Análisis de la encuesta a los padres de familia del centro educativo

Generally the crystal structure of large nanoparticles is the same as the bulk structure with somewhat different lattice parameters. X-ray studies of 80-nm aluminum particles have shown that it has the face-centered cubic (FCC) unit cell shown in Fig. which is the structure of the unit cell of bulk aluminum. However, in some instances it has been shown that small particles having diameters of nm may have different structures. For example, it has been shown that 3-5-nm gold particles have an icosahedral structure rather than the bulk FCC structure. It is of interest to consider an aluminum cluster of 13 atoms because this is a magic number. Figure shows three possible arrangements of atoms for the cluster. On the basis of criteria of maximizing the number of bonds and minimizing the number of atoms on the surface, as well as the fact that the structure of bulk aluminum is FCC, one might expect the structure of the particle to be FCC. However, molecular

Figure 4.6. (a) The unit cell of bulk aluminum; (b) three possible structures of a face-centered cubic structure (FCC), an hexagonal close-packed structure (HCP), and an icosahedral (ICOS) structure.

4.2. METAL NANOCLUSTERS

1.02

1.01

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0.99

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orbital calculations based on the density functional method predict that the icosahedral form has a lower energy than the other forms, suggesting the possibility of a structural change. There are no experimental measurements of the structure to verify this prediction. The experimental determination of the structure of small metal nanoparticles is difficult, and there are not many structural data available. In the late 1970s and early G. D. Stien was able to determine the structure of and nanoparticles. The particles were made using an oven to vaporize the metal and a supersonic expansion of an inert gas to promote cluster formation. Deviations from the face-centered cubic structure were observed for clusters smaller than 8 nm in diameter. Indium clusters undergo a change of structure when the size is smaller than 5.5 nm. Above 6.5 nm, a diameter corresponding to about 6000 atoms, the clusters have a face-centered tetragonal structure with a ratio of 1.075. In a tetragonal unit cell the edges of the cell are perpendicular, the long axis is denoted by and the two short axes by a. Below -6.5 nm the ratio begins to decrease, and at 5 nm = 1, meaning that the structure is face-centered cubic. Figure 4.7 is a plot of versus the diameter of indium nanoparticles. It needs to be pointed out that the structure of isolated nanoparticles may differ from that of ligand-stabilized structures. Ligand stabilization refers to associating nonme- tal ion groups with metal atoms or ions. The structure of these kinds of tructured materials is discussed in Chapter 10. A different structure can result in a

1.05

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DIAMETER (nm)

Figure 4.7. Plot of the ratio of the length of the c axis to the a axis of the tetragonal unit cell of

indium nanoparticles versus the diameter of nanoparticles. [Plotted from data in A. Yokozeki and

Table 4.1. Calculated binding energy per atom and atomic separation in some aluminum nanoparticles compared with bulk aluminum

Cluster Binding Energy Separation 2.77 3.10 Bulk 3.39 2.814 2.75 2.86

change in many properties. One obvious property that will be different is the electronic structure. Table 4.1 gives the result of density functional calculations of

some of the electronic properties of Notice that binding energy per atom in is less than in the bulk aluminum. The cluster has an unpaired electron in the outer shell. The addition of an electron to form closes the shell with a significant increase in the binding energy. The molecular orbital approach is also able to account for the dependence of the binding energy and ionization energy on the number of atoms in the cluster. Figure 4.8 shows some examples of the structure

of boron nanoparticles of different sizes calculated by density functional theory. Figures 4.6 and 4.8 illustrate another important property of metal nanoparticles. For these small particles all the atoms that make up the particle are on the surface. This has important implications for many of the properties of the nanoparticles such as their vibrational structure, stability, and reactivity. Although in this chapter we are discussing metal nanoparticles as though they can exist as isolated entities, this is not always the case. Some nanoparticles such as aluminum are highly reactive. If one were to have an isolated aluminum nanoparticle exposed to air, it would immediately react with oxygen, resulting in an oxide coating of on the surface. X-ray photoelectron spectroscopy of oxygen-passivated, aluminum nanoparticles indicates that they have a 3-5-nm layer of on the surface. As we will see later, nanoparticles can be made in solution without exposure to air. For example, aluminum nanoparticles can be made by decomposing aluminum hydride in certain heated solutions. In this case the molecules of the solvent may be bonded to the surface of the nanoparticle, or a surfactant (surface-active agent) such as oleic acid can be added to the solution. The surfactant will coat the particles and prevent them aggregating. Such metal nanoparticles are said to be passivated, that is, coated with some other chemical to which they are exposed. The chemical nature of this layer will have a significant influence on the properties of the nanoparticle. Self-assembled monolayers (SAMs) can also be used to coat metal nanoparticles. The concept of self-assembly will be discussed in more detail in later chapters. Gold nanoparticles have been passivated by self-assembly using octadecylthiol, which produces a SAM, Here the long hydrocarbon chain molecule is tethered at its end to the gold particle Au by the thio head group SH, which forms a strong S-Au bond. Attractive interactions between the molecules produce a symmetric ordered arrangement of them about the particle. This symmetric arrange- ment of the molecules around the particle is a key characteristic of the SAMs.

4.2. METAL NANOCLUSTERS 81

Figure 4.8. Illustration of some calculated structures of small boron nanoparticles. (F. J. Owens, unpublished.)