Molecular Dynamics Simulation of the Melting Behavior of Crown

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Molecular Dynamics Simulation of the Melting Behavior of Crown-Jewel Structured Au-Pd Nanoalloys Mingjiang Li, and Daojian Cheng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp4062835 • Publication Date (Web): 18 Aug 2013 Downloaded from http://pubs.acs.org on August 20, 2013

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The Journal of Physical Chemistry

Molecular Dynamics Simulation of the Melting Behavior of Crown-Jewel Structured Au-Pd Nanoalloys

Mingjiang Li and Daojian Cheng*

Division of Molecular and Materials Simulation, State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China

*

Authors to whom correspondence should be addressed. Electronic addresses: [email protected] Fax: +86-10-64427616 1

ACS Paragon Plus Environment


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ABSTRACT

Understanding the thermal stability of the novel crown-jewel structured Au-Pd nanoalloys with the Au atoms at the top positions is attractive and significant for their potential application in catalysis. In this work, the melting of crown-jewel structured Au-Pd nanoalloys with atoms from 561 to 2057 is investigated by molecular dynamics simulations, based on the Gupta potential. Melting properties for these clusters are studied based on the indicators such as potential energy curve, specific heat capacity, bond order parameters and deformation parameters. It is found that there is a monotonic decrease of the melting temperature with the concentration of the Au atoms, indicating that doping of Au atoms on the Pd clusters could decrease the thermal stability of the Pd cluster. In addition, linear decrease in cluster melting point with the inverse cluster diameter is predicted for the same kind of cluster, which is well-known as the Pawlow's law.

KEYWORDS: Thermal Stability, Au-Pd Nanoalloy, Crown-jewel Structure, Molecular Dynamics Simulation, Size Effect, Composition Effect, Gupta Potential.

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1. INTRODUCTION Metallic clusters have attracted much attention from both experimentalists and theoreticians for their excellent catalytic performances due to their small size and large surface area.1-3 Bimetallic clusters (or “nanoalloys”) show better catalytic properties compared with the corresponding monometallic clusters due to the synergistic effect of the coexisting different metals.4-5 Generally speaking, the catalytic performance of nanoalloys depends mainly on their structures.6-8 In this respect, increasing efforts have been devoted to improve the catalytic activity and selectivity of nanoalloys by developing new kinds of structures. A number of structural models have been found in nanoalloys by varying their compositional and atomic ordering. In previous work, core-shell (B-A)9-12 and three-shell onion-like (A-B-A)13-15 structures were found in nanoalloys by experimental and theoretical investigations. In addition, the onion-ring structure7 was found for the Pd-Pt nanoalloys with the size of 147 and 309 atoms, where Pd and Pt atoms occupy alternate layers of the clusters. The Quasi-Janus structure was also proposed in several nanoalloys by molecular simulations8,

16-17

and experiments,18

where the cluster presents two well-defined subunits. Recently, a novel crown-jewel (CJ) structure was prepared for Au-Pd nanoalloys based on the galvanic replacement process, showing an excellent catalytic activity for aerobic glucose oxidation.6 In this structure, the Au atoms are located at the top position of the Pd clusters, where the Pd clusters serve as the crowns and the Au atoms serve as jewels decorating the top position of the crowns. However, the detailed structural properties and melting behaviors of the CJ structured Au-Pd nanoalloys are still not well-known, which are important for their potential application in catalysis.

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The thermal stability of nanoalloys depends on not only the size and morphology effects, but also the composition and alloying effects, which makes it difficult to be investigated by experimental methods. Recent advances in theoretical methods make that theoretical calculations and simulations can provide insight into the structural and thermal information of nanoalloys. In previous works, surface pre-melting19 and two-stage melting phenomena20-21 have been found by theoretical calculations. It is found that the melting of clusters is preferred to initiate at the surface where atoms are less coordinated than bulk ones and progressively propagates into the interior, corresponding to the surface pre-melting process.19 In addition, two-stage melting process has been found in Pt−Pd and Au-Pd nanoalloys, where the two melting processes are distinctly separated from each other and proceed independently.20-21 In this work, the thermal properties of the crown-jewel (CJ) structured Au-Pd nanoalloys with atoms from 561 to 2057 are studied by molecular dynamics simulations, based on the Gupta potential. The effects of composition and size on the melting of the CJ structured Au-Pd nanoalloys are discussed. The article is organized as follows. The second section discusses the potential model and the simulation methodology. The calculated results and discussion are presented in the third section. The main conclusions are summarized in the fourth section. 2. SIMULATION DETAILS 2.1 Initial Cluster Configurations In this work, the Pd clusters of interest possess highly symmetric cuboctahedral (Cubo) structures, which are in good agreement with the experimental data.6 Note that the Cubo structure is not the global minimum according to the Gupta model neither for pure Au nor for pure Pd, where truncated octahedron with smaller (100) facets is

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lower in energy than the Cubo structure from the energetic point of view.22 Five compositions were adopted in this work, corresponding to the pure Pd cluster (Pd), a vertex of the cluster occupied by a single Au atom (CJ-1), all vertices of the cluster occupied by Au atoms (CJ-2), all edges of the cluster occupied by Au atoms (CJ-3), and the whole surface of the cluster occupied by Au atoms (Pd@Au). Accordingly, clusters with sizes of 561, 923, 1415, and 2057 were used. Figure 1 depicts the initial configurations of the 561-atom clusters with five compositions of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au. Initially, the lowest-energy atomic ordering of all these clusters is optimized by Monte Carlo simulations at the Gupta empirical potential level,7 and the resulting configurations are used to study the melting properties of these clusters.

Figure 1. Snapshots of the 561-atom cuboctahedral Au-Pd clusters with five compositions of pure Pd (Pd561), CJ-1 (Au1Pd560), CJ-2 (Au12Pd549), CJ-3 (Au108Pd453), and Pd@Au (Au252Pd309). Red spheres, Au; yellow spheres, Pd. For the meaning of CJ-1, CJ-2, CJ-3, and Pd@Au, please see the text. 5



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2.2 Potential Models In MD simulations, the Gupta potential23 was employed to describe the interatomic interactions. The Gupta potential is based on the second-moment approximation of the tight-binding (TB-SMA) model. The potential has been successfully used in our previous studies, demonstrating an accurate description of thermodynamic properties of metal clusters.13, 24 According to the framework of the Gupta potential, the total energy for a system can be written as

E to ta l =

∑ (E

i R

− E Bi )

(1)

i

where ERi and EBi are the Born–Mayer ion–ion repulsions and the band term, respectively. These terms can be written for an atom i as

E Ri =

∑ Ae

− p ( rij / r0 −1)

(2)

j

1/ 2

 −2 q ( r / r −1)  E = ∑ ξ 2 e ij 0   j  i B

(3)

where A, ξ , p, q and r0 are obtained by fitting to the experimental values of the cohesive energy, lattice parameters (by a constraint on the atomic volume), and independent elastic constants for the reference crystal structure at T = 0 K. In addition, r0 is the nearest-neighbor distance in the pure metals (Au and Pd), and taken as the average of the pure ones for the heterometallic interactions (Au-Pd). In this work, the heterometallic Au-Pd parameters were obtained as averages of the pure Pd-Pd and Au-Au parameters, which give a higher degree of phase separation between Au and

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Pd.25 All the potential parameters used here were employed in previous studies with satisfactory results,26-28 and are listed in Table 1.

Table 1: Parameters of the Gupta potential for the Pd-Pd, Pd-Au and Au-Au interactions.

Pd-Pd Pd-Au Au-Au

A (eV)

ξ (eV)

p

q

r0 ( Å)

0.1746 0.19 0.2061

1.718 1.75 1.790

10.867 10.54 10.229

3.742 3.89 4.036

2.7485 2.816 2.884

2.3 MD Simulations MD simulations were performed with a constant number of atoms N with a nearly zero fluctuating pressure P. The temperature was maintained by the Nose-Hoover thermostat. Newton's equations of motion were integrated using the Verlet leapfrog algorithm and the integration time step was set to 1 fs. For the melting of the clusters, simulations were performed in a series of temperature conditions starting from 50 to 1400 K with a temperature increment of 50 K. Near the melting point, the increment was reduced to 10 K. At each temperature, the first 400 ps were used for the atomic structure equilibration, and the next 200 ps were used for statistical averaging. 3. RESULTS AND DISCUSSIONS 3.1 Structural Stability To analyze the energetics and the relative stability of Au-Pd nanoalloys with different compositions, a parameter, ∆ , was normally adopted to represent the relative stability of the clusters,11, 14 which is defined as the excess energy of the cluster with respect to N bulk atoms, divided by N 2 / 3 :

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∆=

N Au , N Pd coh coh Etotal − N Au ε Au − N Pd ε Pd ( N Au + N Pd ) 2 / 3

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(4)

coh is the number and the bulk cohesive energy of Au atoms, where N Au and ε Au coh while N Pd and ε Pd is the number and the bulk cohesive energy of Pd atoms,

respectively. N is the total number of the cluster with N = N Au + N Pd , and N 2 / 3 N Au , N Pd scales approximately as the number of surface atoms in the cluster. Etotal is the

calculated total energy of the cluster at the given composition. Note that the lower the value of ∆ , the more stable the structure of the cluster. Figure 2 shows the values of ∆ per atom at the Gupta level for Au-Pd nanoalloys with five compositions of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au at 50 K. It is found in Fig. 2 that the values of ∆ per atom for CJ-1, CJ-2, CJ-3, and Pd@Au are lower than those of pure Pd clusters. It means that Au atoms located at the surface sites of Au-Pd nanoalloys are favorable, corresponding to the surface segregation of Au atoms, which is in good agreement with previous studies.29-31 This is mainly attributed to the lower surface energy of Au (Au: 1.5 J m-2, Pd: 2.0 J m-2).32 In addition, the lattice parameters of bulk Au and Pd are 4.08 and 3.89 Å, respectively, and thus the smaller Pd atoms tend to occupy the center of the cluster. It is also found in Fig. 2 that there is a monotonic decrease of the value of ∆ per atom with the concentration of the Au atoms. Notably, the lowest value is achieved for Pd@Au cluster, indicating that the whole surface of the cluster occupied by Au atoms (Pd@Au) is relatively stable at the Gupta level among these clusters. In addition, the value of

∆ per atom remains unchanged when the total number of atoms (N) increases for the

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same kind of the cluster. It means that size has little effect on the relative stability of the cluster.

Figure 2. Plot of ∆ per atom against N for Au-Pd nanoalloys with five compositions of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au at 50 K.

3.2 Melting Properties The solid-liquid phase transition can be clearly identified by the sharp rise of the potential energy curve and the abrupt peak of specific heat capacity. To identify the melting temperature, we define the specific heat capacity, Cv , per atom as a function of the potential energy fluctuation, given by33

(E C = v

2

− E

2

)

nk BT 2

9


(5)


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where E is the potential energy, k B is the Boltzman constant, n is the total number of atoms in the cluster, and T is the temperature. In general, the melting point is defined as a temperature at which the specific heat capacity reaches its maximum. Figure 3(a-d) shows the temperature dependence of the average total energy per atom and Cv of Au-Pd nanoalloys containing 561, 923, 1415, and 2057 atoms, respectively. It is found in Fig. 3(a) that the potential energy for 561-atom Au-Pd nanoalloys increases almost linearly with temperature in the early stage. Then, a distinguishable sudden increase in the caloric curve occurs, corresponding to the melting transition of the cluster. For the case of CJ-1 structured Au1Pd560 cluster, the sharp peak with its maximum height at about 960 K in the heat capacity Cv corresponds to the distinguishable sudden increase in the caloric curve. Therefore, we estimate that the melting temperature of CJ-1 structured Au1Pd560 cluster is about 960 K.

Figure 3. Temperature dependence of the average total energy per atom and Cv of Au-Pd nanoalloys with five compositions of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au containing (a) 561, (b) 923, (c) 1415, and (d) 2057 atoms. 10


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Based on the same indicators as those for the CJ-1 structured Au1Pd560 cluster, the melting temperatures of all the Au-Pd nanoalloys are obtained, as listed in Table 2. Melting temperatures are plotted changing with the concentration of the Au atoms in Fig. 4. It is found in Fig. 4 that there is a monotonic decrease of the melting temperature with the concentration of the Au atoms, which is in excellent agreement with the fact that the melting point of pure bulk Pd (1825 K) is higher than that of pure bulk Au (1338 K). As expected, the melting temperature in every composition is lower than that of the corresponding bulk metal, which is a well-known property of nano-sized materials. Accordingly, the highest melting point is achieved for pure Pd cluster.

Table 2: Calculated melting points (in K) for five types of Au-Pd nanoalloys of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au with sizes of 561, 923, 1415, and 2057. N 561 923 1415 2057

Pure Pd 960 1010 1050 1080

CJ-1 960 1010 1050 1070

CJ-2 950 1010 1050 1070

CJ-3 920 980 1010 1060

Pd@Au 850 910 950 980

Figure 4. Melting temperatures of Au-Pd nanoalloys containing 561, 923, 1415, and 2057 atoms changing with the concentration of the Au atoms. Notably, l to 5 in x-axis stands for pure Pd, CJ-1, CJ-2, CJ-3, and Pd@Au, respectively. 11



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Figure 5 show the melting temperatures as a function of N −1/3 for Au-Pd nanoalloys with five compositions of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au. Linear decrease in cluster melting point with N −1/3 is found for all the five compositions of Au-Pd nanoalloys. This behavior is in qualitative agreement with Pawlow’s law.34

Figure 5. Melting temperatures as a function of N −1/3 for Au-Pd nanoalloys with five compositions of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au.

3.3 Structural Evolution upon Melting Here we also employ the bond order parameter method35-37 to analyze the structures of clusters during the melting process. The general idea of bond order parameters is to capture the symmetry of bond orientations regardless of the bond length. The definition of bond order parameters can be found in references.13, 35 The four bond order parameters Q4, Q6, W4 and W6 are designed to identify different structures. Table 3 gives bond order parameters for a number of simple geometries, including

face-centered-cubic

(fcc),

hexagonal-close-packed

icosahedral clusters, as well as liquid structure.

12


(hcp),

Mackay

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Table 3: Bond Order Parameter Values for Various Geometries. Geometry fcc Icosahedron hcp liquid

Q4 0.19094 0 0.09722 0

Q6 0.57452 0.66332 0.48476 0

W4 0.159317 0 0.134097 0

W6 0.013161 0.169754 0.012442 0

Figure 6 shows the temperature dependence of bond order parameters Q4 and Q6 for Au-Pd nanoalloys containing 2057 atoms. It is found in Fig. 6a that Q4 ≈ 0.16 is found for the five cuboctahedral clusters before melting, near to the standard value of the fcc structure shown in Table 3. For all the five clusters, Q4 ≈ 0 is found at the temperatures after melting, indicating the appearance of liquid phase after melting. Interestingly, Pd@Au cluster undergoes an ups and downs process between 810 and 980 K, indicating a two-stage melting process. Figure 6b shows the temperature dependence of bond order parameter Q6 for Au-Pd nanoalloys containing 2057 atoms. At lower temperature, the cluster remains the cuboctahedral structure, characterized by the standard value of Q6. However, at the temperatures near the melting point, Q6 takes small jumps, indicating the structure evolution upon heating before melting. Then giant jumps are found in Q6 during the melting temperatures. At the temperatures after melting, Q6 ≈ 0 is found for the clusters, corresponding to the appearance of liquid phase after melting, characterized by the standard value of Q6.

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Figure 6: The temperature dependence of the bond order parameters (a) Q4 and (b) Q6 for 2057-atom Au-Pd nanoalloys with five compositions of Pd, CJ-1, CJ-2, CJ-3, and Pd@Au.

In analyzing the melting process, the deformation parameter ε def was calculated. The deformation parameter ε def

9, 38

is given by

ε def =

2Q1 Q2 + Q3

(6)

where Q1 , Q2 and Q3 is the eigenvalues of the quadrupole tensor Qij with the descending order of Q1 ≥ Q2 ≥ Q3 . The quadrupole tensor Qij is defined as N

Qij = ∑ Rli Rlj , where N is the total number of atoms in the cluster, and i and j run l

from 1 to 3. Rli and Rlj are the ith and jth coordinates of atom l relative to the coordinates of the cluster centers of mass, respectively. A value ε ≈ 1 stands for a sphere-like system and ε > 1 represents a type of quadrupole deformation. In Fig. 7, we give the temperature dependences of the deformation parameters ε def for Au-Pd nanoalloys containing 2057 atoms. At a lower temperature before melting, ε ≈ 1 is found for all clusters. At higher temperatures near melting, some small jumps in ε def are found for the five clusters, corresponding to the shape changes of the clusters 14


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upon melting, even the pre-melting phenomenon. At the melting points, sharp jumps are found for Au-Pd nanoalloys containing 2057 atoms, indicating the giant shape changes during the melting transition. At the higher temperatures after cluster melting, a quadrupole deformation is found for all the clusters with ε def ≈1.2 , corresponding to the shape changes from a spherical shape to a somewhat oval shape after melting.

Figure 7: The temperature dependence of the deformation parameter ε def for 2057-atom Au-Pd nanoalloys with five compositions of pure Pd, CJ-1, CJ-2, CJ-3, and Pd@Au.

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4. CONCLUSIONS Molecular dynamics simulations were used to investigate the cluster-size and composition effects on the melting of crown-jewel structured Au-Pd nanoalloys with atoms from 561 to 2057, based on the Gupta potential. The melting of these Au-Pd nanoalloys with different sizes and compositions has been characterized by calculating the potential energy curve, specific heat capacity, bond order parameters and deformation parameters. It is found that doping of Au atoms on the Pd clusters could decrease the thermal stability of the Pd cluster, where the melting point of the cluster decreases with the concentration of the Au atoms. It is also found that the melting point of the cluster is associated with a linear decrease with the inverse cluster diameter for the five types of the clusters, corresponding to the Pawlow's law. It is expected that this work can provide valuable information for the potential application of the novel crown-jewel structured Au-Pd nanoalloys as catalysts.

ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (21106003), Beijing Novel Program (Z12111000250000), “Chemical Grid Project” of BUCT and Supercomputing Center of Chinese Academy of Sciences (SCCAS).

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Molecular Dynamics Simulation of the Melting Behavior of Crown

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