1 LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 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 E2C October Budapest

2  Iono-covalent oxides have applications in nuclear energy field  Nuclear fuel: UO 2, PuO 2  Inert matrices for actinide immobilization or transmutation: ZrO 2 -c, MgO, pyrochlores A 2 B 2 O 7,…  Neutron absorber (Gd 2 O 3, Eu 2 O 3,…)  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 Scope E2C 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 (UO 2, Gd 2 O 3,…)  Huge computer time (several days, weeks)  Restricted system size (hundreds of atoms) Ab initio methods (DFT) Empirical methods (interatomic potentials)  Very large system size (thousands or millions of atoms) with Monte Carlo and Molecular Dynamic  Short calculation time  Less detailed and accurate 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 E2C October Budapest We have developed new interatomic potentials for iono-covalent oxides based on the so-called SMTB-Q model

4 E2C October Budapest SMTB-Q: Second Moment Tight-Binding Variable-Charge model (*) + 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. (*) R. Tétot et al., EPL, 83 (2008), Surf. Sci. 605 (2011), Surf. Sci. 616 (2013)  The cohesive energy is minimized with respect to the ionic charges which adapt themselses to their local environment (variable-charge). Charge Equilibration formalism: QEq (2) 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)

5 UO 2 : Bulk properties PropertiesSMTB-QExp. a (Å)5.455 B m (GPa)209 E coh (eV)-22.3 C 11 (GPa) C 12 (GPa) C 44 (GPa) QOQO (ab initio) IONICITY (Pauling ionicity) Parameters of the model are fitted on bulk properties of UO 2 E2C October Budapest  The SMTB-Q model well reproduces the experimental data G. Sattonnay and R. Tétot J. Phys.: Condens Matt 25 (2013) Fluorite structure Oxygen Uranium

6 UO 2 : defect formation energies E2C October Budapest E D F = E box with defect – E perfect box (2592 atoms)  The structure is fully relaxed using a Monte Carlo algorithm MethodO-FPU-FP Schottky defect SMTB-Q DFT-GGA [Freyss 2005] DFT-GGA+U [Crocombette 2012] Exp. estimates [Matzke] Formation energies are close to the experimental data and to the ab initio results, except for the cation Frenkel pair Schottky =1V U +2V O G. Sattonnay and R. Tétot, J. Phys.: Condens Matt 25 (2013)

7 UO 2 : relaxation and charge transfer around a defect E2C October Budapest U interstitial d(U-V O ) > d(U-O) bulk Q U int < Q U bulk O vacancy d(U i -O) < d(U-O) bulk Q U bulk = 2.8 Q O bulk = -1.4 d(U-O) bulk =2.36 Å  charge of the U sublattice is mainly affected by the presence of defects whereas little change is observed for the O sublattice

8 E2C October Budapest E S (j.m -2 )SMTB-QAb initio (1)(2) (111) (110) (100) UO 2 : 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)

9 E2C October Budapest A 2 B 2 O 7 pyrochlores A coordination : 6 O 48f +2 O 8b (C.N. = 8)B coordination: 6 O 48f (C.N. = 6) 1/8 th of the pyrochlore cell (Gd) (Ti,Zr) Aim: investigation of the role played by the defect stability (OFP, CFP, CAS) on the radiation tolerance of Gd 2 Ti 2 O 7 and Gd 2 Zr 2 O 7. 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. (Wyckoff)

10 E2C October Budapest A 2 B 2 O 7 pyrochlores: bulk properties PropertiesSMTB-QExp a (Å) x 48f d Gd-O48f d Ti-O48f B m (GPa) E coh (eV) PropertiesSMTB-QExp a (Å) x 48f d Gd-O48f d Ti-O48f B m (GPa) E coh (eV) ATOM Charge SMTB-Q Bader charge Ab initio* Gd Ti O 48f O 8b ATOM Charge SMTB-Q Bader charge Ab initio* Gd Zr O 48f O 8b Gd 2 Ti 2 O 7 Gd 2 Zr 2 O 7 *(Xiao et al, 2011) Ionicity of Gd 2 Zr 2 O 7 > Gd 2 Ti 2 O 7

11 E2C October Budapest Gd 2 B 2 O 7 (B=Ti,Zr): cation antisite defect Gd 2 Ti 2 O 7 Method SMTB-Q (present work) DFT-GGA (Wang 2011) E F (eV) Gd 2 Zr 2 O 7 Method SMTB-Q (present work) DFT-GGA (Wang 2011) E F (eV) E f AS (Gd 2 Ti 2 O 7 ) < E f AS (Gd 2 Zr 2 O 7 ) ? : Gd : Ti, Zr

12 E2C October Budapest Gd 2 Ti 2 O 7 : cation antisite defect : Gd : Ti Before relaxation C.N. (Ti) = 8 E F =13eV After relaxation C.N. (Ti) = 5 E F = 0.8eV Gd 2 Zr 2 O 7 E F =2.5 eV C.N. (Zr=8) E F =1.3 eV E2C October Budapest

13 E2C October Budapest Gd 2 B 2 O 7 pyrochlores: defects (summary)

14 E2C October Budapest Gd 2 Ti 2 O 7 : amorphisation by CAS defects PERFECT 100% AS Accumulation of CAS defects in Gd 2 Ti 2 O 7  amorphization 10% AS 20% AS 50% AS

15 E2C 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 an enormous gain of cpu time). In Gd 2 Ti 2 O 7, 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 Gd 2 Zr 2 O 7 ). This mechanism could play an important role in driving radiation- induced amorphization in Gd 2 Ti 2 O 7 by point defect accumulation. The 5-fold coordination of Ti in the amorphous phase was confirmed by X-ray absorption spectroscopy in irradiated Y 2 Ti 2 O 7. Very good results are obtained for defects in UO 2 and pyrochlores. These defects play a major role in the behavior of these materials under irradiation.

16 E2C October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France 16 Thank you very much for your attention

17 X-ray absorption fine spectroscopy : Y 2 Ti 2 O 7 irradiated with 92-MeV Xe Farges et al PRB 56 (1997) 1809 Ti pre edge peak Ti K-edge amorphous pyrochlore 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

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

19 E2C October Budapest LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 19 Coulomb energy Ionization energy Covalent energy SMTB-Q: the cohesive energy (E Coh ) Repulsive energy Hopping integral are optimized to describe: -the lattice(s) parameter(s) -the cohesive energy -the bulk modulus (B) -the elastic constants (C ij ) Coulomb interaction J AB (R)

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

21 E2C October Budapest LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 21 Covalent energy  Integral of N A (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 m = oxygen stoichiometry n 0 : shared electronic states between C and O L AL NL EOEO 0 ECEC

22 E2C October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France 22 Ionization energy (ex: TiO 2 ) Coulomb energy Ionization energy Covalent energy

23 E2C October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France 23 Coulomb energy Ionization energy Covalent energy Coulomb interactions J AB

24 E2C October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France 24 Coulomb interactions J AB (ex: TiO 2 )   Ions are described by ns-type Slater orbitals:  Strong screening of Coulomb forces at small distances: R ij < 4 Å  Classic Coulomb law (1/R) at larger distances

25 E2C October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France 25 Coulomb energy Ionization energy Covalent energy M-O covalent energy: E Cov (Q i )

26 E2C October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France 26 E S (j.m -2 )SMTB-QEmpiricalAb initio (1) (2)(3) (111) (110) (100)A (100)B SMTB-Q: surfaces of UO 2 (111)(110) (100)A (100)B (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

27 E2C October Budapest LEMHE/ICMMO CNRS-Univ. Paris-Sud 11 Orsay-France 27 E F (eV)E F (eV)/at OxE F (eV) VO(1) VO(3) VO(4) VO(6) VO(bulk) VU VU(bulk) IO IO(bulk) SMTB-Q: defects at UO 2 (111) UO 2 (111) Oxygen Uranium