Motivation

CECAM workshop on Actinides, Manchester, June 2010

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DFT+U calculations of the electronic structure of perfect and defective PuO2

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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Motivation

• Solid solution (U,Pu)O2 (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 (UO2 and PuO2) 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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PuO2 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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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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UPS spectra T. Gouder et al, Surf Sci Lett. 601, L 77 (2007)


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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 Ueff= 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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24 atom supercell

Pu

O


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DOS for FM PuO2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

DO

S, s

tate

s/eV

Energy, eV

U = 0.0 eV U = 1.0 eV U = 6.0 eV

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 50

2

4

6

8

10

12

14

16

18

20

DO

S,

sta

tes

/eV

En ergy, eV

U = 0 .0 eV

U = 1 .0 eV U = 6 .0 eV

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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Dudarev Exc vs Liechtenstein:AFM structure

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 70

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4

6

8

10

12

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DO

S,

stat

es/

eV

Energy, eV

U = 6.0 eV U = 0.0 eV U = 1.0 eV

-6 -5 -4 -3 -2 -1 0 1 2 3 4 50

2

4

6

8

10

DO

S, s

tate

s/eV

Energy, eV

J = 1.5 eV J = 2.5 eV J = 2.0 eV J = 1.0 eV

AFM PuO2 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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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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Hybrid (PBE0) calculations

-10 -8 -6 -4 -2 0 2 4 6 8 10

-6

-4

-2

0

2

4

6D

OS

, arb

. uni

ts

Energy, eV

Pu 5f O 2p


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Defects in PuO2

• 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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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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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 1.78 1.90 Pu-rich 6.83 6.70Pu vacancy O-rich 3.07 9.0 Pu-rich 13.18 18.5


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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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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, PuO2 and O2 molecule.


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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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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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Thank you for your attention!

Motivation

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