Platinum-Based Nanoalloys PtnTM55ân (TM = Co ... - ACS Publications

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Platinum-Based Nanoalloys PtnTM55−n (TM = Co, Rh, Au): A Density Functional Theory Investigation Maurício J. Piotrowski* and Paulo Piquini Departamento de Física, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil

Juarez L. F. Da Silva*,†,‡ †

Instituto de Química de São Carlos , Universidade de São Paulo, Caixa Postal 780, 13560-970, São Carlos, SP, Brazil Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São Carlos, SP, Brazil

‡

ABSTRACT: Structural and electronic properties of the PtnTM55−n (TM = Co, Rh, Au) nanoalloys are investigated using density functional theory within the generalized gradient approximation and employing the all-electron projected augmented wave method. For TM = Co and Rh, the excess energy, which measures the relative energy stability of the nanoalloys, is negative for all Pt compositions. We found that the excess energy has similar values for a wide range of Pt compositions, i.e., n = 20−42 and n = 28−42 for Co and Rh, respectively, with the core−shell icosahedron-like configuration (n = 42) being slightly more stable for both Co and Rh systems because of the larger release of the strain energy due to the smaller atomic size of the Co and Rh atoms. For TM = Au, the excess energy is positive for all compositions, except for n = 13, which is energetically favorable due to the formation of the core−shell structure (Pt in the core and Au atoms at the surface). Thus, our calculations confirm that the formation of core−shell structures plays an important role to increase the stability of nanoalloys. The center of gravity of the occupied d-states changes almost linearly as a function of the Pt composition, and hence, based on the d-band model, the magnitude of the adsorption energy of an adsorbate can be tuned by changing the Pt composition. The magnetic moments of PtnCo55−n decrease almost linearly as a function of the Pt composition; however, the same does not hold for PtRh and PtAu. We found an enhancement of the magnetic moments of PtRh by a few times by increasing Pt composition, which we explain by the compression effects induced by the large size of the Pt atoms compared with the Rh atoms.

1. INTRODUCTION

good control of the processes that lead to the formation of Ptbased nanoalloys. However, our atomistic knowledge of the bimetallic NPs is still far from satisfactory. From our knowledge, experimental studies of platinum-based nanoalloys have been spread over a large number of PtTM nanoalloys, e.g., PtFe,13 PtCo,13−15 PtNi,16,17 PtCu,18,19 PtRu,20,21 PtRh,22,23 PtPd,24,25 PtAg,26 PtAu.27,28 Most of these studies have focused on the synthesis and control of the size, shape, and composition of the PtTM nanoalloys, as well as on the turnover of particular reactions. Among those

Bimetallic transition-metal (TM) nanoparticles (NPs) have attracted great interest due to the possibility to tune their properties through size, shape, and composition,1−3 which opens the possibility for a wide range of technological applications. Among all bimetallic TM systems,1,2 platinumbased nanoalloys have been widely studied, in particular, because of the interest to improve the figures of merit of Pt for catalytic reactions4 and electrocatalysis,5,6 as well as to reduce the amount of Pt in technological applications because of the high cost of Pt. This interest is made possible because Pt-based NPs with specific facets, size, and composition can be controlled using suitable surfactants,7−9 amphiphilic polymers,10,11 or electrochemical treatments,12 which indicates a © 2012 American Chemical Society

Received: March 25, 2012 Revised: August 3, 2012 Published: August 3, 2012 18432

dx.doi.org/10.1021/jp302844f | J. Phys. Chem. C 2012, 116, 18432−18439

The Journal of Physical Chemistry C

Article

2. THEORETICAL APPROACH AND COMPUTATIONAL DETAILS A. Computational Details. Our spin-polarized total energy calculations are based on DFT60,61 within the generalized gradient approximation62 (GGA) to the exchange-correlation energy functional as formulated by Perdew, Burke, and Ernzerhof63 (PBE). The Kohn−Sham equations were solved using the projector augmented wave (PAW) method,64,65 as implemented in the Vienna ab initio Simulation Package (VASP).66,67 We considered PAW projectors with 3d74s2, 5s14d8, 5d96s1, and 5d106s1 valence electrons for Co, Rh, Pt, and Au, respectively. For the total energy calculations of the bulk and NP systems, we employed a cutoff energy of 268 eV, which was defined based on the highest cutoff energy suggested for the Co, Rh, Pt, and Au elements, i.e., 268, 229, 230, and 230 eV, respectively. To obtain the equilibrium volumes of the bulk systems by minimization of the stress tensor and atomic forces, we employed cutoff energies of 536, 458, 460, and 460 eV, for Co, Rh, Pt, and Au, respectively. For the NP calculations, we used a cubic box with 22 Å, which yields a distance of about 12 Å between NPs, and hence the interaction between the NP and its periodic images is negligible compared with the relative total energies. For example, the relative total energy among two 55atom configurations changes by 2.2 meV by increasing the cubic box size from 22 Å to 26 Å. The Brillouin zone integrations were performed using only the Γ-point for the NP calculations, and a k-mesh of 21 × 21 × 11 for Co in the hexagonal close-packed (hcp) structure37 and 18 × 18 × 18 for Rh, Pt, and Au in the face-centered cubic (fcc) structures.37 For all calculations, the equilibrium geometries are obtained when the forces on each atom are less than 0.025 eV/ Å. We found from our convergence calculations that a tight convergence does not affect our results, e.g., 0.005 eV/Å changes the relative total energy among two 55-atom structures by about 1.0 meV. Furthermore, a poor convergence criteria such as 0.10 eV/Å yields an error in the relative total energy of only 21 meV. B. Atomic Configurations. The search of global minimum structures, in particular TM nanoalloys, is a challenge problem in computational material science due to the large number of local minimum configurations,68 which requires the application of sophisticated global search algorithms such as the Basin Hopping Monte Carlo69 (BHMC) or Genetic Algorithm (GA).70 The application of those techniques require total energy evaluations for thousands of different configurations along the optimization even for 55-atom particles, which are only possible using empirical pair-potentials. 71 BHMC calculations employing the Sutton−Chen71 EPP has been used as structure generator for DFT calculations,72,73 which is an alternative to classical molecular dynamic (MD) simulations to obtain model structures for DFT optimizations. To obtain a reliable set of putative lowest (LOW) energy structures for PtnTM55−n, we considered a set of designing principles, which helps to decrease the number of configurations while keeping the most representative ones. First, we determined the lowest energy structures of the end point NPs, i.e., TMn (n = 0 and 55), which will be used to build up nanoalloy configurations. For TM55, we performed simulated annealing simulations for ∼100 ps from high (∼2000 K) to about zero temperature. Furthermore, we considered a large number of configurations, namely, the icosahedron (ICO) with

nanoalloys, PtCo, PtRh, and PtAu have received great interest due to the possibility of technological applications. For example, PtCo nanoalloys are candidates for ultrahigh-density storage media due to the high magnetic anisotropy and susceptibility29−31 and good stability upon corrosion.29,30 Furthermore, PtCo has been studied as magnetic contrast in magnetic resonance imaging15 and fuel cell electrocatalysis.32 PtRh nanoalloys have been used as a catalyst for the reduction of NOx,33 hydrogenation,34 oxygen reduction in direct methanol fuel cells,5and CO reduction.23 PtAu nanoalloys have been studied for applications in the electrocatalytic oxidation of CO,35 as well as, applications in spherical polyelectrolyte brushes, where they show enhanced catalytic activity as compared to pure gold nanoparticles.28 In addition, PtAu has been studied for methanol and CO electrooxidation36 and fuel cell electrocatalysis.32 Theoretical calculations for PtCo, PtRh, and PtAu have been performed using empirical pair-potentials (EPP), e.g., Gupta,38 (PtCo,39,40 PtRh,41,42 PtAu43−45) and first-principles density functional theory (DFT) calculations (PtCo, 13,46,47 PtRh,46,48−50 PtAu46,51,52), as well as the combination of EPP and DFT calculations, i.e., initial atomic configurations generated using EPP and final geometric optimization using DFT (PtCo,53,54 PtAu,55). Most of those studies have employed bulk-derived structures, such as the cuboctahedron,42,43,49,50,56 icosahedron,13,43,55,57 and decahedron.13,43,55 However, to gain insights into the nanoalloy mechanisms, an important prerequisite is to determine the correct atomic structure of the nanoparticles, which is intimately connected with their electronic structure, binding mechanism, and strain release. Several studies have suggested that PtAu is not miscible at nanoscale,55,58 which is consistent with PtAu bulk alloys, and hence most of the studies of PtAu nanoalloys have focused on the segregation mechanisms of both species.55,58,59 For PtRh, most of the studies have focused on the search of the most stable composition,42,49,50 and to our knowledge, only an electronic structure study has been reported so far.56 In contrast, most of the studies of PtCo nanoalloys have been focused on the magnetic properties as a function of the Co composition; however, there is little information on the atomic structure of those nanoalloys at small scale. Thus, the theoretical understanding of Pt-based nanoalloys is still limited. An explanation of their structural and electronic behavior and an explanation for why alloy particles can show a different structural and electronic (magnetic) behavior from pure nanoparticles is still lacking. Although several theoretical studies have been performed, numerous questions remain open for the PtCo, PtRh, and PtAu systems, in particular, the changes in the electronic states and magnetic properties of the nanoalloys as a function of the Pt composition and a better understanding of the structural mechanisms determining the nanoalloy structure formation. Furthermore, we suggest that simple design principles should be established to improve the study of nanoalloys by DFT calculations. Thus, to contribute to the solution of these questions, in this study, we report a DFT study of the PtCo, PtRh, and PtAu systems using NPs with 55 atoms, i.e., PtnTM55−n (n = 0−55, TM = Co, Rh, Au). 18433



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Ih symmetry74 and cuboctahedron (CUB) with Oh symmetry, and structures reported previously73 for Pt55 and Au55, which were obtained by the combination of structures generated by BHMC-EPP with DFT total energy optimizations. For PtnTM55−n, we selected a set of Pt compositions, i.e., n = 6, 13, 20, 28, 35, 42, and 49, which yields a Pt composition of 10.9%, 23.6%, 36.4%, 50.9%, 63.6%, 76.4%, and 89.1%, respectively. We can define two regions in the 55-atom NP based on the lowest energy TM55 structures, namely, surface and core regions composed of about 42 and 13 atoms, respectively. For particular cases such as Pt20TM35, the main question is the location of the Pt or TM atoms, i.e., are they located at the surface or core region? Using a 55-atom ICO or CUB model, only 13 atoms can be placed in the core region, and hence the remaining atoms must be distributed at the surface region, which can form uniform distributions or segregate at one side of the surface region. Furthermore, based on the lowest structures for Pt55 and Au55,73 reduced core structures can be designed. In addition, structural crossover among the configurations can be used to generate candidate structures, e.g., the lowest energy structure identified for Pt20Rh35 can be tested for Pt20TM35. Molecular dynamics or simulated annealing simulations were not employed as a structure generator scheme for nanoalloys because of the slow diffusion rate of surface atoms to the core region or vice versa. C. Analyses. For the characterization of the local environment (coordination) and bond lengths, we employed the effective coordination concept,75−77 which yields the effective coordination number (ECN), ECNi, and the weighted bond lengths, diav, for a given structure configuration (bulk or particle), where i indicates the atom index. The average results can be obtained by N

ECN =

3. RESULTS A. Bulk: Co, Rh, Pt, Au. The equilibrium lattice parameters (a0, c0), dav, ECN, and total magnetic moments, mT, of the bulk systems in the hcp (Co) and fcc (Rh, Pt, Au) structures are summarized in Table 1. The lattice parameters are in excellent Table 1. Equilibrium Lattice Constants, a0, c0, Weighted Bond Lengths, dav, Effective Coordination Number, ECN, and Magnetic Moments for the TM Bulka bulk system Co Rh Pt Au

dav =

i=1

∑ davi i=1

Econfig tot

(1)

(2)

where and are the total energies of a given configuration and of the icosahedron structure, respectively, and (ii) for PtnTM55−n, we calculated the relative energy stability with respect to the end points (n = 0 and 55), which is commonly called excess energy, Eexc.83 Eexc can be obtained by

nTM55‑n EPt , tot

55 EPt tot ,

n Pt55 55 − n TM55 Etot − Etot 55 55

dav (Å)

ECN

mT/atom (μB)

4.03 (−1.0)

2.49 2.72 2.81 2.95

12.0 12.0 12.0 12.0

1.58 (−8.2)

agreement with experimental37 and theoretical84−86 results, Table 1, which is expected from previous GGA studies.86,87 The atomic radius (dav/2.0) is 1.25, 1.36, 1.41, and 1.48 Å for Co, Rh, Pt, and Au, respectively, which are in good agreement with the radii of ions in 12-coordinated metals,37 i.e., deviations of 0.0%, 0.7%, −2.1%, and 2.9%, respectively. From this data, Co and Rh are smaller than Pt by 11.4% and 3.6%, while Au is larger than Pt by 5%. For Co, we obtained a total magnetic moment, mT, of 1.58 μB/atom, which is smaller than the experimental value (1.72 μB/atom) by about 8%,37 which is consistent with previous GGA calculations (1.61 μB/atom).88 Calculations using GGA +U (Ueff = 3.0 eV) reported 1.83 μB/atom,88 which is 6.4% larger than the experimental result, in particular, due to the increased localization of the 3d-states by the GGA+U functional, which enhances the magnetic moments. HybridDFT calculations employing the HSE functional with 5% of exact exchange yields mT = 1.69 μB/atom.82 In line with GGA +U calculations, an increase in the amount of exact exchange increases the localization of the 3d-states, and hence the magnetic moment increases, e.g., 1.91 μB/atom for 25% of exact exchange. B. TM55: TM = Co, Rh, Pt, Au. The lowest energy structures for TM55 (TM = Co, Rh, Pt, Au) are shown in Figure 1, while the results for ΔEtot, dav, ECN, and total magnetic moments, mT, are summarized in Table 2. The ICO structure yields the lowest energy for Co55 and Rh55 even when compared with configurations obtained from long MD simulations (∼ 100 ps). However, MD simulations identified low-symmetry structures with energies lower than the ICO structure for Pt55 and Au55, which is consistent with results obtained by the combination of BHMC-EPP and PBE calculations.73 The most stable Pt55 and Au55 structures are −5.49 and −2.01 eV lower than ICO. From the nature of the Pt55 and Au55 structures, we found several nearly degenerated configurations for Pt55 and Au55, which differ in the number of atoms in the core region or with slightly different values for ECN. However, for Co55 and Rh55, the second best identified configuration is 3.78 and 0.90 eV higher than the ICO structure, respectively. The ICO structure is strongly favorable for Co55 because of the strong localization of the 3d-states compared with the 4d-states in the Rh55 configuration.

EICO tot

Pt nTM55 − n Eexc = Etot −

(−0.4) (1.3) (1.5) (2.2)

The numbers in parentheses are the relative error (in %) with respect the experimental results.37.

where N is the number of atoms. Using the results for dav, an effective hard sphere radius (dav/2.0) can be estimated for every atom, which can be employed to establish the number of surface atoms, i.e., atoms exposed directly to the vacuum region. The effective coordination concept was recently applied in the study of bulk oxides, e.g., R2O3(ZnO)n (n = 1−6, R = In, Ga),77−79 TM13 clusters,80−82 and Pt55 and Au55 NPs.73 To compare the relative stability of the studied systems, we employed two concepts: (i) for TM55 systems, we define the relative total energy, ΔEtot, config ICO ΔEtot = Etot − Etot

2.50 3.85 3.98 4.17

c0 (Å)

a

N

∑ ECNi,

a0 (Å)

(3)

55 ETM tot

where and are the total energies of the PtnTM55−n, Pt55, and TM55 systems, respectively. For the separate phases, i.e., Pt55 and TM55, Eexc = 0.0 eV. For mixed PtnTM55−n a negative value of Eexc indicates a tendency to form nanoalloys (the mixing is energetically favorable), whereas positive values characterize segregation tendencies, i.e., the separate phases are more stable than the mixture. 18434



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Figure 1. Lowest energy DFT-PBE structures for the PtnTM55−n (TM = Co, Rh, Au) systems. Below every structure, we provided the average weighted bond lengths, dav, (Å), and the average effective coordination number, ECN, for TM (Co, Rh, and Au) atoms in the first line and Pt atoms in the second line.

number of configurations were reduced for about 20−25 model structures for every PtnTM55−n composition. The results for the excess energy, which measure the relative energetic stability of the nanoalloys with respect to the separate phases, are shown in Figure 2. It can be seen that the formation of a mixture is energetically favorable for all compositions for PtnCo55−n and PtnRh55−n, while for PtnAu55−n, we found only a particular composition with a negative excess energy (n = 13), which could be unexpected for PtnAu55−n, as Pt and Au are not mixable in bulk alloys.44

Table 2. Weighted Bond Lengths, dav, Effective Coordination Number, ECN, Magnetic Moments, and Relative Total Energies, ΔEtot, for the TM55 Systems TM55 system

config

ΔEtot (eV)

dav (Å)

ECN

mT/atom (μB)

mT (μB)

Co Rh Pt

LOW LOW LOW ICO LOW ICO

0.00 0.00 −5.49 0.00 −2.01 0.00

2.44 2.66 2.68 2.75 2.81 2.90

8.36 8.40 6.84 8.34 6.54 8.39

1.909 0.091 0.000 0.218 0.018 0.055

105 5 0 12 1 3

Au

For Pt55 and Au55, the reduction of the core size, from 13 to about 7−9 atoms, affects directly the average bond lengths. For example, dav reduces by 2.0, 1.8, 4.6, and 4.7% for Co55, Rh55, Pt55, and Au55, respectively, compared with the bulk values. The large reduction in the values of ECN for Pt55 and Au55 is due to the large number of surface atoms compared with core atoms. The surface atoms have an average ECN of 7.32, 7.33, 6.47, and 6.26 for Co55, Rh55, Pt55, and Au55, while for the core atoms, ECN = 11.72, 11.77, 8.73, and 8.41, respectively. The total magnetic moment of Co55 (1.91 μB/atom) is about 21% larger than that of Co bulk in the hcp structure (1.58 μB/ atom), which is mainly because of the enhancement of the local magnetic moment, mL, of the surface atoms. For example, the average values for mL are 1.74, 1.75, and 1.91 μB/atom for the central atom, first shell, and surface atoms in the 55-atom ICO structure. For Rh55, we obtained a total magnetic moment of 0.09 μB/atom, which is about half the experimental value of ∼0.2 ± 0.10 μB/atom;89 however, the error bar has size similar to the result itself. The zero magnetic moment calculated for Rh bulk in the fcc structure is experimentally recovered only for Rh particles with about 100 atoms.89 For Pt55, mT = 0.0 μB, while for Au55, it is about 0.02 μB/atom. C. PtnTM55−n: TM = Co, Rh, Au. 1. Excess Energy. Following our design principles described in section 2B, the

Figure 2. Excess energy, Eexc, for the PtnCo55−n, PtnRh55−n, and PtnAu55−n nanoalloys. The continuous line (red color) links the lowest energy configurations for every composition as a guide line. 18435



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atoms in the core region are replaced by Pt atoms, which stabilizes the ICO structure instead of the low-symmetry structure with a reduced core. For n = 28, there are 13 Pt atoms at the core, while the remaining 15 Pt and 27 Au atoms are not uniformly distributed on the surface, i.e., there is a phase separation at the surface, Figure 1. By increasing the number of Pt atoms at the surface, we would expect an increase in the strain energy on the Pt core region, and hence the ICO structure would be destabilized, which is in fact found in our calculations for n = 35. For n = 35−49, we have the occurrence of nonicosahedral structures with a smaller core size, which is supported by the ECN results. 3. Density of States Analyses. In our analysis of the local density of states (LDOS), we employed the d-band model proposed by Hammer and Nørskov.90 They suggested that the distance of the center of gravity of the d-states with respect to the Fermi level (zero energy in this work), Cdg , can be correlated with the magnitude of the adsorption energy of an adsorbate to the TM surfaces, which have been used in several studies.91,92 Thus, this analysis can be useful to obtain a better understanding of the electronic character. Here, we calculated Cdg as a function of the Pt composition, which is shown in Figure 3. For all configurations, the atoms are separated into two groups, namely, surface and core atoms.

For PtnCo55−n, the excess energy decreases (increased stability) by increasing the amount of Pt atoms in the nanoalloy, and it reaches a plateau for n = 20−42. In the plateau region, Eexc is slightly more negative for n = 42. Thus, our calculations indicate a wide range of compositions for which the mixture of Pt−Co nanoalloys are energetically favorable compared to the separate phases. Similar trends can be observed for PtnRh55−n. The present trends are explained below. 2. Lowest Energy PtnTM55−n Configurations. The lowest energy structures for every PtnTM55−n composition are shown in Figure 1. Furthermore, we provide in Figure 1 the average coordination and bond lengths, which can be correlated with the location of the Pt and TM atoms. We found that the structural patterns are similar for PtnCo55−n and PtnRh55−n, which can be summarized as follows. For n = 0, both Co55 and Rh55 have an ICO structure with Ih symmetry. For n = 6, we found that the 6 Pt atoms replace Co or Rh atoms at the 6-fold ICO surface sites instead of the 12-fold core sites, which is supported by the coordination analysis. On the basis of our analyses of the bulk dav results, Pt is larger than Co and Rh by 11.4% and 3.6%, respectively, and hence the location of Pt atoms in the core region would contribute to increase the strain energy, while at the surface sites in contact with the vacuum the strain energy can be more efficiently released by relaxation of the surface atoms. Thus, this analysis can also indicate that the external environment might play an important role in the release of the strain energy. When the Pt composition (n = 13) is increased, 12 of the 13 Pt atoms are located at the 6-fold surface sites, while the 13th Pt atom occupies a 8-fold surface site, i.e., all Pt atoms are located at the surface with an ECNPt = 6.11 and dPt av = 2.56 Å for TM = Co. Thus, there is a clear preference of the Pt atoms for an uniform distribution on the surface, which contribute to decrease the strain energy. Further increase in the Pt composition (n = 20) only increases the number of Pt atoms at the ICO surface, reaching a maximum of 42 Pt atoms at the surface for n = 42 (ECNPt = 7.36 for TM = Co), where all Co or Rh atoms are located at the core region (ECNCo = 11.62), leading to the maximum stability observed for the PtCo and PtRh nanoalloys. The lowest energy configurations for Pt42Co13 and Pt42Rh13 are known as core−shell structures and are expected to play an important role in nanocatalysis. For example, a TM atom with smaller atomic size and that is less expensive can be used at the core region, while the Pt atoms are located at the surface, which contributes to reduce the production cost, as well as to change the electronic structure of the Pt NPs. For n = 49, we would expect that 42 Pt atoms will be located at the ICO surface with the remaining 7 Pt atoms at the core region. However, this is observed only for Pt49Co6. In this case the ICO structure is stabilized, which we attribute to the smaller size of the Co atoms, as Pt55 has a low-symmetry structure with a reduced core size of 7−9 atoms. For Pt49Rh6, there are only 4 Pt atoms in the core, while there are 45 Pt atoms in the surface, i.e., the lowest energy structure is likely the one found for Pt55. Thus, the large size of the Rh atoms compared with Co atoms plays an important role at this regime. In contrast with the results for PtnCo55−n and PtnRh55−n, PtnAu55−n shows different structural patterns. For n = 6, the Pt atoms are located at the ICO core region instead of the surface, which can be explained by the atomic size of the Pt and Au atoms, i.e., Au is 4.96% larger than Pt. For n = 13, all the Au

Figure 3. Center of gravity with respect to the Fermi level of the occupied d-states, Cdg , for PtnTM55−n (TM = Co, Rh, Au). The Fermi energy is at zero energy.

The PtnCo55−n is the only system in which there are substantial differences in the Cdg results for the majority (up) and minority (down) spin components. The Cdg results for the down component show a strong dependence on the Pt composition, while the spin-up component changes slightly for a wide range of Pt compositions, which can be explained as follows. For bulk Co, the DOS at the Fermi level is dominated by the spin-down component, and hence it is strongly affected by changes at the DOS near the Fermi level, which are induced by the replacement of Co by Pt atoms. This also explains why Cdg has smaller values for the spin-down component. For n = 35, 18436



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the average Cdg result for the surface atoms is near the result for Pt55, as most of the Co atoms are located at the core region, and only 7 Co atoms are uniformly distributed at the surface. For Pt42Co13 (core−shell structure), the Co atoms located at the core region almost do not affect the average Cdg results for the surface Pt atoms. For PtnRh55−n, except for small deviations at n = 42, we found that Cdg changes almost linearly as a function of the Pt composition, with different slopes for the core and surface atoms. For example, Cdg = −3.33 eV for the core atoms of Rh55, while it is −3.18 eV for the core atoms of Pt55, and hence the center of the gravity will move near to the Fermi level by increasing the Pt composition, which is found by our calculations. In contrast, an opposite behavior is obtained for the surface atoms, i.e., Cdg = −2.05 eV for Rh55 and −2.53 eV for Pt55. Thus, increasing the Pt composition shifts Cdg almost linearly down in energy, as a function of the composition. In contrast with Co55, Rh55, and Pt55, the core and surface atoms of Au55 in the lowest energy configuration, Figure 1, have about the same values for Cdg , which is a consequence of the local environment of the Au atoms in the core and surface regions. For the surface atoms, Cdg = −3.10 eV for Au55 and −2.53 eV for Pt55, and hence the center of gravity moves close to the Fermi level by increasing the Pt composition, which is obtained from the calculations. For the core atoms, the linear behavior is observed only from n = 13−55 due to the reduced and low-coordinated core region. D. Magnetic Moments. The total and local magnetic moments of the lowest energy PtnTM55−n configurations are shown in Figure 4, where the local magnetic moments are separated in four groups, namely, Pt and TM atoms in the core and surface regions. For PtnCo55−n, mT decreases almost linearly for n = 0−49 by reducing Co composition, which is expected as mT is dominated by the Co atoms. The magnetic moments of the Co atoms in the core region are slightly affected by the replacement of Co by Pt atoms at the surface sites (n = 0−42);

however, the Co atoms at the surface region are strongly affected by the replacement of Co by Pt atoms. In contrast with PtnCo55−n, the results for the lowest energy PtnRh55−n configurations are unexpected as the total magnetic moments of PtnRh55−n are substantially larger than the mT results for Pt55 and Rh55. The magnetic moment of Rh55 is enhanced substantially by the replacement of Rh by Pt atoms at the surface, which can be explained through the strain induced by the size difference between the Rh and Pt atoms. For example, the replacement of the Rh surface atoms by Pt atoms create a compression of the Rh−Rh bond lengths, which affects directly the hybridization of the d-states and consequently their magnetic moments. For all the lowest energy PtnRh55−n configurations, we performed fixed total magnetic moment calculations (mT = 5.0 μB). We found that these moment configurations have energies slightly higher than those of high magnetic moment solutions, i.e., differences less 1.0 meV/atom. From Figure 4, it can be seen that the main contribution is due to the Rh surface atoms for lower Pt composition, while Pt surface atoms and Rh core atoms contribute for large values of n. The same effect can be seen in Figure 4 for PtnAu55−n; however, the magnitude of the enhancement is substantially smaller, which can be explained by the similar size of the Pt and Au atoms.

4. SUMMARY In this paper, we report a DFT-PBE investigation of the structural formation, relative stability, density of states, and magnetic properties of the PtnTM55−n systems for TM = Co, Rh, Au, as a function of the Pt composition. For PtnCo55−n and PtnRh55−n, the excess energy has a plateau with similar values for n = 20−42 and n = 28−42, respectively, while the core− shell icosahedron structures (Pt42Co13, Pt42Rh13) have the highest stability. For Pt28Rh27, 13 of the Rh atoms are located at the core region, while the remaining 14 Rh atoms are uniformly distributed at the surface. Thus, both Pt and Rh atoms are exposed directly to the vacuum region and can take part in reactions. Following the results for PtAu bulk alloys,58 for PtnAu55−n, we found a small positive excess energy for almost all compositions, except for Pt13Au42, which is energetically favorable due to the formation of the core−shell icosahedron configuration with the Pt atoms at the core region, due to the small atomic size of the Pt atoms. Thus, for TM = Co, Rh, Au, the formation of the core−shell icosahedron structure plays a decisive role for the stability of the nanoalloys with 55 atoms due to the release of strain energy, which favors the formation of nanoalloys with only one species on the surface, which might not be desirable for particular reactions. Our analyses of the density of states of the PtnTM55−n showed that the position of the center of the gravity of the occupied d-states with respect to the Femi level90,93 can be tuned as a function of the Pt composition. Thus, it indicates that adsorption energy of a particular adsorbate to the surface of the nanoalloys can be tuned, and hence it affects the reactivity of the nanoalloys. We found that the magnetic moments of the PtnCo55−n systems follow the expected trend as a function of Pt composition; however, the same is not true for PtnRh55−n and PtnAu55−n. For PtRh, we observed a clear enhancement of the magnetic moment of the nanoalloys by a few times compared with their separated Pt55 and Rh55 phases. A similar effect is observed for PtnAu55−n, however, with smaller magnitude.

Figure 4. Total and local magnetic moments for the lowest energy PtnTM55−n (TM = Co, Rh, Au) configurations. 18437



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. E-mail: juarez_dasilva@ iqsc.usp.br Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

M. J. Piotrowski and P. Piquini thank the Brazilian financial agencies CNPq and CAPES, and J. L. F. Da Silva thanks the São Paulo Science Foundation - FAPESP.

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