Ordering of Bimetallic Nanoalloys Predicted from Bulk Alloy Phase

Article pubs.acs.org/JPCC

Ordering of Bimetallic Nanoalloys Predicted from Bulk Alloy Phase Diagrams Yuexia Wang†,‡ and Marc Hou*,‡ †

Applied Ion Beam Physics Laboratory, Institute of Modern Physics, Fudan University, Shanghai 200433, China Physique des Solides Irradiés et des Nanostructures, CP 234, Université Libre de Bruxelles, Campus de la Plaine, Boulevard du Triomphe, B-1050 Brussels, Belgium

‡

ABSTRACT: The Metropolis Monte Carlo method is used to demonstrate the relationship between the bulk phase diagram of alloys with limited miscibility and the equilibrium configurations of nanoparticles. Using the Au−Pt system as a case study, an embedded atom potential is parametrized so as to match the phase diagram exactly. The smooth temperature dependence of the short-range order parameter is shown correlated with an onion-like configuration intermediate between solid solution and phase separated states.

1. INTRODUCTION The finite size of nanomaterials is well-known for driving important properties which can be completely different from those of their bulk counterpart. Therefore, they give rise to a broad range of studies in view of applications in chemistry and in physics. Among finite-size systems, nanoalloys, that is, nanoparticles made of different metals, represent a class of materials presently attracting a fast-growing interest.1 All alloys which naturally form as bulk materials have their counterpart at the nanoscale. In addition, nanoalloy systems can be synthesized of elements which are immiscible in bulk materials.2 One of the main advantages of nanoalloys on elemental nanostructures is the possibility of tuning their properties, which is of particular interest in catalysis.3 Given the numerous amounts of different nanoalloy systems which can be synthesized, there is a strong need to establish a link from theory to application by which a fast-growing amount of knowledge fits into well-focused theoretical frameworks. One such framework is provided by phase diagrams. The extent to which a link can be established between macroscopic and nanoscopic phase diagrams is presently an active open question. The evidence for a relationship between macroscopic and finite size properties is however accepted. For instance, the same ordered solid phases as in FCC bulk miscible alloys were both observed experimentally and theoretically.4−6 On the other hand, in systems with limited miscibility, several equilibrium atomic arrangements are possible such as the core−shell7,8 and onion-like and the so-called Janus configurations characterizing the separation of the two compounds by a plane surface.9−12 Theoretically, ordering in nanoalloys is the subject of intense studies using atomistic models4−10 and global minimization searches, recently combined with DFT calculations13 for small clusters. In the present work, we develop an original methodology which allows monitoring the position of solid phase boundaries in the phase diagram by an appropriate © 2012 American Chemical Society

tuning of atomic interactions. This way, the empirical phase diagram can be reproduced, and the relationship between equilibrium configurations in the core of nanoparticles and the bulk equilibrium phase diagram can be revealed.

2. METHOD An obvious method to address this question is the Metropolis Monte Carlo (MMC). It is now commonly used for discussing phase stability and changes in nanoparticles (see ref 1 for a review). We therefore select the case study of the Au−Pt alloy. AuPt nanoalloys are synthesized according to various routes;11,14−16 they are interesting for their catalytic properties11,16−19 and were the subject of several theoretical studies.20−23 The bulk phase diagram of the AuPt alloy is represented in Figure 1. It was derived in ref 24. by a thermodynamic methodology accounting for close to 100 experimental data points for the solid−solid transition in the composition range from 15% to 100% Pt. These data points are shown in ref 24 to closely fit the calculated curve reproduced in Figure 1. In what follows, we show that the same curve can be used to predict the onion-like structure of Au−Pt nanoparticles as an intermediate between the solid solution (SS) and the precipitation phase in the low Pt side of the phase diagram, while the Pt-rich side is governed by Au site segregation. An ideal truncated octahedral (TO) particle composed of 586 atoms was selected as a representative of FCC nanoparticles to study the spatial configuration of Au and Pt atoms as a function of composition and temperature. Equilibrium configurations of both the bulk alloy and the nanoparticle are predicted by MMC with sampling in the Received: March 8, 2012 Revised: April 27, 2012 Published: April 27, 2012 10814

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Figure 1. Bulk and nanoparticle phase diagrams. Solid thick line: ref 24 and revised potential; dotted line: prediction with Johnson's potential. The nanoparticle configurations are given in italics. α′ denotes the Aurich, and α″ denotes the Pt-rich phases, respectively.

Figure 2. SRO parameter, α1, as a function of temperature for the x and (1 − x) Pt fractions as obtained with the Johnson potential (solid symbols and dashed lines) and with the modified potential for the low Pt fractions (open symbols).

isobaric−isothermal ensemble with constant numbers of Au and Pt atoms. The algorithm includes three types of trials: (1) random displacements of all of the atoms in the system; (2) site exchange in one randomly chosen pair of different species; (3) a random change of the system size. The 2 × 106 MMC steps involving a sequence of the aforementioned trials in each one are used in all of the simulations, which is enough to guarantee the convergence of calculation. To characterize the solid solution to the precipitated phase transition seen in the phase diagram, we adopt the generalization of the Cowley parameter25 to finite systems6,26

shown in Figure 1 is close to symmetrical, at variance with the empirical one. Such symmetry is a common feature of most pairwise and many-body semiempirical potential predictions. One noticeable exception is the FeCr alloy for which a change of sign of the mixing enthalpy occurs in the Fe-rich side of the phase diagram, related to magnetic frustration. 31 The embedding function developed in ref 32 and which predicts a symmetrical dependence of mixing enthalpy on composition was successfully modified to account for its change of sign on the Fe-rich side only.33 The mixing enthalpy of Au−Pt alloys is not driven by magnetism, and the asymmetry of the phase diagram has another origin. In the present work, we acknowledge that the density functional in eq 2 warrants a suitable cohesion model for the alloys. On the other hand, the pairwise repulsive term, which is needed to fulfill the equilibrium condition and charge neutrality, is somewhat arbitrary. It turns out however that the heat of solution is most sensitive to its strength.6 Therefore, like in ref 6, we use a scaling parameter, w, to the mixed repulsive term Φαβ when α ≠ β in eq 2, which is unity in the original Johnson potential. Here, to reproduce the correct asymmetry of the Au−Pt phase diagram, we allow w to be a function of composition. Using

αn = 1 − (pnAuPt + pnPtAu )

(1)

where is the probability of finding an A atom in the nth neighbor shell of B atom and we use n = 1. αn is an ensemble average. In a system disordered at short range, α1 = 0, while α1 is maximal in the case of complete phase separation. In this case, the offset of unity is the consequence of the occurrence of an interface. A semiempirical embedded atom model is used to evaluate configuration energies according to Johnson.27 Such models, fitted on both microscopic and macroscopic materials properties, are commonly used for predicting material properties from atomistic modeling. In this framework, the configuration energy of atom i is given by 1 Ei = ∑ Φαβ (rij) − Fα(ρi ) 2 i≠j (2) pAB n

where the N-body term Fα(ρi) is a functional of the local electron density ρi, due to the atoms in the vicinity of atom i, and Φαβ (rij) is an effective two-body function, symmetric in α and β which adds a repulsive component at short distances. With this potential, the energies of (100) and (111) pure Au surfaces are 1.005 J/m2 and 0.911 J/m2, respectively, quite smaller than the corresponding values of pure Pt, 1.804 J/m2 and 1.642 J/m2. The agreement with experimental values is fair.28−30

w(x) = 0.97

0 < x < 0.075

w(x) = (wi + 1 − wi)

xi − xi + 1 xi + 1 − xi

w(x) = 0.997

xi < x < xi + 1

(3)

0.5 < x < 1

the empirical phase diagram in Figure 1 is perfectly reproduced. The interpolation points in eq 3 are w = 0.97, 0.972, 0.983, 0.99, 0.995, and 0.997 for xi = 0.075, 0.1, 0.2, 0.3, 0.4, and 0.5, respectively. The dependence of the actual SRO on temperature is shown for comparison in Figure 2. The pure elemental surface energy difference and size mismatch between species tend to favor surface segregation of Au, which is found indeed well-pronounced by MMC both at the surface of bulk alloys and of the TO nanoparticle. In bulk, at low Pt fractions, a composition oscillation is predicted at the vicinity of surfaces, as often observed in miscible metal alloys.34 The surfaces are pure Au, and below 1000 K, Pt segregates beneath the Au surface as this minimizes the stress, locally. In the nanoparticle the surface shell is made of 46.4% of the 586 atoms. Hence, the whole Pt-rich side of the phase diagram

3. RESULTS AND DISCUSSION The short-range order parameter (SRO) was estimated in bulk Au−Pt with the Johnson potential as a function of temperature over the whole composition range. Selected results are given in Figure 2. The temperature dependencies are similar for x and (1 − x), where x is the Pt fraction. As a consequence, the Au− Pt phase diagram derived from the Johnson potential and 10815

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(x > 0.5) is characterized by the surface segregation of Au. Starting with pure Pt, with increasing the Au concentration, the surface Pt atoms are gradually replaced with Au, at vertices first, then at edges, at (100) facet sites, and finally at (111) facet sites. The process has been depicted in detail, for instance in ref 22, and is typical to surface segregation at polyhedral nanoparticle surfaces. On the Au-rich side of the phase diagram (x < 0.5), the composition and temperature dependencies of configurations involve the core of the nanoparticle, and typical configurations at 300 K and 700 K are shown in Figure 3.

Figure 4. Short-range order parameter, α1, in the nanoparticle as a function of temperature for selected compositions. The dotted line separates the ranges where the Janus and the onion configurations are observed.

composition dependence of the solid solution/precipitation transition temperature in the bulk. Figure 4 shows the temperature dependence of α1 at different compositions. Using α1 = 0.35 as a borderline, this figure allows predicting the nanoparticle configuration. The OC takes place at T ≤ 800 K, when x = 0.1. An OC/JC transition occurs at intermediate compositions and at a temperature which increases with the Pt fraction. There is thus a composition limit determined by the melting point of the cluster beyond which the OC is not possible. To provide further evidence for the relationship between the nanoparticle configuration and the bulk phase diagram, we artificially reduced the transition temperature in Figure 1 by decreasing the w scaling factor by 3%. In this case, the curves in Figure 4 for x = 0.3 and x = 0.4 are shifted downward. α1 is then decreased below 0.35 at all temperatures, and the JC converts to OC accordingly. Decreasing w still further, Pt and Au become fully miscible, the SRO value tends to zero, and the OC vanishes. Hence, the equilibrium OC corresponds to subsurface segregation and can be regarded as an intermediate state during the transformation of the binary nanoparticle from a solid solution to a precipitation state. The OC is possible because the transition from the solid solution to the precipitation phase is gradual with temperature, as attested by the smooth variation of the SRO in Figure 2. In our simulations the range of SRO values where the OC is obtained is 0.35 ≥ α1 ≥ 0.1. The JC is obtained for higher values and the solid solution for lower ones. The nanoparticle phase diagram is sketched accordingly in Figure 1. Since the SRO is directly accessible in bulk by X-ray diffraction and nanoparticle JC and OC by electron microscopy, an experimental assessment of this phase diagram is possible. The same correlation is found between the bulk and the nanoparticle phase diagrams of the Cu−Ni and the Au−Co systems. This is illustrated by Figure 5 with TO nanoparticles containing 586 atoms. The experimental order−disorder transition temperature of Cu0.7Ni0.3 is close to 300 K. At 700 K, we find a solid solution, at 400 K an onion-like configuration and a JC at 100 K. The potential scaling factor (see eq 3) is taken as w = 1. The experimental order−disorder transition temperature of Au0.95Co0.05 is as high as 750 K. The miscibility of the Au−Co system is indeed particularly small. Figure 5 shows that, at 1300 K, a solid solution is found, but at this temperature, the cluster is molten, an onion-like configuration

Figure 3. Snapshots at various Pt fractions at T = 300 K and T = 700 K. Black spheres: Pt atoms.

At 300 K, consistently with the bulk phase diagram, no Pt precipitation takes place in the nanoparticle when x < 0.1 and the SRO value is close to zero. Pt sits preferentially below the low coordinated Au vertices first, then below Au(100) facets, producing a similar composition oscillation as at bulk surfaces. When the Pt fraction is increased further and all sites in a layer beneath a (100) facet are filled, depending on the temperature, two scenarios are possible. At low temperature, α ≥ 0.35, precipitation is favored, and a next subsurface layer builds up. By this mechanism, a Janus-like configuration (JC) is generated. When the temperature is high enough, configurational entropy makes (111) subsurface sites easier accessible to Pt, and rather than the growth of a JC from (100), an onion-like configuration (OC) develops. We checked the relation systematically between the configuration and the temperature over the whole Au-rich composition range, and this allows us to show how the OC equilibrium appears as intermediate between SS (solid solution) and JC. Figure 4 shows the SRO value in the nanoparticle as a function of temperature. At x = 0.1, the onionlike configuration is preserved in the whole range of temperature from 100 K up to 800 K, and α1 remains close to 0.1. Above 1000 K, as in bulk, the ring dissolves, and the SRO decreases further. At this composition, the bulk phase diagram in Figure 1 indicates no precipitation. At x = 0.2, α1 > 0.4 when T ≤ 600 K and a Janus configuration is found. At higher temperature, the configuration is onion-like and α1 < 0.35. For higher concentrations, x ≥ 0.35, the OC is no more observed at any temperature, and only the JC shows up. Clearly, the SRO value α1 = 0.35 represents a turning point between the OC and the JC. It corresponds exactly to the 10816

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diagram on the repulsive component of the interaction between atoms of different kinds, we proposed a new approach which allows using the potential as a parameter, thereby helping to understand the relationship between the nanoalloy and the bulk phase diagrams. We tuned the phase diagram artificially to decrease the bulk transition temperature. This way, the correlation with the ordering in the nanoparticle on a still broader range of compositions could be achieved, and expectedly, we succeeded to predict the same correlation between nanoparticle equilibrium configurations and bulk phase diagrams for the Cu−Ni and Au−Co systems. We anticipate that the methodology applies generally to alloys with limited miscibility, and we hope that the possibility of predicting nanoalloy phase diagrams from their bulk counterpart will be useful in many practical situations.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: ++32 2 6505735. Fax: ++32 2 6505227. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS One of us (Y.W.) is thankful to the support of the China Scholarship Council, of the Natural Science Foundation of China under Grant No. 11175047, and to the Université Libre de Bruxelles for support. This work is part of the European COST MP0903 action on Nanoalloys.

Figure 5. Snapshots of Cu0.7Ni0.3 (left column) and Au0.95Co0.05 (right column) TO nanoparticles at three temperatures where solid solution, onion-like, and Janus configurations are found.

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REFERENCES

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