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CECAM workshop on Actinides, Manchester, June 2010 1 DFT+U calculations of the electronic structure of perfect and defective PuO 2 Eugene Kotomin and Denis Gryaznov Laboratory of Theoretical Physics and Computer Modelling at the Institute of Solid State Physics, University of Latvia Riga, Latvia

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CECAM workshop on Actinides, Manchester, June 2010 2 Motivation Solid solution (U,Pu)O 2 (known as MOX) is nowadays widely used as a commercial nuclear fuel. This is why understanding of the basic physical and chemical properties of MOX and parent materials (UO 2 and PuO 2 ) including radiation-induced defects is of great importance. Accurate theoretical calculations of these 5f-electron materials is a challenge due to strong electron correlation effects.

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CECAM workshop on Actinides, Manchester, June 2010 3 PuO 2 first principles calculations L.Petit et al, Science 301, 498 (2003) SIC LSD method, including defects R.Martin et al, Phys Rev B 76, 033101 (2007): Gaussian code + Periodic Boundary Conditions, HSE (Heyd,Scuseria, Enzerhof) hybrid functionals Jomard et al, Phys Rev B 78, 075125 (2008) GGA+U (PBE functional), ABINIT code

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CECAM workshop on Actinides, Manchester, June 2010 4 Basic experimental data Cubic fluorite structure, a=5.396 A semiconductor, with a gap of 1.8 eV Pu shows no magnetic moment (?) 5f states dominate at the Fermi level – not reproduced in previous studies

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CECAM workshop on Actinides, Manchester, June 2010 5 UPS spectra T. Gouder et al, Surf Sci Lett. 601, L 77 (2007)

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CECAM workshop on Actinides, Manchester, June 2010 6 Present study Spin-polarized GGA+U VASP calculations PAW pseudopotentials, 78 e (Pu), 2e (O) in a core a comparison of Dudarev and Liechtenstein exchange-correlation functionals: rotationally invariant U eff = U – J vs independent U, J parameters Supercells 3, 6, 12 (conventional cell) and 24 atoms, FM and AFM magnetic solutions

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CECAM workshop on Actinides, Manchester, June 2010 7 24 atom supercell Pu O

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CECAM workshop on Actinides, Manchester, June 2010 8 DOS for FM PuO 2 Dudarev functional for a) the cubic structure and b) the tetragonal structure. Spin-up electrons are only shown and the J-exchange parameter fixed at 0.5 eV. The Fermi level is taken as zero

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CECAM workshop on Actinides, Manchester, June 2010 9 Dudarev E xc vs Liechtenstein: AFM structure AFM PuO 2 a) the Dudarev functional at U = 6.0 eV, J=0.5 eV, b) Liechtenstein functional for different J with fixed U = 3.0 eV. Spin-up electrons are only shown. The Fermi level is taken as zero.

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CECAM workshop on Actinides, Manchester, June 2010 10 Optimal parameters Liechtenstein functional, U=3 eV, J=1.5 eV a=5.51 A, c=5.41 A (AFM, tetragonal str.) DOS corresponds to UPS spectra The effective (Bader) charges: 2.48 e (Pu) -1.24 e (O) considerable covalency!

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CECAM workshop on Actinides, Manchester, June 2010 11 Hybrid (PBE0) calculations

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CECAM workshop on Actinides, Manchester, June 2010 12 Defects in PuO 2 Change of supercell volume due to Pu and O vacancies (Å**3). Positive sign means increase of volume, negative its decrease. The values correspond to the complete local structure and lattice parameter optimisation. Numbers in brackets show the defect concentration. Defect 12 atom cell 24 atom Pu vacancy -12.60 (25%) -14.43 (12.5%) O vacancy 4.58 (12.5%) Lattice constant variation 0.8 % (O) vs -2.6% (Pu) 0.9 % (SIC) -3.4% (SIC) (12% of defects)

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CECAM workshop on Actinides, Manchester, June 2010 13 Local lattice, charge perturbations Pu vacancy NN O ions displaced 1.1% charge -0.95e NNN Pu 0.0 2.56 e O vacancy NN Pu ions displaced 1.2 % charge 2.20 e NNN O 0.0 -1.25e Charge redistribution is very local, only NN

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CECAM workshop on Actinides, Manchester, June 2010 14 Defect formation energies, eV O vacancy GGA+U SIC O-rich 3.97 (3.60-24 at.) Pu-rich -1.08-- O interstitial O-rich 1.781.90 Pu-rich 6.836.70 Pu vacancy O-rich 3.07 9.0 Pu-rich 13.1818.5

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CECAM workshop on Actinides, Manchester, June 2010 15 Thermodynamic reference Pu-rich conditions correspond to the chemical potential for excess Pu μ(Pu) = - Ecoh(δ-Pu), μ(O)=½( - Ecoh(PuO2)- μ(Pu)); O-rich condition implies μ(O) = - ½Ecoh(O2) μ(Pu)= - Ecoh(PuO2)- 2μ(O). Defect formation energy definition: Ef = - Ecoh(PunOm) - n μ(Pu) – m μ(O).

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CECAM workshop on Actinides, Manchester, June 2010 16 Analysis Defect formation energy deacreases 10% as concentration increases from 12 to 25% Reasonable agreement of GGA+U and SIC, discrepancy is due to difference in the reference states-cohesive energies of pure Pu, PuO 2 and O 2 molecule.

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CECAM workshop on Actinides, Manchester, June 2010 17 CONCLUSIONS Only use of the Liechtenstein functional within GGA+U permits to reproduce the UPS spectra Defect calculations using GGA+U and SIC agree quite well Hybrid functionals in VASP and GAUSSIAN- PBC give similar results, but this does not help! Defect migration calculations is the next step in multi-scale study of nuclear fuel long-time performance (TRANSURANUS code)

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CECAM workshop on Actinides, Manchester, June 2010 18 Many thanks to L.Petit, A.Svane, M.Freyss, R.A.Evarestov for many stumulating discussions, as well as EC FP7 F-Bridge project for a financial support

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CECAM workshop on Actinides, Manchester, June 2010 19 Thank you for your attention!

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