Riccardo Ferrando

Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles

5.1. Nanoalloys of Group 11 (Cu, Ag, Au) 865 5.1.1. Cu−Ag 866 5.1.2. Cu−Au 867 5.1.3. Ag−Au 870 5.1.4. Cu−Ag−Au 872 5.2. Nanoalloys of Group 10 (Ni, Pd, Pt) 872 5.2.1. Ni−Pd 872 * To whom correspondence should be addressed. Phone: +39010 3536214. Fax:+39010 311066. E-mail: ferrando@fisica.unige.it. † Universita di Genova. ‡ Argonne National Laboratory. § University of Birmingham. | As of October 1, 2007, Chemical Sciences and Engineering Division. Volume 108, Number 3

Collective and single particle diffusion on surfaces

We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism are presented. These first three sections form an introduction to the field of surface diffusion. Section 4 contains subsections that discuss surface diffusion for various systems which have been investigated both experimentally and theoretically. The focus here is not so much on specific systems but rather on important issues concerning diffusion measurements or calculations. Examples include the influence of steps, diffusion in systems undergoing phase transitions, and the role of correlation and memory effects. Obviously, the choice of topics here reflects the interest and expertise of the authors and is by no means exhaustive. Nevertheless, these topics form a collection of issues that are under active investigation, with many important open questions remaining.

Crossover among structural motifs in transition and noble-metal clusters

The energetics of nanoclusters is investigated for five different metals (Ag, Cu, Au, Pd, and Pt) by means of quenched molecular dynamics simulations. Results are obtained for two different semiempirical potentials. Three different structural motifs are considered: icosahedra (Ih), decahedra (Dh), and truncated octahedra (TO). The crossover sizes among structural motifs are directly calculated, considering cluster up to sizes N≃40 000. For all the systems considered, it is found that icosahedra are favored at small sizes, decahedra at intermediate sizes, and truncated octahedra at large sizes. However, the crossover sizes depend strongly on the metal: in Cu, the icosahedral interval is rather large, and it is followed by a very wide decahedral window; on the contrary, in Au, the icosahedral interval is practically absent, and the decahedral window is narrow. The other metals display intermediate behaviors, Ag being close to Cu, and Pd and Pt being close to Au. A simple criterion, which is based on the rat...

Global optimization of bimetallic cluster structures. I. Size-mismatched Ag–Cu, Ag–Ni, and Au–Cu systems

A genetic algorithm approach is applied to the optimization of the potential energy of a wide range of binary metallic nanoclusters, Ag-Cu, Ag-Ni, Au-Cu, Ag-Pd, Ag-Au, and Pd-Pt, modeled by a semiempirical potential. The aim of this work is to single out the driving forces that make different structural motifs the most favorable at different sizes and chemical compositions. Paper I is devoted to the analysis of size-mismatched systems, namely, Ag-Cu, Ag-Ni, and Au-Cu clusters. In Ag-Cu and Ag-Ni clusters, the large size mismatch and the tendency of Ag to segregate at the surface of Cu and Ni lead to the location of core-shell polyicosahedral minimum structures. Particularly stable polyicosahedral clusters are located at size N = 34 (at the composition with 27 Ag atoms) and N = 38 (at the composition with 32 and 30 Ag atoms). In Ag-Ni clusters, Ag32Ni13 is also shown to be a good energetic configuration. For Au-Cu clusters, these core-shell polyicosahedra are less common, because size mismatch is not reinforced by a strong tendency to segregation of Au at the surface of Cu, and Au atoms are not well accommodated upon the strained polyicosahedral surface.

Global optimization of bimetallic cluster structures. II. Size-matched Ag-Pd, Ag-Au, and Pd-Pt systems

Genetic algorithm global optimization of Ag-Pd, Ag-Au, and Pd-Pt clusters is performed. The 34- and 38-atom clusters are optimized for all compositions. The atom-atom interactions are modeled by a semiempirical potential. All three systems are characterized by a small size mismatch and a weak tendency of the larger atoms to segregate at the surface of the smaller ones. As a result, the global minimum structures exhibit a larger mixing than in Ag-Cu and Ag-Ni clusters. Polyicosahedral structures present generally favorable energetic configurations, even though they are less favorable than in the case of the size-mismatched systems. A comparison between all the systems studied here and in the previous paper (on size-mismatched systems) is presented.

Morphological instability of core-shell metallic nanoparticles

Bimetallic nanoparticles (often known as nanoalloys) with core-shell arrangement are of special interest in several applications, such as in optics, catalysis, magnetism and biomedicine. Despite wide interest in applications, the physical factors stabilizing the structures of these nanoparticles are still unclear to a great extent, especially for what concerns the relationship between geometric structure and chemical ordering pattern. Here global-optimization searches are performed in order to single out the most stable chemical ordering patterns corresponding to the most important geometric structures, for a series of weakly miscible systems, including AgCu, AgNi, AgCo and AuCo. The calculations show that (i) the overall geometric structure of the nanoalloy and the shape and placement of its inner core are strictly correlated; (ii) centered cores can be obtained in icosahedral nanoparticles but not in crystalline or decahedral ones, in which asym- metric quasi-Janus morphologies form; (iii) in icosahedral nanoparticles, when the core exceeds a critical size, a new type of morphological instability develops, making the core asymmetric and extending it to- wards the nanoparticle surface; (iv) multi-center patterns can be obtained in polyicosahedral nanoalloys. Analogies and differences between the instability of the core in icosahedral nanoalloys and the Stranski- Krastanov instability occurring in thin-film growth are discussed. All these issues are crucial for designing strategies to achieve effective coatings of the cores.

Searching for the optimum structures of alloy nanoclusters.

Recent advances in computational methods for searching for the most stable structures of alloy nanoparticles are reviewed. A methodology based on extensive global optimization searches within an empirical potential model in conjunction with structure recognition algorithms and subsequent density-functional local relaxation of the lowest-energy structures pertaining to each different structural basin is proposed. Applications to different systems, including Cu-Ag, Cu-Au, Ni-Ag, Co-Ag, Co-Au, Ni-Au and Pd-Pt clusters, are presented.

Searching for low-energy structures of nanoparticles: a comparison of different methods and algorithms

Nanoparticles can have unusual, low symmetry or non-crystalline shapes. Since structure determines nanoparticle physical and chemical properties, many efforts have been devoted to predict what are the most stable structural motifs depending on cluster size and composition. The global optimization of the 3N-dimensional potential energy surface of a nanocluster is nevertheless a very difficult computational problem. Here we depict the scenery of the global optimization strategies applied to the study of nanoclusters, focusing on genetic and Basin-hopping approaches. Moreover, several strategies to improve Basin-hopping efficiency are discussed and compared through the optimization of test-systems with different size and composition.

Size-Dependent Transition to High-Symmetry Chiral Structures in AgCu, AgCo, AgNi, and AuNi Nanoalloys

A class of nanomaterials possessing the highest degree of chiral symmetry, the chiral icosahedral symmetry, is found by a combination of global optimization searches and first-principle calculations. These nanomaterials are core-shell nanoalloys with a Cu, Ni, or Co core and a chiral Ag or Au shell of monatomic thickness. The chiral shell is obtained by a transformation of an anti-Mackay icosahedral shell by a concerted rotation of triangular atomic islands which breaks all mirror symmetries. This transformation becomes energetically favorable as the cluster size increases. Other chiral nanoalloys, belonging to a different structural family of C(5) group symmetry, are found in the size range between 100 and 200 atoms. High-symmetry chiral nanoalloys associate strong energetic stability with potential for applications in optics, catalysis, and magnetism.

Modeling free and supported metallic nanoclusters: structure and dynamics

We compare atomic structure and dynamics of free and supported metallic clusters via molecular dynamics simulations using tight-binding semiempirical potentials for metal–metal interactions and a potential fitted to ab initio calculations for the metal-supported ones, the support being essentially the MgO(100) surface in the case of a nonreactive metal–oxide interface. The structural transition for free Ni, Pd, Pt, Cu, Ag, Au clusters with noncrystalline structures (mainly icosahedral and decahedral) at small sizes to FCC truncated octahedrons for larger sizes is reported as well as the variation of the critical size of transition from 3d to 5d metals. In the case of Pd clusters on the MgO(100) surface, we analyze the substrate-induced modifications in morphology and atomic structure and follow their evolution as a function of cluster size. The mechanism of strain release by misfit interfacial dislocations in 3D clusters is described at the atomic level. Dynamics of growth and melting of free silver clusters are discussed and some effects of the oxide substrate in melting transition are pointed out, notably the delay in melting induced by the epitaxial relation with the support.