Theoretical Study of surface stabilities of CeO2 - a DFT and DFT+U study Yong Jiang 1, James B Adams 2 1,2 Sci. & Engr. of Materials Program 2 Dept. of

Theoretical Study of surface stabilities of CeO2 - a DFT and DFT+U study

Yong Jiang 1, James B Adams 2

1,2 Sci. & Engr. of Materials Program2 Dept. of Chemical and Materials Engineering

Arizona State University

Presented to 2004 APS 4 Corners Fall meeting, UNM, Alburquerque, NM

2

Automobile Emission Limits

Emission regulations of the fossil-fuel burning engines have been tightened since the Clean Air Act was published in 1970's in the US.

Fig.1 NO emission limit published by USA EPA (from http://www.fhwa.dot.gov/environment/aqfactbk/factbk12.htm)

3

Three-way Catalysts (TWC)

Traditional Pt/Rh and Pt/Pd/Rh TWC contains Pt/Pd: for CO and HC oxidation

Rh: efficient at NO reduction Low-cost Pd-only catalysts only work

efficiently in narrow air(O)-to-fuel (A/F) window centered at ratio=14.6

High oxygen storage/release capacity (OSC) material is needed to stabilize the air-fuel ratio about this value

4

CeO2 as OSC Material

Advantages of using pure CeO2 as OSC

- elevated oxygen transport capacity- facile redox ability: CeO2 ↔ CeO2-x (0<x<0.178)- compatibility with noble metals

Nano-size particles with high surface area (in order of ~100 m2/g) is demanded 1

But ceria particles may start to aggregate at T<700K 2

People want to know the stable surfaces at certain chemical environment.

1 Fornasiero, P. et al, J. Catal. 164, 173, (1996)1,2 El Fallah, J., et al. J. Phys. Chem. 98, 5522, 19943 Fornasiero, et al. J. Catal. 1996, 164, 173

5

DFT

- Based on the Hohenberg-Kohn theorems - using Kohn-Sham total energy functional (Exc added):

- solve N one-electron equations self-consistently

- Exchange-correlation Approximation : LDA, GGA (PW91/PBE)

- Ion-electron pseudopotentials: Ultrasoft and PAW

Simulation Theory - DFT

)()()()( rVrVrVrV XCHextKS

drrnrnE xcLDAxc

N

ii rrn

1

2)()(

drrnrnfEGGAxc )(),(

drrrrnT i

N

iis )()(

2

1)]([

1

2*

drrVrnrnErdrdrr

rnrnrnTrnE extXCs )()()]([

||

)()(

2

1)]([)]([

yjiang

The starting point is an approximative description of the single particle functions, P(r). It could be hydrogen-like functions, but usually some better approximation is used. With these starting functions the Hartree-Fock potential is constructed and the eigenvalue equation, Eq.(11), is solved. Then a new set of single-particle functions are obtained and a new Hartree-Fock potential is constructed and again the eigenvalue equation is solved. This is done over and over again until the radial functions as well as the energy eigenvalues are stable. We call this a Self-Consistent Field method.

yjiang

yjiang8/10/2004Density-functional theory is widely accepted as a framework for the study of the electronic ground-state properties of molecules and solids.The total Energy functional is written as E[n]=F[n]+Eext[n]The univeral functional of n, F[n] is written as F[n]= T[n]+Eee[n] in HFHere, F[n] consists of the first three terms. i.e. F[n]=Ts[n]+EH[n]+Exc[n]

yjiang

yjiang8/10/2004The exchange-correlation energy which contains the non-classical electrostatic interaction energy and the difference between the kinetic energies of the interacting and non-interacting systemsThe aim of this separation is that the first two terms can be dealt with simply, and the last term, which contains the effects of the complex behaviour, is a small fraction of the total energy and can be approximated surprisingly well.

yjiang

yjiang8/10/2004One begins with a guessed n(r), constrcuts Veff[n] through Vex[n] and finds a new n(r) from one-electron equations. The total energy can be computered

6

Validation of exchange-correlation

Necessary to test on all available exchange -correlation functionals and pseudopotentials

23.5

28

VASP_PAWi

VASP_PAWGGAi

VASP_PBEi

g1 r( )

g2 r( )

g3 r( )

5428 V1i

V2i

V3i

r r r28 30 32 34 36 38 40 42 44 46 48 50 52 54

28

27.72

27.44

27.16

26.88

26.59

26.31

26.03

25.75

25.47

25.19

24.91

24.63

24.34

24.06

23.78

23.5

Volume (Å3)

Tot

al

En

ergy

(e

V)

PBE-PAW

PW91-PAW

LDA-PAW

a(Å) % Bo(GPa) %

LDA-PAW 5.371 -0.72 193.35 -5.22/-18.07

PW91-PAW 5.479 1.27 182.20 -10.69/-22.80

PBE-PAW 5.380 -0.55 202.40 -0.78/14.24

HF [1] 5.385 -0.46 357 75/51.3

EXP5.41[2]

204[3], 236[4]

[1] Hill, S.E.; Catlow, C.R.A. J. Phys. Chem. Solids. 1993, 54, 411[2] Eyring, L.; Handbook on the Physics and Chemistry of Rare Earths; Amsterdam, 1979, Vol.3, Chap.27[3] Nakajima, A.; Yoshihara,A.; Ishigame,M. Phys. Rev. B. 1994, 50, 13297 (Polarized Raman-scattering at 10k)[4] Gerward, L.; Olsen, J.S.; Powder Diffr. 1993, 8, 127

Fig 2. Validation by reproducing bulk properties of CeO2

7

Simulation Theory – DFT+U

)2

1( iLDA

ii NU

N

E

ii

jijiLDA

NN

NNUNUN

EE2

1

2

)1(

DFT limitation:

VKS continuous, and fixed for all energy bands, not exact for a strongly correlated system - transition or rare-earth metals

DFT+U: the Coulomb d–d or f-f interaction is treated as a separate term 1/2UNiNj as in HF, and the delocalized s, p electrons are described by orbital-independent one-electron potential (LDA or GGA).

8

LDA+U parameters (U and J)

Fig 3. LSDA+U predictions for lattice constant, bulk modulus, and band gaps of bulk CeO2. The dotted lines stand for experimental measurements.

2.3

2.4

2.5

2.6

0.3 0.5 0.7 0.9 1.1 1.3J (eV)

2p -

4f G

ap

5.0

5.1

5.2

5.3

5.4

2p -

5d G

ap

5.30

5.35

5.40

5.45

0 1 2 3 4 5 6 7 8

U - J (eV)

Lat

tice

Con

stan

t (A

)

1.4

1.8

2.2

2.6

3.0

0 1 2 3 4 5 6 7 8U - J (eV)

2p -

4f G

ap

4.0

4.5

5.0

5.5

6.0

2p -

5d G

ap

180

200

220

240

0 1 2 3 4 5 6 7 8

U - J (eV)

Bul

k M

odul

us in

GP

a

The optimal values: U=7, J=0.7 eV

9

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

DOS of CeO2 bulk

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

Figure 2. Comparison of partial electron density of states (PDOS) of bulk CeO2 by LDA (U, J = 0) and LDA+U (U = 7 eV, J = 0.7 eV). The left plot is for cerium ions (magnitude 2), and the right one is for oxygen ions..

LSDA+U

LSDA

5p 5d 4f 5d4f

LSDA+U

LSDA

2s

2p

10

Surface Energy vs. T and PO2

Surface energy is a function of T and PO2.

in which the last two terms are normally ignored.

The temperature dependence of the first two terms can be neglected for T=[ 0,1200 K]. (Tmelt>=2600K)

Our goal is to determine the relative ordering of surface stabilities of all possible surfaces.

)(2

122 STVPNNE

A OOVCeCetot

])(,[2

1222 OOCebulkCeOCetot NNNE

A

200

,0

,2022

022 ln)(/ln ObulkCebulkCeOOOOO PkTHPPkT

f

(1)

(2)

(3)

11

CeO2 Surfaces of interest

Fig 3. Views of the surface structures under study with all stoichiometric surfaces in the 1st row and all non-stoichiometric surfaces in the 2nd row (Red circles: O2-, white circles: Ce4+).

(a) 110 (I) (b) 111 (II) (c) 100 (III) (d) 210 (III) (e) 211 (I) (f) 310 (I)

(g) 100_O (h) 100_Ce (i) 210_O (j) 210_Ce (l) 111_O (m) 111_Ce

yjiang

Type I surfaces: they are stacks of charge neutral planes, each plane retaining the CeO2 stoichiometry, and therefore carry neither charge nor dipole moment normal to the surface. A oxygen-terminated (111) surface, on the other hand, is known as a Type II surface, consists of a neutral repeatable (O-Ce-O) sandwiches and hence zero perpendicular dipole moment. The (100) and (210) surfaces belong to Type III surfaces which on the contrary consist of alternately charged planes, thus with net dipole normal to surface. Such a surface would be unstable as ideally cleaved but can be made stable if half of the oxygen atoms are removed from the outermost plane. The surface models used in our work are shown in Figure 3.

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Surface Energy ResultsUnrelaxed Surface Energy

(111) (100) (110) (210) (211) (310)

DFT-PBE (this work) 0.55 1.89 1.09 1.54 1.92 6.06

DFT-GGA b 0.61 1.98 1.19

DFT-GGA c 0.69 2.37 1.26

DFT-LDA c 1.06 1.55

Ionic Potential d 1.71 3.60 11.58

Relaxed Surface Energy

(111) (100) (110) (210) (211) (310)

DFT-PBE (this work) 0.45 1.28 0.86 0.96 1.21 1.68

DFT-GGA b 0.60 1.43 1.01

DFT-GGA c 0.68 1.57 1.05

DFT-LDA c 1.04 1.35

Ionic Potential d 1.20 1.58 2.48

Ionic Potential e 1.54 3.25 2.45 3.27 2.68 3.57a this work; b Z. Yang, et al, J. Chem. Phys. 120, 7741 (2004); c N. V. Skorodumova, et al, Phys. Rev. B 69, 075401 (2004); d T.X.T. Sayle, et al, Surf. Sci. 316, 329 (1994); e J. C. Conesa, Surf. Sci. 339, 337 (1995)

13

Surface Stabilities at 300K

the stoichiometric (111) has the lowest free energy over almost all the range of pressure up to 1 atm

The cerium-rich (111)_Ce surface

become the most stable one only at UHV.

The O-rich (210)_O may become the most stable one at PO2> 1 atm, but this range is beyond the limitation of our thermodynamic model

0

1

2

3

4

5

6

7

8

-450 -350 -250 -150 -50ln PO2

Sur

face

Ene

rgy

(J/m

2 )

111

111_Ce

111_O

100

100_Ce

100_O

110

210

210_Ce

210_O

211

310

14

Surface Stabilities at 1200K

the transition point moves to higher pressures gradually when temperature increases.

At T= 1200 K, the transition point positions at lnPO2 = ~ -80.

0

1

2

3

4

5

6

7

8

-450 -350 -250 -150 -50

ln PO2

Sur

face

Ene

rgy

(J/m

2 )

111

111_Ce

111_O

100

100_Ce

100_O

110

210

210_Ce

210_O

211

310

15

Surface electronic structure

Figure 5. Charge, ELF, and Projected density of states for Ce and O ions of the stoichiometric (111) by LSDA+U (U = 7 eV, J = 0.7 eV).

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

Surface-Ce 4

5p 5d4f 5d

4f

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

2s

Surface-O 12p Charge ELF

yjiang

(1) very small relaxation has been found on (111) surface, with the top O moving down by 0.02-0.03A(1) only the DOS for the outmost layers differs significantly from that of the bulk(2) band-gap shrink,(3)some occupied Ce4-f and O-2p shift up near to fermi level, corresponding to the surface formation

16

Surface electronic structure, cont’

Figure 6. Projected density of states of the O-rich (210) by LSDA+U (U = 7 eV, J = 0.7 eV).

-20 -16 -12 -8 -4 0 4 8

2s

Surface-O 1 2p

-20 -16 -12 -8 -4 0 4 8

Surface-Ce 4

5p 5d 4f 5d4f

yjiang

(1) very small relaxation has been found on (111) surface, with the top O moving down by 0.02-0.03A(1) only the DOS for the outmost layers differs significantly from that of the bulk(2) band-gap shrink,(3)some occupied Ce4-f and O-2p shift up near to fermi level, corresponding to the surface formation

17

Summary Ceria surface energies are investigated extensively by DFT as a

function of temp and PO2

Our results show that the stoichiometric (111) has the lowest surface energy over almost all the range of pressure

The transition to the cerium-rich (111)_Ce is found at UHV only. The transition point moves to higher pressures gradually when temperature increases.

DFT+U calculation with the optimal U=7 and J=0.7 eV leads to reasonable predictions for all considered physical properties of ceria

Ongoing and future work oxygen vacancy in bulk and on surfaces: energy level in band-gap, vacancy formation energy, equilibrium concentration, and migration…

18

Acknowledgements

Advisor: Dr. James Adams All committee members

- Dr. Mark Van Schilfgaarde

- Dr. Peter Crozier

- Dr. Renu Sharma Dr. William Petuskey

19

Yong Jiang tiger-paw @ asu.edu

Ph.D in Computational Materials Science (4.0/4.0) , ASU, 2001-2005

M.S. in Solid State Device (3.8/4.0) , ASU, 2002-2004

To obtain a research position to broaden my expertise on computational materials science.

Publications

1. Yong Jiang and James Adams, Oxygen Vacancy Formation and Migration in CeO2 bulk, to be

submitted to Physcial Review B.

2. Yong Jiang and James Adams, Theoretical Study of CeO2 Surface Stabilities under the influence of

temperature and oxygen partial pressure, submitted to Journal of Chemical Physics (2004)

3. Yong Jiang, James Adams, and Donghai Sun, Benzotriazole Adsorption on Cu2O (111) Surfaces: a First-Principles Study, Journal of Physical Chemistry B. 108 (2004) 12851

4. Yong Jiang and James Adams, First-Principles Study of Benzotriazole Adsorption onto Clean Cu(111), Surface Science, 529 (2003) 428

5. Yong Jiang, Dashu Peng, Dong Lu, and Luoxin Li, Analysis of Bimetal Sheet Bonding by Cold Rolling, Journal of Materials Processing Technology, 105 (2000) 32

6. Yong Jiang, Dashu Peng, and Langfei Liu, Stream Function Theory Calculations of Clad Sheet Bonding by Cold Rolling. Proceeding of the 6th National Conference on Plastic Deformation Mechanics of Materials, China, (1999)

Documents

Theoretical Study of surface stabilities of CeO2 - a DFT and DFT+U study Yong Jiang 1, James B Adams 2 1,2 Sci. & Engr. of Materials Program 2 Dept. of