First principles modeling of oxygen vacancy formation and mobility in (Ba,Sr)(Co,Fe)O 3-δ δ δ δ perovskites

First principles modeling of oxygen vacancy formation and mobility in (Ba,Sr)(Co,Fe)O _{3-δ δ δ δ} perovskites

R. Merkle ^a , E.A. Kotomin ^a,b , Y.A. Mastrikov ^b,c , M.M. Kuklja ^c , J. Maier ^a

a

MPI Solid State Research Stuttgart,

^b

Inst. Solid State Physics Riga,

^c

University of Maryland

MPI for Solid State Research

Stuttgart

3.80 3.85 3.90 3.95 4.00 4.05

0.00 0.25

0.50 0.75

1.00

0.25 0.50

0.75 1.00 BaxSr1-xCoyFe1-yO3-δ

x Ba y Co

lattice constant

hexagonal perovskite Å

lattice constant/

0.3 0.4 0.5 0.6 0.7

0.00 0.25

0.50 0.75

1.00

0.00 0.25 0.50

0.75 1.00 Ba_xSr_1-xCo_yFe_1-yO_3-δ

x Ba y Co

δ

? δ

600°C pO2= 10^-3bar oxygen deficiency

BSCF permeation membranes

⇔ high D (Z.P. Shao (2000)) test as SOFC cathode

⇔ high k (Z.P. Shao, S.M. Haile (2004))

mechanistic interpretation:

L. Wang, R. Merkle, J. Maier J. Electrochem. Soc. 157 (2010) B1802

* vacancy formation energy increases linearly with Fe content

↔

↔ ↔

↔ difference in band structure

* vacancy migration barriers in good agreement with experiments

* barriers are determined by combination of

geometrical constraints (d

_A*-O*

in transition state) and electronic contribution (vacancy formation energy)

Ba

_1-x

Sr

_x

Co

_y

Fe

_1-y

O

_3-δδδδ

perovskites: high concentration and mobility of V

_o^..

Summary

Acknowledgement

The research leading to these results has received funding from the European Union's Seventh Framework Program FP7/2007- 2013 (NASA-OTM) under grant agreement n°228701 and the US National Science Foundation (NSF) grant n°08 32958. Authors thank NSF for its support through TeraGrid resources provided by the Texas Advanced Computing Center (TACC) and the National Center for Supercomputing Applications (NCSA) under grant number TG-DMR100021. MMK is grateful to the Office of the Director of NSF for support under the IRD Program. Any appearance of findings, conclusions, or recommendations, expressed in this material are those of the authors and do not necessarily reflect the views of NSF. This study was supported also by a grant of computer time at the EMS Laboratory at PNNL (Project No 42498).

Authors are greatly indebted to D. Gryaznov for many stimulating discussions.

1000/T / K^-1

0.9 1.0 1.1 1.2 1.3 1.4 1.5

DVo.. / cm2 s-1

1e-8 1e-7 1e-6 1e-5

Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3-δ

BSF

SF La_0.5Sr_0.5CoO_3-δ

La0.8Sr 0.2CoO_3-δ

LSC: R.A. De Souza et al.,Solid State Ionics 106 (1998) 175 L. Wang et al., Appl. Phys. Lett. 94 (2009) 071908

D

_Vo

.. from

¹⁸

O isotope exchange:

Ea= 0.5 eV

1 1 22

3 3

1 1 22

1 1 A y=1/8

C y=1/2

B

y=1/ 4 X: δδδδ=3/8

y=1/4

3 3 3 1 1 1 222 E

y=3/8 Y:δδδ=1/2δ

y=1/4 Fe

Co

* VASP 4.6 + PAW and plane wave basis set

* PBE-type exchange-correlation GGA functional

* 4x4x4 k-point mesh in the Brillouin zone (Monkhorst-Pack scheme)

* ion charges calculated by the Bader method

* energy cut-off 520 eV

* Ba

₄

Sr

₄

(Co,Fe)

₄

O

_12-δ

supercells (2

×

2

×

2)

* Fe: high spin state, Co: intermediate spin

E. A. Kotomin et al., Solid State Ionics 188 (2011) 1

Computational details

different vacancy configurations in supercell

Electronic structure

Oxygen vacancy formation

Oxygen vacancy migration

SrCo_1-yFe_yO_2.875

Fe fraction y

0.00 0.25 0.50 0.75 1.00

vacancy formation energy / eV

1.0 1.5 2.0 2.5

Ba_0.5Sr_0.5Co_1-yFe_yO_2.875 Co-V_O^..-Co

Co-V_O^..-Fe

Co-V_O^..-Co Co-V_O^..-Fe Fe-V_O^..-Fe O

energy / eV

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

arb. units

-5 0 5

arb. units

-10 0 10

Fe

arb. units

-5 0 5

Co

O px O py O pz dxy + dxz + dyz dz² + d(x²+y²)

dxy + dxz + dyz dz² + d(x²+y²) spin-projected density of states (DOS) for

Ba0.5Sr0.5Co0.75Fe0.25O2.875

A*

B**

A'*

B*

Oh O_h

Ov Ov O*

A*

B**

A'*

B*

Oh O_h

Ov Ov O*

transition state and initial state for Ba0.5Sr0.5CoO2.875

E.A. Kotomin, R. Merkle, Y. A. Mastrikov, M. M. Kuklja, J. Maier, ECS Transact. 35(1) (2011) 823; JES (2011) submitted cartoon of the BSCF band structure (density of states)

oxygen loss for δ

δ δ = 1/8: excess electronsδ

distributed mainly to Co and O

significant (Fe,Co)-O covalency (t

_2g

) Fe: 1 eV gap between occupied

↑↑↑↑

e

_g

and empty

↓↓↓↓

e

_g

BSCF ≈≈≈≈ linear increase of V

_O^..

formation energy with Fe content

⇔

more narrow empty Fe states at higher energy

SCF: slightly higher values

⇔

oversized Ba favours reduction of Fe,Co

transition state:

O* moving through

"critical triangle"

transition state:

e density map in (110) plane for Ba0.5Sr0.5Co0.75Fe0.25O2.875

barriers DFT expt. good BSCF 0.44 eV 0.5 eV* agreement BSF 0.72 eV 1.0 eV*

SCF 0.64 eV 0.65 eV**

geometric factors:

d

_A-O*

compared to BSC*

(cf. SrSr, SrBa and BaBa barriers for BSC)

Ba Ba

Sr Sr

Co O*

electronic factors:

vacancy formation energy (cf. SrBa barriers for BSC, SCF, BSF)

*L. Wang et al., JES 157 (2010) B1802

**Y. Teraoka et al., Mat. Res. Bull. 23 (1988) 51

D.N. Mueller et al., J. Mat. Chem. 19 (2009) 1960

cf. XAS study for Ba

_0.1

Sr

_0.9

Co

_0.8

Fe

_0.2

O

_3-δ

:

charge distribution depends delicately on

δ

(more e to Fe at low T, high pO

₂

)

comparison to expt. data:

E_V

= 0.6 eV for BSF (

δ

= 0.34), 0.5 eV for BSCF (δ = 0.52)

E_V

depends on δ

⇒

extrapolate to δ = 1/8 trend of smaller E

_V

for Co-rich materials confirmed O

_O^x

+ 2 M

_M^x¾

0.5 O

₂

+ V

_O^..

+ 2 M

_M

'

L. Wang et al., ECS Transact, 13(26) (2008) 85

E O Co

Fe

EF(δ ≈1/8) EF(δ= 0) Fermi energy:

EV Em

/ eV / eV B*-O*

/ Å B*-Ov

/ Å B*-Oh

/ Å q(O*)

∆q(O*) / e0

B*-B**

/ Å

A*-O* A*A'*

Sr Ba / Å / Å / Å BSC BaSr

1.21 0.40

SrSr 1.03 0.43

BaBa 1.28 0.75

1.70 -13%

1.71 -12%

1.68 -14%

1.77 -9%

1.79 -8%

1.76 -10%

1.95

±0%

1.95

±0%

1.95

±0%

-0.97 +0.10

-0.96 +0.11

-0.95 +0.12

5.68 +3%

5.48 -1%

5.63 +2%

2.37 2.58 4.12 +6%

2.41 4.19 +7%

2.49 4.12 +6%

BSCF BaSr 1.34 0.42 C*VC->C*VC 1.40 0.46 CVF*->CVF*

1.69 -13%

1.69 -13%

1.77 -9%

1.76 -10%

1.98 +1.5%

1.91 -2%

-0.98 +0.09

-0.95 +0.13

5.75 +4%

5.65 +2%

2.38 2.59 4.10 +5%

2.39 2.57 4.15 +6%

BSF BaSr 2.22 0.72

1.68 -14%

1.78 -9%

1.95

±0%

-0.96 +0.12

5.68 +3%

2.40 2.57 4.14 +6%

SCF SrSr 1.58 0.60 C*VC->C*VC 1.69 0.67 CVF*->CVF*

1.70 -11%

1.70 -11%

1.79 -7%

1.77 -8%

1.92

±0%

1.91 -2%

-0.97

-0.97 5.56 +2%

5.52 +2%

2.38 4.08 +6%

2.38 4.11 +7%

Vacancy formation energy EV, migration barrier Em, and structural parameters of oxygen migration.

* indicates the migrating O and directly connected cations. Italic numbers give the change in the transition state relative to the ideal structure.

∆q(O*) is the change of O* ion charge in the transition state relative to the initial state. For BSCF and SCF, the geometry and barrier from a Co-V_O^..-Co initial state to a Co-V_O^..-Co final state as well as for Fe-V_O^..-Co to Fe-V_O^..-Co (Fe*-O* transition state) is given

0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.0 1.2 1.4 1.6 1.8 2.0 2.2

-0.10 -0.08 -0.06 -0.04 -0.02 0.020.00 0.04

migration barrier / eV

∆r(A*O*) relative to BSC / Å

BSF SrSr F*VF BaSr F*VF BaBa F*VF BSCF5528 BaSr F*VF BSCF5555 BaSr C*VF SCF SrSr C*VC SrSr CVF*

BSCF BaSr C*VC BaSr CVF*

BSC SrSr C*VC BaSr C*VC BaBa C*VC

vacancy form atio n

energy / eV