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Atomistic simulation of oxides of nuclear interest

Atomistic simulation of oxides of nuclear interest. Robert T É TOT Gaël SATTONNAY. Laboratoire d’Étude des Matériaux Hors Équilibre. Institut de Chimie Moléculaire et des matériaux d’Orsay. E2C 2013 27-31 October Budapest. Scope.

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Atomistic simulation of oxides of nuclear interest

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  1. Atomistic simulation of oxides of nuclear interest Robert TÉTOT Gaël SATTONNAY Laboratoire d’Étude des Matériaux Hors Équilibre Institut de Chimie Moléculaire et des matériaux d’Orsay LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France E2C 2013 27-31 October Budapest

  2. Scope • Iono-covalent oxides have applications in nuclear energy field • Nuclear fuel:UO2, PuO2 • Inert matrices for actinide immobilization or transmutation: ZrO2-c, MgO, pyrochlores A2B2O7,… •  Neutron absorber (Gd2O3, Eu2O3,…) • Materials under irradiation  The role of defects is prevailing on their performances  Experimental determination of defect properties is difficult  Atomic scale simulation is a powerful tool E2C 2013 27-31 October Budapest

  3. Modelling iono-covalent oxides at atomic scale  Calculations at the electronic structure level  High accuracy (but treatment of localized f-electrons is not straightforward (UO2, Gd2O3,…)  Huge computer time (several days, weeks)  Restricted system size (hundreds of atoms) Ab initio methods (DFT)  Very large system size (thousands or millions of atoms) with Monte Carlo and Molecular Dynamic  Short calculation time  Less detailed and accurate Empirical methods (interatomic potentials) • Purely ionic models generally used are not satisfactory: • no charge transfer between oxygen and cations • the iono-covalent character of the M-O bonding is not well described We have developed new interatomic potentials for iono-covalent oxides based on the so-called SMTB-Q model E2C 2013 27-31 October Budapest

  4. Alternating Lattice Model (1) • The covalent energy of the oxide is calculated by means of the Tight-Binding approach in the Second-Moment approximation (SMTB). The electronic structure is approximately but correctly described. Charge Equilibration formalism: QEq (2) • The cohesive energy is minimized with respect to the ionic charges which adapt themselses to their local environment (variable-charge). SMTB-Q: Second Moment Tight-Binding Variable-Charge model (*) (*) R. Tétot et al., EPL, 83 (2008), Surf. Sci. 605 (2011), Surf. Sci. 616 (2013) SMTB-Q is based on two main schemes: (1) J. Goniakowski, C. Noguera, Surf. Sci. 31 (1994) (2) A. K. Rappé, W. A. III Goddard, J. Phys. Chem. 95 (1991) + E2C 2013 27-31 October Budapest

  5. UO2: Bulk properties Oxygen Uranium Parameters of the model are fitted on bulk properties of UO2 Fluorite structure G. Sattonnay and R. Tétot J. Phys.: Condens Matt 25 (2013)  The SMTB-Q model well reproduces the experimental data E2C 2013 27-31 October Budapest

  6. UO2: defect formation energies • The structure is fully relaxed using a Monte Carlo algorithm EDF = E box with defect – E perfect box (2592 atoms) Schottky =1VU+2VO Formation energies are close to the experimental data and to the ab initio results, except for the cation Frenkel pair G. Sattonnay and R. Tétot, J. Phys.: Condens Matt 25 (2013) E2C 2013 27-31 October Budapest

  7. UO2: relaxation and charge transfer around a defect U interstitial O vacancy QU bulk = 2.8 QO bulk = -1.4 d(U-O) bulk =2.36 Å QU int < QU bulk d(U-VO) > d(U-O) bulk d(Ui-O) < d(U-O) bulk • charge of the U sublattice is mainly affected by the presence of defects whereas little change is observed for the O sublattice E2C 2013 27-31 October Budapest

  8. UO2: surfaces (1)Evarestov et al. Acta. Mater. 57 (2009) (2)Skomurski et al. Am. Miner. 91 (2006) G. Sattonnay and R. Tétot, J. Phys.: Condens Matt 25 (2013) E2C 2013 27-31 October Budapest

  9. B coordination: 6 O48f (C.N. = 6) A2B2O7 pyrochlores Aim:investigation of the role played by the defect stability (OFP, CFP, CAS) on the radiation tolerance of Gd2Ti2O7 and Gd2Zr2O7. Due to the large number of atoms by unit cell (88) and the presence of f electrons in Gd, ab initio calculations are very difficult to perform. (Gd) 1/8th of the pyrochlore cell (Ti,Zr) (Wyckoff) A coordination : 6 O48f+2 O8b (C.N. = 8) E2C 2013 27-31 October Budapest

  10. A2B2O7 pyrochlores: bulk properties Gd2Ti2O7 Gd2Zr2O7 *(Xiao et al, 2011) Ionicity of Gd2Zr2O7 > Gd2Ti2O7 E2C 2013 27-31 October Budapest

  11. Gd2B2O7 (B=Ti,Zr): cation antisite defect : Ti, Zr : Gd EfAS (Gd2Ti2O7) <EfAS (Gd2Zr2O7)? E2C 2013 27-31 October Budapest

  12. : Ti : Gd Gd2Ti2O7: cation antisite defect Gd2Zr2O7 EF=2.5 eV C.N. (Zr=8) EF=1.3 eV Before relaxation C.N. (Ti) = 8 EF=13eV After relaxation C.N. (Ti) = 5 EF= 0.8eV E2C 2013 27-31 October Budapest E2C 2013 27-31 October Budapest

  13. Gd2B2O7 pyrochlores: defects (summary) E2C 2013 27-31 October Budapest

  14. Gd2Ti2O7: amorphisation by CAS defects 100% AS PERFECT 10% AS 20% AS 50% AS Accumulation of CAS defects in Gd2Ti2O7 amorphization E2C 2013 27-31 October Budapest

  15. Summary and conclusions SMTB-Q is a semi empirical model which is capable of describing bulk, surfaces and defects of insulating oxides. Overall, the obtained results compare well with ab initio calculations (with anenormous gain of cpu time). Very good results are obtained fordefects in UO2 and pyrochlores. These defects play a major role in the behavior of these materials under irradiation. In Gd2Ti2O7, the formation of strong local distorsions around the Ti-antisite defect is associated to a reduction of the Ti coordination number (8→5, not observed for Zr in Gd2Zr2O7). This mechanism could play an important role in driving radiation-induced amorphization in Gd2Ti2O7 by point defect accumulation. The 5-fold coordination of Ti in the amorphous phase was confirmed by X-ray absorption spectroscopy in irradiated Y2Ti2O7 . 15

  16. Thank you very much for your attention 16 LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France

  17. X-ray absorption fine spectroscopy : Y2Ti2O7 irradiated with 92-MeV Xe X-ray absorption fine spectroscopy (XANES+EXAFS) has been performed on irradiated yttrium titanate pellets (SOLEIL synchrotron facility – MARS beamline) Coll. : D. Menut, J-L Béchade, M. Morales, B. Sitaud, D. Chateigner, L. Lutterotti, S. Cammelli Ti pre edge peak Ti K-edge amorphous pyrochlore Farges et al PRB 56 (1997) 1809

  18. Alternating Lattice Model (Goniakowski and Noguera, 1994) • The covalent energy of an oxide MnOm is calculated by means of a Tight-Binding approach in the Second-Moment approximation (SMTB) QEq: Charge Equilibration formalism (Rappé and Goddard, 1991) • Minimization of the cohesive energy with respect to the ionic charges SMTB-Q: A Tight-Binding Variable-Charge model N equations N variables Qi Equalization of chemical potentials (electronegativity) Electrical neutrality + E2C 2013 27-31 October Budapest LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 18

  19. SMTB-Q: the cohesive energy (ECoh) Ionization energy • are optimized to describe: • the lattice(s) parameter(s) • the cohesive energy • the bulk modulus (B) • the elastic constants (Cij) Coulomb energy Covalent energy Repulsive energy Coulomb interaction JAB(R) Hopping integral E2C 2013 27-31 October Budapest LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 19

  20. B AB NB (hopping integral) 0 EC EO No bonding • - Total density of states N(E) • Local DOS NA(E) et NC(E) • are calculated analytically Alternating Lattice Model (ALM): Band description must be valid • The outer atomic orbitals of oxygens (p), on the one hand, and of the cations, on the other hand, have the same energy (EOand EC respectively) crystal-field splitting is neglected. • Alternating nature of the lattice (ALM) electron transfer takes place only betweenoxygens and cations(rC) E2C 2013 27-31 October Budapest LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 20

  21. L AL NL 0 EC EO m = oxygen stoichiometry n0 : shared electronic states between C and O Covalent energy • Integral of NA(E) over VB yields the number of electrons on anions and the charge Q: • The covalent energy is obtained from the integral of EN(E) over VB E2C 2013 27-31 October Budapest LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 21

  22. Ionization energy (ex: TiO2) Ionization energy Coulomb energy Covalent energy 22 LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France

  23. Coulomb interactions JAB Ionization energy Covalent energy Coulomb energy 23 LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France

  24. Coulomb interactions JAB (ex: TiO2) • Ions are described by ns-type Slater orbitals:  • Strong screening of Coulomb forces at small distances: Rij < 4 Å • Classic Coulomb law (1/R) at larger distances 24 LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France

  25. M-O covalent energy: ECov(Qi) Ionization energy Coulomb energy Covalent energy 25 LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France

  26. SMTB-Q: surfaces of UO2 (111) (110) (100)A (1) Abramowski et al. J. Nucl. Mater. 275 (1999) 12 (2)Evarestov et al. Acta. Mater. 57 (2009) 600 (3) Skomurski et al. Am. Miner. 91 (2006) 1761 (100)B 26 E2C 2013 27-31 October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France

  27. Oxygen Uranium SMTB-Q: defects at UO2(111) UO2(111) 27 E2C 2013 27-31 October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France

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