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

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

Atomistic simulation of oxides of nuclear interest

Robert TÉTOTGaël SATTONNAY

Laboratoire d’Étude des Matériaux Hors Équilibre

Institut de Chimie Moléculaireet des matériaux d’Orsay

E2C 2013 27-31 October Budapest

2

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

Scope


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)

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


We have developed new interatomic potentials for iono-covalent oxides based on the so-called SMTB-Q model

4E2C 2013 27-31 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

UO2: Bulk properties

Properties SMTB-Q Exp.

a (Å) 5.455 5.455

Bm (GPa) 209 209

Ecoh (eV) -22.3 -22.3

C11 (GPa) 389 389.3

C12 (GPa) 118 118.7

C44 (GPa) 59 59.7

QO -1.40 -1.40

(ab initio)

IONICITY 0.64 0.67

(Pauling ionicity)

Parameters of the model are fitted on bulk properties of UO2


The SMTB-Q model well reproduces the experimental data

G. Sattonnay and R. TétotJ. Phys.: Condens Matt 25 (2013)

Fluorite structure

Oxygen

Uranium

6

UO2: defect formation energies


EDF = E box with defect – E perfect box (2592 atoms)

The structure is fully relaxed using a Monte Carlo algorithm

Method O-FP U-FPSchottky

defectSMTB-Q 4.4 6.1 6.1

DFT-GGA [Freyss 2005]

3.6 11.8 5.6

DFT-GGA+U [Crocombette 2012]

4.2 6.4

Exp. estimates [Matzke]

3.0-4.6 6.0-7.0

Formation energies are close to the experimental data and to the ab initio results, except for the cation Frenkel

pair

Schottky =1VU+2VO

G. Sattonnay and R. Tétot, J. Phys.: Condens Matt 25 (2013)

7

UO2: relaxation and charge transfer around a defect


U interstitial

d(U-VO) > d(U-O) bulk

QU int < QU

bulk

O vacancy

d(Ui-O) < d(U-O) bulk

QU bulk = 2.8

QO 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


ES (j.m-2) SMTB-Q Ab initio

(1) (2)

(111)

(110)

(100)

1.08

1.75

1.92

0.94 0.461

0.846

1.194

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)


A2B2O7 pyrochlores

A coordination : 6 O48f+2 O8b (C.N. = 8) B coordination: 6 O48f (C.N. = 6)

1/8th of the pyrochlore

cell

(Gd)

(Ti,Zr)

Aim: investigation of the role playedby the defect stability (OFP, CFP, CAS)on the radiation tolerance of Gd2Ti2O7

and Gd2Zr2O7. Due to the large number of atoms byunit cell (88) and the presence of f electrons in Gd, ab initio calculations are very difficult to perform.

(Wyckoff)


A2B2O7 pyrochlores: bulk properties

Properties SMTB-Q Exp

a (Å) 10.185 10.185

x48f 0.3262 0.3263

dGd-O48f 2.525 2.524

dTi-O48f 1.961 1.961

Bm (GPa) 182 186

Ecoh (eV) -78 -75

Properties SMTB-Q Exp

a (Å) 10.536 10.535

x48f 0.347 0.343

dGd-O48f 2.461 2.462

dTi-O48f 2.126 2.125

Bm (GPa) 151 156

Ecoh (eV) -79 -81

ATOM Charge

SMTB-Q

Bader charge

Ab initio*

Gd 2.13 2.05

Ti 2.02 2.25

O48f -1.18 -1.23

O8b -1.23 -1.23

ATOM Charge

SMTB-Q

Bader charge

Ab initio*

Gd 2.37 2.08

Zr 2.11 2.56

O48f -1.30 -1.33

O8b -1.18 -1.33

Gd2Ti2O7 Gd2Zr2O7

*(Xiao et al, 2011)

Ionicity of Gd2Zr2O7 > Gd2Ti2O7


Gd2B2O7 (B=Ti,Zr): cation antisite defect

Gd2Ti2O7

MethodSMTB-Q

(present work)

DFT-GGA(Wang 2011)

EF (eV) 0.8 1.38

Gd2Zr2O7

MethodSMTB-Q

(present work)

DFT-GGA(Wang 2011)

EF (eV) 1.30 1.7

Ef AS (Gd2Ti2O7) < Ef AS (Gd2Zr2O7)?

: Gd : Ti, Zr


Gd2Ti2O7: cation antisite defect

: Gd : Ti

Before relaxation C.N. (Ti) = 8 EF=13eV

After relaxationC.N. (Ti) = 5 EF= 0.8eV

Gd2Zr2O

7

EF=2.5 eV

C.N. (Zr=8)EF=1.3 eV



Gd2B2O7 pyrochlores: defects (summary)

O-FP AS AS+O-FP Gd-PF B-PF

0

5

10

15

20

25 Gd

2Zr

2O

7 unrelaxed

Gd2Ti

2O

7 unrelaxed

Gd2Zr

2O

7 relaxed

Gd2Ti

2O

7 relaxed

spontaneous recomb.

DE

FE

CT

FO

RM

AT

ION

EN

RE

GY

(eV

)

DEFECT TYPE


Gd2Ti2O7: amorphisation by CAS defects

0 2 4 6 8 10

0

2

4

6

8

g(r)

r(Angstr.)

Gd-O

0 2 4 6 8 10-2

0

2

4

6

8

10

12

14

g(r)

r(Angstr.)

Ti-O

0 2 4 6 8 10

0

1

2

3

4

g(r)

r(Angstr.)

O-O

0 2 4 6 8 10

0

2

4

6

8

O-O

g(r)

r(Angstr.)

0 2 4 6 8 100

2

4

6

8

10

12

14

16

Gd-O

g(r)

r(Angstr.)

0 2 4 6 8 10

0

2

4

6

8

10

12

14

16

18

20

22

24

26

Ti-O

g(r)

r(Angstr.)

0 2 4 6 8 10

0

2

4

6

8

10

12

14

16

18

20

22

24

26

Ti-O

g(r)

r(Angstr.)

0 2 4 6 8 10

0

2

4

6

8

10

12

14

16

18

20

22

24

26

Ti-O

g(r)

r(Angstr.)

0 2 4 6 8 10

0

2

4

6

8

10

12

14

16

18

20

22

24

26

Ti-Og(

r)

r(Angstr.)

PERFECT 100% AS

Accumulation of CAS defects in Gd2Ti2O7 amorphization

10% AS

20% AS

50% AS

15E2C 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 an enormous gain of cpu time).

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 .

Very good results are obtained for defects in UO2 and pyrochlores.These defects play a major role in the behavior of these materials under irradiation.

16E2C 2013 27-31 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 : Y2Ti2O7 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

18E2C 2013 27-31 October Budapest LEMHE/ICMMO CNRS-Univ Paris-Sud 11 Orsay-France 18

SMTB-Q: A Tight-Binding Variable-Charge model

+

A

CohNA Q

EQQ

)()...( 1 0

1

N

i

iQ

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 MnOm is calculated by means of a Tight-Binding approach in the Second-Moment approximation (SMTB)


Coulomb energy

Ionization energy

Cij rrijpairs ij

ijijij

Cov

N

BAABBA

N

AAAAAAA

Coh

r

rpA

E

RJQQ

QJQE

E

1exp

)(

0

21

1

202

100

Covalent energy

SMTB-Q: the cohesive energy (ECoh)

Repulsive energy

21

2)

B(R

Bζ

Bn

ΦAB

R)

A(R

Aζ

An

ΦB

dRA

dR(R)AB

J

)exp(1 RRN nn

Slatern

ARn eff412

1exp

00OM

OMijMO r

rq

Hopping integral

IJIJ

IeffII

pq

RJ

,,

,,

0

00

are optimized to describe:-the lattice(s) parameter(s)-the cohesive energy-the bulk modulus (B)-the elastic constants (Cij)

Coulomb interaction JAB(R)


Alternating Lattice Model (ALM):

No bonding

CBCE

OE

VB

(hopping integral)

- Total density of states N(E) - Local DOS NA(E) et NC(E) are calculated analytically

B AB

NB

EO0

22 4 OOC ZEE

EC

The outer atomic orbitals of oxygens (p), on the one hand, and of the cations, on the other hand, have the same energy ( EO and EC respectively) crystal-field splitting is neglected. Alternating nature of the lattice (ALM)

electron transfer takes place only between oxygens and cations (rC)

Band description must be valid


Covalent energy

Integral of NA(E) over VB yields the number of electrons on anions and the charge Q:

22

0

4)(12

OOC

OC

ZEE

EE

m

nQ

Q

m

nQZmE OCov 022

22

2

04)(

4

OOC

O

ZEE

ZnE

Cov

The covalent energy is obtained from the integral of EN(E) over VB

QQ 2m = oxygen stoichiometry

n0 : shared electronic states between C and O

L AL

NL

EO0

22 4 OOC ZEE

EC


Ionization energy (ex: TiO2)

eV 12.162 eV 7.543 0

0 OOO J

Coulomb energy

Ionization energy

)()...(1

2120

210

1 0 iCOV

N

A

N

BAABBAAAAAAAN QEJQQQJQEQQE

Covalent energy

-2 -1 0 1 2 3 4

0

20

40

60

80

100

(b)

Ionization energy Fit used in this work

En

erg

y (

eV

)

Charge Ti (e)

(hardness)0

and gativity)(electrone0

ofion Determinat AAA J

eV 10.572 eV 0.0 0

0 TiTiTi J

-2 -1 0 1-4-202468

101214

(a)

Ionization energy Fit used in this work

En

erg

y (e

V)

Charge O (e)


Coulomb energy

Ionization energy

)()...(1

2120

210

1 0 iCOV

N

A

N


Covalent energy

Coulomb interactions JAB


Coulomb interactions JAB (ex: TiO2)

Ions are described by ns-type Slater orbitals:

Strong screening of Coulomb forces at small distances: Rij

< 4 Å

0 1 2 3 4 5 6 7 8

0

2

4

6

8

10

12

14

14.4/RAB

coulomb O-O Ti-O Ti-Ti

J AB(e

V)

RAB

(Ang)

)exp(1 RRN nn

Slatern

ARn eff412

ÅOReff 6.0

ÅTiReff 77.0

2On

3Tin

Classic Coulomb law (1/R) at larger distances

21

2)

B(R

Bζ

Bn

ΦAB

R)

A(R

Aζ

An

ΦB

dRA

dR(R)AB

J


Coulomb energy

Ionization energy

)()...(1

2120

210

1 0 iCOV

N

A

N


Covalent energy

M-O covalent energy: ECov(Qi)


ES (j.m-2) SMTB-Q Empirical Ab initio

(1) (1) (2) (3)

(111)

(110)

(100)A

(100)B

1.08

1.75

1.92

2.40

1.27

2.0

2.81

3.11

0.89

1.28

1.43

1.91

0.94 0.461

0.846

1.194

SMTB-Q: surfaces of UO2

(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


EF (eV) EF (eV)/at Ox EF (eV)

VO(1)

VO(3)

VO(4)

VO(6)

VO(bulk)

9.9

11.1

9.9

8.6

8.8

VU

VU(bulk)

-5.6

-6.2

IO

IO(bulk)

-2.9

-4.1

SMTB-Q: defects at UO2(111)

UO2(111)

Oxygen

Uranium

Documents

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