Ab initio calculations

of proton migration

properties in

Gd-doped BaCeO3

SSPC 16 – SEPTEMBER 2012

Jessica Hermet1,2, François Bottin1, Grégory

Geneste1, Guilhem Dezanneau2

1 CEA, DAM, DIF, F-91297 Arpajon, France

2 Laboratoire SPMS, CNRS-UMR8580, ECP, Grande Voie des

Vignes, 92295 Châtenay-Malabry Cedex, France

OUTLINE

Structure of BaCeO3

Ab initio calculations of barriers

Parameters

Results

- stable positions,

- energy barriers

KMC Simulations

Parameters and assumptions

Results

- mechanisms frequencies,

- location of defects,

- diffusion coefficients

Conclusion

| PAGE 2 SSPC 16 | SEPTEMBER 2012

STRUCTURE OF BACEO3

Structure: distorted perovskite (Pnma) Orthorhombic structure up to 550 K (low symmetry)

2 tilts (a-b+a-)

BaCeO3 : good protonic conductivity Especially when doped with a trivalent element

Creation of oxygen vacancy

Hydration:

⇒ Gd:BaCeO3 = Electrolyte for

Protonic Ceramic Fuel Cell | PAGE 3 SSPC 16 | SEPTEMBER 2012

+ H2O Gd

Gd

Vo

dry

Gd

Gd

H+

H+

hydrated

AB INITIO CALCULATIONS

Parameters

Abinit Code (plane-waves)

PAW method

GGA-PBE exchange correlation

Spin-polarized (because of Gd)

Highly parallelized

80 atoms supercell

Calculations

One geometry optimization per configuration

- (1 proton, 1 dopant)

- (1 oxygen vacancy, two dopants)

Energy barrier between two configurations using the string method

- (to find Minimum Energy Path)

| PAGE 4 SSPC 16 | SEPTEMBER 2012

AB INITIO CALCULATIONS

Energetics Hydration enthalpy = - 1.42 eV (per H20 molecule)

Stable positions for the proton

16 differents positions are found

- 8 “close” to the dopant Gd

- 8 “far” from the dopant

Hermet,J. ; Bottin, F.; Dezanneau, G.; Geneste, G. Physical Review B, 2012, 85, 205137

| PAGE 5 SSPC 16 | SEPTEMBER 2012

1a 1b 1c 1d 2a 2b 2c 2d

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Positions of the proton

Rela

tive e

nerg

y (

eV

)

Gd

Ce1

Ce2

Ce3

AB INITIO CALCULATIONS

Proton diffusion mechanisms

Energy barrier calculations (=84 values)

3 kinds:

Reorientation

Intra-octahedra hopping

Inter-octahedra hopping

| PAGE 6 SSPC 16 | SEPTEMBER 2012

Mechanism Emoy

(eV)

Intra hopping 0.38

σ=0.08

Inter hopping 0.19

σ=0.04

Reorientation 0.23

σ=0.16

KMC SIMULATIONS

Kinetic Monte Carlo (KMC) Method to simulate the time evolution of a system where processes can occur with a

known rate

Conditions and assumptions: Parameters:

Simulation box = 8*8*8 cubic cell (2560 atoms)

10 000 000 steps per simulation (= from 20 ns up to 1 µs)

Temperature from 300K up to 1500K (no longer Pnma structure experimentally)

Doping rate between 1/64 (1.5%) and 1/4 (25%)

Assumptions:

Oxygen vacancies and Gadolinium dopants are fixed (initially randomly distributed)

No long-range electrostatic interactions

One oxygen can only welcome one proton

- choice based on : i/ proton repulsion, ii/ 2 protons on the same oxygen is not a stable

configuration

- NB: simulations with the possibility of 4 protons per oxygen lead to similar results

Main Goal : activation energy and protonic conductivity

how dopant affects conduction

| PAGE 7 SSPC 16 | SEPTEMBER 2012

KMC SIMULATIONS

Relative frequencies of the different mechanisms

Temperature dependence

Doping rate dependence

| PAGE 8 SSPC 16 | SEPTEMBER 2012

0

20

40

60

80

100

Reo Intra Inter

300K

600K

900K

1200K

1500K

0

10

20

30

40

50

60

70

80

Reo Intra Inter

1.56%

3.13%

6.25%

12.50%

T=900K δ=6.25%

KMC SIMULATIONS

Location of protonic defects

Close or far from the dopant

Assuming a fully-hydrated system (no oxygen vacancy)

Number of possible protonic sites : 8*8*8*3*4 = 6144

Number of protons between 8 (δ=1.5625%) and 128 (δ=25%)

Occupation of close sites (to be compared with the percentage of close sites)

Average on ten million KMC steps (minus equilibration time depending on T)

| PAGE 9 SSPC 16 | SEPTEMBER 2012

Doping rate=

(Percentage

of close sites)

1.5625%

(3.13%)

3.125%

(6.25%)

6.25%

(12.37%)

12.5%

(23.31%)

25%

(43.62%)

300K 50% [16.0] 57% [9.1] 69% [5.5] 79% [3.4] 91% [2.1]

600K 17% [5.4] 28% [4.5] 43% [3.5] 60% [2.6] 78% [1.8]

900K 9% [2.9] 18% [2.9] 31% [2.5] 48% [2.1] 69% [1.6]

1200K 7% [2.2] 14% [2.2] 26% [2.1] 42% [1.8] 63% [1.4]

1500K 7% [2.2] 12% [1.9] 23% [1.9] 38% [1.6] 60% [1.4]

KMC SIMULATIONS

Location of protonic defects

Initially randomly distributed

Relaxation time to get the equilibrated

distribution

- Long at low temperature (≈1 000 000 steps)

- Short at high temperature (≈ 1000 steps)

| PAGE 10 SSPC 16 | SEPTEMBER 2012

At T=300K, δ=6.25%

Initial After 10 000 steps After 100 000 steps After 1 000 000 steps

“Close” proton “Far” proton Dopant

KMC SIMULATIONS

Diffusion coefficients ν=ν0 exp[-ΔE/kBT]

<r²>=6Dt

D=D0 exp[-Ea/kBT]

Previous calculation with ν0=1013Hz 6.25% : Ea= 0.37 eV

12.5% : Ea= 0.36 eV

25% : Ea= 0.34 eV

Previous study 0% : Ea= 0.49 eVa

10% : Ea= 0.45 eVb

Calculations with ν0=kBT/h

6.25% : Ea= 0.45 eV

12.5% : Ea= 0.44 eV

20% : Ea= 0.43 eV

25% : Ea= 0.42 eV

aMünch, W.; Kreuer, K.-D.; Seifert, G. & Maier, J. Solid State Ionics, 2000, 136-137, 183 - 189

b Kreuer, K.; Schönherr, E. & Maier, J. Solid State Ionics, 1994, 70-71, Part 1, 278 - 284 | PAGE 11 SSPC 16 | SEPTEMBER 2012

3E-11

3E-10

3E-09

3E-08

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Dif

fus

ion

co

eff

icie

nt

(m2

/s)

1000/T

6.25%

12.50%

20.00%

25.00%

CONCLUSION AND PROSPECTS

| PAGE 12 SSPC 16 | SEPTEMBER 2012

Conclusion

Proton diffusion is more efficient with inter-octahedral transfer (due to tilted structure)

Proportion inter/intra-octahedral hopping decreases with doping rate

Proportion hopping/reorientation increases with temperature

Protonic defects are preferentially located near a dopant

But not completely trapped (or all of them will be near a dopant)

And activation energy slightly decreases with doping rate, suggesting an easier

diffusion as we put more dopant in the material.

On-going work

Implementation of Ewald summation in KMC code

To take into account electrostatic interaction more accurately

Path Integral Molecular Dynamics (PIMD)

To take into account the quantum nature of proton

Path before iteration

Path after iteration

2) Re-parametrization

1) Move images according to

atomic forces

STRING METHOD

AB INITIO CALCULATIONS

Conditions Uncharged supercell

More realistic representation of the material

No need to apply corrections

[1 proton for 1 dopant] or [1 vacancy for 2 dopants]

Limits of our study Only one proton in a supercell ( no effect of two protons)

NB: tests with two proton facing each other, or on the same oxygen lead to

unstable configurations.

Only one dopant

configurations where two or more dopants are neighbors are not taken into

account

No oxygen vacancy around

| PAGE 14 SSPC 16 | SEPTEMBER 2012