Читать книгу Superatoms - Группа авторов - Страница 11

Puru Jena1, and Qiang Sun2,3

1 Physics Department, Virginia Commonwealth University, Richmond, Virginia, USA

2 School of Materials Science and Engineering, Peking University, Beijing, China

3 Center for Applied Physics and Technology, Peking University, Beijing, China

Atomic clusters are a group of homo‐ or hetero‐nuclear atoms that form in the gas phase when a hot plume of atoms cool through collisions with noble gas atoms. Once mass is isolated in a quadrupole or time of flight mass spectrometer, these clusters are studied with atomic precision. Although both molecules and atomic clusters are composed of a group of atoms, the similarity ends there. Molecules are found in nature and are stable under ambient conditions, while clusters are produced in the laboratory and are stable only when held in isolation. In addition, unlike molecules, clusters of any size and composition, in principle, can be formed. The early motivation for studying clusters was to understand how properties of matter evolve, one atom at a time. It was soon realized that the structure and properties of clusters are unique and do not resemble their bulk properties until their sizes are very large. Equally important, their properties vary nonmonotonically and unpredictably with size, shape, and composition. This realization gave clusters their own identity, and they came to represent a new phase of matter intermediate between the atoms and their bulk matter. The field of cluster science, born over half a century ago, has attracted scientists from different disciplines to study, understand, and manipulate their properties by changing size, shape, composition, charge, and environment [1–136]. More than 200 000 papers have appeared in this field with about 10 000 papers appearing per year over the past decade. Clusters now bridge disciplines, and their role in the design and synthesis of novel materials with tailored properties is the subject of this book.

In 1992 in an article in Physical Review Letters, Shiv Khanna and Puru Jena showed that a cluster with specific size and composition could mimic the properties of an element in the periodic table and named such a cluster as a “superatom” [137]. They further suggested that these superatoms could be used to build a three‐dimensional periodic table with superatoms forming the third dimension [138]. Furthermore, a new class of materials, called “cluster‐assembled materials” [138], can be formed by using superatomic clusters as building blocks, much as conventional materials are formed by using atoms as building blocks. This concept originated from a seminal experiment in the field of cluster science by Walter Knight and his group in 1984 [139]. These authors measured the mass spectra of Na clusters and observed that clusters containing 2, 8, 20, 40, . . . atoms are more abundant than their neighbors (see Figure 1.1). They noted that the nuclei with the same number of nucleons were already known to be very stable. In analogy with the nuclear physics, the authors termed these very stable clusters as magic clusters and showed that the origin of the magic numbers in Na clusters is due to electronic shell closure, just as the magic numbers in nuclei are due to nuclear shell closure.

Knight et al. described the electronic shell structure of Na clusters using the jellium model where the clusters were assumed to have spherical symmetry with the charges of the positive ion core distributed uniformly inside the sphere (see Figure 1.2) [140]. They assumed that valence electrons in Na clusters would behave like free electrons, similar to the conduction electrons in a Na metal. In the jellium model of a cluster, the charge density n ⁺(r) of the positive ions is given by,

Figure 1.1 Sodium cluster abundance spectrum, (a) experimental data of Knight et al. (b) Second derivative of the total energy, dashed line using Woods‐Saxon potential; solid line using the ellipsoidal shell (Clemenger‐Nilsson model).

Source: Adapted with permission from Ref. [130]. Copyright 1993 American Physical Society.

Figure 1.2 Schematic diagram of an atom and atomic orbitals (left panel) where the positively charged nucleus is localized at a point, and jellium model of a cluster where the positive charge is smeared over a sphere of finite radius with corresponding electronic orbitals (right panel).

Source: Adapted with permission from Ref. [140]. Copyright 2013 American Chemical Society.

where n ₀ is the density of the positive charge and R is the radius of the sphere. Θ(r − R) = 1 for r ≤ R and Θ(r − R) = 0 for r > R. The electrons responding to this charge distribution occupy orbitals similar to those in the atoms. The major difference is that in this case the orbitals of clusters are characterized as 1S 1P 1D 2S 1F 2P . . . . shells. Because the number of free electrons in a Na cluster is equal to the number of Na atoms, the magic numbers observed in Na clusters, namely 2, 8, 20, 40, . . . correspond to electronic shell closure of 1S², 1S² 1P⁶, 1S² 1P⁶ 1D¹⁰ 2S², 1S² 1P⁶ 1D¹⁰ 2S² 1F¹⁴ 2P⁶, . . . . orbitals, respectively. The validity of the jellium model has since been established in simple as well as noble metals. Of particular note is the Al₁₃ ⁻ cluster, which contains 40 electrons. Will Castleman and coworkers noted that Al₁₃ ⁻ with a conspicuous peak in the mass spectra is indeed a very stable cluster [141] and is much less reactive toward oxygen than the neighboring clusters (Figure 1.3). In addition, Al₁₃, having an icosahedral geometry, also represents an atomically shell closed structure. The extraordinary stability of Al₁₃ ⁻, therefore, derives from both electronically and atomically closed shell system.

The above findings led Khanna and Jena to propose that neutral Al₁₃ cluster, with 39 electrons should behave the same way as a halogen atom, as both need one extra electron to close their electronic shells, the former being consistent with the jellium rule and the latter being consistent with the octet rule [137]. Indeed, calculations and experiments showed that the electron affinity of Al₁₃, namely 3.57 eV, is identical to that of Cl [142, 143]. That Al₁₃ mimics the chemistry of halogens that was later shown theoretically [144] by studying its interaction with K. KAl₁₃ was shown to be an ionically bonded cluster just like KCl. Experimental confirmation that KAl₁₃ is indeed ionically bonded validates the superatom concept [145].

For the sake of history, it should be mentioned that properties of clusters have been linked to atoms as early as 1981 when Gutsev and Boldyrev [146] showed that the electron affinity of a cluster with composition MX _{k + 1}, where M is a metal atom with valence k and X is a halogen atom, can exceed that of a halogen atom. Note that MX _{k + 1} cluster, just like a halogen atom, would need an extra electron to close its electronic shell. Because the size of MX _{k + 1} cluster is larger than that of a halogen atom, the Coulomb repulsion experienced by the extra electron decreases as the size increases. Hence, the electron affinity of MX _{k + 1} is larger than that of X. The authors coined the word “superhalogen” to describe these clusters. In a subsequent publication, Gutsev and Boldyrev also showed that the ionization potential of a cluster with composition M _{k + 1}X is less than that of the alkali atom, M where k is the valence of atom X, and coined the word “superalkali” to describe these clusters. Thus, superhalogens and superalkalis that mimic the chemistry of alkali and halogen atoms in the periodic table, respectively, can be regarded as the first demonstration of what is now commonly termed as “superatoms.” Figure 1.4 shows an example of a three‐dimensional periodic table where superhalogens and superalkalis constitute the third dimension representing Group 1 and Group 17 elements [147].

Figure 1.3 Series of mass spectra showing progression of the etching reaction of Al anions with oxygen in 0.0 SCCM (a), 7.5 SCCM (b), and 10.0 SCCM s(c).

Source: Leuchtner, et al. [141]. © AIP Publishing.

A few years later, Saito and Ohnishi [148] noted that Na₈ satisfying electronic shell closure (1S² 1P⁶) according to the jellium model should be chemically inert like the noble gas atoms, which have their outermost s and p shells closed. Similarly, Na₁₉ lacks an electron to achieve electronic shell closure and should behave like a halogen atom. The authors termed these as “giant atoms.” However, atomic clusters neither have spherical geometries nor do their electrons behave as if they are free electrons. On the contrary, the electrons are confined within the cluster. A later calculation that took explicit account of the cluster geometry showed that Na₈ retains its geometry up to 600 K on a NaCl substrate, but it spontaneously collapses forming an epitaxial layer on a Na (110) surface [149]. When two Na₈ clusters interact, instead of remaining as individual clusters, they coalesce and form a Na₁₆ cluster. Similarly, no evidence exists to demonstrate that Na₁₉ can form a salt‐like molecule, analogous to KAl₁₃, while interacting with an alkali atom.

Figure 1.4 Three‐dimensional periodic table with superatoms mimicking the chemistry of halogens and alkalis. Examples are those of superalkalis designed using the octet rule (Li₃O, Na₃O, K₃O, Rb₃O, Cs₃O) and jellium rule (Al₃) and superhalogens designed using the octet rule (AuF₆, LiF₃, MnCl₃, BO₂) and Wade‐Mingos rule (B₁₂H₁₃).

In later years, superatoms have been described in terms of their molecular orbital structures specific to their optimized geometries. Instead of using the jellium model and identifying superatoms as they fill the jellium orbitals, superatoms are regarded as a single unit with their molecular orbitals filled much the same way as electrons fill orbitals of a single atom. The chemistry of the superatoms is then determined by the outer molecular orbitals. As an example, consider Al₁₃I₂ ⁻ [150]. Since Al₁₃ behaves as a halogen, one could regard Al₁₃I₂ ⁻ mimicking a triiodide I₃ ⁻ ion. Indeed, the outer electronic orbitals of Al₁₃I₂ ⁻ and I₃ ⁻ ion have similar features. Similarly, Al₁₄I⁻ can be viewed as Al₁₄ ²⁺.3I⁻, where Al₁₄ ²⁺ behaves like an alkaline‐earth element. Considerable research over the past couple of decades has led to the design of superatoms using electron counting rules such as the octet rule, the 18‐electron rule, Hückel's aromatic rule, and the Wade‐Mingos rule [147].

“Magnetic superatoms,” the name coined by Vijay Kumar and Yoshi Kawazoe [151], is another example of how a cluster could possess a magnetic moment just as transition and rare earth metal atoms do. An early realization of this concept dates back to the work of Rao et al. [152] who showed a Li₄ cluster confined to a tetrahedral geometry has a total spin 1 while its rhombus ground state structure has a total spin 0. That the geometry of a cluster can be linked to its underlying spin structure gives scientists an unprecedented opportunity to design magnetic superatoms where the constituent atoms are not even magnetic. Similarly, clusters of antiferromagnetic elements such as Mn can be ferromagnetic while the magnetic moments of transition metal clusters can far exceed that of their bulk value [153].

Knowing that superatoms can have properties different from the atoms, one can envision a new class of materials where these superatomic clusters are used as building blocks. One of the basic requirements for this purpose is that the superatomic clusters must be stable when assembled to a form a bulk material. This class of materials is called “cluster‐assembled materials.” The advantage of cluster‐assembled materials over atom‐assembled materials is that their underlying electronic structure is different from the electronic structure of atoms. In Figure 1.5 we present the electronic orbitals of an Al atom and compare it to that of an Al₁₃ superatom [140]. We note that the energy spacing between molecular orbitals and atomic orbitals as well as their degeneracies and energy gap between highest occupied and lowest unoccupied molecular orbitals (HOMO–LUMO) are different. As these energy levels overlap and broaden when individual atoms and superatoms are brought together, the resulting energy bands would be very different. Thus, the electronic structure of cluster‐assembled materials would be different from that of atom‐assembled materials, even though the cluster is composed of the same elemental atoms. A good example is crystals made of carbon atoms and that of C₆₀ fullerene. Graphite, the ground state of atom‐assembled carbon is metallic and made of honeycomb arrangements of layers coupled weakly with each other. Fulleride, a crystal of C₆₀, on the other hand, forms an insulating fcc lattice with weakly bonded C₆₀ clusters. Alkalization of fulleride crystal gives rise to a superconductor while intercalation of graphite by alkali atoms does not. In addition to the different electronic structure between atoms and superatoms, there are other features that contribute to the unique properties of cluster‐assembled materials. For example, in a conventional crystal there is only one length scale, namely the lattice constant, while in a cluster‐assembled material, there are two length scales – the intra‐cluster distance and the inter‐cluster distance. Clusters due to their nonspherical shape can influence the potential energy surface due to their rotational degree of freedom, while in a conventional crystal, the atoms, being spherical, do not have that freedom. The phonons generated from the lattice vibration and their coupling with electrons can also render unusual properties depending upon whether the crystal has atoms vs superatoms as building blocks.

Figure 1.5 Spin polarized electron orbitals of Al atom (left panel) and the Al₁₃ cluster (right panel).

Source: Jena [140]. © American Chemical Society.

The central question then is: how to ensure that the superatoms retain their geometry after assembly? This can be accomplished in a number of ways: (i) The superatoms should be very stable (e.g., C₆₀) and must not coalesce or deform as they come together to form a crystal. Electron counting rules as well as atomic shell closure rules can be used to identify such superatoms. Stability of clusters satisfying the jellium shell closure rule is one such scheme that is discussed in the above. However, stable superatoms can also be designed by satisfying other electron counting rules such as the octet rule for simple elements (s² p⁶), the 18‐electron rule for transition metal elements (s² p⁶ d¹⁰), 32‐electron rule for rare earth elements (s² p⁶ d¹⁰ f¹⁴), the aromatic rule for organic molecules, and the Wade‐Mingos rule for boron‐based and Zintl clusters. (ii) Endohedral doping of metal atoms can also be used as an effective strategy to stabilize clusters. (iii) Atomic clusters can be soft‐landed on a substrate and kept apart by limiting their density or (iv) coated with ligands that protect the core when assembled. In the latter two cases, it is likely that the substrate and the ligands can interact with the atomic clusters and can affect both their geometry and properties. Instead of viewing such interactions as undesired, they can be used to tailor the properties of atomic clusters by choosing the right substrate and the ligands.

In the following 11 chapters, various authors discuss how to design superatoms by using simple electron counting rules, how to stabilize them by endohedral doping of metal atoms, and how to protect them from coalescing with each other by coating them with suitable ligands, or soft‐landing them on a chosen substrate to form cluster‐based thin films. Cluster‐assembled materials and how their properties can be tailored to produce novel catalysts, magnetic materials, and materials for energy production, storage, and conversion are also discussed. The concluding chapter describes outstanding problems and provides an insight into the future developments.