Hongqing Shi and Catherine Stampfl

School of Physics, The University of Sydney, Sydney, Australia

First-principles Investigation of the Stability of Surface Gold

Oxides on Au(111)

• UHV results often thought to be transferable to “real” high-pressure, high temperature catalysis

• Dynamic environment + labile surface morphology at corresponding partial pressure and temperature need to be included.

• Nanometric-size gold particles act as catalysts at or below room temperature [1]

22 CO1/2O CO

• Quantum size effects

• Charging of the gold particles by interaction with defects in the oxide

• Availability of low coordinated sites, and strain

• Combined effects of the gold particles and the oxide support

M. Valden et al. Sci. 281, 1647 (1998).

“Pressure-gap, temperature-gap”

Efficient Gold-based catalysts: e.g.

322 SO1/2OSO ;

[1] M. Haruta, Catal. Today, 36, 153 (1997).

“Structure-gap, materials-gap, water-gap”

Aim and Theoretical Approach To investigate chemisorption of oxygen on Au(111) and the stability of surface oxides taking into account the effect of pressure and temperature

Density-functional Theory (DFT)• The pseudopotential and plane-wave method

VASP [1,2]• Projector augmented-wave method (PAW)• Generalized gradient approximation (GGA) for the

exchange-correlation functional • Energy cutoff of 36.75 Ry (500 eV)• Equivalent k-point sampling, 21 k-points in (1x1) IBZ• Full atomic relaxation of top three Au layers and O

atoms with 5 layers slab, vacuum region of 15 Å

[1] G. Kresse et al., PRB 47, 558 (1993); 49, 14251 (1994);54, 11169 (1996); 59, 1758 (1999).[2] G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).[3] P. E. Blöchl, PRB 50, 17953 (1994).

On-surface and sub-surface oxygen adsorption

tetra II

tetra I

octa

Ofcc/Otetra-I

vacancy structure

Surface oxide structures: (4x4)(4x4)Au3O2

(4x4)Au3O2+OF+OH

(4x4)Au3O2+OH (4x4)Au3O2-Au3O

Electronic structure of surface oxide phases0.06 ML

0.11 ML

0.25 ML

1.0 ML

Ofcc/Otetra-I On-surface fcc

(4x4)Au3O2-Au3O

(4x4)Au3O2-Au3O

Ab initio atomistic thermodynamics

OOMMMM/OO A1

)( μμμ NNGGG ΔΔ

Two chemical reservoirs are used:

1. Chemical potential of oxygen, μO from ideal gas, O2

2. Chemical potential of metal, μM from bulk metal, M

CONFTOT

CONFVIBROTTRANSTOT

),(

),(

FETpG

pVFFFFETpG

By defining ,2O2

1OO EμμΔ

OOMMbOOO 22

1

A1

)( μμμ ΔΔΔΔ NNENG

⇅

⇅BULK

SURFACE

O2 GAS

⇅

⇅

⇅

⇅BULK

SURFACE

O2 GAS

C. Stampfl, Catal. Today, 105 (2005) 17; W.X. Li, C. Stampfl and M. Scheffler, Phys. Rev. Lett. 90 (2003) 256102; K. Reuter and M. Scheffler, Phys. Rev. B, 65 (2002) 035406

• For atmospheric pressure and temperature <360 K, thin oxide-like structures are stable• For atmospheric pressure, T>360 K, no stable species

Propose thin Au-oxide-like structures could play a role in the low temperature catalytic reactions

Ab initio surface phase diagram

Conclusion

• Acquired the ab initio (p,T) phase diagram for O/Au(111) system

• On/Sub-surface oxygen overlayer structures unstable

• At atmospheric pressure, thin surface oxide-like structures are stable up to 360 K

• Could play an important role in low temperature catalytic reactions

Outlook

• Investigate chemical reactions (e.g. CO oxidation) on the most stable surface oxide

Acknowledgements

We gratefully acknowledge support from:

• the Australian Research Council (ARC)

• the National Supercomputing Facility (APAC)

• the Australian Centre for Advanced Computing and Communications (ac3)

DFT Functional a0 (Å) B (GPa) Ecoh (eV/atom)

PAW-GGA Plane waves 4.175 132 3.04

LDAa DZS 4.054 207

LDAb Plane waves 4.07 172

LDAc Plane waves 4.07 185 4.39

GGAa DZS 4.181 152

GGAb Plane waves 4.19 132

Exp.d 4.08 170 3.81

Convergence tests

Table I. Convergence tests for fcc bulk gold of our first principles DFT method. The first line is our present calculation. The parameters a0, B and Ecoh are the lattice constant, bulk modulus and cohesive energy, respectively. The DZS represents the basis function of double- for the s orbital.

a. Reference 33.b. Reference 34.c. Referecne 35. The calculation used VASP.d. Reference 36.33. J. M. Soler, M. R. Beltrán, K. Michaelian, I. L. Garzón, P. Ordejón, D. Sánchez-Portal, and E. Artacho, Phys. Rev. B 61, 5771 (2000).34. B. D. Yu and M. Scheffler, Phys. Rev. B 46, R15 569 (1997).35. L. L. Wang and H. P. Cheng, Phys. Rev. B 69, 165417 (2004).36. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996).

Convergence tests

Table II. Structural and energetic data for clean Au(111) surface. The parameters , Esurf, d12 and d23 are the work function, surface energy, the first and second interlayer distance relaxation for the clean Au(111) surface, respectively.

a. Reference 39.b. Reference 40.c. Reference 41. The value comes from our calculation with their equation and parameter.

35. L. L. Wang and H. P. Cheng, Phys. Rev. B 69, 165417 (2004).38. Y. Yourdshahyan, H. K. Zhang, and A. M. Rappe, Phys. Rev. B 63, 081405 (2001).39. G. V. Hansson and S. A. Flodstrom, Phys. Rev. B 18, 1572 (1978).40. M. A. Van Hove and S. Y. Tong, Surface Crystallography by LEED: Theory, Computation, and Structural Results (Springer-Verlag, Berlin, 1979).41. S. G. J. Mochrie, D. M. Zehner, B. M. Ocko, and D. Gibbs, Phys. Rev. Lett. 24, 2925 (1990).

(eV) Esurf

(eV/Å2) d12 (%) d23 (%) d34 (%) d12

This work 1×1

5.184 0.044 1.2906 -0.3306 -0.4439 2.44155

This work 2×2

5.195 0.044 1.1405 -0.4769 -0.5056 2.43793

This work 3×3

5.192 0.044 1.1190 -0.5288 -0.5848 2.43741

This work 4×4

5.195 0.044 1.0283 -0.5145 -0.6169 2.43523

LDA (Ref. 35)

5.54 0.071 0.37 -0.36 0.05

LDA (Ref. 38)

0.101 0.97 -0.48 0.07

Exp. 5.26a 0.096b 0.0b 2.4276c

Convergence tests

VASP

1.23

-3.14

1558

Appendix

• A sufficiently high energy cut-off is crucial for accurate surface binding/adsorption energy calculations particularly for low coverage.

• High quality quantitative calculation is necessary. In VASP, set tag PREC=High. ref. VASP manual at http://cms.mpi.univie.ac.at/vasp/vasp/vasp.html

Ab Initio Atomistic Thermodynamics

MOTIVATION: To bridge the “pressure” gap, ie. to include finite temperature and pressure effects.

OBJECTIVE: To use data from electronic structure theory (eg. DFT-calculated energies) to obtain appropriate thermodynamic potential functions, like the Gibbs free energy G.

ASSUMPTION: Applies “only” to systems in thermodynamic equilibrium.

C. Stampfl, Catal. Today, 105 (2005) 17; W.X. Li, C. Stampfl and M. Scheffler, Phys. Rev. Lett. 90 (2003) 256102; K. Reuter and M. Scheffler, Phys. Rev. B, 65 (2002) 035406

Computation of Gibbs free energy

G(p,T) = ETOT + FTRANS + FROT + FVIB + FCONF + pV

For condensed matter systems,

ETOT Internal energy DFT-calculated value

FTRANS Translational free energy M∝ -1 → 0

FROT Rotational free energy M∝ -1 → 0

FVIB Vibrational free energy phonon DOS

FCONF Configurational free energy “menace” of the game

pV V = V(p,T) from equation of state (minimal variation) → 0 for p < 100 atm

To simplify calculations,

We set FTRANS = FROT = zero and FVIB will be calculated by finite-differences and approximated by the Einstein model.

Hence the Gibbs free energy of a condensed matter system, G(p,T) ≈ ETOT + FCONF at low temperatures.

⇅

⇅BULK

SURFACE

O2 GAS

Surface in contact with oxygen gas phase

MMOOMM/OA1

),( μμ NNGGTpG ΔΔ

Two chemical reservoirs are used:

1. Chemical potential of oxygen, μO from ideal gas, O2

2. Chemical potential of metal, μM from bulk metal, M

Neglecting FVIB and FCONF for the moment,

By defining ,2O2

1OO EμμΔ

OOMMbOOO 22

1

A1

)( μμμ ΔΔΔΔ NNENG

MMOOMM/OA1

),( μμ NNEETpG ΔΔ