Ramanathan Sh. (Ed.) Thin Film Metal-Oxides: Fundamentals and Applications in Electronics and Energy

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304 T.P. Holme et al.

10.1 Introduction

Selection of catalyst materials with optimal properties is a combinatorial problem.

Trial and error by brute force searches are expensive and do not yield greater sci-

entiﬁc understanding about what makes a good catalyst. The efﬁciency and at least

semiquantitative accuracy of ab initio simulations imply that calculations may help

to search the large space of materials combinations, and furthermore calculations

may give insight that enable intelligent catalyst design. The work of Hammer and

N¨orskov laid the foundations for this ﬁeld by elucidating the relation between the

transition metal electron d-band energy with the adsorption strength for adsorption

reactions [1].

The oxygen dissociation reaction is especially important in intermediate and low-

temperature fuel cells such as solid oxide fuel cells (SOFCs) that are promising

devices for clean, efﬁcient energy conversion. To reduce cost, SOFCs that run efﬁ-

ciently at lower operating temperatures must be developed.

Sluggishness of the electrochemical oxygen dissociation reaction at the cathode

is a signiﬁcant barrier to lower temperature operation. Commercial SOFC cathodes

are typically mixed electronic-ionic conductors such as La

1x

1y

.To

enhance intermediate temperature catalysis, noble metal cathodes have been in-

vestigated [2]. The present contribution presents a method to design catalysts for

heterogeneous dissociative adsorption reactions, and demonstrates the technique to

ﬁnd a compound Ag–Pt catalyst that is superior under nearly reversible conditions

to the standard Pt catalyst for oxygen dissociative adsorption.

Quantum simulations are an effective tool to study catalysis because they allow

the direct calculation of transition-state structures and energies, and visualization

of orbitals participating in the catalytic reaction to build intuition in the design of

optimal catalysts. Among many previous studies of Pt clusters, work by Xu shows

that clusters assume metallic behavior for clusters larger than seven atoms [3]. Stud-

ies have examined oxygen reduction on Pt clusters [4], Pt slabs [5],andAgslabs

[6]. In this study, quantum chemical simulations were used to determine the relative

ability of Pt

clusters and PtAg

slabs of differing composition to catalyze the

dissociative adsorption of oxygen on catalysts that occurs at an SOFC cathode. As

a benchmark, similar calculations were performed on clusters and slabs of pure Pt

and Ag of varying size.

Catalytic activity of a metal cluster depends upon the size of the catalyst particle:

as a cluster grows in size from one atom, the metallic bonding forms low-energy

states for catalysis; however, there is an optimum in catalytic activity, as surface

atoms in nanoclusters are more reactive than bulk material. This optimum was found

experimentally for Au clusters [7]. Therefore this study considers Ag and Pt clusters

of varying sizes.

To enable ﬁne-tuning of control over desired properties that may be not found

in elemental compounds, creation of alloys and bilayers has been used to achieve

higher catalytic activity [8]. Precise control over bilayers with surface layers of one

or less than one monolayer has been demonstrated [9]. This study examines a Pt/Ag

bilayer to study the electronic structure of such bilayers. A random alloy is also

studied for comparison with bilayer structures.

10 Design of Heterogeneous Catalysts and Application to Oxygen Reduction Reaction 305

Finally, as Mavrikakis shows, adsorption strength depends upon the strain state

of the metal surface [10]. The strain of PtAg

surfaces was examined by X-ray

diffraction (XRD), and the strain effect was taken into account in calculations to

show that the alloying effect, rather than the strain effect, is responsible for the

enhanced activity of PtAg

catalysts.

From the base cases of Ag

and Pt

clusters, this study varies the following

parameters one by one: cluster size and composition, strain, and system spin multi-

plicity. The study considers Ag, Pt, and AgPt random alloy low surface energy (111)

slabs and an Ag/Pt bilayer. Oxygen adsorption, and dissociation, when possible, is

studied and compared with experiment.

10.2 Theory

Optimal catalytic activity is often exhibited by materials that are able to form bonds

of intermediate strength with adsorbates.

A balance should be struck by the metal surface: it must be reactive enough

with the adsorbate to catalyze the reaction but for a sufﬁciently weak bond with the

reaction products that they are free to desorb. One way to reﬁne this criteria is to

require that the adsorption process be thermodynamically reversible .G

rxn

D 0/

to minimize losses. From this requirement, we may derive an optimal adsorption

energy. For an isothermal, reversible reaction,

G

rxn

D H

rxn

 TS

rxn

D 0:

As the entropy of adsorbed species is much lower than the entropy of gaseous

species, S

rxn

is approximated to be the entropy of the adsorbate in the gas phase

S

rxn

 S

.g/

. For oxygen, at T D 200

Cand400

C, a reasonable range of operat-

ing temperatures for low-temperature SOFCs, this translates to adsorption energies

of H

rxn

 1:1 and 1.6 eV, respectively. It is noted that this simplistic estimate

neglects the entropy of adsorbed species, resulting in a prediction of reversible ad-

sorption at somewhat greater adsorption energies than should be targeted.

Transition metal valence electron states are characterized by a half-ﬁlled s-band

and increasingly ﬁlled d-band states across the series. The s-band is relatively broad

and constant for different transition metals; trends in the chemistry of transition

metals arise mainly as a result of d-electron interaction. According to the model

proposed by Hammer and Nørskov [1], metals with d-electrons of low energy are

unable to donate much charge to adsorbed molecules, resulting in a weak bond.

Metals with intermediate d-band levels donate more charge to adsorbates, resulting

in a stronger bond. Metals with very energetic d-electrons are strong charge donors

to adsorbates, resulting in a weaker bond as charge is donated into antibonding

orbitals. Therefore, a requirement on the bond strength between an adsorbate and a

metal implies a requirement on metal d-band level.

306 T.P. Holme et al.

Table 10.1 Electron d-band centroid and Fermi level for common catalyst transition metals

Fe Co Ni Cu Zn

D4:40 "

D5:06 "

D5:27 "

D4:87 "

D4:05

D1:42 "

D1:30 "

D1:27 "

D2:20 "

D7:14

Ru Rh Pd Ag Cd

D5:06 "

D5:14 "

D5:37 "

D4:54 "

D3:75

D2:08 "

D2:09 "

D1:71 "

D3:94 "

D8:66

Os Ir Pt Au Hg (liquid)

D5:34 "

D5:58 "

D5:77 "

D5:33

D2:48 "

D2:61 "

D2:24 "

D3:27

Fermi level ."

/ and d-band centroid ."

/ givenineV,"

referenced to vacuum, "

referenced to the

Fermi level

Using the metal d-band as a guide to reactivity with adsorbates, an algorithm

to design a reversible catalyst may be developed. Table 10.1 shows the valence

d-band center and Fermi level ("

and "

, respectively) for common catalyst tran-

sition metals. When combined with experiments, calculations, or published values

of adsorption strength of a reactant on different metal surfaces, a volcano plot of cat-

alytic activity may be constructed by plotting the d-band center against adsorption

strength. A catalyst may then be designed to have an "

that gives high activity by

alloying elements on either side of the peak in the volcano plot. The alloying effect

of mixing two elements is to form a material with an intermediate "

. An alternative

strategy is to use the strain effect explained in Ref. [10], which describes that ma-

terials under tensile strain have a higher "

, whereas materials under compressive

strain exhibit lower "

. One may envision depositing nonequilibrium or nonlattice-

matched epitaxial structures of an element with a nearly ideal "

to optimize "

with

the strain effect.

As an example, this method is applied for the test case of oxygen dissociation.

Pure Pt forms a bond with oxygen that is too strong for oxygen to be readily released

after dissociation. To weaken the O–Pt bond, the d-band of Pt should be lowered, so

it may be alloyed with an element with a lower d-band. Ag is chosen in this case.

10.3 Details of Calculations

10.3.1 Cluster Model

The B3LYP method [11, 12] was chosen for its good performance/efﬁciency ratio.

The selection of basis sets is limited to basis sets that are available for the relatively

heavy metals Ag and Pt. The available basis sets were tested for their accuracy in

predicting the adsorption energy .E

ads

/ of oxygen on Ag

C Ag

! Ag

2.ads/

10 Design of Heterogeneous Catalysts and Application to Oxygen Reduction Reaction 307

These single-point calculations were performed on geometry optimized at the

B3LYP/LANL2DZ level. By comparing with the highly accurate QCISD(T)/

LANL2DZ results, it was found that the LANL2DZ basis set [13] afforded the

best compromise between accuracy and efﬁciency. The addition of basis functions

to oxygen beyond 6–21G further increased the predicted absolute adsorption en-

ergy beyond B3LYP/LANL2DZ, lowering accuracy, as density functional methods

tend to overestimate bond energy. Therefore, LANL2DZ was chosen to represent

oxygen as well. Gaussian ’03 was used for all cluster calculations [14].

The adsorption energy of oxygen on metal clusters was calculated from the

formula

ads

D E

 E

With this deﬁnition, stronger adsorption is more negative.

To ﬁnd adsorption-, dissociation-, and transition-state energies, the following

procedure was utilized:

1. Individually relax the geometry of O

and the metal cluster

2. Introduce oxygen to the vicinity of the metal cluster and relax the geometry

3. Search for the transition state for O–O cleaving

4. Split molecular oxygen to 2O

.ads/

and relax the geometry

10.3.2 Slab Model

Electronic states were expanded in plane waves with energy cutoffs of 400eV for

all simulations. For small supercells used for lattice relaxation, a Monkhorst-Pack

[15] 8  8  8k-point sampling scheme was used; for larger supercells used for

surface relaxation, a Monkhorst-Pack 8  8  1 sampling was used, and for the

largest supercells considered for oxygen adsorption, a Monkhorst-Pack 4  4  1

sampling was employed.

Ultrasoft pseudopotentials in the GGA scheme were used with the Perdew-Wang

91 exchange correlation functional [16]. Methfessel-Paxton order 1 smearing was

used with a smearing width of 0.2 eV. The ab initio code VASP was used for all slab

calculations [17].

Lattice constants were found for primitive cells for each material by relaxing the

supercell volume. Slabs of four atomic planes were constructed where the bottom

two layers were ﬁxed to their bulk distances and the top two layers were allowed

to relax. Slabs were separated by at least 15

A of vacuum to minimize interaction

between slabs. For adsorption calculations, molecular oxygen was brought near an

adsorption site in a vertical (superoxo-) or horizontal (peroxo-) conﬁguration and

allowed to relax, while the top two metal layers were simultaneously relaxed. Dif-

ferent adsorption sites were tested, and results presented are for the most favorable

site found.

Adsorption energy is found by

ads

D E

 E

;

308 T.P. Holme et al.

Fig. 10.1 Potential energy of an electron above the Ag(111) surface as a function of z, the surface

normal, found by averaging the potential in the xy plane. Positions of the ions are marked with

arrows, as is the vacuum potential

where E

is the energy of the clean surface, E

is the energy of O

in the gas

phase, and E

is the energy of the adsorbed system.

The work function of each system was found from the following equation:

 D "

 E

vac

;

where "

is the calculated Fermi level of the system and the potential energy of an

electron in vacuum, E

vac

was found from the potential energy determined by the

self-consistent electron density. The potential energy was averaged in the xy plane

and plotted as a function of z, the surface normal direction, as shown in Fig. 10.1,

illustrated for silver.

The center of the d-band, "

, was found from the usual deﬁnition of the centroid:

˛

."/d"

1

."/d"

;

where n

."/ is the density of d-band states.

10.4 Details of Experiments

Sputter targets of Pt, Ag, Pt

0:4

0:6

,andPt

0:25

0:75

were fabricated by Kurt

Lesker Co. (99.99%) and used for DC sputtering of porous electrodes on thin-

ﬁlm solid oxide supports according to the method described by Huang [18]. I–V

performance data of the fuel cells was measured using a Solartron 1260/1287 in

galvanodynamic mode at a scan rate of 0:2 A=s.

10 Design of Heterogeneous Catalysts and Application to Oxygen Reduction Reaction 309

Analysis of electronic structure of the valence band of catalysts was done with

X-ray photoemission spectroscopy (XPS) with an SSI S-Probe Monochromatized

XPS Spectrometer, which uses Al.K

/ radiation (1486 eV) as a probe. XPS was

done on samples after a thin surface layer was sputtered off in UHV to ensure there

was no oxide or other surface contamination; survey scans conﬁrmed that only the

pure metals remained.

Analysis of strain was performed with XRD (Phillips PANalytical X’Pert PRO)

using the Cu K

’

line (1.54184

A) at 45 kV and 40 mA. XRD was performed on the

bulk sputtering targets;  2 scans were performed after the zero of 2 was aligned

to the detector.

10.5 Results

The following sections present the results of calculations on clusters and slabs of Pt,

Ag, and PtAg

compounds.

10.5.1 Cluster Model

The effect of varying cluster size, composition, and spin are explored for the oxygen

adsorption reaction on Ag

.n D 4; 6; 8; 14/; Pt

.m D 2; 4; 8/,andAg

[.n; m/ D .4; 2/, (6, 2), (4, 4)].

The clusters were constructed by extracting the desired number of atoms from

their bulk conﬁguration and relaxing the ion positions. Stable geometries found for

the Ag clusters are shown in Fig. 10.2.ForAg

and Ag

, the atoms assume a conﬁg-

uration similar to what they would have in a close-packed plane. In Ag

, the atoms

Fig. 10.2 Stable states for

(from left to right and top

to bottom) Ag

; Ag

and Ag

310 T.P. Holme et al.

Fig. 10.3 Stable states for

; Pt

,andPt

Fig. 10.4 Stable states for Ag

; Ag

,andAg

. Ag atoms are shown in white and

Pt in gray

begin to assume the tetrahedral coordination they would have in the fcc structure,

and the Ag

structure is very close to a full unit cell of fcc bulk Ag. Ag clusters are

more stable in low-spin states of multiplicity 1.

The geometries of the Pt clusters are shown in Fig. 10.3. Again, the similarity of

the optimum geometry of the cluster to the bulk conﬁguration is evident. Pt clus-

ters were found to be more stable in high-spin states, in agreement with Kua and

Goddard [19].

The geometries of the AgPt alloys are shown in Fig. 10.4. The clusters were

made by taking a silver cluster of the appropriate size and randomly substituting Pt

atoms for Ag atoms. The geometry was then allowed to relax. As noted by Chris-

tensen et al. [20], and in agreement with the phase diagram by Okamoto [21], Pt

impurities in an Ag matrix are thermodynamically driven to form a bulk alloy. As

can be seen in Fig. 10.4, Pt atoms are incorporated into the Ag cluster. One possible

driving force for this reaction is that the Pt gains a negative charge in Ag (shown

by Mulliken charge analysis [22]) and experience a Columbic repulsion between

negatively charged Pt atoms.

10 Design of Heterogeneous Catalysts and Application to Oxygen Reduction Reaction 311

The geometries and energies of stable structures are highly dependent upon the

spin state of the system. Singlet silver clusters are most stable, whereas platinum

clusters favor high spin states. The alloyed clusters considered also favor singlet

states. Oxygen is most stable in the triplet state when isolated, but when it nears

the catalyst cluster, lower energy conﬁgurations are found for singlet states in some

cases. In all the ﬁgures, the energies and geometries given correspond to the spin

state with lowest energy.

10.5.1.1 Cluster Size

Electronic Structure

The energy of occupied electron eigenstates in silver and platinum clusters is shown

in Fig. 10.5. It is clear that by Ag

, the cluster has not converged to metallic proper-

ties, as the DOS of Ag

has a considerably lower HOMO-1 energy than does Ag

Without simulating a larger cluster, it cannot be determined whether the Ag

clus-

ter can be considered to represent bulk silver. The eigenvalues of HOMO-1 states

are s-states. The relatively higher eigenvalue of the s-states of Ag

may account for

the very weak bonding with O as will be discussed later.

The DOS of Pt

and Pt

are signiﬁcantly different, showing that Pt

is not fully

metallic. According to Xu, once Pt clusters grow above seven atoms, their elec-

tronic structure becomes largely similar to bulk Pt [3]. Therefore this Pt

cluster is

considered to represent metallic Pt.

Oxygen Adsorption

Geometries and energies of oxygen adsorption on Ag clusters and on Pt clusters

are shown in Fig. 10.6. The coordination of the site consistently inﬂuences the

properties of the adsorption reaction. The site with lower coordination is the more

energetically favorable site for adsorption. The atoms of lower coordination are

more able to donate electrons to oxygen because they share electrons with other

metal atoms in the cluster to a lesser degree than sites with higher coordination.

Adsorbed oxygen on Ag

has a shorter O–O bond and a longer O–Ag bond

than the other adsorbed states, correlating with higher adsorption energy. Weak ad-

sorptiononAg

may be explained by referring to Fig. 10.5, which shows that the

HOMO-1 eigenstates have higher energy in the Ag

cluster than the other silver

clusters. An orbital analysis shows that the HOMO of Ag

; Ag

,andAg

is primarily composed of Ag-s mixed with O-p states, whereas Ag

HOMO-3

to HOMO states have very little contribution from O states. The HOMO-4 level

of Ag

has mostly O-p to O-p bonding and lies 2.9 eV below the HOMO level,

explaining the weak adsorption on Ag

312 T.P. Holme et al.

Fig. 10.5 Energy of

eigenstates of electrons in

(a)Agclustersfor

; Ag

,andAg

and (b)Ptclustersfor

; Pt

,andPt

Energy of adsorption on Ag clusters falls within the range of experimental values

0.4–1.1eV reported by Campbell [23] and Wang [24], respectively. An exception is

the unusually weak bonding on Ag

as explained earlier.

Adsorption on Pt clusters becomes less favorable for larger clusters, as the Pt

atoms become less reactive when they share more bonds with neighboring Pt atoms.

Adsorption is generally in a side-on conﬁguration, as found experimentally by

Gland et al. [25]. The steady-state adsorption of O

on Pt at high coverage is ex-

perimentally 1:5 ˙ :4 eV from Brown and King [26]. The high-coverage regime

most closely corresponds to adsorption on Pt

, for which the adsorption is found to

be 1.4 eV, in good agreement with Brown and King.

10 Design of Heterogeneous Catalysts and Application to Oxygen Reduction Reaction 313

Fig. 10.6 Stable energies

and structures of O

2.ads/

for oxygen adsorbed at

different sites on (a)Ag

clusters and (b) Pt clusters.

Agatomsinwhite,Ptingray,

and O in black

O–O and O–M bond lengths, as well as total Mulliken charge on the two oxy-

gen atoms, are given in the Table 10.2. In all cases, adsorbed oxygen gains a partial

negative charge. The degree of charge transfer correlates relatively well with adsorp-

tion strength, in contrast with the model proposed by Hammer and N¨orskov. In the

Hammer-N¨orskov model, weaker adsorption on silver entails more charge transfer

to adsorbates. The reader is referred to Ref. [1] for more details.

The correlation between adsorption energy and charge, and adsorption energy

and O–M and O–O length is notable: a greater O

net charge, longer O–O bond,

and shorter O–M bond correlate well with stronger adsorption. The extra charge

density donated to the oxygen p orbitals lengthens and weakens the O–O bond in

the adsorbed state. Therefore, in systems with strong adsorption, there is greater

charge donation, weakening of the O–O bond, and stronger O–M bonding.