Structure, Electronic, and Magnetic Properties of Binary PtnTM55ân

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Structure, Electronic, and Magnetic Properties of Binary Pt TM (TM = Fe, Co, Ni, Cu, Zn) Nanoclusters: A Density Functional Theory Investigation Diego Guedes Sobrinho, Ricardo Kita Nomiyama, Anderson Silva Chaves, Maurício Jeomar Piotrowski, and Juarez L. F. Da Silva J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b02242 • Publication Date (Web): 11 Jun 2015 Downloaded from http://pubs.acs.org on June 16, 2015

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The Journal of Physical Chemistry

Structure, Electronic, and Magnetic Properties of Binary PtnTM55-n (TM = Fe, Co, Ni, Cu, Zn) Nanoclusters: A Density Functional Theory Investigation Diego Guedes-Sobrinho,† Ricardo K. Nomiyama,‡ Anderson S. Chaves,¶ Maurício J. Piotrowski,§ and Juarez L. F. Da Silva∗,† São Carlos Institute of Chemistry, University of São Paulo, PO Box 780, 13560 − 970, São Carlos, SP, Brazil, Department of Materials Engineering, São Carlos School of Engineering, University of São Paulo, 13560 − 970, São Carlos, SP, Brazil, São Carlos Institute of Physics, University of São Paulo, PO Box 369, 13560 − 970, São Carlos, SP, Brazil, and Department of Physics, Federal University of Pelotas, PO Box 354, 96010 − 900, Pelotas, RS, Brazil E-mail: [email protected] Phone: +55 (16) 3373 6641. Fax: +55 (16) 3373 9952

Abstract

chemical order parameter follows nearly a parabolic behavior as a function of the Pt concentration with a minimum at nearly 50 % for both properties and all systems. From our structural analysis, the difference in the atomic size of the Pt and TM chemical species contributes to increase the segregation, which reaches its maximum for the ICO core-shell configuration, and hence, an ideal homogeneous distribution cannot be reached. Except for PtZn, we found that the average bond lengths increase almost linearly by replacing TM by Pt atoms in the Ptn TM(55-n) systems, and hence, it follows approximately the Vegard’s law. We found that the center of gravity of the occupied d-states of the surface atoms changes almost linearly for PtCo, PtNi, and PtZn, and hence, the d-band center can be tuned by controlling the composition of the chemical species, while there are deviations from the linear behavior for PtFe and PtCu.

Bimetallic platinum-based transition-metal (PtTM, TM = Fe, Co, Ni, Cu, and Zn) nanoclusters are potential candidates to improve and reduce the cost of Pt-based catalysts, however, our current understanding of the binary PtTM nanoclusters is far from satisfactory compared with binary surfaces. In this work, we report a density functional theory investigation of the structural, energetic, and electronic properties of binary PtTM nanoclusters employing 55-atom model systems (Ptn TM(55-n) ). We found that the formation of the binary PtTM nanoclusters are energetically favorable for all systems and compositions. Except small deviations at the icosahedron (ICO) core-shell configuration, Pt42 TM13 , we found that the excess energy, which measures the relative stability, and the ∗ To

whom correspondence should be addressed of São Paulo ‡ University of São Paulo ¶ University of São Paulo § Federal University of Pelotas † University

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Keywords

Although, the binary nanoclusters have been widely studied by experimental and theoretical approaches, our atomistic understanding of those systems is still far from complete compared with bimetallic surfaces, in particular due to the challenges to identify reliable model structures for binary nanoclusters. For example, experimental techniques have difficulties to access directly the atomic structure of nanoclusters due to the lack of long range symmetry, while the number of local minimum configurations increases almost exponentially with the number of atoms, and hence, a hard problem even for global optimization algorithms employing empirical pair-potentials. To obtain a better understanding of the structural and electronic properties of the binary PtTM (TM = Fe, Co, Ni, Cu, and Zn) nanoclusters, and how their properties are related with the parent compounds, we performed a theoretical investigation of binary 55-atom PtTM nanoclusters (diameter of about 1.0 nm) employing density functional theory (DFT) calculations. To obtain the atomic structure models, which plays a crucial role in the quality of our results, we employed a set of ab-initio based structural design principles, which takes into account all available information from the unary 55atom nanoclusters to build up the initial binary configurations.

Nanoalloys, Ab-initio simulations, Density functional theory

I

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Introduction

Bimetallic platinum-based transition-metal (PtTM) systems have attracted great attention due to the wide range of applications of Pt in heterogeneous catalysis and electrochemistry. 1–5 The formation of TM alloys, which includes extended systems such as bimetallic TM surfaces 5–8 and finite binary TM systems 9–14 (clusters, nanoclusters, and nanoparticles) opens the possibility to tune their electronic properties, in particular, the center of gravity of the occupied d-states and the magnitude of the density of states near to the Fermi level of external layers (surfaces) or shell (particles), which affects directly the reactivity of chemical reactions. 15,16 In contrast with the Pt(111)/Cu(111) and Pt(111)/Au(111) substrates, in which the inplane compressive or tensile strain plays a crucial role, 6–8,17,18 the formation of binary nanoclusters (from 1 nm to 10 nm) opens the possibility to release the strain energy by large structure relaxations and/or the formation of core-shell, onion-like, januslike, and homogeneous distribution configurations. 14,19–21 Among a wide range of binary PtTM nanoclusters, which includes 3d, 4d, and 5d TM elements, the combination of Pt and TM 3d systems have received special interest in the last years, in particular, the following systems, PtFe, 22–28 PtCo, 11,23,29–35 PtNi, 9,36–42 PtCu, 13,34,38,42–46 and PtZn. 47,48 Among several important chemical reactions, all those systems have been studied mainly with the aim to improve oxygen reduction reactions (ORR), 24,27,28,49 which plays a crucial role for the development of fuel cells. 34,50 Beyond that, few of those systems such as PtFe and PtCo have also been investigated as potential candidates for magnetic storage due to the high magnetic anisotropy. 23,33

II

Theoretical Approach and Computational Details

A Total Energy Calculations Our calculations are based on spin-polarized DFT 51,52 within the semilocal Perdew-BurkeErnzerhof 53 formulation for the exchangecorrelation energy functional. The KohnSham (KS) equations were solved using the all-electron projected augmented wave 54,55 (PAW) method as implemented in the Vienna ab-initio simulation package 56,57 (VASP) employing the PAW projectors provided within VASP. 58 Spin-orbit coupling was not taken


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into account for the valence states. For the total energy calculations of the bulk and nanocluster systems, we employed a plane-wave cutoff energy of 300 eV, however, to obtain the equilibrium volume of the bulk systems by minimization of the stress tensor and atomic forces, we used a cutoff energy of 600 eV due to the slow convergence of the stress tensor as a function of the number of plane-waves. Further details and total energy convergence are discussed in the supporting information. For the bulk systems, we employed the well known ground state structures, 59 namely, Fe in the body-centered cubic (bcc), Co and Zn in hexagonal close-packed (hcp), and Ni, Cu, and Pt in the face-centered cubic (fcc) structure. We modeled the 55-atom unary and binary nanoclusters using a cubic box with 22 Å, which yields a distance of about 12 Å between the nanoclusters surfaces, and hence, the interactions among the nanocluster and its image are negligible. For example, the relative total energy between two 55-atom configurations changes only 0.04 meV/atom upon an increasing in the cubic box size from 22 Å to 26 Å. The Brillouin zone integration for the nanocluster calculations were performed using only the Γ-point as there is no dispersion in the electronic states, however, high density k-meshes were used for the bulk systems in their respective ground state bulk structures, namely, 27×27×10 for Co and Zn, and 22×22×22 for Fe, Ni, Cu, and Pt. For all calculations, we employed a total energy convergence of 10−5 eV, and the equilibrium geometries are obtained once the forces on each atom are less than 0.025 eV/Å.

55-atom requires the local optimization (total energy evaluations) of thousand configurations, which is computationally demanding for ab-initio DFT calculations. To minimize the computational cost, we employed a set of ab-initio based structural design principles, which takes into account all available information from the 55-atom nanoclusters to build up the initial binary configurations. Initially, we calculated about 30 configurations for each TM55 system (TM = Fe, Co, Ni, Cu, Zn, Pt), which includes the icosahedron (ICO) with Ih space group, 64 cuboctahedron (CUB) with Oh space group, 64 few distorted reduced core (DRC) structures with about 10-atom in the core region instead of 13-atom, 20 polytetrahedral (PTH), 65 wheelshaped (WHE), 66 and etc. Furthermore, we also included the putative global minimum configurations reported for Fe55 , 67,68 Co55 , 11,69 Ni55 , 66,70 Cu55 , 71,72 Zn55 , 73 and Pt55 . 11,20 The most relevant configurations are shown in the supporting information. Once the putative lowest energy configurations for the unary compounds were obtained (i.e., n = 0, 55), the following steps were performed. We considered only seven compositions for Ptn TM(55-n) , namely, n = 6, 13, 20, 28, 35, 42, 49. For all the structural models mentioned above, we can define two regions in the 55-atom nanoclusters, namely, a surface region with 42 (45 − 46) atoms exposed to the vacuum for ICO, CUB, and etc (for DRC), while the core contains 13 (10 − 9) atoms. In this work, the surface region is defined only by the atoms exposed directly to the vacuum region using the hardsphere model. 74 Once the two regions are defined, it is important to establish the trends for the distribution of the Pt and TM atoms within the core and surface regions. For example, for the Pt13 TM42 composition, the following configurations were designed using an ICO model: (i ) Pt13 and TM42 located in the core and surface regions, respectively (i.e., core-shell configuration - segregation); (ii ) TM13 located in the core region, while Pt13 and TM29 form a homogeneous distribution or segregate in the nanocluster sur-

B Nanocluster Atomic Configurations The search for the global minimum configuration for systems like Ptn TM(55-n) requires the use of global optimization algorithms such as the basin hopping Monte Carlo 60,61 (BHMC) or genetic algorithms 62,63 (GA). The application of those techniques for systems like


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Those results are in good agreement with previous DFT-GGA results. 80,81 It has been suggested that the size of the atomic radius, RTM , plays a crucial role in the location of the TM atoms within the nanoalloys, 11,82–84 and hence, it is important to obtain RTM directly from our calculations. In this work, we employed the hard-sphere model, 74 in which RTM can be calculated from the nearest-neighbor distances. Thus, it is important to calculate the nearest-neighbor distance for a given atomic configuration. For symmetric structures such as Ni, Cu, and Pt in the fcc structure or 55-atom ICO and CUB nanoclusters, the number of nearestneighbors and the nearest-neighbor distance can be easily calculated by defining a cutoff radius, however, it is not the case for distorted nanoclusters or bulk systems with a small separation between the first and second nearest-neighbor shells such as in the bcc structure or hcp structures with a large c0 /a0 ratio, Table 1. To overcome this problem, we employed the effective coordination concept, 85,86 which yield the average weighted nearest-neighbor distance, d av , and the average effective coordination number, ECN, which is given in number of nearestneighbors (NNN). Further details are discussed in the supporting information and elsewhere. 86 Using the hard-sphere model (RTM = d av /2), we obtained RTM = 1.26, 1.25, 1.25, 1.29, 1.38, and 1.41 Å for Fe, Co, Ni, Cu, Zn, and Pt, respectively, which deviates slightly compared with 12-coordinated metals (e.g., from 0.0 % for Ni to 1.4 % for Pt). 59 Thus, DFT-PBE yields that Fe, Co, Ni, and Cu are smaller than Pt by 10.6, 11.3, 11.3, and 8.5 %, respectively, while RZn and RPt differs only by 2.1 %. As expected, we obtained ECN = 12 for Co, Ni, Cu, and Pt in the fcc structure, however, we found ECN = 11.6 for Fe. Thus, the second nearest-neighbor contributes to increase ECN from 8 to 11.6 in the bcc structure, while the large c0 /a0 ratio decreases ECN from 12 to 11 for Zn. The cohesive energy behavior from Fe to Zn can be explained by the occupation of the bonding and anti-bonding

Table 1: Bulk properties: equilibrium lattice constants, a0 and c0 , average weighted bond lengths, d av , effective coordination number, ECN, in number of nearest neighbors, total magnetic moment per atom, mT , and the cohesive energy per atom.

Fe bcc Co hcp Ni fcc Cu fcc Zn hcp Pt fcc

a0 (Å) 2.83 2.49 3.52 3.63 2.66 3.98

d av (Å) 2.52 2.49 2.49 2.57 2.75 2.81

ECN 11.6 12.0 12.0 12.0 11.0 12.0

mT (µB ) 2.17 1.58 0.62 0.00 0.00 0.00

Ecoh (eV) −4.89 −5.01 −4.62 −3.49 −0.94 −5.62

face; (iii ) Pt7 TM6 and Pt6 TM36 form a homogeneous distribution in the core and surface regions, respectively. Thus, several configurations were designed with Pt atoms in the core or surface region for all the studied compositions. Furthermore, we considered the crossover among the systems, i.e., the lowest energy configuration identified for a particular system was used as an initial configuration for a different system. Although the number of configurations is finite, it provides a good representation to study the evolution of the structural, energetic, electronic, and magnetic properties as a function of composition for nanoalloys with diameter of 0.9 Å to 1.3 Å, which can be accessed by experimental techniques nowadays. 75–79

III

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Results

A Bulk Sytems: Fe, Co, Ni, Cu, Zn, Pt The main bulk properties are summarized in Table 1. The Fe and Co lattice constants are smaller than experimental results by about 0.8 % to 1.4 % and nearly 0.0 % for Ni, however, DFT-PBE yields larger lattice constants than experimental for Cu, Zn, and Pt, in which the relative error increases from Cu (0.6 %) to Pt (1.5 %). 59 We found c0 /a0 = 1.614 and 1.880 for Co and Zn, respectively.


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Figure 1: Putative global minimum DFT-PBE configurations for the binary Ptn TM(55-n) (n = 0, 13, 20, 28, 35, 42, 49, and 55) nanoclusters. The Fe, Co, Ni, Cu, Zn, and Pt atoms are indicated by yellow, purple, green, blue, red, and black spheres. The core-shell configurations, Pt42 TM13 , are formed for the following nanoalloys: PtFe, PtCo, PtNi, and PtCu. Table 2: Unary 55-atom nanoclusters properties: relative total energies, ∆Etot , average weighted bond lengths, d av , effective coordination number, ECN, in number of nearestneighbor, and total magnetic moments per atom, mT .

Fe55 Co55 Ni55 Cu55 Zn55 Pt55

ICO ICO ICO ICO DRC ICO DRC ICO

∆Etot (eV) 0.00 0.00 0.00 0.00 −5.75 0.00 −5.58 0.00

d av (Å) 2.50 2.43 2.44 2.52 2.66 2.72 2.67 2.74

ECN 8.15 8.36 8.39 8.38 7.27 8.42 6.84 8.34

B Unary TM55 Nanoclusters The putative lowest energy TM55 structures are shown in Figure 1, while the results Config. i for relative total energy (∆Etot = Etot − ICO Etot ), d av , ECN, and mT are summarized in Table 2. We found that the ICO structure is the lowest energy configuration for Fe55 , Co55 , Ni55 , and Cu55 , while Zn55 and Pt55 adopt the DRC structure, which is −5.75 and −5.58 eV lower in energy than ICO, and hence, in good agreement with previous results. 20,89 In the ideal ICO structure, there are 13 atoms in the core region with ECN = 12 (i.e., a bulk-like behavior), while the surface atoms are separated into two groups, namely, 30 atoms with ECN = 8.0 and 12.0 atoms with ECN = 6.0, which results in ECN = 8.5. It can be seen in Table 2 a slight reduction in the ECN values obtained for Fe55 , Co55 , Ni55 , and Cu55 , which can be explained by

mT (µB ) 2.73 1.90 0.73 0.04 0.00 0.11 0.00 0.22

d-states. 59,87,88


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the reduction of the bond lengths of the surface atoms, which is expected due to the lowcoordination of the surface atoms. In contrast, there is a large reduction in the ECN values for Zn55 and Pt55 in the DRC structure, which can be explained by the reduction of the number of atoms in the core region and the disorder of the structure, in particular, for Zn55 . We found that d av decreases compared with the bulk values by −0.79, −2.40, −2.01, −1.94, −3.27 and −4.98 % for Fe, Co, Ni, Cu, Zn and Pt, respectively, which can be explained mainly by the reduction of the bond lengths of the surface atoms as the core region has ECN = 12 (bulk-like region). The magnitude is similar for Fe, Co, Ni, and Cu, however, there is a substantial increase for Zn and Pt, which is due to the low-coordination of the atoms located in the core region.

C

0.2 0.0 -0.2 PtnFe55-n

-0.4 0.1 0.0

Excess energy (eV/atom)

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0.0 -0.2

PtnNi55-n

0.1

PtnCu55-n

0.0 -0.2 -0.4

PtnZn55-n

0

10

20

30

n

40

50

60

Figure 2: Excess energy for the Ptn TM(55-n) systems (TM = Fe, Co, Ni, Cu, and Zn) as a function of the composition. The continuous lines in color connect the excess energy values for the lowest energy configurations, while the continuous black lines were obtained using a parabolic fitting from the lowest energy curves. The open symbols are the excess energies for the high energy configurations.

1 Energetic Properties One of the key parameters in the study of alloys is the excess energy, Eexc , which measures the relative stability of a particular alloy configuration with respect to parent compounds. 11,90 The Eexc per atom was calculated using the following equation, Pt

PtnCo55-n

0.2

-0.1 0.2

The putative lowest energy structures for the 55-atom PtTM nanoclusters are shown in Figure 1. Below, we will discuss the energetic, structural, electronic, and magnetic properties as a function of the Pt composition.

Ptn TM(55-n)

-0.1

0.0

Binary PtTM Nanoclusters

TM

−n n Etot55 − 5555 Etot 55 − 55 , Eexc = 55 (1) Ptn TM(55-n) Pt55 TM55 where Etot , Etot , and Etot are the total energies of the Ptn TM(55-n) , Pt55 , and TM55 systems, respectively. From its definition, Eexc = 0.0 eV for n = 0, 55, and a negative (positive) value indicates that the alloy is energetically favorable (unfavorable). The Eexc results are shown in Figure 2. We found that the formation of the binary Ptn TM(55-n) nanoclusters are energetically fa-

Etot

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vorable for all systems and compositions as the excess energy is negative for all cases. Using a parabolic fitting of the lowest excess energies, we obtained that the excess energy follows nearly a parabolic behavior in which Eexc decreases (increases stability) by replacing TM atoms by Pt atoms in the nanocluster, and it reaches a minimum at n ∼ = 28 (nearly 51 % of Pt) for TM = Fe, Co, Ni, Cu


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and n = 26 (nearly 47 % of Pt) for TM = Zn, and then, Eexc increases (decreases stability) and reaches 0.0 eV at n = 55. Small deviations from the parabolic behavior can be seen in Figure 2, in particular, for TM = Ni. For example, initially Eexc decreases by increasing Pt composition, however, it reaches a plateau (n = 20 − 42), in which the excess energy decreases very slightly and reaches maximum stability at n = 42, which correspond to the core-shell structure. Using the compositions that yield the minimum excess energy (not from the parabolic fitting), we found Eexc = −0.35, −0.15, −0.20, −0.12, −0.36 eV/atom for Pt35 Fe20 , Pt28 Co27 , Pt42 Ni13 , Pt20 Cu35 and Pt20 Zn35 . Thus, the stability is larger for PtFe and PtZn systems, which might be related with charge transfer among the chemical species for PtZn and to the strong binding energy and magnetic interactions for PtFe. For example, Pauling eletronegativities are 1.83 (Fe), 1.88 (Co), 1.91 (Ni), 1.90 (Cu), 1.65 (Zn), and 2.28 (Pt), 91 and hence, the largest electronegativity difference occurs for PtZn.

1.2 PtnFe55-n

0.8 0.4 0.0 1.2

PtnCo55-n

0.8

Chemical order parameter

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0.4 0.0 1.2 PtnNi55-n

0.8 0.4 0.0 1.2

PtnCu55-n

0.8 0.4 0.0 1.2

PtnZn55-n

0.8 0.4 0.0

2 Structural Properties

0

To characterize the distribution of the Pt and TM atoms in the nanoclusters, we calculated the chemical order parameter, σ, which is defined as follows, 12,92,93 σ=

NPt-Pt + NTM-TM − NPt-TM , NPt-Pt + NTM-TM + NPt-TM

10

20

30

n

40

50

60

Figure 3: Chemical order parameter for the binary Ptn TM(55-n) systems as a function of the composition. The continuous lines in color connect results for the lowest energy configurations, while the continuous black lines were obtained using a parabolic fitting. The open symbols are the chemical order parameter for the high energy configurations.

(2)

where NA-B (A, B = Pt, TM) is the total number of bonds between the A and B atoms in the nanoclusters considering only nearestneighbour bonds obtained from the effective coordination concept. From its definition, for n = 0, 55, there is no Pt−TM bonds, and hence, σ = 1. For nanoalloys, we can obtain σ = +1 (complete segregation) only in the case that an initial mixture of Pt and TM atoms separate completely along the geometric optimization and two unary nanoclusters are formed, which is possible only for systems with Eexc > 0 and using global opti-

mization algorithms. 60–62 It can be seen that for nanoalloys with bonds only among the Pt and TM atoms, σ = −1, which implies a complete homogeneous distribution of the Pt and TM atoms. The σ results are shown in Figure 3, which show the same behavior for all studied Ptn TM(55-n) systems. We obtained that σ calculated for the lowest energy configurations has a nearly ideal-parabolic behavior as a function of the composition with a minimum


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value for n = 28 (σ ∼ = 0 for n = 28) for all systems. Except for the deviations in the parabolic behavior of the excess energy (formation of the core-shell structures), we can observe a correlation between the minimum in the excess energy and the minimum values in the chemical order parameter. The distribution of the Pt and TM atoms in the 55atom nanoalloys for n = 28 (σ ∼ = 0) is at the same distance from the ideal homogeneous (σ = −1) and segregation (σ = +1) distributions, which indicates that the Pt28 TM27 systems contain features of both cases. For example, it contains segregation features as the core region is formed only by the TM atoms, except for PtZn, while in the surface region the Pt and TM atoms form an homogeneous distribution. To quantify the distribution of the Pt and TM atoms within the nanocluster, we calculated the radial distribution function (RDF) with respect to the center of gravity of the nanocluster (r = 0). Our RDF results indicate that PtFe, PtCo, PtNi, and PtCu behave very similar, while PtZn show a different trend. Thus, only the results for PtFe and PtZn are shown in Figure 4, while the RDF results for the remaining systems are reported in the supporting information. It has been known that the 55-atom ICO structure has five non-equivalent atoms, 20,64 which are located at different distances from the center of gravity (e.g., for Fe55 , 0.00, 2.44, 3.70, 4.29, 4.76 Å), Figure 4, however, as expected from Figure 1, Zn55 and Pt55 shows a complete different behavior due to the low-symmetry of the DRC structures. For example, there is no Zn or Pt atoms located in the center of gravity, which is the case of the ICO structure. Our PtTM (TM = Fe, Co, Ni, and Cu) results show clearly that initially Pt atoms replace TM atoms located in the surface, in particular, those TM atoms located far from the center of gravity. Then, the addition of Pt atoms replace TM atoms located in the surface region up to the limit in which all the surface atoms are Pt and the core region is composed entirely by TM atoms, which yields a partial segregation of the Pt and TM atoms, and

Radial distribution function (arbitrary units)

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Fe55

Zn55

Pt6Fe49

Pt6Zn49

Pt Fe

Pt Zn

Pt13Fe42

Pt13Zn42

Pt Fe

Pt Zn

Pt20Fe35

Pt20Zn35

Pt Fe

Pt Zn

Pt28Fe27

Pt28Zn27

Pt Fe

Pt Zn

Pt35Fe20

Pt35Zn20

Pt Fe

Pt Zn

Pt42Fe13

Pt42Zn13

Pt Fe

Pt Zn

Pt49Fe6

Pt49Zn6

Pt Fe

Pt Zn

Pt55

Pt55

0 1 2 3 4 5 6 70 1 2 3 4 5 6 7 r (Å) r (Å)

Figure 4: Radial distribution function (arbitrary units) for the lowest energy Ptn Fe(55-n) and Ptn Zn(55-n) (n = 0 − 55) configurations. r = 0 is the center of gravity of the nanocluster.


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the formation of a core-shell structure with the following composition, Pt42 TM13 . Further Pt atoms will replace TM atoms in the core region, and finally, it reaches the DRC Pt55 structure. A simple mechanism to explain these trends are far from trivial, in particular, because different mechanisms can play a role, namely, cohesive/surface energy, relative strength of the homo- and heterobondings, electronegativity, segregation energy, and atomic radii of the chemical species, etc. As discussed below, our results can be explained by the differences in the size of the atomic radius of the Pt and (Fe, Co, Ni, Cu) atoms and partially by the segregation energy of those chemical species in 55-atom Pt nanoclusters. 14,19 For example, the Fe, Co, Ni, and Cu atoms have smaller atomic radius than Pt, which contributes to release the strain energy due to the compression induced by the Pt surface on the core region, which can be up to few GPa. 94 The segregation energy of Fe (0.82 eV), Co (0.94 eV), Ni (0.42 eV) in 55-atom Pt particles is positive, which indicates a strong preference of Fe, Co, and Ni by the core region (the magnitude of the preference is proportional to the segregation energy). 14,19 Thus, it is consistent with our results for PtFe, PtCo, and PtNi. In contrast with PtFe, PtCo, and PtNi, Cu in Pt55 has a negative segregation energy (−0.24 eV), and hence, the Cu atoms would have a preference for shell sites and not for the core region as obtained by our calculations. The segregation energies results were obtained employing a CUB structure, 19 which is one of the high energy configurations for Pt55 , and hence, it might affect the accuracy of those results, in particular, for the cases in which the segregation energy is relatively small. Furthermore, based on the cohesive/surface energy mechanism, we would expect that the TM with the smallest cohesive/surface energy would located in the surface shell, however, it is not the case for PtCu. For example, Cu(111) has a smaller surface energy than Pt(111), 80 while we found from our calculations that the Cu atoms are located

2.8

9.0

2.6

7.5 PtnFe55-n

2.4 2.8 2.6

Average bond length (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PtnCo55-n

2.4 2.8 2.6

PtnNi55-n

2.4 2.8 2.6

PtnCu55-n

2.4

6.0

Effective coordination number (NNN)

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9.0 7.5 6.0 9.0 7.5 6.0 9.0 7.5 6.0

2.8

9.0

2.6

7.5 PtnZn55-n

2.4

0 10 20 30 40 50 60

n

6.0 0 10 20 30 40 50 60

n

Figure 5: Average weighted bond length and effective coordination number in number of nearest neighbors (NNN) as a function of the composition. The continuous line connect the results for the lowest energy configurations, while the open symbols are the results for the high energy configurations. in the core region. In contrast, the RDF results follow a different trend for PtZn. For example, initially Pt atoms replace Zn atoms located in the core and surface regions, however, at the ICO core-shell composition, namely, Pt13 Zn42 or Pt42 Zn13 , both Pt and Zn atoms are located in the core and surface regions. Thus, the ideal ICO core-shell structure with 13 atoms in the core cannot be formed for PtZn, however, the replacement of few Zn by Pt atoms, Pt49 Zn6 , induces the formation of a core-shell configuration in which all the Zn atoms are located in the core along with few Pt atoms, which can be explained by the smaller atomic size of the Zn atoms. To understand the local environment (bond lengths, coordination) effects as a function of the Ptn TM(55-n) composition, we also


9


employed the effective coordination concept, 85,86 which takes into account the wide range of bond lengths properly, in particular for low-symmetry configurations. The d av and ECN results are shown in Figure 5. Except for PtZn, d av increases almost linearly by increased Pt concentration in the nanoalloys, which can be explained by the larger atomic radius of Pt compared with Fe, Co, Ni, and Cu atoms, and hence, it follows the Vegard’s law 95 observed for bulk alloy systems. 96,97 However, d av is nearly constant for PtZn, which can be explained by the similar atomic radius and the lowest energy DRC configurations. As discussed above for the unary TM55 systems, ECNICO = 8.15 (Fe) and 8.42 (Zn) are the highest values obtained for the compact configurations. From our ECN results in Figure 5, it can be seen that most of the lowest energy configurations adopt an ICO-like structure (i.e., ECN = 8.11 to 8.42), however, for high Pt concentration, ECN reduces nearly to the value of the DRC configuration (i.e., ECN = 6.84), which is expected as the structure is mainly dominated by the Pt55 features. The PtZn follows the features of the unary Zn55 and Pt55 structures, namely, the ECN results oscillates slightly among the parent compound ECN values.

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Center of gravity of the occupied d-states (eV)

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PtnCu55-n

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3 Electronic Structure

PtnZn55-n

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To obtain insights from the electronic structure, we calculated the center of gravity of the occupied d-states, ǫd , with respect to the highest occupied molecular orbital (HOMO) for every atom in the nanocluster (majority, up ǫd , and minority, ǫddn , spins), which were used to obtain the averaged results for the core and surface atoms. Based on the d-band model proposed by Hammer and Nørskov, 98 the center of gravity of the occupied d-states correlates with the magnitude of the adsorption energy of an adsorbate on the TM surface. The ǫd results for the surface atoms (average over the chemical species) are shown in Figure 6, while the results for the core atoms are shown in the supporting information.

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Figure 6: Center of gravity of the occupied d-states with respect to the highest occupied molecular orbital for the surface atoms in the lowest energy Ptn TM(55-n) configurations. The continuous lines in color connect results for the lowest energy configurations, up ǫd (filled symbols) and ǫddn (open symbols), while the continuous black lines were obtained using a linear fitting. As expected, due to the nature of the localization and number of electrons in the d-


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fects and a shift of the center of gravity of the d-states towards the HOMO level, which is consistent with our results for the center of gravity and linear change in the average bond lengths. The results for Ptn Cu(55-n) show interesting features. For example, for Pt42 Cu13 , the Cu atoms are located in the core, while all the Pt atoms are located in the surface, however, the center of gravity of the surface atoms differs by 0.20 eV compared with the Pt55 , which can be attributed to the differences in the structure (i.e., ICO core-shell for Pt42 Cu13 and DRC for Pt55 ) and charge transfer among the species due to the difference in electronegativity. The largest change was obtained for Pt28 Cu27 , in which the center of gravity was displaced near to the HOMO state by about 0.60 eV. It can be attributed to the compression 94 of the Pt atoms on the Cu atoms, which contribute to increase the localization of the d-states and shifts the center of gravity up. This effect contributes also to increase the magnetic moment for this composition, see below. Furthermore, we would like to mention that this particular energy difference (0.20 eV) is very small compared with the changes due to the strain of Rh, Pd, Ir, and Pt monolayers supported on Cu(111) and Au(111) surfaces. 8,101–103

states, the Fe, Co, Ni, Cu, Zn, and Pt systems have different center of gravity. For exup ample, ǫd = −2.53 eV and ǫddn = −1.34 eV for Fe55 , −2.46 and −1.47 eV for Co55 , −1.81 and −1.34 eV for Ni55 , while ǫd = −2.25, −7.15, −2.62 eV for Cu55 , Zn55 , and Pt55 , respectively. In principle, we would expect that ǫdCu < ǫdPt as the Cu d-states are fully occupied, however, the localization of the Cu 3d-states are stronger than the Pt 5dstates, which shifts the center of gravity of the Cu 3d-states in the direction of the HOMO state. Thus, in principle, we would expect a stronger bind to the Cu sites instead of the Pt sites, however, this is not the case due to the full occupation of the Cu 3d-states. 99 For the cases in which strong relaxation or surface reconstruction is not present, we can assume that the changes in the center of gravity of the surface atoms depend only on the number of Pt and TM atoms located in the surface region. Thus, the replacement of TM by Pt atoms in the nanocluster surface can yields a linear shift of the center of gravity in the direction of the center of gravity of the Pt55 nanocluster as the Pt atoms preferentially replace TM atoms located in the surface. In fact, we obtained a linear change of the center of gravity for Ptn Zn(55-n) , Ptn Ni(55-n) , and nearly linear for Ptn Co(55-n) , while there are strong deviations for Ptn Fe(55-n) and Ptn Cu(55-n) . Thus, for particular cases, the center of gravity can be estimated based on the results for the unary nanoclusters, and hence, we can tune the center of gravity of the surface atoms by tuning the composition, which affects the adsorption energy of chemical species on the surfaces. 98 We found that the center of gravity of the surface Pt55 atoms shift towards the HOMO level by replacing the surface Pt atoms by Fe, Co, and Ni atoms, which is expected to enhance the adsorption energy of molecular species to the surface, and hence, it can affects the reactivity. Experimental studies for PtNi and PtCo systems have reported an enhancement in the reactivity due to the addition of Co and Ni in Pt particles, 34,41,49,100 which have been explained by geometric ef-

D Magnetic Moments For bulk Fe, Co, and Ni in the bcc, hcp, and fcc structures, as expected, we obtained ferromagnetic solutions with a total magnetic moment per atom of 2.17, 1.58, and 0.62 µB , respectively, Table 1, which deviates from experimental results by −2.25, −8.13, and 1.64 %, 59 and are consistent with previous DFT-GGA results. 104,105 Once the Fe55 , Co55 , and Ni55 nanoclusters are formed, there is an increase in the magnetic moment per atom by 25.81, 20.25, and 17.74 % compared with the respective bulk systems, Table 2, which is mainly due to the enhancement of the contribution of the surface atoms for Fe and Co. For example, the local magnetic moment of the surface atoms are 2.85 and 1.90 µB ,


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3.0 Magnetic moment (µB/atom)

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sition, Figure 7. For the PtCu and PtZn systems, the total magnetic moment is zero for almost all compositions, except for core-shell Pt42 Cu13 configuration, in which the total magnetic moment is different from zero due to the increased localization of the Cu and Pt d-states. Thus, the present results show clearly that the magnitude of the magnetization of binary nanoclusters can be tuned by the composition.

PtnFe55-n PtnCo55-n PtnNi55-n PtnCu55-n PtnZn55-n

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Summary

We performed a DFT-PBE investigation of the structural, energetic, and electronic properties of binary PtTM 55-atom nanoclusters for TM = Fe, Co, Ni, Cu, and Zn, as a function of the Pt concentration, in gas-phase. In this work, we found that Fe55 , Co55 , Ni55 , and Cu55 systems adopt the ICO structure as the lowest energy configuration, while Zn55 and Pt55 adopt a DRC structure, which are −5.75 and −5.58 eV lower in energy than their ICO configurations, respectively. Based on a set of ab-initio based structural design principles, the atomic configurations of the binary Ptn TM(55-n) systems were designed. The formation of the binary Ptn TM(55-n) nanoclusters are energetically favorable for all systems and compositions. Except for small deviations, we found that the excess energy and the chemical order parameter follows nearly a parabolic behavior as a function of the Pt composition with a minimum at n ∼ = 28 for TM = Fe, Co, Ni, Cu, and n = 26 for TM = Zn (i.e., nearly 50 % for all systems). Thus, it indicates that the maximum stability of the binary nanoclusters is reached by maximizing the homogeneous distribution of the Pt and TM atoms in the nanocluster configurations. Furthermore, as expected, the charge transfer among the chemical species can contribute to the stability of the nanoclusters as the Pt atom has a higher electronegativity, in particular, than Zn. From the analysis of the RDF results, the Pt atoms replace initially TM atoms located in the surface of the TM55 particles, while the

60

Figure 7: Total magnetic moments per atom for the Ptn TM(55-n) nanoalloys as a function of the composition. The continuous coloured lines connect the results for the lowest energy configurations, while the open symbols are the results for the high energy configurations. The continuous black lines were obtained using a parabolic fitting from the lowest energy curves. which is larger than in the respective bulk systems. For Ni55 , the enhancement occurs for the core and surface atoms, which is in contrast with Fe55 and Co55 . This behavior can be explained by the increased localization of the d-states due to the coordination reduction of the surface atoms. In contrast with Fe55 , Co55 , and Ni55 , the magnetic moment is zero for Zn55 and Pt55 , while it is nearly zero for Cu55 , which is expected as their respective bulk phases are nonmagnetic. The total magnetic moment per atom for the binary nanoclusters are shown in Figure 7. As expected, once Pt atoms replace the Fe, Co, and Ni atoms in the Fe55 , Co55 , and Ni55 nanoclusters, the magnetic moment per atom decreases as Pt55 is not a magnetic system. We found that the decreasing of the magnetic moment per atom of the lowest energy PtFe, PtCo, and PtNi structures follows nearly a parabolic behavior, instead of a linear decreasing as a function of the Pt compo-


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TM atoms remain located in the core region, which can be explained by the larger atomic radius of the Pt atoms and segregation energy, except for PtCu. Thus, the atomic radius of the Pt and TM atoms contribute to increase the segregation of the Pt and TM atoms in the nanoclusters, which is maximized in the formation of the ICO core-shell configurations with 13 TM atoms in the core and 42 Pt atoms located in the surface. Except for PtZn, we found that the equilibrium bond lengths from TM55 increases almost linearly by replacing TM by Pt atoms (i.e., it follows approximately the Vegard’s law). We found that the center of gravity of the occupied d-states of the surface atoms changes almost linearly for PtCo, PtNi, and PtZn, while there are deviations for PtFe and PtCu. Thus, based on the d-band model, it is possible to tune the magnitude of the adsorption energy by tuning the Pt concentration, and hence, those results can be used to understand experimental results, as well as to help in the designing of new catalyts. 106 We would like to point out that our results were obtained in gas-phase, however, the addition of environment effects can affect the preference of the Pt atoms by core or surface region, and hence, it can affects the most favorable compositions. 107

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Acknowledgement Authors thank the São Paulo Research Foundation (FAPESP), Rio Grande do Sul Research Foundation (FAPERGS), National Council for Scientific and Technological Development (CNPq), and Coordination for Improvement of Higher Level Education (CAPES) for the financial support. Authors thank also the Laboratory of Advanced Scientific Computing (University of São Paulo) and the Department of Information Technology - Campus São Carlos, for hosting our cluster. Supporting Information Available: Extra results for the geometric and electronic properties are shown in the supporting information. This material is available free of charge via the Internet at http://pubs.acs.org/.


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Structure, Electronic, and Magnetic Properties of Binary PtnTM55ân

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