Phase Stability, Melting, and Alloy Formation of Au−Ag Bimetallic

May 10, 2010 - The molecular dynamic method has been used to simulate the phase stability, melting, and alloy formation of bimetallic Au−Ag nanopart...
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Phase Stability, Melting, and Alloy Formation of Au-Ag Bimetallic Nanoparticles W. H. Qi†,‡ and S. T. Lee*,† COSDAF (Center of Super-Diamond and AdVanced Films) & Department of Physics and Materials Science, City UniVersity Hong Kong, Hong Kong SAR, China, and School of Materials Science and Engineering, Central South UniVersity, Changsha 410083, China ReceiVed: NoVember 30, 2009; ReVised Manuscript ReceiVed: April 12, 2010

The molecular dynamic method has been used to simulate the phase stability, melting, and alloy formation of bimetallic Au-Ag nanoparticles (NPs) with cuboctahedral, decahedral, icosahedral, and spherical shapes. The alloy NPs have more negative formation energy than the core/shell NPs, indicating the former is more stable than the latter. During melting, both core/shell and alloy NPs start to melt from the surface and then the core. The melting temperature of cuboctaheral, icosahedral, and decahedral NPs is similar, indicating the small influence of shape on melting temperature. During the alloying process, the alloy formation ability follows cuboctaheral > icosahedral > decahedral NPs, revealing the significant effect of particle shape on alloying formation. Only the surface was found to become alloy whereas the core remains pure components after annealing. It is shown that the UV-vis method alone is not enough to characterize the alloy formation in the entire NP, but only in the surface shell. I. Introduction Bimetallic nanoparticles (NPs) can exist in either a core/shell or a mixed alloy structure.1 NPs of different phases have different applications; for instance, Cu/Pt core/shell NPs are used as catalysts for fuel cells.2 Since such NPs are composed of an inexpensive metal (Cu) core and an expensive metal (Pt) catalytic shell, they offer the potential to improve catalytic activity via using a decreasing amount of the precious metal on the catalytic shell. On the other hand, Au-Ag alloy NPs have special optical and catalytic applications. The plasmonic absorption for spherical Au and Ag NPs is around 520 and 400 nm, respectively, while the absorption of Au-Ag alloy NPs can be tuned continually from 520 to 400 nm via changing the alloy composition.3 Furthermore, recent studies show that Au-Ag alloy NPs have a higher catalytic activity than pure Au and Ag NPs for CO oxidation.4 For some applications, bimetallic core/shell NPs are needed, while alloy NPs in other cases. Obviously, phase stability of both core/shell and alloy NPs is an important issue in applications. Recently, Wang et al. prepared Au-Ag alloy NPs from Ag/ Au core/shell NPs.5 They first prepared Ag NPs by thermal reduction of AgNO3 in oleylamine and then deposited Au on Ag NPs by reduction of HAuCl4 with oleylamine at 50 °C. The core/shell structured Ag/Au NPs were heated at 100 °C in oleylamine to increase diffusion in the core/shell structure for the formation of Au-Ag alloy NPs. Since the UV-vis peaks of Au-Ag alloy NPs are different from those of core/shell NPs, the authors used UV-vis absorption to determine the alloy formation in NPs. However, since the UV-vis absorption spectrum is derived mainly from surface plasmonic resonance, therefore it only reveals the composition of the surface layer but cannot identify whether the inner core is alloyed or not. This point will be discussed further below. We show in this

work that the phase transition between core/shell and alloy NP is also important. While it is difficult experimentally to study phase stability and phase transition at atomic level, the relevant theoretical study is readily accessible by atomic simulation and extremely useful. For example, Liu et al. studied the phase stability of Au-Pt NPs6 by molecular dynamic simulation and found the Pt-core/ Au-shell structure is more stable than the Pt-Au alloy structure. Kim et al. simulated the solid-to-liquid transition of Ag-Pd bimetallic nanocluster7 and calculated the corresponding phase diagram. Evteev et al. investigated the effect of surface segregation phenomena at 1000 K on the structure of Pd alloy nanoparticles containing 30 at. % Ni8 and found such nanoparticles form a surface-sandwich structure via interdiffusion. In the present work, we take Au-Ag bimetallic NPs as an example to study the phase stability and the alloy formation process of core/shell NPs. We investigate further whether the final alloy NPs is fully mixed or only mixed in the surface after interdiffusion. II. Simulation Details The molecular dynamics simulation package, MATERIALS EXPLORER,9 was used in present work. The simulation was performed in NVT ensemble with tight binding potential (Φ) developed by Cleri and Rosato,10 which has the following form

Φ)

(1)

i

where

Eir )

[ (

r

)]

∑ ARβ exp -pRβ rRβij - 1 j

* Corresponding author. E-mail: [email protected]. † City University Hong Kong. ‡ Central South University.

∑ (Eib + Eir)

is the two-body term and

10.1021/jp9113442  2010 American Chemical Society Published on Web 05/10/2010

0

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Eib ) -√Fi Fi )

[ (

r

TABLE 1: Tight-Binding Potential Parameters for Au-Ag System11

)]

∑ ζRβ2 exp -2qRβ rRβij - 1 j*i

0

Au-Au Au-Ag Ag-Ag

is the many-body term. R and β represent the atomic species i and j, respectively. ARβ, ζRβ, pRβ, and qRβ are the potential parameters, r0Rβ denotes the nearest-neighbor distance, and rij is the distance between atoms i and j. Values of the parameters for Au-Ag system are listed in Table 1.11 This potential function can be used to simulate the properties of elements and binary alloys. To elucidate the size and composition effects on phase stability, we simulated the spherical NPs with 555 atoms and 959 atoms in different compositions. To study the shape effects on phase stability, three common shapes of Ag-Au NPs were constructed, which are 561-atom cuboctahedron, 584-atom decahedron, and 561-atom icosahedron (the NPs with different shapes are shown in Figure 1). We also constructed pure element, core/shell, and alloy NPs in above-mentioned shape and size. Our simulation consists of three parts: the first is to relax the structure at 0 K to calculate the formation energy, the second is to melt the core/shell and alloy NPs, and the third is to anneal the system at a fixed temperature to study the alloying process in a long time. The total energy curves and the pair correlation functions have been used to characterize the structure variations. III. Results and Discussion A. Phase Stability. The phase stability can be described by formation energy (FE), which is defined as the energy difference between the final bimetallic system and the initial pure components. The general formula for formation energy (∆Hf) is as follows:

∆Hf ) EAB - xEB - (1 - x)EA

(2)

where EAB, EB, and EA are the cohesive energy of bimetallic system, pure component A and B. x is the atomic concentration. If there are several phases, the simple way to find the most stable phase is to compute the FE, and the phase with the lowest FE is the most stable one. To study the phase stability of Au-Ag NPs by molecular dynamic method, we first kept each system at 300 K for 200 ps to relax their structures, decreased the temperature to 0 K in the following 700 ps, and then kept the system at 0 K for 100 ps to obtain the energy. The simulation results for cuboctahedral, decahedral, icosahedral, and spherical Ag-Au bimetallic NPs are listed in Table 2. For cuboctahedral NPs with 561 atoms, as shown in Table 2, the mean cohesive energy for pure Ag and Au NPs are -2.8103 and -3.6802 eV, both of which are higher than the corresponding bulk value at -2.96 eV (Ag) and -3.81 eV (Au).12 It suggests that the stability of pure NPs decreases when the size is in nanoscale. The experimental cohesive energy of Mo and W NPs also confirmed the decreasing phase stability in the nanoscale.13 For alloy and core-shell NPs, the cohesive energies lie in the middle of pure Ag and Au NPs, and the FE can be computed by eq 2. It is found that both alloy and core/ shell NPs have negative FE, suggesting that all they are more stable than the pure component. More rigorously, both Ag and Au core/shell NPs have higher FE than the corresponding alloy

ARβ (eV)

ζRβ (eV)

pRβ

qRβ

rRβ 0 (nm)

0.2096 0.1490 0.1031

1.8153 1.4874 1.1895

10.139 10.494 10.850

4.033 3.607 3.180

0.7738 0.7350 0.7751

NPs in same atomic concentration. The FE of 253-Au/308-Ag core/shell NP is -19.3028 eV, which is higher than -23.3893 eV of 253-Au/308-Ag alloy NPs, while the FE of 308-Au/253Ag core/shell NP is -10.6546 eV, which is also higher than -24.4079 eV of 308-Au/253-Ag alloy NP. The present numerical results show that the alloy NPs are more stable than the core/shell structured NPs. Table 2 also give the FE of decahedral, icosahedral, and spherical NPs, in which similar results to cuboctahedral NPs are obtained. The alloy NPs also have a more negative FE than the core/shell structured NPs, which suggests the alloy NPs are more stable. Apparently, if we exert enough driving force (such as increasing the temperature), the core/ shell NPs may become alloy NPs; i.e., phase transformation from core/shell NPs to alloy NPs may take place. It should be mentioned that the FE calculation just gives the necessary condition, but not the sufficient condition for transformation. Alloy formation also depends on the kinetic process. To investigate the size and composition effect on FE, we studied the Ag-Au bimetallic NPs of 555 atoms and 959 atoms, as shown in Figure 2. The FE of mixed Au-Ag NPs first decreases and then increases with increasing Au concentration; the most negative FE lies at x ) 0.5. For the two particles of 555 atoms and 959 atoms, the latter has a lower FE than the former in almost all composition range, indicating that the large NPs are more stable than the small ones with the same composition. Figure 2 also shows that the absolute values of the FE of the Ag/Au core/shell NPs are very small compared with the absolute values of the corresponding mixed NPs; however, the FEs of the Au/Ag core/shell NPs are close to those of the mixed NPs. These results indicate that the mixed NPs are the most stable structure compared with Au/Ag and Ag/Au core/shell NPs. Consequently, on exerting enough driving force the core/shell NPs would change to alloys. As mentioned above, Wang et al. prepared Ag-Au alloy from Ag/Au core/shell NPs by annealing the system at 398 K.5 To simulate this alloying process, we adopted the following approach. Since the real system is too large to handle by simulation, we thus simulate a smaller but realistic system to study the alloying process. As the annealing was performed at 398 K for 24 h, which is impractically lengthy for simulation, we thus anneal the system at a higher temperature to increase atomic interdiffusion. Smaller particle size and higher annealing temperature were thus selected to simulate the large size and long time of a real system. To determine the annealing temperature, we need to determine the melting temperature of NPs first, and the annealing temperature should be chosen to be lower than but as close as possible to the melting temperature. B. Melting Temperature. To simulate the melting process of bimetallic NPs, we increased the temperature of both alloy and core/shell NPs from 100 to 1400 K at 100 K temperature interval. At each temperature, the NPs were relaxed for 200 ps to reach thermodynamic equilibrium. Near the melting point, the temperature interval of 10 K was chosen. For the cuboctahedral shape, their energy variation curve is shown in Figure 3, and for decahedral, icosahedral, and spherical shapes, their energy variation curves are similar to cuboctahedral shape. As shown in Figure 3, the energy of both alloy and core/ shell increases almost linearly with temperature before 700 K.

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Figure 1. Geometrical configurations of the initial Ag nanoparticles: (a) cuboctahedron, (b) decahedron, (c) icosahedron, and (d) sphere.

TABLE 2: Formation Energies of Au-Ag Bimetallic Cuboctahedral, Decahedral, and Icosahedral Nanoparticles at 0 K morphology of NPs cuboctahedral

decahedral

icosahedral

spherical

structure pure Ag pure Au Au-Ag alloy Au-Ag alloy Au/Ag core/shell Ag/Au core/shell pure Ag pure Au Au-Ag alloy Au-Ag alloy Au/Ag core/shell Ag/Au core/shell pure Ag pure Au Au-Ag alloy Au-Ag alloy Au/Ag core/shell Ag/Au core/shell pure Ag pure Au Au-Ag alloy Au-Ag alloy Au/Ag core/shell Ag/Au core/shell

component 561 561 253 308 253 308 584 584 282 302 282 302 561 561 252 309 252 309 555 555 321 234 321 234

Ag Au Au Au Au Au Ag Au Au Au Au Au Ag Au Au Au Au Au Ag Au Au Au Au Au

308 253 308 253

Ag Ag Ag Ag

302 282 302 282

Ag Ag Ag Ag

309 252 309 252

Ag Ag Ag Ag

234 321 234 321

Ag Ag Ag Ag

In the range of 700-750 K, the energy curves have a sudden change, which corresponds to the melting process, i.e., the solidto-liquid phase transition. The curve of Ag308/Au253 core/shell NP is close to that of Ag308Au253 alloy NP, and that of Au308/ Ag253 core/shell NP is close to that of Au308Ag253 alloy. It shows that both alloy and core/shell NPs have similar melting

Figure 2. Formation energies of Au-Ag bimetallic spherical nanoparticles with 555 and 959 atoms at 0 K. The black cubes are for mixed structure, the blue spheres for Ag/Au core/shell NPs, and red triangles for Au/Ag core/shell NPs. The solid symbols are for 959 atoms and open symbols for 555 atoms.

mean cohesive energy per atom (eV)

total formation enthalpy (eV)

-2.8103 -3.6802 -3.2443 -3.3314 -3.3223 -3.2216 -2.8124 -3.6874 -3.2780 -3.3072 -3.2583 -3.2942 -2.8193 -3.6818 -3.2488 -3.3385 -3.3272 -3.2259 -2.8098 -3.6837 -3.3518 -3.2178 -3.3455 -3.1988

0 0 -23.3893 -24.4079 -19.3028 -10.6546 0 0 -25.1604 -24.7132 -13.6556 -17.1212 0 0 -23.5995 -24.7587 -18.4194 -10.7526 0 0 -20.2881 -21.9474 -16.7916 -11.2110

temperature. For core/shell, the shells melt first and then the cores. To support this conclusion, we calculate the pair correlation function of the core and the shell for cuboctahedral Ag/Au core/shell NP of 561 atoms, with the results shown in Figure 4. It shows that both the core and the shell keep the FCC structure at 100 K, as evidenced by the sharp characteristic peaks. At 700 K, all the peaks of the core remains, indicating that its structure has long-range order and still keeps the FCC structure. However, for the shell, the characteristic peaks of FCC disappear, indicating the disappearance of long-range order and

Figure 3. Energy variation of cuboctahedral NPs during melting.

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Figure 5. Energy variation of cuboctahedral core/shell NPs upon annealing at 600 K. Figure 4. Pair correlation functions of core and shell for cuboctahedral Ag/Au core/shell NPs of 561 atoms at 100, 700, and 750 K.

melting of the shell. At 750 K, the curves show both shell and the core become liquid. The present simulation results for the Ag-Au system are consistent with those of Pd-Pt bimetallic NPs.14 After melting, the final structure is a mixed solution, and there is no apparent segregation in the surface. The surface segregation can be predicted by Reyes-Nava’s model,15 which is based on the difference between atomic properties of the constituent elements. It is predicted there is no segregation of Ag in an Au host, which is well consistent with our simulation results. For decahedral (584 atoms), icosahedral (561 atoms), and spherical (555 atoms) core/shell NPs, the melting temperature is about 700-750 K, whereas for spherical NP of 959 atoms, the melting temperature is about 770-830 K. It suggests that the size is the main factor, but the shape is the minor one in affecting the melting temperature of NPs. There are several models to account for the melting of NPs, such as BOLS model,16 latent heat model,17 liquid drop model,18 and bond energy model,19,20 etc. In the bond energy model,20 the formula of melting temperature (Tm) is proposed by considering the relation with cohesive energy, which has the following form

(

Tm ) Tmb 1 -

3Rd D

)

(3)

where Tmb is the melting temperature of the corresponding bulk, d and D are the diameters of atom and NP, respectively, and R is the shape factor to account for the shape effect on melting temperature, which is a modified factor to consider the shape difference between nonspherical and spherical NPs. For spherical NPs, R ) 1, and for cubic NPs, R ) 1.24. Since the cuboctahedral shape may grow up as FCC structure (the large NPs in experiments are in FCC structure5), therefore, we predict the melting temperature of cuboctahedral shape NP (R ) 1.10420). Furthermore, we have d/D ) f1/3n-1/3, f is the atomic packing factor, and f ) 0.74 for FCC. Equation 3 can be rewritten as Tm ) Tmb(1 - 3Rf1/3n-1/3). According to the Au-Ag phase diagram,21 the bulk melting temperatures of Au0.55Ag0.45 (Au308Ag253) and Au0.45Ag0.55 (Au253Ag308) are about 1340 and 1330 K. Then the calculated melting temperature for Au308Ag253 and Au253Ag308 are about 840 and 850 K, which is about 100 K higher than the simulated value 700-750 K. The difference between theoretical predictions and

simulated results may be due to the fact that the NPs are fully relaxed in simulation but not in bond energy theory. On the basis of above discussion, it is safe to choose the annealing temperature to be below the melting temperature for all NPs studied. Here we choose the annealing temperature as 700 K for the spherical 959-atom NP and 600 K for the cuboctahedral 561-atom, decahedral 584-atom, icosahedral 561-atom, and spherical-555-atom NP; both temperatures are higher than the annealing temperature of 373 K used in experiment.5 At this high temperature, the interatomic diffusion increases, so that the annealing time required is much shorter than that in the real experiment. C. Alloying Formation from Core/Shell Structure. To study the alloy process, we annealed the core/shell NPs of the four shapes at 600 K for 58 ns. The energy variation curve of cuboctaheral NP is shown in Figure 5. For Ag/Au core/shell NP, the energy is about -2.765552 × 10-16 J in the first 14 ns, then decreases dramatically in the time range of 14-28 ns, and then approaches to a constant value -2.844432 × 10-16 J. The energy fluctuation is 3.659096 × 10-19 J at the initial stage, which is 0.13% of the total energy. At the final stage, the energy fluctuation is 2.916144 × 10-20 J, which is 0.01% of the final total energy. The small energy fluctuation suggests the system approaches to thermodynamic equilibrium. For the Au/Ag core/ shell NP, the initial energy is -2.830982 × 10-16 J, and the energy fluctuation is 2.990438 × 10-19 J. The final energy is -2.909058 × 10-16 J, and the final energy fluctuation is 3.562205 × 10-20 J. The ratio between fluctuation energy and total energy decreases from 0.1% to 0.01%. On the basis of the simulation results, we can get the atomic information during alloying process. Figure 6 gives four snapshots and corresponding pair correlation functions during the annealing process of Au/Ag core/shell cuboctahedral NPs. At 300 K, the structure is the ideal core/shell, and the corresponding pair correlation function curves have sharp peaks, which suggest the atoms lay in FCC lattice sites (Figure 6a). At 600 K before annealing, the structure still keeps FCC but with some surface point defects. After 19 ns of annealing, the core is still FCC, but the order of surface decreases. After 58 ns at 600 K, the peaks of pair correlation function become sharp again, which suggests the structure becomes ideal FCC again. From the snapshot of Figure 6d, Au atoms move from the core to surface during the alloy process, which suggests the surface has formed alloy. Figure 7 gives the snapshots and pair correlation functions of Ag/Au core/shell cuboctahedral NPs during the alloy process.

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Figure 6. Snapshots of alloying process and corresponding pair correlation function of Au/Ag core/shell cuboctahedral NPs: (a) at 300 K, (b) at 600 K before annealing, (c) at 600 K after 19 ns, and (d) at 600 K after 58 ns. The blue lines are for Au-Au pairs, black lines for Ag-Ag pairs, and red lines for Au-Ag pairs. In the snapshots, the orange spheres denote Au atoms and green spheres Ag atoms.

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Figure 7. Snapshots of alloying process and corresponding pair correlation function of Ag/Au core/shell cuboctahedral NPs: (a) at 300 K, (b) at 600 K before annealing, (c) at 600 K after 14 ns, and (d) at 600 K after 58 ns. The blue lines are for Au-Au pairs, black lines for Ag-Ag pairs, and red lines for Au-Ag pairs. In the snapshots, the orange spheres denote Au atoms and green spheres Ag atoms.

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Figure 8. Snapshots of cross section of final NPs after annealing for 58 ns: (a) Ag/Au core/shell NPs; (b) Au/Ag core/shell NPs.

Similar to Au/Ag core/shell NP, the initial structure of Ag/Au core/shell NP are ideal FCC. At 600 K before annealing, some surface point defects appear. After 14 ns at 600 K, a lot of Ag atoms moved from core to surface. After 58 ns, the pair correlation functions of Au-Au, Au-Ag, and Ag-Ag become sharp again, indicating the structure becomes ideal FCC again. The relative height of Ag-Au peaks in Figure 7d is higher than that in Figure 6d, which means more Ag-Au pairs have formed in Ag/Au than in Au/Ag core/shell NPs. The reasons may be as follows. (1) The formation energy difference between Ag/ Au core/shell NP and corresponding alloy NP is 13.75 eV, which is much larger than that between Au/Ag core/shell and corresponding alloy NP at 4.09 eV. The FE difference can be regarded as driving force for the alloying process; therefore, the amount of formed alloy in the Ag/Au core/shell NP is more than that in the Au/Ag core/shell NP. (2) The surface energy of Ag (78 meV Å-2) is less than that of Au (97 meV Å-2), which favors surface enrichment by Ag.1 In other words, more Ag atoms in the surface can decrease total energy. The snapshots of the alloying process suggest that the surface finally becomes alloy for cuboctahedral core/shell NPs. But whether the core is alloy or not is still unknown. From the pair correlation function in Figure 6d, the Au-Au pairs are more than Au-Ag or Ag-Ag pairs in Au/Ag core/shell NP, where Au atoms are in the core of the initial structure. In Figure 7d, the pair correlation function shows that Ag-Ag pairs are more than Au-Ag or Au-Au pairs in Ag/Au core/shell NP, where the Ag atoms are in the core in its initial structure. One direct way to determine the core composition of the final structures is to observe the cross section of the final NPs, as shown in Figure 8. One can find that the cores of both annealed NPs are still pure components rather than full alloy, although the shells have become alloy. The alloying formation is a kinetic process, as mentioned, which needs driving force to complete. For the present Au/Ag or Ag/Au core/shell NPs, the alloying driving force, from the FE difference between alloy and core/shell NPs, decreases with continual alloying process. In the final stage, the alloying process would stop due to small driving force, and thermodynamic equilibrium cannot be reached. Therefore, the final structure is still surface-mixed rather than fully mixed. According to Reyes-Nava’s model,15 the Ag-Au NPs should be fully mixed without surface segregation, which however only indicates the thermodynamic (similar to our calculation in section III.A) rather than the kinetic results. If the driving force could make the NPs reach thermodynamic equilibrium, then the final product would be fully mixed NPs. As mentioned above, since the UV-vis method is based on surface plasma resonance, only the composition of the surface shell can be characterized. That the peaks in UV-vis spectrum stopped shifting only suggests the alloy was completely formed in the surface but gives no information about the core. Similar to our simulation, the surface formed alloy, but the core remained as pure component. Therefore, one can conclude that

Qi and Lee the UV-vis method is not enough to characterize the alloy formation in the full NPs but only that in the surface shell. To characterize the alloy formation in the full NPs, other techniques are needed. We also annealed the decahedral and icosahedral NPs at 600 K for 58 ns. The total energy variation during annealing process is similar to cuboctahedral NPs. However, for decahedral NPs, the final structure after annealing remains a core/shell structure with pure components, indicating the driving force from the FE difference between the core/shell and alloy NPs is not enough to start the alloying process. For this point, the thermodynamics and the kinetics can be explained more clearly. Since the core/shell and the alloy decahedral NPs have negative FE, thus they are more stable than the respective pure components. As the alloy NPs are more stable than the core/ shell NPs, the latter would become the former if the driving force is large enough. Annealing the decahedral core/shell NPs at 600 K for 58 ns yields fairly small final energy fluctuation, which suggests the final structure cannot become alloy NPs. Therefore, the negative FE can only give necessary but not sufficient condition for alloy formation. For icosahedral NPs, there are no Au atoms on the surface of Au/Ag core/shell NPs, which suggests interatomic diffusion is difficult in this system. But for Ag/Au core/shell NPs, some Ag atoms appear on the surface after annealing, indicating the driving force in the Ag/ Au core/shell NPs is larger than that in the Au/Ag core/shell NPs. For the three shapes studied, the formation ability of the core/shell structure is in the following sequence: cuboctaheral > icosahedral > decahedral. To further study the size effects on alloying process, we compared spherical NPs of 555 atoms (321Au/234-Ag core/shell and 321-Ag/234-Au core/shell) to NPs of 959 atoms (555-Au/404-Ag core/shell and 555-Ag/404-Au core/shell). After annealing, the surface of Ag/Au core/shell NP of 555-atom becomes a mixed structure after relaxation; however, the surface of Au/Ag core/shell NP of 555-atom remains pure Ag. For 959-atom NPs, the results are similar to 555-atom NP; i.e., after annealing, the surface of Ag/Au core/ shell NP becomes alloy, but that of Au/Ag core/shell NP almost keeps pure core/shell structure. These are similar to the above discussion on alloying of cuboctahedral NPs. Then one may conclude that the main factor affecting alloying process is the driving force, i.e., the formation enthalpy difference between core/shell and mixed structure. The Boltzmann-Arrhenius dependence of diffusivity (D) on temperature follows

(

D ) D0 exp -

∆Hd kT

)

(4)

where k is the Boltzmann constant, ∆Hd the activation enthalpy of diffusion for bulk material, and D0 the preexponential factor.22 According this equation, we can see D at higher temperature is larger than low temperature. For instance, the diffusivity at 600 K is about 108 times larger than that at 373 K at a fixed size. In general, the energy quantity of NPs is (1 - r/R) times that of the corresponding bulk materials, where r and R are the diameters of atoms and NP, respectively. Therefore, the sizedependent activation enthalpy follows ∆Hd(1 - r/R), and eq 4 becomes D ) D0 exp (-∆Hd(1 - r/R)/kT). Apparently, the diffusivity will be larger for small NPs than for larger NPs. These discussions confirm our previous assumption; i.e., simulation of smaller NPs at higher annealing temperature would produce comparable results as larger NPs annealing at low temperature for a long time.

Au-Ag Bimetallic Nanoparticles IV. Conclusions The molecular dynamic method has been used to simulate the phase stability, melting, and alloy formation of bimetallic Au-Ag NPs with cuboctahedral, decahedral, icosahedral, and spherical shapes. It is found that all core/shell and alloy NPs have negative formation energy, suggesting they are all stable. Further, the alloy NPs are more stable than the corresponding core/shell NPs. During melting, both core/shell and alloy NPs begin melting in the surface and then the core. The particle shape has a minor effect on the melting temperature. For alloying, the formation ability follows cuboctaheral > icosahedral > decahedral NPs, which suggests the shape significantly affects alloy formation. In the final structure of annealed cuboctahedral NPs, only the surface becomes alloy while the core remains pure components. The present results show that the UV-vis method alone is not capable of characterizing alloy formation in the full NPs, but only that in the surface shell. Acknowledgment. This work was supported by Research Grants Council of HKSAR (No. CityU5/CRF/08), NSF-RGC Joint Research Scheme (No. N_CityU108/08), Hunan Provincial Natural Science Foundation of China (No. 09JJ3106), and China Postdoctoral Science Foundation (No. 200801344). References and Notes (1) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. ReV. 2008, 108, 3. (2) Wei, Z. D.; Feng, Y. C.; Li, L.; Liao, M. J.; Fu, Y.; Sun, C. X.; Shao, Z. G.; Shen, P. K. J. Power Sources 2008, 180, 84. (3) Mallin, P.; Murphy, C. J. Nano Lett. 2002, 2, 1235.

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