1 FIRST-PRINCIPLES KINETIC MONTE CARLO STUDY OF NO OXIDATION ON

Pd(100) AND PdO(101)(√5×√5)R27°-Pd(100)

1.1 Introduction

The development of diesel and lean-burn gasoline engines has been spurred by increasingly

stringent requirements for fuel economy since increased fuel efficiency can be achieved by combusting

hydrocarbons at high air/fuel ratios89,90. However, toxic NOx exhaust gases dramatically increase as the

air/fuel ratio increases (>14.7:1), and these pollutants cannot be completely removed with conventional

three-way catalysts under oxygen-rich conditions. One of the strategies of handling the higher NOx

levels in lean burn automotive emissions is a NOx storage reduction (NSR) system91,92. Noble metals like

platinum and palladium have been used as the active metal components in NSR catalysts due to their

performance at low temperature, and their thermal stability55-58. Although Pd has been shown to

demonstrate even better performance at low temperature than Pt56, Pd, unlike Pt, may form an oxide

under NO oxidation conditions93. Ribeiro et al. suggested that formation of oxides on small Pt particles

was detrimental to their activity and resulted in poor performance. 23 However, in their DFT based micro

kinetic modeling examination of Pt, Ir, Os and their oxides, Hu et al. reported that metal oxides may

exhibit comparable activity to metal surfaces for NO oxidation and, in fact, IrO 2 out performs Ir26.

Previously in the DFT based ab initio thermodynamics examination of Pd over a range of O2 and NO

partial pressures, Jelic and Meyer found that bulk PdO is thermodynamically stable under the typical NO

oxidation mode of a NSR catalyst (600 K, 1 atm O2, 0.001 atm NO).27 However, grazing incidence X-ray

diffraction results from Lungren et al. indicated that no bulk oxide was observed to form under 1 atm of

O2 (without the presence of NO) and 600 K after one hour due to kinetic limitations. 28 From these

observations, it was suggested that a thin film surface oxide (√5×√5)R27°PdO(101) is an appropriate

model for the catalytic surface for NO oxidation in the NSR cycle.29, 30 We have used this model in DFT

based kinetic Monte Carlo simulations and found that, as in Hu et al.’s examination of the bulk oxide

terminations, the turnover frequency of the PdO(101)/Pd(100) surface oxide is on par with metal

surfaces.26, 29 The role of the surface oxide in NSR catalysis is of further interest due to the transient

nature of the process. When the surface cycles between the oxidizing regime and the reducing regime,

the surface oxide must be created and destroyed. Modeling this process explicitly is difficult given the

time scales involved. However, we can gain insight into this process by using a first principles kinetic

Monte Carlo technique. The role of surface oxides in CO oxidation has been previously debated by

Frenken et al., and Goodman et al.32-35.While Frenken’s work with in situ STM and SXRD reactor of Pd

single crystals showed significant roughening with a concomitant increase in activity, the PM-IRAS and

reactivity data from work of Goodman suggest that the active phase is metallic. More recently

Rupprechter and co-workers examined CO oxidation on Pd, PdOx<1 and PdO nanoparticles on alumina

support and concluded that oxygen covered metallic palladium contributes the highest catalytic activity

based on the experimental results that Pd and PdOx<1 have almost equally high catalytic activity while

PdOx<1 can be reduced completely to Pd even under low partial pressure of CO36. In a prior study of CO

oxidation, it was found that CO oxidation led to the formation of a region of meta-stability in which the

phase transformation (either from the surface oxide to the metal or from the metal to the surface oxide)

that is predicted thermodynamically is hindered kinetically.94 This result suggests that the answer to the

debate over the nature of the active surface is a combination of both surfaces rather than a single

surface. Now we will move this examination to determine how NO oxidation differs from CO oxidation

given that CO is a much stronger reductant than NO. We will also seek to determine if the nature of the

surface can be identified in NSR catalysis and determine if or how meta-stability plays a role.

1.2 Theory

1.2.1 First-principles kinetic Monte Carlo simulations

A first-principles kinetic Monte Carlo method is used herein to examine the surface stability under

reaction conditions by analyzing the steady-state coverage of NO and O in micro-kinetic models as a

function of thermodynamic conditions (T, PNO, PO2, PNO2). However, unlike mean field micro-kinetic

models, the spatial distribution of the surface species is explicitly determined and accounted for.

Furthermore, kinetic Monte Carlo simulations allow one to follow the time evolution of the catalytic

surface by coarse graining rare-event dynamics80, 95-97. It has been previously used successfully to

improve understanding of the activity and stability of specific structures under particular

thermodynamic conditions84, 86, 94.

Without accounting for the short-time dynamics of the system in between states, one kinetic Monte

Carlo step corresponds to the execution of a single rare event and each state is independent as the

system retains no knowledge of the preceding step. A complete list of relevant elementary processes

with their corresponding rate constants, kp, is required to create for a kMC model where kp characterizes

the probability of transition from the current state by the process p. The mathematic algorithm is

detailed in a review by Reuter80 and will be briefly described here. First a total rate constant, ktot, is

calculated by summing all possible rate constants for individual processes kp for a given initial

configuration: ktot = ∑pkp. The executed process is then chosen by the following inequality:

Σp=1q k p≥ρ1 k tot≥Σp=1

q−1 k p ，(2.1)

where ρ is a random number between 0 (not including 0) and 1. The configuration is updated by

executing the chosen process i and time evolution can be obtained by

t→t – ln(ρ2)/ ktot ， (2.2)

herein, ρ2∈(0,1] is a second random number98.

The above mentioned rate constants are essential to a meaningful kinetic Monte Carlo simulation

and they can be obtained from DFT based transition-state theory (TST) calculations. Based on our

models for NO oxidation over Pd(100) and (√5×√5)R27°PdO(101) four different types of elemental

process have been included: adsorption, desorption, diffusion, and reaction.

1.2.2 Rate Constants

1.2.2.1 Adsorption

The rate constant of adsorption k i , stads (T , pi )of species i with partial pressure

pi on a surface site of

type st is a function of the impingement rate and the local sticking coefficient~S i , st as shown in equation

(2.3):

k i , stads (T , pi )=

~S i , st (T )pi A

√2πmi k BT . (2.3)

Herein A is the surface area of the unit cell; mi is the mass of species i; k B is the Boltzmann constant,

and T is the temperature of the system. The sticking coefficient gives a statistical average fraction of

the impinging particles that stick to a given free site of the specified site st at temperatureT as

described in following equation:

~S i , st (T )=f i , stads Ast ,i

Aexp(−

ΔE i , st , j

kB T).(2.4)

In equation (2.4),A st , i is the active area such that the ratio of Ast,i/A represents a geometric factor of the

fractional surface area which is available for the molecules for adsorption when impinging on the

surface and ΔE i , st , j is the adsorption barrier (if any) along the minimum energy pathway (MEP). f i , st

adsis

an efficiency factor which describes the fraction of impinging gas phase molecules that travel along the

MEP as opposed to those which do not and therefore experience a higher barrier. Herein, as in previous

work, it is simplified to 1 since most of the molecules do follow the MEP84, 86, 87, 94.

1.2.2.2 Desorption

The desorption process is the time-reversed process of adsorption, therefore the desorption rate

constant is relative to the adsorption rate constant by equation (2.5):

k i , stdes (T , pi )=k i , st

ads (T , pi )exp (−ΔG i , st (T , pi )

kB T).(2.5)

The change in the Gibbs free energy, ΔG i , st (T , pi ) can be approximated by the difference between the

chemical potential of the species i in the gas phase and the binding energy of species i in the adsorbed

state: ΔG i , st (T , pi )=μgas , i(T , pi )−E st , ibind

.

1.2.2.3 Diffusion

Once adsorbed on the surface, species i can diffuse to other surface sites with a barrier

obtained by transition state theory identifying the saddle point along the diffusion pathway. The

diffusion rate constant for species i from site st to site st’ can be written as

ki , st →st 'diff (T )=f

i , st →st 'diff ,TST (T )(

kB Th

)exp(−ΔE i ,st → st '

diff

kB T).(2.6)

In equation (2.6), f

i , st →st 'diff , TST

is the ratio of the vibrational partition functions in the transition state and

that in the initial state, which is generally smaller than but very close to 1. Considering the error from

DFT, using 1 instead of the real value off

i , st →st 'diff , TST

is an acceptable approximation. Therefore in our work,

the diffusion rate constant is simplified as:

ki , st →st 'diff (T )=(

kB Th

)exp (−ΔE i , st→ st '

diff

kB T)

.(2.7)

1.2.2.4 Reaction

Finally, species on the surface can react with each other. The barrier for reaction can be determined

by using transition state theory if a suitable reaction coordinate can be identified that contains a saddle

point. The rate constant can be calculated as written in equation (2.8):

k i→ freac(T )=f i→ f

reac ,TST (T )(kB T

h)exp(−

ΔE i→freac

k BT).(2.8)

In equation (2.8), ΔE i→ freac

is the reaction process barrier, the energy difference in the transition and

initial state and f i→freac , TST

is ratio of the partition functions in the transition and initial states. Again, in

our work we artificially assign f i→freac , TST

equal to 1. Of course both forward and reverse reaction rates

must be considered.

1.2.2.5 Computational setup

The Vienna Ab Initio Simulation Package (VASP) utilizing a plane wave basis set with a

cutoff energy of 500 eV has been employed to perform the DFT calculations99, 100.The projector-

augmented wave (PAW)101 pseudopotentials were adopted in this work and all calculations have

been done using the Perdew-Burke-Ernzerhof (PBE)102 exchange-correlation functional. The

Climbing Nudged Elastic Band (NEB) method has been used to determine the reaction paths and

barriers103. Calculation of the energies of molecules (O2, NO, NO2) was done in a 10Å cube with

a 1×1×1 k-point grid sampling.

For Pd(100), pure palladium metal surface models used in this work are inversion-symmetric slabs consisting of five Pd(100) layers with

potential adsorbates (NO, O etc) on both sides, with the middle layer fixed. A uniform 7×7×1 k-point grid is employed for the

Brillouin zone104 with a (2×2) unit cell.

The surface oxide will use the previous employed model of Todorova et al a

(√5×√5)R27°PdO(101) structure above Pd(100). 30 A 1×1 unit cell of the √5 surface is used with a 5 layers

Pd(100) slab beneath a single oxide layer. All atoms are set to relax except the very three center layers

of palladium metal. The slabs are separated by approximately five layers of vacuum. A uniform 7×7×1 k-

point grid is used for the Brillouin zone. Lattice constants are consistent with the experimental values.

Geometries are considered to be optimized once a force less than 0.02eV/Å is achieved.

1.2.3 Kinetic Monte Carlo model

Appropriate lattice models are required to perform kinetic Monte Carlo simulations. Herein a

(1x1) Pd(100) surface shown in Figure 2.1 is adopted as a model for the clean metal surface

while a monolayer of PdO(101) above the Pd(100) surface (known as the √5 structure shown in

Figure 2.2) is applied as the model of ultra-thin surfaceoxide30.

1.2.3.1 Pd(100)

Considering strong lateral interactions between surface species105 and the morphology

transformation caused by high coverages of O (≥0.5 monolayer (ML)106, the coverage has been

limited to a range of 0-0.5 ML. Previous experimental107 and theoretical108 studies both indicate

that O preferably adsorbs on the fourfold hollow sites at Pd(100) for O coverages of 0-0.5 ML.

However, for NO, the evolution of coverage is more complicated. Core level photoemission and

LEED data from Jaworowsk and co-workers109 shown that NO prefers fourfold hollow site at

coverage up to 0.25-0.30 ML, while NO only occupies bridge sites when the NO coverage rises

to 0.5 ML. Based on above observations, in our kMC model for Pd(100) O is fixed to exclusively

adsorb on fourfold hollow sites while NO can adsorb on either hollow sites or bridge sites.

Nearest-neighbor positions have been blocked for oxygen adsorption and diffusion processes

since the lateral interactions between nearest-neighbor sites are very strong (up to 1.0

eV)according to Zhang and coworkers108. Occupation of second-nearest-neighbor sites is allowed

despite the fact that moderately repulsive interaction exists108. Therefore O2 dissociative

adsorption requires an ensemble of eight empty sites known as the 8-site rule110-113. The nearest-

neighbor sites are also blocked for NO adsorption and diffusion due to lateral interactions.

For NO oxidation on Pd(100), there are 18 possible processes including adsorption,

desorption, diffusion, and reaction events included in the model. The data for the event list are

given in Table 2.1.

Figure 2.1: Top view of the Pd(100) surface. The white square area is for one unit cell of 1×1 Pd(100) surface.

ΔEO2 , hol−holadd

= 0.00 ΔE NO, hol

add= 0.00

ΔE NO, bradd

= 0.00ΔE NO2, br

add= 0.00

ΔEO2 , hol−holdes

= -2.51ΔE NO, hol

des= -2.08

ΔE NO, brdes

= -2.08ΔE NO2 ,hol

des

= -1.42

ΔEO,hol→holdiff

= 0.28ΔE NO,hol→ hol

diff= 0.28

ΔE NO,br →brdiff

= 0.56ΔE NO, br→hol

diff= 0.09

ΔE NO, hol→brdiff

= 0.10ΔE NO2 ,hol→hol

diff

=0.37

ΔE NOhol+Oholreac

= 0.75ΔE NObr+Ohol

reac= 0.81

ΔE NO2→NOhol+Oholdiss

= 0.42ΔE NO2→ NObr+Ohol

diss

= 0.62

Table 2.1: Summary of DFT binding energies, diffusion and reaction barriers on Pd(100). All values are in eV.

1.2.3.2 √5 surface oxide

The monolayer surface oxide structure (√5×√5)R27°PdO(101)-Pd(100), described in detail

by Todorova and coworkers23 has been previously adopted as a model for an ultra-thin surface

oxide30, 72, 86, 87. Previously, the unit cell of the √5 surface oxide in the kMC model has been

constructed to be half the size of the true unit cell of the √5 oxide film to simplify the structure.

Since differences in the adsorption energies of species on the two different “upper” (hollow) sites

are often smaller than 0.05 eV, these two sites herein can be considered as equivalent. Similarly,

the difference in adsorption energies of O or NO on the two different bridge sites are less than

0.1 eV and therefore the two bridge sites are also considered as equivalent. The surface structure

is shown in Figure 2.2.

For the kMC model of√5 surface oxide, the available adsorption sites for oxygen and NO are

Pd atop sites, bridge, and hollow sites (which are produced by removing the top O from the

surface). However, the binding energies of NO on Pd atop sites (0.9 eV and 0.5 eV respectively

for atop 2f site and atop 4f site (site designations are shown in Figure 2.2)) are much lower than

that on bridge sites (1.55 eV) and hollow sites (2.31 eV). Such a small NO adsorption energy on

the Pd atop site implies that NO would diffuse to the bridge or hollow site before any reaction

can occur at the atop sites at steady state. O atoms are extremely stable on the hollow site with a

-1.97 eV binding energy, which seems logical since it will make the surface stoichiometrically

complete. Comparing to the binding energy of O on to the surface at hollow and bridge sites, O

on atop sites (0.4 eV and 0.2 eV respectively for atop 2f site and atop 4f site) are very weak,

which leads to the need to consider only O on the bridge and hollow sites being considered in our

model.

The coverage of the higher position oxygen is an indicator of the stability of the monolayer

of surface oxide and the simulation specifically allows for their occupancy to change. However,

we do not explicitly calculate the reconstruction of the PdO(101) surface. Therefore in this kMC

model, positions of all Pd atoms and lower position oxygen atoms are fixed. When the

simulation is initialized, the upper oxygen atoms are removed and oxygen atoms, NO and NO2

molecules as well as empty sites are randomly assigned to these locations to give a starting

configuration for the system.

In this NO oxidation model, there are 38 possible elementary processes including adsorption,

desorption, diffusion, and reaction events. The values for each elementary processes were

calculated by the same method introduced in Rogal et al.’s work87. For NO oxidation, there are

seven adsorption processes in total: non-dissociative adsorption of NO on the bridge sites and

hollow sites, non-dissociative adsorption of NO2 on the bridge sites and hollow sites and

dissociative adsorption of O2 to hollow-hollow sites, hollow-bridge sites and bridge-bridge sites.

From the adsorption data shown in Table 2.2, it is obvious that only O2 dissociative adsorption

onto bridge-bridge sites has a barrier. Desorption from the surface was also calculated using the

adsorption energies shown in Table 2.3. From the data, we can easily conclude that all species

prefer adsorbing on hollow sites created by removing the higher position oxygen. Diffusion of

species on the surface can take place between bridge and bridge sites, bridge and hollow sites,

and hollow and hollow sites as shown in Table 2.4. Table 2.5 lists the four pathways of NO 2

formation that have been calculated in our work, with varying locations for NO and O:

NOhol+Ohol , NOhol+Obr , NObr+Ohol , NObr+Obr . Each NO2 formation reaction has a corresponding

reverse reaction of NO2 dissociation into NO + O, also shown in Table 2.5.

Figure 2.2: (a) Top view of the PdO(101)/Pd(100) surface oxide structure; (b) Side view of the PdO(101)/Pd(100) surface oxide structure. The oxygens with black circles are the higher position oxygens, which can be removed during the kMC simulation leaving a hollow site. The white square area represents one unit cell of the √5 surface oxide, which is split by the dashed line in the middle.

ΔEO 2 , hol−holadd

= 0.00 ΔEO 2 , hol−bradd

= 0.00 ΔEO 2 , br−bradd

=1.90

ΔE NO, holadd

= 0.00 ΔE NO, bradd

= 0.00

ΔE NO2, holadd

= 0.00 ΔE NO2, bradd

= 0.00

Table 2.2: Adsorption barriers of NO, O2 and NO2 on the √5 surface oxide.

ΔEO 2 , hol−holdes

= -3.94 ΔEO2 , hol−brdes

= -2.66 ΔEO 2 , br−brdes

= -1.38

ΔE NO, holdes

= -2.31 ΔE NO , brdes

= -1.55

ΔE NO2, holdes

= -1.27 ΔE NO2, brdes

= -1.15

Table 2.3: Desorption energies of NO, O2 and NO2 on the √5 surface oxide

ΔEO,br →brdiff

= 1.17 ΔEO , br→holdiff

= 0.41 ΔEO , hol→brdiff

= 1.69 ΔEO ,hol→holdiff

= 1.92

ΔE NO ,br→brdiff

= 0.44 ΔE NO, br→holdiff

= 0.51 ΔE NO, hol→brdiff

= 1.27 ΔE NO ,hol→ holdiff

= 1.16

ΔE NO2 ,br→brdiff

= 0.80ΔE NO2 ,br→hol

diff

= 0.40ΔE NO2 ,hol→br

diff

= 0.52ΔE NO2 ,br→br

diff

= 0.90

Table 2.4 Diffusion barriers of NO, O2 and NO2 on the √5 surface oxide

ΔE NObr+Ohol→NO2 holreac

= 1.08 ΔENObr+Obr→ NO2 brreac

= 1.31ΔE NOhol+Ohol→ NO2 hol

reac

=1.75 ΔE NOhol+Obr→NO2 brreac

= 0.54

ΔE NO2 hol→ NObr+Oholdiss

= 0.6ΔE NO2 hol→ NOhol+Ohol

diss

= 0.48ΔE NO2 br→ NObr+Obr

diss

= 2.06 ΔE NO2 br→ NOhol+Obrdiss

= 1.03

Table 2.5 Reaction barriers of NO + O → NO2 and dissociation barriers of NO2→ NO + O on √5 surface oxide

1.2.4 Simulation setup

The Pd(100) kinetic Monte Carlo simulations are performed through the kmos framework114

while reported results for √5 surface oxide work are obtained by our internally developed fortran

based kMC code and verified by kmos framework for √5 surface oxide. All simulations were

performed in (20×20) unit cells employing a periodic boundary condition. The grid size has been

confirmed large enough since no differences were observed in the steady state occupancies or

reaction rates when the cell size was increased to 40×40. The goal for this simulation is to

determine the average surface occupations θ̄i , st of species i on site st, and TOFs under steady-

state condition for a given thermodynamic condition(T , pNO , pO2

, pNO2). The average surface

occupations θ̄i , st of nth step of kinetic Monte Carlo simulation in the time step of Δtn can be

obtained through following equation:

θ̄i , st=∑n

θ i , st , n⋅Δtn

∑nΔtn .(2.9)

In Equation (2.9), θi , st , n is the coverage of species i at site st at nth kMC step after steady state has been

reached. Different initial configurations (clean surface, O-fully-covered surface and random-filled-

surface) have been tested and no multiple steady-state phenomena have been observed.

1.3 Results and Discussion

The stability of two surface structures, Pd(100) and (√5×√5)R27°PdO(101)-Pd(100) surface oxide,

under reaction conditions has been evaluated by monitoring the oxygen occupancy in the kMC

simulations.

1.3.1 Pd(100)

In our Pd(100) model, dynamic formation of surface oxide from pristine metal surface

Pd(100) cannot be observed with changes in partial pressure of O2 since the surface structure has

been fixed. Instead we applied an easy to observe indicator to determine whether the surface

oxide has been formed or not. The Pd(100) surface is expected to be stable when the coverage of

O on the surface is smaller than 0.25 ML which is representative for the experimentally

characterized p(2×2) overlayer28, 11328, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528,

115(Zheng and Altman, 2002a, Lundgren et al., 2004), 115In other words, the pristine metal surface

Pd(100) is considered stable only when coverage of O θ̄O ,hol is no larger than 0.25 ML (0.25 ML

is shown as a dotted line in Figure 2.3(a)). Based on the above assumption, a map of coverage of

O has been constructed for NO partial pressures ranging from 10-7to 1 atm and O partial

pressures from 10-7to 1 atm at 600 K. The oxygen coverage varies as a function of NO and O2

partial pressures in an intuitively expected distribution. For a fixed NO partial pressure, when the

partial pressure of O2 increases, the coverage of O on the surface gradually increases. As Figure

2.4 (a) shown at a fixed partial pressure of O2 (P(O2) = 1.0 atm), and P(NO2) = 10-13 atm, the

reaction order of NO is close to 1 when 10-5 ≤ P(NO) ≤ 0.1 atm. When P(NO) exceeds 0.1 atm,

the reaction order decreases. When P(NO) is fixed at 1 atm and P(NO2) = 10-13 atm, the reaction

order of O2 is close to 1 in the O2 pressure range 0.1 ≤ P(NO) ≤ 1.0 atm as shown in Figure 2.4

(b).

(a) (b)

Figure 2.3: (a) O coverage holO, on Pd(100) as a function of partial pressure of NO and O2 at 600 K. The

dotted black line between pink region and red region is the starting point of decomposition of surface

oxide; (b) O coverage holO, on the √5 surface oxide as a function of partial pressure of NO and O2 at

600 K and the dotted black line between pink region and red region is the starting point of formation of surface oxide.

(a) (b)

Figure 2.4: (a) The NO oxidation rate on Pd(100) as a function of the partial pressure of NO with fixed P(NO2) = 10-13 atm and P(O2) = 1.0 atm at T = 600 K; (b) The NO oxidation rate on Pd(100) as a function of the partial pressure of O2 with fixed P(NO) = 1.0 atm and P(NO2) = 10-13 atm atT = 600 K.

Figure 2.5: Average coverage of O on hollow sites as a function of the partial pressure of NO with fixed P(O2) = 0.2 atm and P(NO2) = 10-13atm at 600 K. Black squares indicate the results of simulations with the

reaction barriers obtained from DFT calculations(ΔE NObr+Ohol→ NO2 hol

reac

=1.08 eV, ΔE NOhol+Obr→NO2 br

reac

=0.54 eV);

Red diamonds represent the results of simulations with reduced reaction barriers(ΔE NObr+Ohol→NO2 hol

reac

=0.98

eV, ΔE NOhol+Obr→NO2 br

reac

=0.44 eV).

Figure 2.6: O coverage holO, on the √5 surface oxide as a function of the partial pressures of NO and O2

at 600 K (a) and at 450 K (b).

(a) (b)

Figure 2.7: Average coverage of O as a function of temperature and oxygen pressure on the √5 surface oxide model. (a)Average coverage of O as a function of temperature at P(O2) = 0.2 atm (black squares) and P(O2) = 0.00001 atm (red diamonds); (b) Average coverage of O as function of temperature and oxygen pressure.

1.3.2 √5 surface oxide

Just as in the case of Pd(100), we cannot explicitly observe the reconstruction of the surface

oxide as the film decomposes. Instead, we use a fixed lattice and apply a decomposition criteria

to mark the transition from the oxide to the metal 27. We set the decomposition condition to

match previous studies of CO oxidation87 whereby decomposition of surface oxide occurs when

the average coverage of O in the hollow siteθ̄O ,hol falls below 90%. Following this criteria, if

θ̄O ,hol ≥ 90%, the √5 surface oxide is considered as stable under the thermodynamic conditions,

but if theθ̄O ,hol drops below 90% then the transition to the metal surface is considered to have

occurred (0.90 ML is shown as a dotted line in Figure 2.3 (b)). The value for θ̄O ,hol chosen here

is not critical, the quantitative numbers for the transition pressures almost remain in the same

magnitude even when we set the 70% as the value for θ̄O ,hol in the O2 rich region (70% coverage

is shown in a dashed line in Figure 2.3 (b)). When we manually decrease the barriers of two most

important reactionsNObr+Ohol→ NO2 hol

andNOhol+Obr→ NO2 br

(

NObr+Ohol→NO2 holis dominant because the strong preference for O to the hollow sites29)

by 0.1 eV, the surface decomposes faster but will remain stable at P(NO) = 10 -3 atm shown as

Figure 2.5. From the ab initio thermodynamics based phase-diagram, the region of √5 surface

oxide is found to be very small because of the ample stability of bulk PdO27. Our kMC model

focuses on the region where both Pd(100) and the √5 surface oxide could appear, which spans

from NO partial pressures of 10-7 to 1 atm and oxygen partial pressures of 10 -7 to 1 atm. Again,

the oxygen coverage intuitively reflects the coverage variations with partial pressures. Starting

from an intact surface oxide, when the partial pressure of O2 decreases, the coverage of O on the

surface gradually decreases as well with fixed NO pressure. Simulation results show that the

region of a stable √5 surface oxide ties well with the results from thermodynamic prediction27

and the surface oxide is stable under a typical operating condition ( T = 600 K, PNO = 0.001 atm,

PO2 =1 atm) as shown in Figure 2.3 (b). In order to understand the effect of temperature on the

stability of the surface oxide, simulations at 450 K also have been performed. Results show that

across a range of reaction temperatures , a higher partial pressure of NO is required in order to

reduce the surface oxide at a higher temperature as shown in Figure 2.6, which is consistent with

previous observations of CO oxidation on the √5 surface that higher temperature stabilized the

surface oxide.87 This is likely due to the shorter lifetime of the reductant on the surface as the

temperature increases. A screening of the stability of the palladium thin film oxide at various

temperature under a pure oxygen environment P(O2) =0.2 atm indicates that the palladium thin

film oxide starts decomposing at T = 1100 K while when oxygen pressure decrease to P(O2)

=0.00001 atm, the thin film oxide starts decomposing at T = 950 K as indicated in Figure 2.7(a).

Weaver and coworkers found their PdO(101) thin films which grew on Pd(111) decomposed

completely at T = 923 K under UHV condition116. As reported by Wang and coworkers, a higher

oxygen partial pressure would require a higher temperature to decompose palladium oxide as

they observed the decomposition temperature of PdO increased from 750 to 810 ⁰C as the

oxygenpartial pressure increased from 5 to 20 kPa117. This is further confirmed by our calculation

results shown in Figure 2.7 (b) that higher temperature is required in order to decompose the

oxide under higher oxygen pressure. The reaction orders of NO and O2 have been examined at

various partial pressures excluding the presence of NO2 in the gas phase (a discussion of NO2

will follow below). Previous work from Weiss and Iglesia have shown that the orders for NO, O2

and NO2 are 1, 1, and -1 respectively93. kMC simulation results (Figure 2.8 (1)) show that

reaction order of NO is 1 up to P(NO) = 1000 Pa with constant P(O2) = 5000 Pa and the reaction

order of O2 is 1 up to P(O2) = 1000 Pa with constant P(NO) = 112 Pa when we applied original

data from DFT calculation, which is consistent with previous experimental result. However, the

data also show that when partial pressure of O2 exceeds 1 kPa, the reaction order gradually

decreases and is zero order for P(O2) ≥ 0.1 atm. This deviation from the experimental results of

Weiss and Iglesia likely results from over prediction of the adsorption energy from DFT. Using

RPBE instead of PBE, for example, has been recommended by Norskov and co-workers for a

more accurate assessment of the binding energy of oxygen on d-band transition metal surfaces

(although one may argue RPBE is guilty of under prediction of adsorption energies)118. The

adsorption energy of O on hollow site decreases to 3.67 eV when using RPBE compared to 3.84

eV using PBE. However by using this data, deviation from experimental results still exits. To

address this issue, we artificially decrease the adsorption energy to determine, to what extent our

results must be perturbed to reproduce the 1st order dependence in oxygen observed by Weiss

and Iglesia. By decreasing the adsorption energy of O on hollow site by 0.3 eV, the oxygen

pressure region that indicates first order dependence of O2 could be extended to 1 kPa and

completely re-produce Iglesia and coworker’s data93 as shown in Figure 2.8 (2).

(1)

(a) (b)

(2)

Figure 2.8: (1)(a) The NO oxidation rate on the √5 surface oxide as a function of the partial pressure of NO with fixed P(NO2) = 56 Pa and P(O2) = 5000 Pa at T = 600 K; (b) The NO oxidation rate on the √5 surface oxide as a function of the partial pressure of O2 with fixed P(NO) = 112 Pa and P(NO2) = 56 Pa atT = 600 K; (2) The NO oxidation rate dependence on O2 partial pressure on the √5 surface oxide with fixed P(NO) = 112 Pa and P(NO2) = 56 Pa at T = 600 K using a lower adsorption energy for O (see text).

1.3.3 Combining the result from Pd(100) and the √5 surface oxide

It is obvious that at given oxygen partial pressure, a much higher NO pressure is required to

decompose a formed surface oxide than the pressure observed for which a surface oxide may

start to form. This phenomena is also observed experimentally and theoretically for CO

oxidation94, 119, 120. Pd(100) is considered stable only when coverage of O does not exceed 0.25

ML which corresponds to a coverage regime representative for a p(2×2) over-layer28, 115. The

dotted line between 0.2 ML and 0.3 ML coverage of O in Figure 2.3 (a) indicates a 0.25 ML

coverage of O. Hence any gas-phase conditions to the upper left of this line are expected to result

in a stable Pd(100) surface. As stated previously, the √5 surface oxide is considered to begin its

decomposition when the coverage of O is smaller than 0.9 ML. The dashed line indicating 0.9

ML O coverage is drawn in the red area of Figure 2.3 (b) and any gas-phase conditions to the

down-right of this line are expected to result in a stable surface oxide. By combing Figure 2.3 (a)

and Figure 2.3 (b), we obtain an area of bistability where both Pd(100) and the surface oxide are

predicted to be stable depending upon which surface is initially considered, as shown in Figure

2.9. This type of hysteresis phenomena has been previously observed in CO oxidation49, 51-53.

Similar observations of hysteresis in the rate have been made by Frenken and coworkers for CO

oxidation on Pd and Pt when the conditions allowed both oxide and metal surface to co-exit.88, 119,

121, 122 In the low-pressure region, atomic-scale restructuring of the catalyst surface could cause

spontaneous and self-sustained oscillations in the rate while spontaneous and periodic switching

from metal surface to oxide surface is the reason for the oscillations at atmospheric pressure

region121, 122. Compared to the previous work on CO oxidation, a larger bi-stability region exists

for NO oxidation. Despite the apparent simplicity of the reaction, NO oxidation itself still has

several intrinsic differences from CO oxidation. First NO2 can bond to surface much stronger

than CO2and it is actually endothermic to form NO2 on the surface for a typical NSR operating

condition (P(O2) = 0.2 atm, P(NO) = 0.001 atm and T = 600 K) when P(NO2) > 10-4 atm. Such an

effect has been artificially suppressed removing gas phase NO2 from the simulation27, 29. The

kMC simulations did not reveal obvious differences in the oxide surface stability up to P(NO2) =

10-3 atm. However, by setting P(NO2) to more realistic pressures, we do observe an effect of

NO2 on the TOF. As Figure 2.10 shows at P(NO) = 0.1 atm, the presence of NO2 lowers the TOF

on the thin film surface oxide. The decrease in the TOF can be attributed to the reverse reactions

of NObr+Ohol↔ NO2 hol

andNOhol+Obr↔ NO2 br

, as the barriers for dissociation of

NO2 are much lower than the barriers to form NO2. (as listed in Table 2.5). A higher P(NO2) will

lower the total TOF for NO oxidation. However, our model failed to predict the experimentally

observed reaction order for NO2 of -1 determined by Weiss and Iglesia when we search in the

pressure region of 10-7≤P(NO2) ≤ 10-3 atm with fixed P(NO) and P(O2). Our results show NO2

has a slightly negative order while previous experimental data shows a much stronger inversely

proportional relationship. The work of Weiss and Iglesia suggests that the NO2 pressure is

critical since NO2 determines the concentration of the vacancies required for O2 activation25, 93, 123.

From Table 2.3 we can see that NO2 bonding strength on the surface is weaker than either of O

and NO. In the kMC model, the chance for a process to be selected depends on the rate constant

of the elementary step80 (in addition to the concentrations of surface species and their

arrangements). This implies that the NO2 desorption step has a high chance of selection if NO2 is

on the surface. Therefore for the typical simulation times that we employ, NO2 adsorbs and

desorbs many times before any dissociation reaction occurs. The reaction barriers of NO

oxidation are higher than that of CO oxidation, which indicates kinetically, it is more difficult to

reduce a surface oxide. The TOF on both surfaces at P(O2) = 0.2 atm indicates that both surfaces

are active for NO oxidation at ambient pressure as shown in Figure 2.11 and similar to CO

oxidation case. In the low P(NO) regime, the metal surface is more active than surface oxide

while in the oxygen rich region surface oxide is superior124. From our results showing a large bi-

stability region and the comparable TOFs at the relevant environmental pressures, we may

conclude that both the surface oxide and the pristine metal could be the active surface for NO

oxidation. However, due to the error associated with the DFT calculation, the exact region for

this bistability cannot be located. At this point there is no detailed experimental work for NO

oxidation on Pd catalysts which identifies the nature of surface during NSR process to further

support our simulation data as there is for CO oxidation32-35, 88, 119, 123, 125-129. Nevertheless, we can

conclude that the surface oxide plays an important role during NO oxidation and oscillation

between these two surfaces may be the real condition when NO oxidation is carried out over Pd

catalysts.

Figure 2.9: Surface structure map as a function of the partial pressures of O2 and NO at 600 K. The Pink region is the possible region of bi-stability.

Pd(100)

√5 oxide surface

Figure 2.10: NO oxidation TOF on the √5 surface oxide as a function of oxygen partial pressure at a fixed P(NO) = 0.1 atm. Reddots indicate the TOF at P(NO2) = 10-13 atm; Black square indicate the TOF at P(NO2) = 10-3 atm.

Figure 2.11: Comparison of the intrinsic TOFs of Pd(100) surface and the √5 oxide surface with fixed P(O2) = 0.1 atm at T = 600 K.

1.4 CONCLUSIONS

First-principles kinetic Monte Carlo simulations have been applied to examine the coverage of O on

Pd(100) and the (√5×√5)R27°PdO(101)-Pd(100) surface oxide in the steady state NO oxidation reaction.

The decomposition pressure of the surface oxide matches well with phase-diagram constructed by

thermodynamic methods27. Fixing the partial pressure of oxygen, the NO pressure for surface oxide

decomposition is much higher than that when the surface oxide starts forming, which indicates a kinetic

limitation for the formation the surface oxide. By examining the partial pressures of NO and O from 10 -7

to 1 atm at temperature of 450 K and 600 K, higher temperatures were found to stabilize the thin film

surface oxide. Comparing the average coverage of oxygen on Pd(100) and the √5 surface oxide, a

bistability region was found to exist in which both Pd(100) and PdO(101) could be the active surface for

reaction NO + O → NO2 in the practical operation.