B, Hickel T, Neugebauer J, Kresse G, Janotti A, Van de Walle CG (2014) First-principles calculations for point defects in solids. Rev Mod Phys 86:253–305

    Article  ADS  Google Scholar 

  • Geng HY, Chen Y, Kaneta Y, Iwasawa M, Ohnuma T, Kinoshita M (2008) Point defects and clustering in uranium dioxide by LSDA+U calculations. Phys Rev B 77:104120

    Article  ADS  Google Scholar 

  • Georges A, Kotliar G, Krauth W, Rozenberg MJ (1996) Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev Mod Phys 68:13

    Article  ADS  MathSciNet  Google Scholar 

  • Gofryk K et al (2014) Anisotropic thermal conductivity in uranium dioxide. Nature Comm 5:4551

    Article  Google Scholar 

  • Govers K, Lemehov S, Verwerft M (2008) In-pile Xe diffusion coefficient in UO2 determined from the modeling of intragranular bubble growth and destruction under irradiation. J Nucl Mater 374:461–472

    Article  ADS  Google Scholar 

  • Goyal A, Phillpot SR, Subramanian G, Andersson DA, Stanek CR, Uberuaga BP (2015) Impact of homogeneous strain on uranium vacancy diffusion in uranium dioxide. Phys Rev B 91:094103

    Article  ADS  Google Scholar 

  • Grimes RW, Catlow CRA (1991) The stability of fission products in uranium dioxide. Philos Trans R Soc London Ser A 335:609–634

    Article  ADS  Google Scholar 

  • Guéneau C, Baichi M, Labroche D, Chatillon C, Sundman B (2002) Thermodynamic assessment of the uranium–oxygen system. J Nucl Mater 304:161–175

    Article  ADS  Google Scholar 

  • Hellman O, Abrikosov IA, Simak SI (2011) Lattice dynamics of anharmonic solids from first principles. Phys Rev B 84:180301(R)

    Google Scholar 

  • Henkelman G, Jónsson H (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113:9978–9985

    Article  ADS  Google Scholar 

  • Henkelman G, Uberuaga BP, Jónsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113:9901–9904

    Article  ADS  Google Scholar 

  • Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened coulomb potential. J Chem Phys 118:8207–8215

    Article  ADS  Google Scholar 

  • Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871

    Article  ADS  MathSciNet  Google Scholar 

  • Jones RO (2015) Density functional theory: its origins, rise to prominence, and future. Rev Mod Phys 87:897

    Article  ADS  MathSciNet  Google Scholar 

  • Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138

    Article  ADS  MathSciNet  Google Scholar 

  • Kresse G, Joubert J (1999) From ultrasoft pseudopotentials to the projector augmented wave method. Phys Rev B 59:1758–1775

    Article  ADS  Google Scholar 

  • Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186

    Article  ADS  Google Scholar 

  • Kudin KN, Scuseria GE, Martin RL (2002) Hybrid density-functional theory and the insulating gap of UO2. Phys Rev Lett 89:266402

    Article  ADS  Google Scholar 

  • Langreth DC, Perdew JP (1980) Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works. Phys Rev B 21:5469–5493

    Article  ADS  Google Scholar 

  • Langreth DC, Mehl MJ (1983) Beyond the local-density approximation in calculations of ground-state electronic properties. Phys Rev B 28:1809–1834

    Article  ADS  Google Scholar 

  • Lany S, Zunger A (2008) Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: case studies for ZnO and GaAs. Phys Rev B 78:235104

    Article  ADS  Google Scholar 

  • Laskowski R, Madsen GKH, Blaha P, Schwarz K (2004) Magnetic structure and electric-field gradients of uranium dioxide: an ab initio study. Phys Rev B 69:140408

    Article  ADS  Google Scholar 

  • Lassmann K (1980) The structure of fuel element codes. Nucl Eng Des 57:17–39

    Article  Google Scholar 

  • Lawrence GT (1978) A review of the diffusion coefficient of fission-product rare gases in uranium dioxide. J Nucl Mater 71:195–218

    Article  ADS  Google Scholar 

  • Liu XY, Uberuaga BP, Andersson DA, Stanek CR, Sickafus KE (2011) Mechanism for transient migration of xenon in UO2. Appl Phys Lett 98:51902

    Article  Google Scholar 

  • Ma PW, Woo CH, Dudarev SL (2008) Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron. Phys Rev B 78:024434

    Article  ADS  Google Scholar 

  • Ma PW, Dudarev SL (2014) Dynamic magnetocaloric effect in bcc iron and hcp gadolinium. Phys Rev B 90:024425

    Article  ADS  Google Scholar 

  • Mei ZG, Stan M, Pichler B (2013) First-principles study of structural, elastic, electronic, vibrational and thermodynamic properties of UN. J Nucl Mater 440:63–69

    Article  ADS  Google Scholar 

  • Meredig B, Thompson A, Hansen HA, Wolverton C, van de Walle A (2010) Method for locating low-energy solutions within DFT+U. Phys Rev B 82:195128

    Article  ADS  Google Scholar 

  • Miao Y, Gamble KA, Andersson D, Mei ZG, Yacout AM (2018) Rate theory scenarios study on fission gas behavior of U3Si2 under LOCA conditions in LWRs. Nucl Eng Design 326:371–382

    Article  Google Scholar 

  • Miao Y, Gamble KA, Andersson D, Ye B, Mei ZG, Hofman G, Yacout A (2017) Gaseous swelling of U3Si2 during steady-state LWR operation: a rate theory investigation. Nucl Eng Design 322:336–344

    Article  Google Scholar 

  • Middleburgh SC, Grimes RW, Lahoda EJ, Stanek CR, Andersson DA (2016) Non-stoichiometry in U3Si2. J Nucl Mater 482:300–305

    Article  ADS  Google Scholar 

  • Miekeley W, Felix FW (1972) Effect of stoichiometry on diffusion of xenon in UO2. J Nucl Mater 42:297–306

    Article  ADS  Google Scholar 

  • Mills G, Jónsson H, Schenter GK (1995) Reversible work transition state theory: application to dissociative adsorption of hydrogen. Surf Sci 324:305–337

    Article  ADS  Google Scholar 

  • Nerikar P, Watanabe T, Tulenko J, Phillpot S, Sinnott S (2009a) Energetics of intrinsic point defects in uranium dioxide from electronic-structure calculations. J Nucl Mater 384:61–69

    Article  ADS  Google Scholar 

  • Nerikar PV, Liu XY, Uberuaga BP, Stanek CR, Phillpot SR, Sinnott SB (2009b) Thermodynamics of fission products in UO2±x. J Phys Condens Matter 21:435602

    Article  Google Scholar 

  • Noordhoek MJ, Andersson D, Chernatynskiy A, Middleburgh S, Besmann TM (2016) Phase equilibria in the U-Si system from first-principles calculations. J Nucl Mater 479:216–223

    Article  ADS  Google Scholar 

  • Pang JWL, Buyers WJL, Chernatynskiy A, Lumsden MD, Larson BC, Phillpot SR (2013) Phonon lifetime investigation of Anharmonicity and thermal conductivity of UO2 by neutron scattering and theory. Phys Rev Lett 110:157401

    Article  ADS  Google Scholar 

  • Perdew JP (1985) Accurate density functional for the energy: real-space cutoff of the gradient expansion for the exchange hole. Phys Rev Lett 55:1665–1668

    Article  ADS  Google Scholar 

  • Perdew P, Wang Y (1986) Accurate and simple density functional for the electronic exchange energy: generalized gradient approximation. Phys Rev B 33:8800–8802

    Article  ADS  Google Scholar 

  • Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868

    Article  ADS  Google Scholar 

  • Rashid Y, Dunham R, Montgomery R (2004) Fuel analysis and licensing code: FALCON MOD01. Technical report EPRI 1011308, Electric Power Research Institute

    Google Scholar 

  • Rashid J, Yagnik S, Montgomery R (2011) Light water reactor fuel performance modeling and multi-dimensional simulation. JOM 63:81–88

    Article  Google Scholar 

  • Sanati M, Albers RC, Lookman T, Saxena A (2011) Elastic constants, phonon density of states, and thermal properties of UO2. Phys Rev B 84:014116

    Article  ADS  Google Scholar 

  • Souvatzis P, Eriksson O, Katsnelson MI, Rudin SP (2008) Entropy driven stabilization of energetically unstable crystal structures explained from first principles theory. Phys Rev Lett 100:095901

    Article  ADS  Google Scholar 

  • Söderlind P, Grabowski B, Yang L, Landa A, Björkman T, Souvatzis P, Eriksson O (2012) High-temperature phonon stabilization of γ-uranium from relativistic first-principles theory. Phys Rev B 85:060301(R)

    Google Scholar 

  • Taylor SE, Bruneval F (2011) Understanding and correcting the spurious interactions in charged supercells. Phys Rev B 84:075155

    Article  ADS  Google Scholar 

  • Thompson AE, Wolverton C (2011) First-principles study of noble gas impurities and defects in UO2. Phys Rev B 84:134111

    Article  ADS  Google Scholar 

  • Thompson AE, Wolverton C (2013) Pathway and energetics of xenon migration in uranium dioxide. Phys Rev B 87:104105

    Article  ADS  Google Scholar 

  • Tonks MR, Andersson D, Phillpot SR, Zhang Y, Williamson R, Stanek CR, Uberuaga B, Hayes SL (2017) Mechanistic materials modeling of nuclear fuel performance. Ann Nucl Energy 105:11–24

    Article  Google Scholar 

  • Turnbull JA, Friskney CA, Findlay JR, Johnson FA, Walter AJ (1982) The diffusion coefficients of gaseous and volatile species during the irradiation of uranium dioxide. J Nucl Mater 107:168–184

    Article  ADS  Google Scholar 

  • Vanderbilt D (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 41:7892–7895

    Article  ADS  Google Scholar 

  • Vathonne E, Wiktor J, Freyss M, Jomard G, Bertolus M (2014) DFT+U investigation of charged point defects and clusters in UO2. J Phys Condens Matter 26:325501

    Article  Google Scholar 

  • Vathonne E, Andersson DA, Freyss M, Perriot M, Cooper MWD, Stanek CR, Bertolus M (2017) Determination of krypton diffusion coefficients in uranium dioxide using atomic scale calculations. Inorg Chem 56:125

    Article  Google Scholar 

  • Wang BT, Zhang P, Lizarraga R, Marco ID, Eriksson O (2013) Phonon spectrum, thermodynamic properties, and pressure-temperature phase diagram of uranium dioxide. Phys Rev B 88:104107

    Article  ADS  Google Scholar 

  • Williamson RL, Hales JD, Novascone SR, Tonks MR, Gaston DR, Permann CJ, Andrs D, Martineau RC (2012) Multidimensional multiphysics simulation of nuclear fuel behavior. J Nucl Mater 423:149–163

    Article  ADS  Google Scholar 

  • Yin Q, Savrasov SY (2008) Origin of low thermal conductivity in nuclear fuels. Phys Rev Lett 100:225504

    Article  ADS  Google Scholar 

  • Yu J, Devanathan R, Weber WJ (2009) First-principles study of defects and phase transition in UO2. J Phys Condens Matter 21:435401

    Article  ADS  Google Scholar 

  • Yun Y, Kim H, Kim H, Park K (2008) Atomic diffusion mechanism of Xe in UO2. J Nucl Mater 378:40–44

    Article  ADS  Google Scholar 

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Acknowledgments

This work was supported in part by the US Department of Energy, Office of Nuclear Energy, and Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the US Department of Energy under Contract No. DE-AC52-06NA25396.

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Correspondence to David Andersson .

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Andersson, D. (2018). Density Functional Theory Calculations Applied to Nuclear Fuels. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_117-1

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