Density functional theory global optimization of chemical ordering in AgAu nanoalloys

Highlights

• Optimal chemical ordering in small AgAu nanoalloys depends on the cluster shape.

• Strong surface enrichment in Au for icosahedral nanoalloys.

• Charge transfer and stress effects are at the origin of chemical ordering behaviour.

Abstract

The chemical ordering in AgAu nanoalloys is determined by global optimization searches at the DFT level. A simulation code based on the Basin Hopping algorithm is developed and applied to truncated octahedral nanoalloys of 38 atoms and to icosahedral nanoalloys of 55 atoms. The optimization results show a different behaviour of these clusters for what concerns the optimal chemical ordering on the Ag-rich side. In the truncated octahedron, up to two Au atoms are accommodated in the cluster core, while in the icosahedron, all atoms are placed on the surface. When increasing Au content, string-like Au patterns form on the cluster surface. The different behaviours of the icosahedron and of the truncated octahedron are rationalized in terms of the electronic properties of these nanoalloys, which demonstrate that a subtle interplay of charge transfer and stress effects is taking place.

Introduction

Binary metallic clusters and nanoparticles, often referred to as nanoalloys, have been recently the subject of intense research activity both experimentally and computationally [1,2]. In particular, the AgAu system has been studied in view of applications to catalysis (for example in CO oxidation [3,4]) and to plasmonics, because of its sharp and tunable surface plasmon resonance [[5], [6], [7]].

In general, catalytic and optical properties of nanoalloys crucially depend on chemical ordering. Chemical ordering is the pattern in which the two atomic species are arranged in the nanoalloy. Several types of chemical ordering are possible, from phase-separated to intermixed (alloyed) ones, to intermetallic compounds. At equilibrium, AgAu is a highly miscible system in the bulk, forming solid solutions for all compositions [8]. For this reason, intermixing may be expected at the nanoscale. But in cluster and nanoparticles, the number of surface atoms is often comparable (if not larger) than the number of inner atoms, so that non-trivial effects may occur [9]. In particular, in AgAu, surface segregation effects may induce some kind of phase separation.

Chemical ordering in AgAu nanoalloys has been studied in several experiments [[5], [6], [7],10]. Experimentally, it may be difficult to determine whether a nanoparticle structure reflects thermodynamic equilibrium or the formation kinetics. Indeed, there are cases in which the final chemical ordering is determined by kinetic effects [11]. Anyway, the determination of the equilibrium configurations is of great importance since it gives the reference state to which kinetically formed clusters should tend in the long time limit. If temperature is sufficiently low, equilibrium is dominated by low-energy structures. The problem of determining the lowest-energy structure of a cluster of given size and composition is known as the global optimization problem [12]. For nanoalloys, the general global optimization problem implies find both the optimal cluster shape and the optimal chemical ordering [1,2]. For many applications, such as in catalysis, the optimal chemical ordering is indeed of crucial importance, especially for what concerns the composition of the surface and subsurface shells [13].

In this paper we focus on the optimization of chemical ordering of AgAu clusters of given geometric structure. This is what is usually termed as the search of the best homotop [14], since homotops are isomers differing for their chemical ordering but not for their geometric structure (apart from local relaxations). We describe the interactions in our clusters by using Density Functional Theory (DFT) methods. We consider both fcc truncated octahedral clusters and icosahedral clusters, of sizes of 38 and 55 atoms, respectively. Global optimization searches are performed by the Basin Hopping (BH) method [15]. DFT-based global optimization is computationally demanding, being limited now to cluster sizes of a few ten atoms [16].

DFT results about very small clusters indicated that Au prefers to occupy low-coordination sites [17,18]. This result, confirmed also in calculations for clusters of a few hundred atoms [19,20], is somewhat surprising, since Ag has lower cohesion and surface energies than Au, so that Ag surface enrichment might be expected [1], at least in the bulk limit. The preferred occupation of low-coordination sites by Au was attributed to charge-transfer effects [18,19]. If charge transfer is not included, atomistic modelling results by the second-moment tight-binding potential (SMTB, also known as Gupta potential) show that low-coordination sites are preferentially occupied by Ag [21], in contrast with DFT results [18,19,22]. The experimental data about the synthesis of AgAu nanoalloys in the size range between 1 and a few nanometers show indeed that the transition towards the bulk behaviour, in which Ag segregation is prevalent, is not yet accomplished. In fact, for these sizes, several types of chemical ordering have been produced (see for example [1]). When preparing core@shell clusters as initial configuration, a considerable intermixing of the core and shell materials has been observed, which has been especially strong in Ag@Au clusters [6]. The transition towards the bulk-like behaviour is likely to be completed for somewhat larger sizes, of about 10 nm [10], but the actual transition size range is not precisely determined yet.

Since the experimentally produced structures show this quite complex behaviour, calculations can be useful to understand what are the most favourable structures from the energetic point of view. To this end, DFT calculations are necessary, since atomistic modelling is not sufficiently accurate especially for cluster sizes of a few ten atoms. In the following we will perform a full-DFT searches of the lowest-energy chemical ordering in AgAu nanoalloys, considering two sizes, 38 and 55 atoms, corresponding to face-centered-cubic (fcc) and icosahedral clusters, respectively. For each size, we consider several compositions.