1 H2 OXIDATION AT Pd(100): A FIRST-PRINCIPLES CONSTRAINED

THERMODYNAMICS STUDY

1.1 Introduction

Oxidation reactions are ubiquitous in heterogeneous catalysis. The nature of the active metal surface

under steady state conditions for oxidation reactions of different species has been intensively studied.22,

27, 30, 34, 35, 70, 72, 115, 116, 119, 127-129, 131-145For example, CO oxidation over Pd(100) has been well studied by Reuter

and co-workers using a constrained ab initio thermodynamics approach.72 In those studies it was found

that a monolayer thick surface oxide of PdO(101) supported above Pd(100) was the most stable surface

for a large portion of the phase diagram, particularly in the range of partial pressures of CO and O 2 and

at temperatures representative of technological operation. This work demonstrated that the proper

surface termination (which may be predicted from thermodynamics) must be considered when trying to

use density functional theory calculations to evaluate the kinetics of the catalytic mechanism, and that

the proper surface termination may be an oxide when considering oxidation reactions over d-band

transition metal catalysts.

More recently, we have attempted to expand this approach to examine the oxidation of NO over

Pd(100) and Pd(111).27 In contrast to the CO oxidation case, we found that the bulk oxide, i.e. thick bulk-

like oxidic overlayers, dominates the phase diagram when NO is the reducing agent. This stems from the

fact that NO is a weak reductant compared to CO, and therefore the reaction equilibrium for NO +

PdObulk ↔ Pdbulk + NO2 is shifted to higher NO partial pressures compared to an analogous reaction

statement for CO oxidation. Furthermore, the product, NO2, is not volatile as in the case of CO oxidation.

This complicates the analysis of the proper surface termination because NO2 cannot be assumed to

desorb.

Another common reductant is hydrogen. Due to its important role in heterogeneous catalysis, metal

corrosion and surface electrochemistry, hydrogen oxidation has been well studied over Pd surfaces by

several groups ever since Langmuir’s early work in 1922.146, 147, 148, 149, 150, 151, 152, 153, 154, 155 A palladium oxide

thin film above pristine metal has been investigated as a potential active surface for hydrogen oxidation,

but only under ultra-high vacuum conditions or using density-functional theory (DFT).135, 48However,

experiments on palladium methane oxidation catalysts suggest that the surface may be covered with

hydroxyl groups under reaction conditions.116 Although, Blanco Rey et al. did examine the stability of the

oxide in mixture atmospheres of H2 and O2,48 a complete surface termination map across a wide range of

conditions has not been developed, and in particular a map that would rationalize the appearance of

hydroxylated surfaces.

Therefore, DFT calculations linked to ab initio thermodynamics52, 53 have been employed herein to

examine a variety of surface structures and compositions on Pd(100) and to build a thermodynamic map

of surface termination under different partial pressure of O2 and H2. Using this method, we can

determine what the most appropriate surface termination to consider for a particular application.

1.2 Computational Methodology

DFT calculations were performed using the Vienna Ab Initio Simulation Package (VASP).99, 100A

plane wave basis set with a cutoff energy of 500 eV and the projector-augmented wave (PAW)101

pseudopotentials were used, and all calculations have been done using the Perdew-Burke-

Ernzerhof (PBE)102 exchange-correlation functional.

Pure palladium metal surface models used in this work are inversion-symmetric slabs

consisting of five Pd(100) layers with the adsorbate (H, O etc) on each side and with the middle

layer fixed. A uniform (7×7×1) k-point grid is used for the Brillouin zone integration within a 2×2 unit

cell.

The thin film surface oxide model was based upon the (√5×√5)R27°PdO(101)-Pd(100) structure

previously employed by Reuter et al.27, 29, 30, 72, 86, 87 For the structure optimization calculation, a

‘mirror’ structure with five-layers of Pd(100) and one-layer of PdO(101) on both sides has been

created in order to cancel the polarity from the oxide. All atoms are set to relax except the three

center layers of palladium metal. The slabs are separated by approximately 11 Å, equivalent to the

thickness of five layers of Pd(100). A uniform (5×5×1) k-point grid is used for the Brillouin zone

integrations.104 Geometries will be considered to be optimized once all residual forces fall below 0.02

eV/Å.

A four-atom fcc unit cell was adopted to calculate the energy of bulk Pd by sampling in a (9×9×9) k-

point grid. The optimized DFT result for the lattice constant is 3.95 Å in good agreement with

experimental data (3.89 Å)156 and previous calculation result157. Bulk PdO is a simple tetragonal structure

with lattice constants a = 3.03 Å and c = 5.33 Å at ambient conditions.158, 159, 160 PdO was calculated by

sampling in a (9×9×7) k-point grid and the optimized DFT result gave lattice constants of a = 3.05 Å and c

= 5.48 Å, in good agreement with experimental data. Calculation of energies of molecules (O 2, H2, H2O)

were performed in a 10 Å cubic super cell with Gamma k-point grid sampling.

For the determination of the surface termination we follow the surface ab initio thermodynamics

approach established by Scheffler and co-workers.72, 27, 52, 28, 161, 162, 163The underlying principle for this

approach is that the observed termination for a given gas-phase of defined (T, Pi) is the one with lowest

surface free energy, where T is temperature and Pi are the partial pressures of species i. Specifically

considered is a constrained equilibrium, in which the surface is separately in equilibrium with i gas

reservoirs of the i gas phase species, and therefore no provision exists for gas-phase reactions (and

concomitant equilibration between the different gas reservoirs). The normalized surface free energy Ω

of a given surface termination at the given gas-phase conditions is then obtained by the following

expression

Ω(T, Pi) = [ Gslab(T, Ni, Pi) – ΣiNiμi(T, Pi)] / 2A , (3.1)

where Gslab denotes the Gibbs free energy of the specific surface slab, μi(T,Pi) are the chemical potentials

of species i for a given temperature T and partial pressure Pi, and Niis the number of atoms (or

molecules) of species i present in the system. The surface free energy is normalized by the surface area,

2A, where A is the area of the surface unit-cell, and the factor of 2 accounts for the fact that all slabs are

modeled as mirror structures with two equivalent surfaces.

The chemical potential of gas-phase species i can be obtained by the following equation:

μi(T, P) = ΔH(T, Pº) + Egas – TΔS(T,Pº) + kBT ln(P/Pº), (3.2)

where Egas is the total energy of the isolated gas phase molecule i, ΔH and ΔS represent the changes in

enthalpy and entropy associated with the temperature of the system at standard pressure P°, and the

final term describes the free energy change with respect to the actual partial pressure of the gas phase

species. In practice ΔH and ΔS were calculated by the Shomate equation using the data from the NIST

database.164,165 Rigorously, Gslab can be expressed as

Gslab = Etotal + Fvib- T Sconf + pV, (3.3)

where Etotal is the total energy of the slab, Fvib is the vibrational free energy, and Sconf is the configurational

entropy. As previously discussed in detail by Reuter and Scheffler, 72 Equation (3.1) may be simplified

greatly by recognizing that the difference in the Gibbs free energy between the slab and clean metal, the

free energy contributions cancel to a large degree. Therefore equation (3.1) can be approximated as

follows:

Ω = [Etotal – ΣNi μi(T, Pi)] / 2A, (3.4)

where Etotal is given by the DFTcalculations. Utilizing Equation (3.4), surface energies for different

structures at various thermodynamic conditions (T, PO2, PH2) are obtained.

In this study a large number of candidate surfaces were evaluated and a comparison of their

stability was examined over a large range of partial pressures of both O 2 and H2 for a given temperature,

following the previous examples of Reuter et al. and Jelic and Meyer.72, 27As will be shown, only a certain

sub-set of these candidate structures were actually found to be most stable in the range of chemical

potentials examined. However, as always, we are limited here by our need to calculate ordered

structures with defined stoichiometry in unit cells of finite size, and it is certainly possible that there are

stable structures which we did not consider.

Finally, the stability of an adsorption structure can also be expressed through its binding energy 72.

For example, for gas-phase species i adsorbed at the Pd(100) surface its binding energy ∆Ei@Pd(100) is given

by

) /( @ (100)@ (100) (100) itotal total totalE NE E E iii Pdi Pd Pd N

(3.5)

Where

Ei @Pd (100 )total

is the total energy with species i at the Pd(100) surface,

EPd (100 )total

is the total

energy of the clean Pd(100) surface, and Etotal

is the total energy of an isolatedmolecule i. ni is the

number of species i on one surface unit cell.

1.3 Results and Discussion

First, different adsorption structures of oxygen were examined for Pd(100) within the constrained

thermodynamic equilibrium approach. In this work, three different ordered adsorption structures

containing dissociated O in a p(2×2), c(2×2), (3√2×√2) R45°, (1×1) arrangement, as well as the

(√5×√5)R27°PdO(101)-Pd(100) surface oxide have been calculated. The p(2×2), c(2×2), (3√2×√2) R45°,

(1×1) structures are the expected structures for coverage of O on Pd(100) at 0.25 monolayer

(ML), 0.50 ML, 0.67 ML and 1.00 ML, respectively. The binding energies were calculated by eq. (5)

with respect to the O2 gas phase molecule. Previous studies115, 52indicated the adsorption of oxygen on

the fourfold hollow site as most stable one and based on these results, only O adsorption at the fourfold

hollow site of Pd(100) was considered in this work. All adsorption energies calculated by above methods

are shown in Table 3.1 and the corresponding structures are shown in Figure 3.1. The calculated

adsorption energies for the p(2×2) and c(2×2) structure agree with the data from previous

calculations.72 It is obvious that the adsorption energy decreases as the O coverage increases from 0.25

ML to 1.00 ML. This decrease is associated with repulsive interactions between adsorbed O atoms 108. A

closer look at the side view in Figure 3.1 shows that the Pd(100) surface structure with 1.00 ML

adsorbed O restructures in response to the adsorbate. The palladium atoms have been pulled out from

the (100) surface by the surrounding oxygen, which is indicative of the formation of a surface oxide. In

fact experimentally, coverages of O above 0.5 ML are not found to be stable as Low Energy Electron

Diffraction and Scanning Tunneling Microscopy experiments indeed indicate the formation of surface

oxides starting at an O coverage of ~ 0.5 ML.115,106

Coverage Θ Ebind(eV)

Pure O structures

p(2×2)-Ohol 0.25 -1.26

c(2×2)-Ohol 0.50 -1.06

(1×1)- Ohol 1.00 -0.88

Pure H structures

p(2×2)-Hbr 0.25 -0.34

p(2×2)-Hhol 0.25 -0.41

c(2×2)-Hhol 0.50 -0.47

(3√2×√2) R45°- Hhol 0.67 -0.45

(1×1)- Hhol 1.00 -0.45

Mixed O/H structures

(2×2)-Ohol-Hhol 0.50 -1.73

Table 3.1: Adsorption energies (per atom) of O/H atom on Pd(100). For the mixed adsorption structure, energies are given by one surface.

Figure 3.1: View of different O adsorption on Pd(100) structure; (a) top view of p(2×2), representing 0.25 ML coverage; (b)top view of c(2×2),representing 0.50 ML coverage; (c) top view of (1×1), representing 1.00 ML coverage; (d) side view of p(2×2) ; (e)side view of c(2×2); (f) side view of (1×1). Red (dark gray) spheres indicate the oxygen atoms while blue (light gray)spheres are the palladium atoms.

For H adsorbed at Pd(100), we first compared the stability of H on atop sites, bridge sites and hollow

sites within a p(2×2) arrangement. The obtained energetic preference for the four–fold hollow site

agrees with Hennig and Lober’s previous results.166 Results for higher coverage of H on Pd(100) including

c(2×2), (3√2×√2)R45° and (1×1) arrangements with H always in hollow sites were consequently

obtained. Calculated adsorption energies are listed in Table 3.1 and corresponding structures

are shown in Figure 3.2. The adsorption energy of H reaches a maximum at 0.50 ML. This is in

agreement with the experimental observation that hydrogen islands with the c(2×2) structure

are formed at the coverage near 0.5 ML indicating attractive lateral interactions are present at

this coverage.167

Figure 3.2: Top view of different H adsorption structures on Pd(100) ; (a) top view of p(2×2), representing 0.25 ML coverage; (b)top view of c(2×2),representing 0.50 ML coverage; (c) top view of (1×1) ; (d) top view of (3√2×√2) R45°, representing 0.67 ML coverage. White (white) spheres are hydrogen atoms while blue (light gray) spheres are palladium atoms.

Co-adsorption of H and O on Pd(111) has been previously studied with scanning tunneling microscopy,

indicating repulsion between H and O leading to formation of O islands and H islands on the surface. 149,

150, 151, 152, 153However, Pd(100) has seen considerably less study. Co-adsorption of ordered H and O on the

Pd(100) surface has been calculated in our work. Adsorption energies of H and O co-adsorption are

lower than sum of the adsorption energies of the respective pure ad-layers of O and H except in the case

of 0.25 ML of H and 0.25 ML O co-adsorption. In this case, the adsorption energy is slightly higher due to

the low density of adsorbates on the surface. However, with increasing coverage, the surface becomes

more crowded and repulsive lateral interactions lead to decreasing adsorption energies, which shows H

and O have similar behavior on Pd(100) as on Pd(111) though Pd(100) is more open. Previous work by

Nyberg and Tengstal indicates that O and H will form an ordered structure when co-adsorbed at low T

and annealed to 275 K with p(2×2) symmetry.147

Once the O coverage has reached 0.5 ML, a surface oxide will be the thermodynamically favored

phase. The oxide thin film model structure (√5×√5)R27°PdO(101)-Pd(100) has multiple high-symmetry

sites, top, bridge and hollow as discussed in Reuter et al. (all sites are shown in Figure 3.4).30 Adsorption

of O on the monolayer oxide film has previously been addressed. It has been determined that

adsorption on the bridge sites on the √5 surface has been found to be -0.04 eV at 0.20 ML O coverage.

At higher coverage (0.40 ML O coverage) where O is adsorbed on both bridge sites of the unit cell at the

same time, O adsorption is thermodynamically unfavorable.

Ohol-Hhol 2Ohol-Hhol Ohol-2Hhol 2Ohol-2Hhol

Figure 3.3: Top view of considered coadsorbed overlayer structures of O and H on Pd(100). White (white) spheres are hydrogen atoms, red (dark gray) spheres are oxygen atoms and blue (light gray) spheres are palladium atoms.

Figure 3.4: Top view of high-symmetry adsorption sites on the (√5×√5)R27°PdO(101)-Pd(100) surface oxide structure. Red (dark gray) spheres are oxygen atoms while blue (light gray) spheres are palladium atoms.

Although hydrogen and oxygen adsorption has been well studied on Pd metal surfaces, only UHV

studies have examined co-adsorption on the oxide. Hakanoglu et al. observed H2 adsorption and

dissociation (via water formation) on their four-layer of PdO(101) thin film model grown above

Pd(111).135 However, in this case, the oxide film is multi-layer as opposed to the single layer oxide thin

film. Previous X-ray diffraction results indicate that monolayer of PdO is stable under 600 K and 1 atm O 2

over one hour but that the bulk oxide will not form under these conditions.28 Using DFT calculations,

Blanco-Rey et al. found that H2 is unable to adsorb on to the monolayer oxide surface because of the

repulsive electrostatic force on H2 caused by charge accumulation.48 However, dissociative adsorption of

H2 whereby H atoms bond atop to O in the PdO film to form hydroxyl groups is favored. Results from our

calculation confirmed that no molecular adsorption of H2 on the monolayer oxide model can occur while

the molecular adsorption of H2 on the four-layer model is possible.151 In a similar fashion, the adsorption

of H atoms has been examined on all sites. H adsorption on the bridge sites is possible though it is also

very weakly bound (binding energies in two bridge sites are -0.05 eV and -0.02 eV referenced to gas

phase H2). H adsorption is unstable on any of the atop sites or hollow sites and when performing

geometry optimizations starting in configurations with adsorption on those sites, upon relaxation the

adsorbed H atom always moves to the respective neighboring bridge site. As in the case of O, the

adsorption of two H on neighboring bridge sites on the √5 surface is thermodynamically unfavorable.

From kinetic studies of CO oxidation, it is known that reduction of the oxide surface may result in

removal of a fraction of the oxygen atoms and surface restructuring.86 As shown above, H adsorption on

the pristine metal Pd(100) surface is stronger than on any site of PdO(101). Based on the idea of

“reducing” the surface oxide, the upper oxygen atoms were removed and H atom adsorption was

examined at the hollow sites left by O. Results show that H atoms are more stable on this hollow site (-

0.38 eV) than on the bridge site (-0.05 eV/-0.02 eV). However, the adsorption energy of H to the hollow

site is much weaker than for O (-1.81 eV) to the same site, which implies O will preferentially occupy the

hollow sites when the two adsorbates compete for this site.

Comparing aforementioned structures by applying Equation (4) at various partial pressures of H2 and

O2, a phase diagram under different thermodynamic condition (T, pO2, pH2) has been constructed to

reflect the stable region of a particular surface termination and the diagram is shown in Figure 3.5. The

phase diagram as presented can be translated from chemical potential to T, P by setting the

temperature constant and viewing the changes in chemical potential as changes in the partial pressures

of the gas species. As indicated in Figure 3.5, if the temperature is assumed to be 600 K then the partial

pressure of H2 can be varied from ultra-high vacuum conditions to pressures well exceeding normal

reaction conditions along the y-axis. Similarly, following the x-axis across from the left to the right, one

can follow the increase in oxygen pressure. Starting in the lower left corner at low partial pressure for

both species, and moving from the left to right, one can examine the change from pristine Pd (100) to,

p(2×2)-O/Pd(100) and ultimately to(√5×√5)R27°PdO(101)-Pd(100) as the O2 pressure is increased. The

disappearance of c(2×2) from the phase diagram indicates this is a metastable surface produced

by the exposure kinetics according to Scheffler and co-workers.72Alternatively, when

maintaining an extremely low chemical potential (partial pressure) of O2 and increasing the H2

pressure (chemical potential), the surface will change from pristine Pd(100) to

c(2×2)-H/Pd(100), then to (1×1)-H/Pd(100).

Figure 3.5: Phase diagram for Pd (100) system in contact with gas reservoirs of H2 and O2 at T = 600 K assuming considering co-adsorption of H and O only.

In addition to these stable phases involving one of the adsorbates, there are also stable

phases that involve both oxygen and hydrogen. Without considering formation of OH on the

surface, co-adsorbed hydrogen and oxygen on Pd(100) at 0.25 ML coverage appears on the

phase diagram. Co-adsorbed O and H is only stabilized in a narrow area then disappears as

increasing O coverage results in the formation of the surface oxide. Phases involving H

adsorbed oxide surfaces are possible when the partial pressures of H2 and O2 both extremely

high (107 atm). For the primary conditions of interest however, around 1 atm for both H2 and

O2, for example, the phase diagram indicates the surface oxide will be present (but without any

adsorbed H). This result gives yet another example of the stability of thin oxide films even

under a significant reductant partial pressure.

In addition to the stable surfaces, one must consider the formation of bulk phases (oxides,

hydrides). For example, in extreme oxidizing conditions, bulk PdO would form. In our case, PdO

will form when

EPdObulk

¿ EPdbulk+μo , (3.6)

which defines the transition from the Pd to PdO at increasing oxygen pressure indicated by the vertical

line at ∆μO = - 0.96 eV. Similarly, this bulk oxide will decompose due to reduction by H 2 once the

following condition is met

EPdObulk +μH2

<EPdbulk+μH 2O

(3.7)

and

μH 2

is sufficiently high. Since Etotal

O2

and Etotal

HHH 2

and under the

assumption of no reaction between H2 and O2 in gas phase for this so called “constrained equilibrium”

approach, expression (3.6) and (3.7) can be written respectively in Equation (3.8) and (3.9)

Δμo ¿ EPdObulk −EPd

bulk−EO2

total

(3.8)

ΔμH ¿−EPdObulk +E Pd

bulk+EO2

total+EH2Obind −EH 2

bind−12

EO2

bind

(3.9)

Conversely, in extreme reducing conditions, bulk PdH would form. There are two palladium

hydride phases: α and β168. In our calculation, only β palladium hydride has been considered.

The structure of β palladium hydride adopted herein is PdH. PdH will form when

EPdHbulk

¿ EPdbulk+μH

. (3.10)

Equation (3.10) defines the transition from the Pd to PdH at increasing hydrogen pressure indicated by

the vertical line at ∆μH = - 0.14 eV. Similarly, this bulk hydride will decompose due to oxidation by O 2

once the following condition is met

EPdHbulk +0.5 μO<EPd

bulk+0. 5 μH2O

(3.11)

As discussed,

EO2

total

,

EH 2

total

,

EO2

bind

,

EH 2

bind

are obtained by DFT calculation of the molecules in

vacuum. Previous work shows that palladium hydride can be formed at very low H2 partial pressure and

the start forming pressure is increasing with the ratio of H and temperature. 168-170 Formation of β PdHx

starts at around P(H2) = 0.01 atm at 300 K according to the phase-diagram obtained by Lewis while

Schogl found β PdHx formed at 1 mbar at 320 K.168,171 Obviously H/Pd ratio x and temperature affect the

formation pressure dramatically. Our result indicates formation of bulk PdH starts at P(H 2) = 102.2 atm at

300 K while at 600 K, required pressure of H2 is about 104.8 atm. Over-binding of H2 as calculated by GGA

functionals leads to PdHX formation pressures that are much higher compared to experimental data,

which also observed in a ReaxFF investigation of hydride formation in Pd nanoclusters from Senftle and

co-workers.172

Overall, the basic shape of the H2-O2 phase diagram of Pd(100) is very close to the CO-O2

phase diagram.72 The partial pressure of H2 required to decompose the bulk oxide at 600 K and

PO2 = 1 atm is only 0.0001 atm indicating that H2 is strong reductant like CO which requires an

even lower partial pressure of about 10-7 atm to decompose the bulk oxide under the same

conditions. This is in sharp contrast to NO which required a pressure of 10 10 atm at 600 K and 1

atm O2 to decompose bulk PdO. However, compared to CO or NO adsorption, H adsorption on both

Pd(100) and the PdO surface is very weak and therefore the portion of the phase diagram that involves

adsorption of the reducing gas is small.

In either CO oxidation or NO oxidation, there is no intermediate produced, but for H 2 oxidation, the

intermediate OH was observed as a stable species on the Pd (100) surface147 by EELS under 215 K. DFT

calculation results show the binding energy of OH to surface is up to 1.98 eV. Therefore in our work, we

also examined surface structures with OH to determine how the phase diagram would change. Table 3.2

shows the calculated adsorption energies of OH with different coverage on the surface and detailed

structures are shown in Figure 3.6 at various OH coverage, 0.25 ML, 0.50 ML, and 1.00 ML. Obviously

repulsive interactions between OH groups become stronger as the coverage increases, which is

indicated by the decreasing binding energies for increasing coverage. For H adsorption on the surface

oxide, there are additional sites, atop the four O atoms on the surface, which are not available for CO.

Results show that the oxide thin film structure is stable when the H binds to the higher O atom, which is

not true when H binds to the lower O atom. The binding energy is~0.5 eV for both cases. As shown in

Figure 3.7, inclusion of OH terminated structures, dramatically changes the phase diagram in the region

of medium to high chemical potentials of both O2 and H2, where the formation of OH becomes available.

In either the low O2 pressure area or low H2 pressure zone, the phase diagram is essentially unchanged

since either the low chemical potential of H2 or O2 makes the formation of OH unlikely. However, the

predominant surface in the primary region of interest is no longer the bare surface oxide but one which

is covered by OH groups at the bridge sites. The formation of OH on Pd(100) has been previously studied

by Nyberg and Tengstal.155 They found that no reaction occurs between O and H below 275 K under

ultrahigh vacuum conditions. At 300 K O and H will react, but did not form stable OH groups on the

surface, and instead formed H2O directly which then desorbs. In contrast, the reaction of O and H 2O on

the Pd(100) surface at 110 K formed OH which was then stable up to 300 K. This result indicates that OH

formation from O and H on Pd(100) is kinetically limited. While our diagram shows a vast region

dominated by OH groups, there are kinetic limitations which may prevent its observation under reaction

conditions. OH groups have been observed previously on the surface of Pd nanoparticles under CH 4

oxidation conditions by Ciuparu et al..173

Coverage Θ Ebind(eV)

Pure OH structures

p(2×2)-OHhol 0.25 -1.98

c(2×2)-OHhol 0.50 -1.79

(1×1)- OHhol 1.00 -1.20

Pure H2O structures

p(2×2)- H2O hol 0.25 -0.18

c(2×2)- H2O hol 0.50 -0.24

Table 3.2: Adsorption energies (per OH group) of OH atom on Pd(100) and adsorption energies of H2O on Pd(100).

Ebind(eV) Ebind(eV)

Hbr -0.05(-0.03) Obr -0.04(-0.01)

OHbr -1.86

H2Obr -0.13 2OHbr -3.08

Table 3.3: Calculated binding energies of different species (H, O, OH) at bridge sites on the √5 surface.

Figure 3.6 Top view of different OH adsorption on Pd(100) structure; (a) top view of p(2×2), representing 0.25 ML coverage; (b)top view of c(2×2),representing 0.50 ML coverage; (c) top view of (1×1), representing 1.00 ML coverage. White (white) spheres are hydrogen atoms while blue (light gray) spheres are palladium atoms and Red (dark gray) spheres are oxygen atom.

Figure 3.7: Phase diagram for Pd (100) system at T = 600 K considering the possible formation of OH intermediates.

In the cases for CO oxidation and NO oxidation, the formed product on the surface, either CO 2 or NO2

has been assumed to be readily transported away.72, 27Water adsorption may be stabilized on metal

surfaces154, 174 and on oxide surfaces like PdO(101)146 as well. Therefore structures with molecular water

have also been considered in our work. Formation of a hydrogen bond between the surface and the

water molecule makes the higher coverage on Pd(100) favored when the coverage of H 2O goes from

0.25 ML to 0.50 ML, the binding energy changes from -0.18 to -0.24 eV per water molecule. According to

Nyberg and Tengstal, an intermolecular hydrogen bond forms with increasing coverage of H2O and an

ice-like two-dimentional adsorption layer may form on Pd(100).147 The binding energy of H2O in the

bridge site on the √5 surface is -0.13 eV. Calculation of various coverages of OH/H 2O done by Weaver et

al. indicated a combination of HO-H2O at a coverage of 0.5 ML is most stable for the four layer PdO(101)

surface.116 Most of the phase-diagram is dominated by H2O termination, if one does not consider its

desorption. However, under typical reaction conditions (600 K, 1 bar), the free energy gain through

removal of H2O from the surface to the gas phase would outweigh the adsorption energy by 1.10 eV at

600 K and 1 atm. Note that the approach presented here is a constrained thermodynamic approach as it

does not connect the H2 and O2 reservoirs in the gas phase with a corresponding H2O reservoir.

Obviously given the highly exothermic formation of water from H2 and O2, relaxing that constraint would

lead to a trivial result.

1.4 Conclusions

Density functional theory calculations linked to thermodynamic methods have been applied to explore

the stability of different surface structures under various thermodynamic conditions (T, PO2, PH2). A

complete surface phase diagram has been constructed. H2 is a strong reductant, like CO, and therefore

the bulk oxide formation region is small compared to NO oxidation. In contrast to NO and CO oxidation,

the phase diagram of H2 oxidation is dominated by surfaces involving the presence of a surface

intermediate, OH. Under typical reaction conditions, the favored surface termination will be a

hydroxylated monolayer oxide film. This result seems to be in agreement with previous experimental

results of Pd methane oxidation catalysts.