driving force for surface segregation in bimetallic catalysts

Surface Science Letters 278 (1992) L125-L130 North-Holland surface sc ience

letters

Surface Science Letters

Driving force for surface segregation in bimetallic catalysts

A n n M. Schoeb, T o d d J. Racke r , Liqiu Yang , Xi Wu, Te r ry S. King and A n d r e w E. DePr i s to

Ames Laboratory, USDOE and Departments of Chemistry and Chemical Engineering, Iowa State University, Ames, IA 50011, USA

Received 22 June 1992; accepted for publication 14 August 1992

The catalytic properties of bimetallic clusters are influenced by the detailed structure of the cluster surface. We briefly describe two methods developed to treat this problem, from the computationally demanding corrected effective medium (CEM) theory (a non-self-consistent density functional based method) to the computationally simple method of surface modified pair potentials (SMPP). Parametrization of the latter is accomplished using the former. Comparisons of theoretical predictions with experimental data are made for the heat of formation in RhxPt I -x alloys and for surface segregation behavior in Rh0.9Pt0j(lll). Results on the shape, site composition and surface micromixing are shown for 201 atom clusters (dispersion of 0.6) and RhxPt I _x(lll).

A fundamental point follows from the fact that the CEM calculated cohesive energy of Rh is slightly smaller than that of Pt, but the surface energy of Rh is significantly larger: the driving force for surface segregation is the relative surface energies not the relative cohesive energies. In general, one can predict surface energy differences by properly accounting for the variation of the bond energy with coordination.

1. Introduction

Bimetallic clusters in the range of 200-2000 atoms form the fundamental constituents of bimetallic catalysts [1]. Experimental data on such clusters is extremely difficult to obtain, and indeed there are no direct measurements of metal atoms' positions in these clusters. Theoretical predictions of the structure and energies of these clusters depends upon an accurate and computationally efficient description of metal-metal bonding.

The large number of electrons and the low symmetry of such systems precludes ab initio calculations. In this Letter, we demonstrate the ap- plicability of an approximate non-self-consistent density functional theory, the corrected effective medium (CEM) method [2-4]. These calculations are just barely feasible on modern massively par- allel supercomputers for the cluster sizes of inter- est here [5]. Thus, we also show that the CEM method can be used to determine the parameters in the empirical surface modified pair potential (SMPP) model [6-8]. Applications of the latter

can be done very efficiently on even a low-end workstation or high-end personal computer.

We consider the R h - P t bimetallic system in this Letter. Mixing in Rh0.gPt0.1(lll) and 201 atom clusters of RhxPt]_ x are treated and the former is compared to recent experimental data. The latter is used to test the adequacy of the SMPP approach by comparison to the much more costly CEM calculations. The R h - P t system is interesting technologically, of course, but also fundamentally behavior, not simply complete segregation with bulk immiscibility driven by AHma >> 0 or compound formation driven by A Hm~ , << 0.

2. Theory

We give a brief overview of the two theories, CEM and SMPP, used to describe bimetallics in this letter. The reader interested in more details should consult the references, especially refs. [2b] and [2d] for the fundamental CEM development and ref. [4] for construction of embedding func-

0039-6028/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

L126 A.M. Schoeb et aL / Drit:ing force fbr surface segregation in bimetallic catalysts

tions. Applications of a simpler CEM method to bimetallic surfaces can be found in ref. [3], but we shall not consider this here, leaving extensive comparisons to future publications. For the SMPP method, the reader should consult refs. [6-8] for an overview.

For a set of N-atoms, {A~, i = 1 . . . . , N}, the CEM theory utilizes the following equations to calculate the interaction energy:

N

ae({A,}) = E a ,.MTo(A, n,) i-I

N N I

+ 7 E E K( i, J) + aG({A,}), i = 1 j ~ i

(1)

l N

ni= ~ i j . ~ i f n ( r - R i ) n ( r - R i ) dr, (2)

n ( r - R i) is the unpolarized atomic electron density distribution (from Har t r ee -Fock calculations) while Z i and R, are the atomic number and nuclear position, respectively. This equation is valid under the assumption that the total system electron density can be approximated as the su- perposition of atomic electron densities.

The first term is the sum of the embedding energy for each atom, each term of which is solely a function of the average electron density environ- ment of that particular type of atom. The subscript " L M T O " indicates that these functions are pro- vided by forcing the CEM method to duplicate the results of self-consistent linearized muffin tin orbital density functional calculations on the cohesive energy of the homogeneous bulk solid at lattice constants from 30% expansion to 10% contraction [4a]. Since these embedding energies are a major component of the system interaction energy, it is important to determine them accu- rately and this procedure does so, at least for electron density environments like surfaces and bulk. For very low coordinations or more properly at very small n~, it is necessary to supplement the LMTO calculated values with experimental data from the diatomic binding curve [4b]. Such

low density regions do not play a role in the bimetallic systems considered here.

The second term consists of pairwise additive Coulombic energies. Vc(i, j ) is the sum of elec- t ron-electron, e lect ron-nuclear and nuclear- nuclear Coulomb interactions between atoms A i and Aj. These are determined solely from the electron densities of each atom and are not ad- justed to fit any experimental or calculated value.

The last term, AG, is the difference in kinetic-exchange-correlation energies of the N- atom and atom-in-jellium systems. It is a true many body term whose evaluation entails a multi-center, three-dimensional integral over all space that varies explicitly with any change of the atomic coordinates. It is also specified by the atomic electron densities and is thus not ad- justed.

Computationally, the CEM theory is much faster than ab initio methods but still rather slow compared to simple empirical pair potential methods. Four orders of magnitude more time are needed for the calculation of AG than the combined total for the other two terms in the CEM interaction energy [5]. At a rate of 100 Mflops, the CPU time required for one calculation at each nuclear geometry is (1-100)N 2 s, indicating that calculations for systems of up to N = 100 are feasible. To be more specific, for a 64 atom Ni cluster, it takes approximately 35 s to evaluate the energy and forces on each atom using a 64 processor nCUBE 2 computer. The time decreases to 2.3 s for 1024 processors. Since many energy and force evaluations are needed for each simulation, the CEM method is just fast enough to provide an accurate comparison for simpler methods at this point. It is definitely not fast enough for use on current workstations to predict the structure of bimetallic clusters.

A central aspect of metallic bonding is the delocalized electrons. If one tries to discuss metallic bonding in terms of pairwise bonds, then this delocalized bonding leads to the strengthen- ing of the meta l -meta l bond between neighbors as the coordination decreases. This fundamental aspect lies at the heart of the SMPP method which calculates the energy of an atom by count- ing the bond energies with each of its nearest

A.M. Schoeb et al. / Driving force for surface segregation in bimetallic catalysts L127

neighbors, adjusting the strength of each bond according to the number of neighbors. In this method, the working equation for a system of one atom type (or when one ignores differences in bonding between unlike and like atoms) is

A E ( { A i } ) = E N / e ( A i ; N/), (3)

where e (h i ; N i) is the energy atom A i con- tributes to each of its N i nearest neighbor bonds. This equation must be supplemented with the interchange energy when there are different types of atoms [6]. Note that bond lengths are not required in the application of this method be- cause the interatomic potential is a function of coordination rather than distance. However, this approach does require that the metal particle maintains a fixed lattice type during the simulation. This would become less adequate when the sizes of the bimetallic atoms differ considerably. In the results reported below the simulations are fixed in a fcc lattice.

The connection between these methods is that the CEM theory can be used to provide the partial bond energies by using selected calculations on various metal surfaces and metal vacancy formation [9]. This is explained in detail in ref. [9] so we just provide an outline here. In order, we use the cohesive energy,

AEco h = 12e12

to find e~2, and then the vacancy energy,

AEva c = 12(l lEll -- 12e12 )

to determine e11. Solving for the unknown e in the first term on the right hand side, we have the surface energies, ~(i jk) , as given by

t r ( l l l ) A ( l l l ) = 9e9 -- 12e12

tr(100) A(100) = 8% - 12E12

t r ( l l 0 ) A ( l l 0 ) = 7e 7 + l l e l l - 24~12

t r (210)A(210) = 6e 6 + 9 , 9 + l l e H - 36e12

where A( i j k ) is the surface unit cell area for the " i jk" face. The binding energy of a tetrahedral cluster is

AE 4 = 12E 3

while the energy of chemisorption A E c of the same type of metal atom on the (ijk) plane is

AEc(100 ) = 4E 4 + 36E 9 - 32%

AEc(111) = 30El0 + 3E 3 - 27E 9

AE~( l l0 ) = 5% + 32% + 12e12- (28E 7+ l l e l l ).

These equations provide the partial bond energies. The left hand quantities are calculated by the CEM theory. Clearly, the above procedure is not unique since calculations in other geometries can be used to find the e i (i < 7).

3. Results and discussion

Consider the RhPt system. The bulk cohesive energy and lattice constant are (5.75 eV, 3.80 ,A) and (5.84 eV, 3.92 ,A) for Rh and Pt, respectively. The surface energies (in J / m 2) predicted by CEM are 2.37, 2.52 and 2.71 for Rh ( l l l ) , Rh(100), Rh(l l0) , respectively [4a]. The values are 1.94, 2.05 and 2.20 for P t ( l l l ) , Pt(100), Pt( l l0) , respectively. Experimental data on surface free energies of polycrystalline samples [10] at the metal's melt- ing point and at 298 K can be used to extrapolate to 0 K with the result being 2.94 and 2.49 J / m 2 for Rh and Pt, respectively. The CEM predictions are rather good, especially for the difference between Rh and Pt. For example, the experimental and CEM ratios of Rh to Pt surface energies are 1.18 and 1.22-1.23, respectively.

It is especially important to note that CEM predicts that Rh has a much bigger surface energy even though it has a slightly smaller cohesive energy. This effect is not trivially related to the smaller size of Rh since this would yield a ratio of (5.75/3.802)/(5.84/3.922) or a factor of only 1.04. The reason for the increase is the difference in bond variation with coordination which is well illustrated by the SMPP partial bond energies as shown in fig. 1. The slope of the line for Pt is larger than that for Rh while the values at N = 12 are nearly the same. Thus, Pt strengthens its bonds substantially more than the Rh atom does as the coordination lowers, leading to lower surface energies for Pt.

L128 A.M. Schoeb et al. / Dri~,ing force for surface segregation in bimetallic catalysts

- 0 . 4

g - 0 . 6

I .U

- 0 . 8 o

o

o - 1 , 0

- 1 . 2

j

• CEM input: Rh CEM input: Pt

n omp i r { co I i npu t : P t

o empldcol input: Rh

, , , , , J , i , i , i , , , i , i

2 5 4 5 6 7 8 9 10 11 12 15 N

Fig. 1. Partial bond energies for Pt and Rh as determined from CEM calculations and the relationships given at the end of the theory section. Previous values using a quadratic form

(in N) fit to surface energies are also shown.

/ . ~ , ~ " o D 6 0

, 0 0 ~ O? 05 0 : ) ~ ~ t~ , ] . ' 08 09 "

Fig. 2. Surface fraction of Rh in RhxPt l_~ clusters with 201 total atoms as predicted by the SMPP model at 973 K. The dotted line separates enrichment (above) and depletion (be-

low) regions.

The CEM predictions of the mixing energy are -0 .9 , - 1 . 7 and - 1 . 6 kJ /mol for Rh0.25Pt0.75, Rh0.50Pt0.50 and Rh0.75Pt0.25. Since Pt and Rh form miscible solutions even at low temperatures, this small negative mixing energy is very reasonable. Indeed, the SMPP formulation uses a value of - 0.00691 eV for the interchange energy, yield- ing - 2 kJ /mol for the mixing energy in Rh0.sPt0. 5. This is in excellent agreement with the CEM predictions.

Using CEM calculations of the various Pt and Rh systems yields the partial bond energies shown in fig. 1. For comparison, partial bond energies using a quadratic fit to limited experimental data are also shown. The agreement is quite good except at very low coordinations where the empirical approach involves extrapolation.

Predictions of the surface fraction of Rh in R h / P t n_x bimetaUics cluster with 201 total atoms are shown in fig. 2 based upon Monte Carlo simulations at 973 K. These are calculated using the partial bond energies assuming that the cluster retains an fcc lattice arrangement of atoms. Even though these simulations allow the structure of the particle to deviate from the initial cubo-octahedral shape, no such morphology change occurred due to the thermodynamic sta- bility of that arrangement. Note that the surface of the small cluster is depleted of Rh at all concentrations with a maximal depletion at x - - 0.5.

To test the SMPP results, a single simulation was performed at x - -0 .5 , using both molecular dynamics for continuous distance relaxation along with MC switching for atom exchange, in which the full CEM theory was used. The temperature was 600 K and yielded SRh = 0.40. The compara- ble SMPP value at 600 K is 0.34, thus providing confidence that the use of the SMPP model with an fcc lattice is generally adequate for this system.

In fig. 3, we show the fraction of edge and corner sites in the RhxPt~_ x cluster with 201 total atoms at T = 973 K. Note that Rh segregates to the corner sites while Pt segregates strongly to the edge sites. This unusual behavior

v

B

• !

~g r _mr . . . .

0 C I S {; 5 2/ ' o 9 3 9

Fig. 3. Fractional coverage of Rh at edge and corner sites in RhxPt~ -x clusters with 201 total atoms as predicted by the SMPP model. There are 36 edge and 24 corner atoms in the

cluster.

A.Mo Schoeb et al. / Driving force for surface segregation in bimetallic catalysts L129

in the micromixing is explained from the e i. In particular, note that 7E 7 - - 12E12 controls the fraction of edge versus bulk atoms while 6E 6 - 12e]2 determines the fraction of corner versus bulk atoms. These values are shown in table 1, and indicate the preference for Pt over Rh at the edge sites but the reverse at the corner sites. Such unusual micro-segregation could have quite important consequences for catalytic reaction ki- netics. The full CEM simulation yields an edge fraction of 0.18 at x = 0.5 in excellent agreement with the SMPP values, but a corner fraction of 0.29 which is a depletion of Rh instead of the enhancement predicted by SMPP. Continuous distance relaxation in the CEM simulation a n d / o r the use of the (210) face to parametrize the SMPP model may contribute to this difference.

Experimental verification of these predictions is problematic. Only surface composition measurements have been at tempted leaving site pop- ulation and micromixing properties to specula- tion. The standard surface science tools such as Auger electron spectroscopy (AES) are not feasible due to the very nature of the particles. In addition, traditional methods of estimating surface composition using selective chemisorption are known to significantly perturb these bimetallic systems [6]. In certain simple systems a combi- nation of I H NMR and hydrogen chemisorption have indicated the predictions give reasonable results [11]. We can apply the predictions to low-index plane simulations that are more easily verified experimentally, however. The fcc (111) surface of Rh0.qPt0.1 was simulated with the SMPP

Table 1 Site energies (in eV) from SMPP partial bond energies as predicted by the CEM theory

Site type Formula Rh Pt

Bulk 12E [2 - 5.750 - 5.840 111 plane 9e 9 - 12e12 0.925 0.806 100 plane 8~ s - 12~[2 1.138 0.982 Edge 7~ 7 - 12~12 1.589 1.382 Corner 6~ 6 - 12¢1~ 1.505 1.528

10

~o6 ~o5 ~o4

2 h 0 3

~02

0,1

0 . 0 4 0 0

Fig.

09

08

07

Rho 9Pto 1 I i 11 ~1 Rho:sPto 5~111 l

i h i , i i i i i i i , i i

6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0 T e m p e r a t u r e ( K )

4. Surface fraction of Rh in Rho.gPto.1(111) and Rho.sPto.5(111) as predicted by the SMPP model.

method in a similar manner as the 201 atom particle discussed above (but taking into account the fixed chemical potential versus fixed number of particles). The results are shown in fig. 4. Recently, Fisher and coworkers have used AES and ion scattering spectroscopy to determine that the surface composition of this system is = 70% Rh in the 1200 K temperature range [12], which is in good agreement with our predictions. Note also that the Rho.sPt0.5(lll) surface displays greater segregation at all temperatures than the Rh0. 9 Pto. l ( l l l ) one.

We conclude with a brief comparison to recent measurement of Siera et al. [13] on the fcc (111) surface of Rh0.75Pt0.25. They find depletion of Rh in the top layer to 54% at T = 990 K rising to 72% at T = 1250 K. The SMPP predictions are 54% at 973 K and 58% at 1250 K. The difference is significant. To see why, consider the perfect mixing model result using the CEM predicted surface energies (or the SMPP partial bond energies in table 1). This yields the following equation

3

SRh = 3 + exp(1.4 × 1 0 3 K / T ) (4)

for the surface fraction of Rh. To obtain a value of SRh =0.72 at T = 1250 K requires a much smaller difference in surface energies than 1.4 × 103 K. But this difference of 1.4 × 103 K is also very close to the measured difference (1.5 x 103 K) for polycrystalline samples of Rh and Pt [10].

L 130 A.M. Schoeb et al. / Dri~,ing force for surface segregation in bimetallic catalysts

Furthermore, the very fast decrease in SRh with decreasing T in the Seria et al. data requires a much larger value than 1.4 × 103 K in this perfect mixing model.

To describe their data, Siera et al. use an equation of the form

3

SRh = 3 + exp(--ASvi b + A E / T ) ' (5)

where AE = 3020 K is given in ref. [13]. Using the value SRh = 0.72 at T = 1250 K yields ASvi b = 2.26. With these values, the above equation makes the easily testable prediction that Rh will enrich the surface for T > 1335 K. At 1500 K, the value is SRh = 0.81. Unfortunately, the data in ref. [13] are reported only till 1250 K. Furthermore, the magnitude of A E still appears to be inconsistent with the surface energies in the R h - P t system. The data is also not consistent with the predictions of the full MC simulation using the SMPP model.

Acknowledgements

This work was supported by the Biological and Chemical Technologies Research Program (Ad- vanced Industrial Concepts Division) of the US Department of Energy through the Ames Labo- ratory, which is operated for the US DOE by Iowa State University under Contract No. W- 7405-Eng-82. The more extensive CEM calculations were performed on the nCUBE 2 hyper- cube at the Scalable Computing Laboratory of Iowa State University and the Ames Laboratory.

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driving force for surface segregation in bimetallic catalysts

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