Au Alloy Nanoparticles from a Density Functional

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Structure of Pd/Au Alloy Nanoparticles From a DFT-Based Embedded-Atom Potential Remi Marchal, Alexander Genest, Sven Krueger, and Notker Roesch J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 27 Sep 2013 Downloaded from http://pubs.acs.org on September 29, 2013

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The Journal of Physical Chemistry

Structure of Pd/Au alloy nanoparticles from a DFT-based embedded-atom potential Rémi Marchal,1 Alexander Genest,2,3 Sven Krüger,3 and Notker Rösch2,3*

1

Department Chemie & Institut für Siliziumchemie, Technische Universität München, 85747 Garching, Germany

2

Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore

3

Department Chemie & Catalysis Research Center, Technische Universität München, 85747 Garching, Germany

Abstract Based on DFT results for a set of representative bulk, surface, and cluster systems, we determined a new embedded-atom potential for Pd/Au alloys. This embedded-atom approach accurately reproduces DFT properties of such alloy systems. We applied this potential in Monte-Carlo simulations to study effects of temperature and composition on the structure and bonding of Pd/Au alloy nanoparticles with up to 5 nm in diameter. We characterized the structure of those particles by evaluating the gold concentration at the surface and in the interior, the coordination numbers of atoms, the nature of Pd entities at the surface, and the number of suggested active sites for vinyl-acetate formation.

Keywords: alloy nanoparticles, palladium, gold, embedded atom method, Monte-Carlo

* To whom correspondence should be addressed. E-mail: [email protected]

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1

Introduction Metal nanoparticles are finding great interest for their widespread applications, ranging

from optoelectronic

devices and fluorescence

marking to molecular electronics,

electrocatalysis and catalysis.1 In heterogeneous catalysis and electrocatalysis, bimetallic nanoalloy particles opened new perspectives,2,3 as these systems exhibit properties, tunable via their composition, often reaching higher catalytic activity and selectivity than their monoelementary counterparts. Among such alloy nanoparticles, Pd/Au mixtures have demonstrated particular catalytic activities and selectivities for various reactions, e.g., aromatic hydrogenation,4 CO oxidation,5,6 and vinyl-acetate formation.7-9 Using various experimental techniques, both PdcoreAushell and AushellPdcore particles have been synthesized, in addition to pure Pd and Au particles.10-14 However, high resolution electron microscopy revealed that such synthesis mostly leads to heterogeneous compositions, cluster shapes and sizes.14,15 Goodman et al.7-9 demonstrated that the catalytic formation of vinyl acetate by Pd/Au particles is structure sensitive. They postulated a type of active sites on the surface of such particles where the reactants, ethylene and acetic acid, initially each adsorb at isolated palladium atoms that are suitably separated by gold atoms, i.e., two next-nearest palladium centers on (100) facets, each fully surrounded by gold atoms in the first coordination shell. Therefore, to understand and optimize the catalytic activity, it is necessary to understand in detail the surface composition of such alloy nanoparticles. Yet, the structure of bimetallic Pd/Au catalyst particles is still not well established although promising activities of such materials have been demonstrated in experiment.9 Available experimental data regarding composition and structure often do not suffice for interpreting the behavior of nanoparticles. Thus, theoretical chemistry approaches have been applied in addition.16-20 While pure nanoparticles have successfully been described at the DFT level, using small or medium sized clusters21-24 or surface models,25-27 the case of alloyed nanoparticles28,29 is much more complex, due to the number of possible compositions and structural elements that evolve in a combinatorial way.2 To go beyond the limits of conventional DFT treatment and to apply an atomistic simulation to segregation, defects and diffusion of large truly nano-sized systems, force-field methods coupled with Monte-Carlo simulations are still the most commonly used approaches.16-19 Among the variety of force fields,30 the embedded-atom method31,32 (EAM) has been demonstrated to be particularly accurate for metallic systems and alloys.33-37 However, as most EAM parameterizations mainly aim at bulk properties, such methodology may fail for nanoparticles where low-coordinated surface atoms are of particular interest. Recently, Shan et al.16 presented an EAM force-field for Pd/Au systems derived from DFT results collected on a reference set of representative bulk, surface, and cluster systems. 2 ACS Paragon Plus Environment

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Coupling this potential to a Monte-Carlo procedure, they examined the temperature dependence of Au segregation, for clusters of various sizes and compositions, and the Pd surface species for one cuboctahedral cluster of nuclearity 5083. However, in their MonteCarlo procedure, Shan et al. allowed only permutations of atoms, but did not account for structure relaxation. With these simulations, they showed that Au atoms mainly segregate to the surface and that this surface segregation is temperature dependent. For the single example of a cluster with 5083 atoms they also analyzed the distribution of the Pd atoms on the cluster surface. However, the EAM parameters published in Ref. 16 appear to be, at least in part, erroneous,38 as the Pd-Au interaction potential cannot be reproduced. On the other hand, the results of the applications seem to be correct. In this paper we report a new EAM potential for Pd/Au alloys, parameterized with the help of DFT results that were collected on an improved set of representative bulk, surface, and cluster systems. Compared to the previous work discussed above,16 our set of cluster systems contains more alloyed systems and the surface systems include defects, to achieve a better representation of low-coordinated atoms. As an application of our new potential, we explored Pd/Au nanoparticles with up to 5083 atoms based on Monte-Carlo simulations. Compared to the previous study,16 we employed a more sophisticated Monte-Carlo procedure that also permitted structure relaxation steps. Furthermore, we here provide a considerably extended evaluation and rationalization of the results. In addition to the previously discussed Au segregation to the surface, we analyzed statistically averaged properties, such as coordination numbers, the concentration and distribution of various Pd species at the surface and in the interior of the particles as function of the temperature and the particle size. As a practical application, demonstrating the benefit of a more thorough evaluation of the structure of such alloys particles, we examined the number of suggested active sites for forming vinylacetate.7-9 2

Theoretical approach First, we describe the systems used to produce the reference data set for determining the

EAM parameterization, the corresponding DFT calculations, the underlying EAM formalism, the procedure for fitting the EAM force field, and finally details of the Monte-Carlo simulations. 2.1

Computational details of the DFT calculations Self-consistent density-functional calculations were carried out on a set of representative

systems intended as references for fitting the EAM parameters. For these calculations we used the Vienna Ab-initio Simulation Package, VASP.39-42 We applied the Perdew-BurkeErnzerhof (PBE)43,44 variant of the generalized-gradient approximation (GGA), as this 3 ACS Paragon Plus Environment


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exchange-correlation functional is particularly well suited for metallic systems.45 Ionic cores were represented by the projector-augmented wave method.46,47 Electronic single-particle wave functions were represented by plane waves, using an energy cutoff of 400 eV. To facilitate the convergence of the SCF procedure, a fractional occupation number technique was invoked,48 using a broadening function with a width of 0.15 eV. Final total energies were determined by extrapolating to T = 0 K.48 The geometry optimizations were terminated when the Hellmann-Feynman force49,50 on each atom was less than 0.05 eV/Å. In the SCF procedure the convergence criterion for the energy was set to 10-6 eV. For the fitting of the EAM parameters, we studied various bulk, surface, and cluster systems of pure and alloyed compositions. 9×9×9, 4×4×1, and 1×1×1 k-point meshes were used to sample the first Brillouin zone for bulk, surface, and cluster systems, respectively. The set of reference systems includes the pure systems of bulk Pd and Au, and the bulk alloys Pd3Au, Pd1Au1, and PdAu3; the latter are the only stable alloy phases observed experimentally.51 We assume a L12 structure for Pd3Au and PdAu3 and a L10 structure for Pd1Au1.52 The DFT optimized lattice constants of 394.8 pm (Pd) and 417.1 pm (Au) slightly overestimate the experimental values, 388 pm and 407 pm, respectively, as is often the case for GGA results. The calculated DFT cohesive energy for Pd, -358.0 kJ·mol-1, agrees well with the experimental value, -376 kJ·mol-1.53 However, the PBE result for the cohesive energy of gold, -288.5 kJ·mol-1, strongly underestimates the experimental value, -366 kJ·mol-1.54 This effect, already noted for all-electron scalar-relativistic DFT results, is not a consequence of the specific choice of the exchange-correlation functional; a variety of other functionals do so as well.45,55 In the present study we have to take into account that underestimating the Au-Au interaction compared to the Pd-Pd interaction may favor Au segregation somewhat too strongly compared to experiment. Surface systems were set up as four-layer repeated slab models, separated by 1.1 nm to avoid notable image interactions between the slabs. The two “bottom” layers of a slab, mimicking the bulk side, were either pure Pd or pure Au and were fixed to the optimized bulk lattice constant of the corresponding pure metal. The “top” two layers were allowed to relax; see Figure S1 of the Supporting Information (SI). For these surface models, we considered various unit cells: 2×2 for regular structures without defects, 3×3 for stepped, and 4×4 for surfaces with kinks of various compositions. We include such structural surface defects in order to account for low-coordinated atoms that occur at the surface of nanoparticles, in our force field parameterization. We considered two surface orientations, (100) and (111), which appear on cube-octahedral nanoclusters of fcc metals. Several compositions are represented in the data set: pure surfaces, Pdn-1Au configurations in which the heteroatom sits at step or kink 4 ACS Paragon Plus Environment

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sites, and finally configurations where the upper-most layer is covered by the alloying element. All configurations included in the data set for the EAM parameterization are depicted in Figure S1 of the SI. Finally, we also included some clusters in the data set for the EAM parameterization. Those cube-octahedral and truncated octahedral clusters exhibit Oh symmetry and comprise 55, 79, 140, and 147 atoms. We choose the pure clusters of both elements, Pd and Au, as well as AucorePdshell and PdcoreAushell configurations, resulting in the species Pd55, Pd42Au13, Pd13Au42, Au55; Pd79, Pd60Au19, Pd19Au60, Au79; Pd140, Pd96Au44, Pd44Au96, Au140; as well as Pd147, Pd92Au55, Pd55Au92 and Au147. Moreover, we also selected a set of alloy clusters where the (100) facets are covered by the alloying element; see Figure S2 of the SI. For all clusters, we used a simulation box of 24×24×24 Å3, to avoid image interactions. For the largest cluster studied, Au147, images are separated by 7 Å and thus can be considered as simulating clusters in the gas phase. 2.2

Embedded atom model Among various force-field strategies, the embedded atom method31,32 has emerged during

the last decades as one of the most efficient potentials for pure and alloyed extended metallic systems.33-37 In the EAM method one defines the total energy of an N-atom system as the sum of two contributions: embedding energies Fi, which represent the energy needed to embed atom i in the host electronic density ρi created by the surrounding atoms, and the pairwise interaction energies Φij at interatomic distance Rij between atoms i and j: N

N

i =1

i =1 j > i

Etot = ∑ Fi (ρi ) + ∑∑ Φij ( Rij )

(1)

Among the various functional forms developed to describe the embedding energy and the pairwise interaction energy,30 the formalism developed by Johnson et al. has been demonstrated to be particularly accurate for bulk, surface, and thin film systems.35-37 Our EAM approach is based on a slight reformulation of this formalism;16 details are given as SI. The EAM parameters have been optimized using a simplex-downhill method.56,57 The target function g(x) to be minimized is the sum of the norms of the residual differences between EAM and DFT cohesive energies of the 77 reference systems just described (Section 2.1 and Table S1 of the SI). As convergence criterion C of the simplex method we used:56  1 m +1 2 C= ( g ( xi ) − g ( x ) )  ∑ m + 1 i =1  

1/ 2

(2)

where g(xi) are the values of the target function at the simplex vertex i, m is the number of parameters to be optimized and thus m+1 is the number of simplex vertices. ̅ is the centroid 5 ACS Paragon Plus Environment


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of the simplex in the m+1 dimensional space. The simplex optimization procedure is supposed to be converged if C < 10-8 eV. All geometry optimizations at the EAM level, used in the parameterization, were carried out with the Large-scale Atomic/Molecular Massively Parallel Simulator software LAMMPS58 and the Polak-Ribiere conjugate-gradients method.59 Optimizations were considered as converged when the force on each atom was less than 10-8 eV/Å. 2.3

Monte Carlo simulations For studying the structure of Pd/Au nanoparticles, we employed a Monte-Carlo

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procedure based on the Metropolis algorithm.61 An MC approach is particularly advantageous compared to molecular dynamics when aiming at phase space profiles in case of (relatively) slow dynamic processes, e.g., diffusion and segregation. In the spirit of models, we examine here nanoparticles of cube-octahedral shape; such shapes have been observed in experiment.15, 62-64 The initial lattice constant of the alloyed particles is estimated according to Vergard’s law, i.e., by interpolating the bulk optimized Au and Pd inter-atomic distances.65 We initially create a random distribution of Pd and Au atoms in the nanoparticle. At each MC step, one of the following two configuration changes is attempted: (1) A randomly selected atom is displaced from its position (x, y, z) in a random direction, restricted by three random numbers (dx, dy, dz) with |di| ≤ dmax (i = x, y, z). The maximal absolute displacement dmax is reevaluated on the fly so that the acceptance rate of new configurations is about 50%.66 (2) A randomly selected pair of (Pd, Au) atoms is permuted. Operation (1) allows geometric relaxation of the nanoparticle while operation (2) accounts for diffusion processes in the particle. As structure relaxations are expected after each permutation step, we admit more relaxation operations than permutations by fixing a probability of 90% for operations (1) to occur. To reduce the number of steps needed for reaching equilibration, we initially anneal the system by starting the simulation at a temperature T1 = T + 800 K where T is the intended simulation temperature. Then the system is progressively cooled down in 104 MC steps until T1 = T. The energies before (E1) and after (E2) configuration changes are computed using the EAM potential. If the new configuration is more stable, E2 < E1, it is always accepted. Otherwise the new configuration is accepted only if exp[(E1 – E2)/kBT] is greater than a random number selected from a uniform distribution in the range [0,1]. This procedure is repeated for 3·106 steps for each system treated. We observed that the simulations are energetically equilibrated after about 106 MC steps and thus the equilibrated phase of the 6 ACS Paragon Plus Environment

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simulation covers ~2·106 MC steps, which should be enough to analyze the properties of such nanoparticles. The final structure and properties of the nanoparticles were obtained by averaging over snapshots taken every 100 MC steps over the whole equilibrated phase. 3 3.1

Results and discussion Accuracy of the EAM potential Table 1 lists the optimized parameters of the EAM potential. The corresponding electron

density ρ, embedding energy F, and pairwise interaction potentials Φ are shown in Figure S3 of the SI. For evaluating the accuracy of our EAM parameterization, we compared the cohesive energies, Ecoh, of various systems at the EAM and DFT levels. The cohesive energy of a system of n = x + y atoms is defined as the average atomization energy per atom. At the DFT level, this energy is DFT Ecoh =

1 DFT  E (Pd x Au y ) − xE DFT (Pd) − yE DFT (Au)  n

(3)

where EDFT(PdxAuy) refers to the DFT energy of the system and EDFT(Pd) and EDFT(Au) to the DFT atomic energies of Pd and Au atoms, respectively. At the EAM level, the cohesive energy is defined as: DFT Ecoh =

1 EAM E (Pd x Au y ) n

(4)

where EEAM(PdxAuy) is the EAM energy of the system; atomic energies vanish by definition. For extended systems, the various quantities are defined in analogous fashion. For bulk systems, our EAM cohesive energies for Pd, Pd3Au, Pd1Au1, PdAu3, and Au, -357, -349, -333, -312, and -288 kJ·mol-1, respectively, fit well the corresponding DFT values, -358, -345, -330, -312, and -289 kJ·mol-1; the maximum deviation, 4 kJ·mol-1, occurs for Pd3Au. Thus, due to the accurate parameterization of DFT results, also the EAM calculations will tend to overestimate Au segregation. In the same vain, the EAM equilibrium interatomic distances of 280.8, 283.1, 286.5, 291.2 and 296.3 pm, for Pd, Pd3Au, Pd1Au1, PdAu3, and Au bulk, respectively, agree with the corresponding DFT values, 279.2, 283.3, 286.9, 290.7 and 294.9 pm; the maximum deviation, 1.6 pm, occurs for Pd. Figure S4 of the SI shows the cohesive energy for Pd, Pd1Au1, and Au as a function of the lattice constant. As seen from those figures, our EAM potential also accurately describes out of equilibrium properties of pure and alloy bulks. Figure 1 illustrates the correlation between EAM and DFT cohesive energies for the surface and cluster systems used for the parameterization of the EAM. Slight differences 7 ACS Paragon Plus Environment


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Figure 1. Correlation between DFT and EAM cohesive energies for the set of (a) surface and (b) cluster systems used in the parameterzation.

between EAM and DFT can be observed for the cohesive energies, as the axes intercept of the trend lines are 3.06 kJ·mol-1 for surfaces and -3.67 kJ·mol-1 for particles. Those values are quite small. Moreover, our EAM approach accurately reproduces the evolution of the cohesive energy with system size and composition; the correlation coefficients and slopes of the trend lines are close to unity: r2 = 1.00 and 0.96 for surfaces and clusters, respectively; the corresponding slope values are 1.01 and 0.99. The deviations in cohesive energies between EAM and DFT results are at most 2.3 kJ·mol-1 for surfaces and 11.3 kJ·mol-1 for clusters, and the corresponding RMS deviations are 1.3 kJ·mol-1 and 4.2 kJ·mol-1, respectively. We conclude that our EAM approach is able to reproduce quite accurately the DFT energy properties of the set of systems used for the parameterization. Of course, one expects such accuracy as the EAM parameters were fitted with regard to these systems. How does our EAM approach work for systems that have not been included in the parameterization? To answer this very important question, we checked our EAM potential against DFT results for a set of test systems that comprises additional surface and cluster 8 ACS Paragon Plus Environment

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systems; see Figures S5 and S6 of the SI. For this purpose, we selected four-layer slab models of (111) surfaces using a 2x2 unit cell. The two “bottom” layers were built of Pd atoms, fixed at the optimized bulk positions. For the two “top” layers, we considered all possible alloy configurations, ranging from Pd7Au to PdAu7. Excluding configurations equivalent by symmetry, one obtains 33 configurations, as depicted in Figure S5 of the SI. Figure S7a of the SI reports a comparison of the DFT and EAM cohesive energies for this set of surfaces; the correlation between them is shown in Figure S7c. For each composition, the Au segregation to the surface increases from the left to the right in Figure S7a. Although not included in the parameterization process, our EAM potential is able to reproduce accurately the DFT cohesive energies for these surfaces; correlation coefficient and slope of the trend line in Figure S7c are close to unity. The maximum absolute and RMS deviations between DFT and EAM cohesive energies are 1.0 kJ·mol-1 and 0.53 kJ·mol-1, respectively, for this part of the test set. Note that DFT and EAM predict Au to prefer to segregate to the surface layer. The test set of particles consists of small pure Mn clusters (M = Pd, Au; n = 13, 14, 19, 20, 31, 35, 38) and of larger alloyed clusters. We selected 9 configurations of the icosahedral cluster Pd43Au12, treated without symmetry constraints, and varied the Au positions from all Au atoms at the surface to all Au atoms in the second shell. Additionally we treated a set of 6 configurations of the truncated-octahedral cluster Pd78Au, also varying the position of the Au atom, see Figure S6 of the SI. To assist the reader in distinguishing the configurations of these alloyed clusters, we also provide in the SI the Cartesian coordinates of the atoms and their DFT and EAM cohesive energies. Figure S7b of the SI displays DFT and EAM cohesive energies of the various configurations considered for the cluster Pd43Au12. Although slightly underestimating the DFT cohesive energies, the EAM approach is able to reproduce nicely the segregation behavior of such systems; the trend of the DFT and EAM curves are the same. Figure S7d displays the correlation between EAM and DFT cohesive energies; slope and correlation coefficient of the trend line are close to unity, demonstrating good agreement between DFT and EAM cohesive energies of clusters. The maximum absolute and the RMS deviations for this set of test systems are 17.4 kJ·mol-1 and 6.7 kJ·mol-1, respectively. In summary, we demonstrated in this section that our EAM approach is able to reproduce DFT cohesive energies with reasonable accuracy, also for systems outside the training set used in the parameterization.

3.2

Systems studied Having established the accuracy of our EAM potential, we went on to apply it in MC 9 ACS Paragon Plus Environment


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simulations of a series of cube-octahedral alloy clusters with 55, 147, 309, 561, 923, 1415, 2057, 2869, 3871, and 5083 atoms. To evaluate how the composition affects the structure of these particles, we considered three compositions, namely Pd0.75Au0.25, Pd0.5Au0.5 and Pd0.25Au0.75. We choose those three compositions as these are the only ones for which structures have been determined in the bulk phase.51 Moreover, to inspect the temperature dependence of the structures, we carried out MC simulations at various temperatures, i.e., at 273 K (room temperature), 423 K (close to the temperature used in the synthesis of vinylacetate), 523 K, and 723 K.

3.3

Energetics Differences between the binding energies (per atom) of finite-size metal clusters and the

corresponding bulk cohesive energy are related to the reduced coordination of the surface atoms.67,68 As the surface-to-volume ratio decreases for pure metal clusters of increasing nuclearity n, the cohesive energy of the clusters changes linearly with n-1/3 (or the inverse of the particle radius), and approaches the bulk value with n → ∞: E coh = k coh n − 1/ 3 + E bulk

(5)

The intercept of the linear function provides an estimate of the bulk cohesive energy Ebulk. The scaling of the cluster cohesive energy with n-1/3 was demonstrated for pure clusters of various metals,45, 69 but do alloy clusters exhibit the same behavior? To answer this question, we optimized the last snapshot of the MC simulation for 273 K at the EAM level for each cluster size just mentioned. We probed the effect of choosing only a single initial configuration for the Pd0.5Au0.5 particle with 561 atoms. We optimized 10 configurations selected at regular intervals from the beginning of the equilibrated phase to the end of the MC simulation. For an average value of -310.1 kJ·mol-1 of the cohesive energies, maximum and minimum values of these 10 optimized structures were calculated to differ by 0.13 kJ·mol-1 only. Figure S8 of the SI reports the evolution of the cohesive energy as a function of n-1/3 for the various particles studied. The individual values and the parameters of the linear trend line are reported in Table S2 of the SI. The resulting correlation coefficients show that the cohesive energy increases perfectly linearly with n-1/3 and the extrapolated values agree very well with EAM bulk simulations, with a maximum absolute deviation of 2.8 kJ·mol-1 for Pd0.5Au0.5. Thus, we conclude that also alloyed particles show the same energy scaling behavior with size as monometallic particles. An important criterion of the stability of bimetallic systems is the mixing energy Emix, also known as excess energy.70 For PdxAuy nanoparticles, Emix is defined as 10 ACS Paragon Plus Environment

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Emix (Pd x Au y ) = Ecoh (Pd x Au y ) −

x y Ecoh (Pd x +y ) − Ecoh (Au x +y ) x+ y x+ y

(6)

where Ecoh(z) is the cohesive energy of particle z. Accordingly, a negative value of Emix reflects the fact that alloying of Au and Pd atoms in a mixed-metal particle is favorable relative to the corresponding monometallic clusters. The individual values of Emix of all particles studied are reported in Table S2 of the SI. As all systems exhibit negative values of Emix, we conclude that Pd and Au atoms easily form stable bimetallic particles. We determined the largest mixing effect for Pd0.5Au0.5, in agreement with previous DFT results on small clusters.71 The values Emix slightly increase with cluster size because the stabilizing Au surface segregation contributes less (per atom) as the surface-to-volume ratio decreases; see Section 3.4. Recall that these energies are expected to be underestimated due to the underestimation of the Au cohesive energy. Yet, the present values are negative as the (unknown) exact values have to be, or it would be impossible to synthesize such an alloy material.

3.4

Structure Our MC simulations on small clusters, i.e., with 55 and 147 atoms, result in a transition

from cub-octahedral to icosahedral shapes. The aim of the present work is to explore cuboctahedral nanoparticles. As (relatively) small systems of nuclearities 55 and 147 are commonly not targeted in experiments on nanoparticles9 and can be examined using more sophisticated approaches at the DFT level, we will restrict the discussions of this section to the results obtained for particles of at least 309 atoms.

Surface composition. Figure 2 shows the evolution of the Au concentration at the particle surface as a function of cluster size and temperature for various alloy compositions. Dotted lines correspond to the maximum gold concentration that the system is able to reach. In general, for the compositions Pd0.75Au0.25 and Pd0.5Au0.5, the surface concentration of Au increases sharply for small nuclearities and approaches a quasi-asymptotic plateau at large particle sizes. In the case of Pd0.25Au0.75, the surface is completely covered by gold, even for small particles. Also for composition Pd0.5Au0.5, a full Au surface coverage is reached for the largest clusters at 273 K. Only for composition Pd0.75Au0.25, the surface gold coverage remains considerably below the possible maximum value (Figure 2). The Au surface segregation increases with the Au concentration of the particle. As example, for a simulation of a particle with 2057 atoms at 423 K, the surface Au concentration grows from 60% to 95%, and finally to 100% by increasing the Au concentration from Pd0.75Au0.25 to Pd0.5Au0.5 and Pd0.25Au0.75. Comparing the results with increasing temperature, one observes that the Au segregation to the surface slightly decreases 11 ACS Paragon Plus Environment


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at 723 K by up to 7%, 8% and 0.5% compared to the results at 273 K for the compositions Pd0.75Au0.25, Pd0.5Au0.5, and Pd0.25Au0.75, respectively. Thus, PdAu particles seem to prefer a PdcoreAushell structure, in agreement with previous studies with EAM16 and Gupta potentials20 and with XPS observations on uncalcined particles.72 However, calcination strongly disturbs the initial uncalcined structure, leading to Pd-rich shell/Au-rich core particles.72 Figure 3 shows the evolution of the Au concentration in the various shells of the larger 12 ACS Paragon Plus Environment

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particles studied, with more than 2000 atoms, as a function of the cluster size for the three compositions treated at 423 K. The Au concentration oscillates for the three outer shells, as previously mentioned for Pd/Au16 and also found for Pd/Pt and Pd/Ir alloy surfaces.73 The same behavior also occurs for the smaller particles; see Figure S9 of the SI. The surface

Figure 3. Au concentration, including standard deviations, of different layers of larger particles from MC simulation at 423 K for compositions (a) Pd0.75Au0.25, (b) Pd0.5Au0.5, and (c)Pd0.25Au0.75 (c). Layer 1 refers to the surface layer, layer 2 to the first subsurface and so on. Squares, circles, triangles and rhombuses represent cluster sizes of 2057, 2869, 3871 and 5083 atoms, respectively. Dashed lines mark the Au concentration for a random distribution of Pd and Au.

appears as Au-rich. These oscillations vanish in the core region, leading to a relatively constant Au concentration. Note that the core concentration is always below the value for a reference cluster with purely randomly distributed Pd and Au atoms (dashed lines in Figure 3); this lower concentration of Au in the inner core of the clusters is a result of the Au 13 ACS Paragon Plus Environment


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segregation to the surface. The high gold concentration of the surface can be rationalized by the fact that the bulk cohesive energy of Au (-288 kJ·mol-1) is lower than that of Pd (-357 kJ·mol-1), at the EAM and the DFT levels of theory. Thus, it is easier to form low-coordinated Au atoms than Pd atoms at the particle surface. The Pd-rich composition of the first subsurface layer can also be understood in terms of cohesive energies which for bulk alloy systems are higher than for pure Au systems, at the DFT and EAM levels. The Pd-Au interaction is also stronger than the Au-Au interaction, as the mixing energies are all negative. This reflects the fact that the mixing of Au and Pd atoms in bimetallic systems is favorable relative to the corresponding monometallic cluster. Therefore, as all atoms in the subsurface layer exhibit coordination 12, the system is stabilized if the number of Pd-Au contacts increases at the expense of Au-Au contacts. By the same token, one can understand the gold enrichment of the second subsurface shell, compared to the average inner shells concentration. Au is attracted by Pd-rich regions, as Pd-Au interactions are stronger than Au-Au interactions (Figure S3 of the SI). This effect enhances the Au concentration below the Pd-rich subsurface layer, even above the average of Au concentrations of 0.75%, 0.50%, and 0.25 % of the corresponding compositions (Figure 3).

Coordination numbers. The evolution of the average coordination numbers of Au and Pd atoms at 423 K as a function of the particle size are depicted in Figure 4. This figure also shows a decomposition of the coordination numbers in terms of homogeneous (Au-Au and Pd-Pd) and heterogeneous (Au-Pd) contacts. First, as expected, the total coordination numbers increase with particle size due to the decreasing surface-to-volume ratio. As Au segregates to the surface, Pd atoms are on average higher and Au atoms lower coordinated compared to a random distribution of Pd and Au in the particles (dashed lines in Figure 4). Thus, a higher concentration of Pd atoms is found in the inner region of the particles. In general, Au and Pd coordination numbers increase with system size, except the number of Pd-Pd contacts in the case of Pd0.5Au0.5 and Pd0.25Au0.75. For the compositions Pd0.75Au0.25 and Pd0.5Au0.5, the total coordination numbers of Pd atoms increase in the small cluster regime and finally level off close to the bulk coordination number, 12. The same behavior is observed for Au atoms approaching an asymptotic value of about 10. These different average coordination numbers for Pd and Au can be rationalized because Au segregates to the surface and Pd atoms are mainly found in the inner core. For the Pd0.25Au0.75 composition, the total Pd coordination number is always close to 12, even for small clusters (Figure 4e). This can be understood by the fact that the Au concentration is high enough that already for small clusters the surface is nearly totally covered by gold and thus Pd atoms are mainly situated in the inner core, hence are fully coordinated. 14 ACS Paragon Plus Environment

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Figure 4. Evolution of coordination numbers of Pd (panels a, c, e) and Au (panels b, d, f) atoms with size of the particles and decompositions as a function of different interactions. Results extracted from MC simulations at 423 K. Panels (a) and (b) – composition Pd0.75Au0.25; panels (c) and (d) – composition Pd0.5Au0.5; panels (e) and (f) – composition Pd0.25Au0.75. Squares, circles and triangles indicate total coordination numbers, homo-atomic interactions (Pd-Pd, Au-Au), and hetero-atomic interactions (Pd-Au), respectively. Empty symbols (dashed lines) show the corresponding values in the case of a purely random distribution of Pd and Au. 15 ACS Paragon Plus Environment


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For the composition Pd0.75Au0.25, the Pd average coordination number is dominated by PdPd contacts. This is related to the fact that most Au atoms are at the surface of the particle and the remaining amount of Au atoms is relatively small; see Figure 3a. Thus, most of the Pd-Au interactions correspond to contacts between the surface and the first subsurface layer while the inner-core Pd atoms are mainly coordinated by other Pd atoms, leading to a high number of Pd-Pd contacts. In consequence, the Au coordination number for the same composition is dominated by Au-Pdf interactions and the average number of Au-Au contacts is below 2. In the same spirit, but reversing the roles of Au and Pd, one can rationalize the coordination numbers of the composition Pd0.25Au0.75.

Figure 5. Snapshot of the MC simulation at 423K of a particle with 5083 atoms and composition Pd0.75Au0.25. Purple, green, grey, and red refers to Pd monomers at the (100) facet, Pd monomers at the (111) facet, Pd dimers, and Pd islands, respectively. Pink could also be considered as a potential active site for VAF as two Pd monomers on the (100) surface are separated by 403 pm.

Surface structure. The catalytic activity of alloy nanoparticles can be strongly correlated with the morphology of the surface. Indeed, Goodman et al. demonstrated that vinyl-acetate formation (VAF) over PdAu nanoalloy particles is structure sensitive.7-9 From their experimental findings, they postulated active sites where two neighboring Pd atoms have to be close, but sufficiently separated. Too short an interatomic distance prevents co-adsorption of the reactants ethylene and acetic acid. Thus, they proposed active sites for VAF to comprise a pair of non-contiguous Pd monomers, i.e., two Pd atoms as next-nearest neighbors, exclusively surrounded by Au atoms in their first coordination shell. Using geometric considerations, they also postulated the ideal distance between the two Pd atoms to be ~3.3 Å.7 In our MC simulations, we found that the average distances between two nextnearest neighbor Pd monomers at facets of (100) and (111) orientations are 4.0 Å and 4.8 Å, respectively. Thus, by slight structural adjustment, the two reactants should be able to assume a favorable mutual arrangement on a (100) facet, whereas the distance between Pd monomers on (111) facets seems to be too large to permit a reaction. Indeed, VAF was demonstrated to be unlikely on a (111) surface.7-9 16 ACS Paragon Plus Environment

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Thus, knowledge of the distribution of Pd atoms at the surface of alloy nanoparticles is a prerequisite for understanding their catalytic activity in VAF as the catalytic process is driven by Pd centers at the surface.7 In this context, recall that the surfaces of Pd0.25Au0.75 particles are completely covered by Au atoms (Figure 2c). The concentration of Pd in the surface of these particles will be small, even if Au segregation tends to be overestimated in the present study due to the underestimation of the Au-Au interaction (Section 2.1). Thus, we will focus on the analysis of the surface of particles with compositions Pd0.5Au0.5 and Pd0.75Au0.25. We considered various Pd species when analyzing the morphology of particle surfaces. Pd monomers are defined as Pd centers where all nearest-neighbor sites are occupied by Au atoms. Pd dimers comprise a pair of two nearest-neighbor Pd centers, otherwise completely surrounded by Au atoms, and Pd islands refers to at least 3 bonded Pd atoms. Figure 5 shows examples of such Pd species. In the following, we will discuss surface concentrations defined as C i j = ni j / ntotj

(7)

where Ci j is the concentration of species i at surface structural motif j, i.e., on (100) facets, (111) facets, edges, or corners. ni j is the number of species i at motif j, and ntotj is the total number of atoms associated with surface motif j. When we do not distinguish surface motifs, e.g. for dimers and islands, ntotj equals the total number of surface atoms (Figure 6). Figure 6 shows how the concentrations of various Pd species evolve at the surface of Pd0.75Au0.25 particles, as function of temperature and system size. Figure 6e depicts how the surface concentration of Pd atoms changes for various surface structural motifs. The Pd concentration increases in the following order: corner < edge < (100) facet < (111) facet. As already mentioned, Pd atoms are expected to occupy preferentially higher coordinated sites as the cohesive energy of Pd is larger than that of Au. Our results for alloy nanoparticles confirm this expectation as sites on (111) facets exhibit a higher coordination (9) than sites on (100) facets (8) as well as on edges (7) and corners (5). The preferred location of single Pd centers at (111) facets over (100) facets has previously been demonstrated at the DFT level, using medium-size model clusters with up to 92 atoms.74 However, Figures 6a and 6b demonstrate that the concentration of Pd monomers is higher at (100) facets than at (111) facets. This can be rationalized by the high amount of Pd at the (111) facets where Pd thus forms more dimers or islands; see Figures S9 and S10 of the SI. In general, concentrations of Pd monomers and dimers at (111) facets hardly change with increasing temperature. The concentration of Pd monomers at (100) facets decreases with increasing temperature, although the Pd surface concentration increases. On the other hand, 17 ACS Paragon Plus Environment


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Figure 6. Evolution of the surface concentration (including standard deviations) of various surface motifs with temperature and particle size for Pd0.75Au0.25 particles. (a) Pd monomers at (100) facets, (b) Pd monomers at (111) facets, (c) Pd atoms involved in Pd dimers, (d) Pd atoms involved in Pd islands. Squares, circles, triangles, and rhombuses refer to results of MC simulations at 273, 423, 523 and 723 K, respectively. Panel (e) shows how the Pd surface concentration evolves at 423 K at different structural motifs; see text for the definition. Squares, circles, triangles, and rhombuses refer to (100) facets, (111) facets, edges, and corners, respectively. the concentration of Pd islands increases with temperature even stronger than the overall Pd concentration at that surface. We conclude that by increasing the temperature, Pd monomers at (100) facets tend to coagulate and form preferentially larger ensembles, i.e., islands (Figure S9 of the SI). On (111) facets, the decomposition of the Pd concentration into contributions from monomers, dimers, and islands is essentially independent of the temperature (Figure S11 of the SI). Note also that the Pd concentration at (111) facets is above the expected value in a purely random distribution (75%) for small clusters, indicating a preference of Pd to occupy 18 ACS Paragon Plus Environment

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Figure 7. Evolution of the surface concentration (including standard deviations) of various surface motifs with temperature and particle size for Pd0.5Au0.5 particles. Lay-out as in Figure 6.

(111) facets for such systems; this is due to fact that the small number of Au atoms in the Pd0.75Au0.25 clusters are preferentially found at corners and edges. Figure 7 shows the same evolution with increasing size of the concentration of various Pd surface entities for particles of Pd0.5Au0.5 composition. As a general observation, the surface concentrations of Pd monomers, dimers, and islands at (100) facets, increase with temperature 19 ACS Paragon Plus Environment


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Figure 8. Evolution of the numbers (including standard deviations) of possible active sites for the formation of vinylacetate as a function of particle size and temperature for compositions (a) Pd0.75Au0.25 and (b) Pd0.5Au0.5. Squares, circles, triangles, and rhombuses refer to results of MC simulations at 273, 423, 523 and 723 K, respectively.

and decrease with increasing cluster size. On the other hand, the surface concentration of Pd monomers at (111) facets decreases with increasing temperature for particle sizes up to 1415 atoms, but an opposite trend is observed for larger particles. As for the composition Pd0.75Au0.25, Figure 7e shows that the concentration of Pd decreases as follows: (111) facets > (100) facets > edges > corners, due to the difference in cohesive energy between Pd and Au. The Pd concentration is again higher at (111) facets than at (100) facets; in consequence, the concentration of Pd monomers is higher at (111) than at (100) facets. The Pd concentrations on (100) and (111) facets are decomposed in similar fashion into monomers, dimers, and islands (Figures S11 and S12 of the SI). At both types of facets, concentrations of monomers, dimers, and islands increase with the temperature and decreases with particle size. Sites for vinyl-acetate formation (VAF). As an application, we finally consider the occurrence of sites appropriate for the formation of vinyl-acetate, as postulated earlier.7-9 Accordingly, VAF is supposed to occur at active sites of (100) facets with two next-nearest neighbor Pd monomers; for an example, see Figure 5. Figure 8 depicts how the concentration of such sites evolves as a function of particle size and temperature. For nanoalloy particles with composition Pd0.75Au0.25, the potential activity, i.e. the number of active sites, increases 20 ACS Paragon Plus Environment

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with the particle size and decreases with increasing temperature. These trends agree with the changes of the concentration of Pd monomers at (100) facets, although this concentration decreases slightly with cluster size at 273 K (Figure 6a). Indeed, for larger clusters, the Pd monomer concentration at (100) facets is essentially independent of the particle size, resulting in an increasing total number of monomers as the size of the (100) facets increases. For Pd0.5Au0.5 particles, the number of active sites is quite small and the standard deviations are relatively high in simulations at 723 K. At lower temperatures, the number of active sites per particle is lower than one; hence, in a set of particles, only a few of them should exhibit active sites. At temperatures below 723 K, the average number of active sites decreases with particle size and marginally increases with temperature. This finding reflects the fact that the concentration of Pd monomers at (100) facets decreases with increasing cluster size and increases with temperature (Figure 7a). However, at 723 K, the number of active sites of smaller clusters slightly increases with cluster size and reaches a quasiasymptotic level for large particles, although the concentration of Pd monomers decreases with particle size. Nevertheless, as we tend to overestimate Au segregation to the surface, also for Pd0.5Au0.5 particles a small number of active sites is expected. In general, the number of potentially active sites is larger for Pd0.75Au0.25 than for Pd0.5Au0.5 particles, due to the larger concentration of Pd monomers at (100) facets of Pd0.75Au0.25 particles. 4

Conclusion We have parameterized a new EAM potential for studying Pd/Au nanoalloy particles. This

force field was shown to reproduce DFT results for bulk, surface, and cluster systems accurately, even for systems not included in the parameterization. Applying Monte-Carlo simulations at the EAM level, we studied effects of cluster size and temperature on the structure and the composition of Pd/Au alloy particles of 55 to 5083 atoms. We demonstrated that Au in general prefers to segregate to the surface, due to its lower cohesive energy compared to Pd. The surface of Pd0.25Au0.75 particles is completely covered by Au. For the two other compositions, the Au concentration at the surface is enhanced to more than 90% for Pd0.5Au0.5 and more than 60 % for Pd0.75Au0.25. The surface segregation increases with particle size and decreases with increasing temperature. As a result of the Au surface segregation, the shell-wise concentrations of Au and Pd exhibit damped oscillations toward the interior of the particles, with the subsurface shell being enriched in Pd. The lower cohesive energy of Au compared to Pd is also reflected in the distribution of both metals at the surface. While Au atoms preferentially occupy low-coordinated edge and corner sites, one finds the highest Pd 21 ACS Paragon Plus Environment


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concentration at the close-packed (111) facets. By analysis of the surface, we also showed that the surface concentration of Pd monomers at (100) facets, which is supposed to be responsible for the high catalytic activity of Pd/Au alloys for VAF, is higher for Pd0.75Au0.25 than for Pd0.5Au0.5 particles. Acknowledgment. R.M. is grateful for financial support by the Institut für Siliciumchemie at TU München. We thank Leibniz Rechenzentrum München for providing generous computing resources. Supporting Information Information on the EAM formalism; tables (1) comparing DFT and EAM cohesive energies of the systems used in the parameterization, and (2) showing EAM cohesive energies of nanoalloy clusters used for studying the scaling of the cohesive energy; figures depicting all surface systems and clusters used in the EAM parameterization, characteristics of EAM contributions as function of the electron density, cohesive energies of bulk alloys, obtained by the EAM method as a function of the lattice constant, the test systems not included in the EAM training set and an evaluation of their energies, the scaling of the cohesive energies of pure and alloyed clusters with size, the decomposition of the surface concentration of Pd atoms into various local motifs, varying with temperature, for various facets of nanoalloy particles. This material is available free of charge via the Internet at http://pubs.acs.org.


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Table 1. Parameters of the EAM potential.

re (Å) fe (eV/Å) ρe (eV/Å) α β A (eV) B (eV) κ λ Fm0 (eV) Fm1 (eV) Fm2 (eV) Fm3 (eV) Fn0 (eV) Fn1 (eV) Fn2 (eV) Fn3 (eV) F0 (eV) F1 (eV) F2 (eV) F3 (eV) Fe (eV) η ρm

Pd

Au

Pd-Au

2.8003 1.5000 19.9736 8.6124 4.6615 0.4017 0.5779 0.6034 0.7656 -1.5113 -0.6296 3.5685 2.6868 -2.2323 -0.5091 1.1839 0.2348 -2.2725 0.0072 1.4407 -2.6195 -2.2674 0.9015 0.3199

2.9629 1.1572 15.3701 8.1504 4.6606 0.2535 0.3577 0.4339 0.7612 -2.0730 -0.2097 1.8633 0.0000 -2.0880 -0.4737 -2.5789 -0.1723 -2.1299 0.0072 1.8183 -0.3263 -2.1277 1.3002 0.8154

2.8492 – – 10.2291 3.7923 0.1635 0.3385 0.2505 0.7417 – – – – – – – – – – – – – – –



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Table of Contents Graphic


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Au Alloy Nanoparticles from a Density Functional

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