Nanostructured Crystals

In this section we discuss the properties of crystals made of ordered arrays of nanoparticles.

6.2.1. Natural Nanocrystals

There are some instances of what might be called "natural nanocrystals." An example is the 12-atom boron cluster, which has an icosahedral structure, that is, one with 20 faces. There are a number of crystalline phases of solid boron containing the B|2 cluster as a subunit. One such phase with tetragonal symmetry has 50 boron atoms in the unit cell, comprising four B12 icosahedra bonded to each other by an intermediary boron atom that links the clusters. Another phase consists of B!2 icosahedral clusters shown in Fig. 6.22 arranged in a hexagonal array. Of course there are other analogous nanocrystals such as the fullerene Qo compound, which forms the lattice shown in Fig. 5.7 (of Chapter 5).

6.2.2. Computational Prediction of Cluster Lattices

Viewing clusters as superatoms raises the intriguing possibility of designing a new class of solid materials whose constituent units are not atoms or ions, but rather clusters of atoms. Solids built from such clusters may have new and interesting properties. There have been some theoretical predictions of the properties of solids made from clusters such as AI12C. The carbon is added to this cluster so that it has 40 electrons, which is a closed-shell configuration that stabilizes the cluster. This is necessary far building solids from clusters because clusters that do not have closed shells could chemically interact with each other to form a larger cluster. Calculations of the face-centered cubic structure A112C predict that it would have a very small band gap, in the order of 0.05 eV, which means that it would be a semiconductor. The possibility of ionic solids made of KA1I3 clusters has been considered. Since the electron affinity of AI13 is close to that of CI, it may be possible for this cluster to form a structure similar to KC1. Figure 6.23 shows a possible body-centered structure for this material. Its calculated cohesive energy is 5.2 eV which can be compared with the cohesive energy of KC1, which is 7.19eV This cluster solid is quite stable. These calculations indicate that new solids with clusters as their subunits are possible, and may have new and interesting properties; peihaps even new high-temperature superconductors could emerge. New ferromagnetic materials could result from solids made of clusters, which have a net magnetic moment.

Figure 6.22. The icosohedral structure of a boron cluster containing 12 atoms. This cluster is the basic unit of a number of boron lattices.

6.2.3. Arrays of Nanoparticles in Zeolites

Another approach that has enabled the formation of latticelike structures of nanoparticles is to incorporate them into zeolites. Zeolites such as die cubic mineral, faujasite, (Na2,CaXAl2Si4)Oi2 ■ 8H20, are porous materials in which die pores have a regular arrangement in space. The pores are large enough to accommodate small clusters. The clusters are stabilized in the pores by weak van der Waals interactions between the cluster and the zeolite. Figure 6.24 shows a schematic of a cluster assembly in a zeolite. The pores are filled by injection of the guest material in the molten state. It is possible to make lower-dimensional nanostructured solids by this approach using a zeolite material such as mordenite, which has the structure illustrated in Fig. 6.25. The mordenite has long parallel channels running through it with a diameter of 0.6 nm. Selenium can be incorporated into these channels, forming chains of single atoms. A trigonal crystal of selenium also has parallel chains, but the chains are sufficientiy close together so that there is an interaction between them. In the mordenite this interaction is reduced significandy, and the electronic structure is different from that of a selenium crystal. This causes the optical absorption spectra of the selenium crystal and die selenium in mordenite to differ in the manner shown in Fig. 6.26.

Figure 6.23. Possible body-centered structure of a lattice made of Al13 nanoparticles and potassium (large circles). [Adapted from S. N. Khanna and P. Jena, Phys. Rev. 51, 13705 (1995).]
Figure 6.24. Schematic of cluster assemblies in zeolite pores. (With permission from S. G. Romanov et al., in Handbook of Nanostwctured Materials and Nanotechnology, H. S. Nalwa, ed., Academic Press, San Diego, 2000, Vol. 4, Chapter 4, p. 236.)

1.813 nm mordenite

Figure 6.25. Illustration of long parallel channels in a crystal of mordenite, an orthrorhombic variety of zeolite (Ca,Na2,K2)(AI2Si10)O24 7H20. (Adapted from S. G. Romanov et al., in Handbook of Nanostructured Materials and Nanotechriology, H. S. Nalwa, ed., Academic Press, San Diego, 2001, Vol. 4, Chapter 4, p. 238.)

1.813 nm mordenite

Figure 6.25. Illustration of long parallel channels in a crystal of mordenite, an orthrorhombic variety of zeolite (Ca,Na2,K2)(AI2Si10)O24 7H20. (Adapted from S. G. Romanov et al., in Handbook of Nanostructured Materials and Nanotechriology, H. S. Nalwa, ed., Academic Press, San Diego, 2001, Vol. 4, Chapter 4, p. 238.)

Figure 6.26. Optical absorption spectra of chains of selenium atoms in mordenite (solid line, Se-M) and in crystalline selenium (dashed line, t-Se) showing the shift in thepeak of the absorption, and the change in shape. [With permission V. N. Bogomotov, Solid State Comrmin. 47,181,(1983).]

6.2.4. Crystals of Metal Nanoparticles

A two-phase water toluene reduction of AuCl4~ by sodium borohydride in the presence of an alkanetiriol (Ci2H25SH) solution produces gold nanoparticles Aum having a surface coating of thiol, and embedded in an organic compound. The overall reaction scheme is

AuCVCaq) + N(CgHn)4 + (QH5Me) -> N(CgH17)4 + AuClT^HjMe) (6.10)

Essentially, the result of the synthesis is a chemical compound denoted as c-Au:SR, where SR is (Ci2H25SH)„(C6H5Me), and Me denotes the methyl radical CH3. When the material was examined by X-ray diffraction it showed, in addition to the diffuse peaks from the planes of gold atoms in the nanoparticles Aum, a sequence of sharp peaks at low scattering angles indicating that the gold nanoparticles had formed a giant three-dimensional lattice in the SR matrix. The crystal structure was determined to be a body-centered cubic (BCC) arrangement. In effect, a highly ordered symmetric arrangement of large gold nanoparticles had spontaneously self-assembled during the chemical processing.

Superlattices of silver nanoparticles have been produced by aerosol processing. The lattices are electrically neutral, ordered arrangements of silver nanoparticles in a dense mantel of alkylthiol surfactant, which is a chain molecule, n-CH3(CH2)mSH. The fabrication process involves evaporation of elemental silver above 1200°C into a flowing preheated atmosphere of high-purity helium. The flow stream is cooled over a short distance to about 400 K, resulting in condensation of the silver to nanocrys-tals. Growth can be abruptly terminated by expansion of the helium flow through a conical funnel accompanied by exposure to cool helium. The flowing nano-crystals are condensed into a solution of alkylthiol molecules. The material produced in this way has a superlattice structure with FCC arrangement of silver nanoparticles having separations of <3nm. Metal nanoparticles are of interest because of the enhancement of the optical and electrical conductance due to confinement and quantization of conduction electrons by the small volume of the nanocrystal.

When the size of the crystal approaches the order of the de Broglie wavelength of the conduction electrons, the metal clusters may exhibit novel electronic properties. They display very large optical polarizabilities as discussed earlier, and nonlinear electrical conductance having small thermal activation energies. Coulomb blockade and Coulomb staircase current-voltage curves are observed. The Coulomb blockade phenomenon is discussed in Chapter 9. Reduced-dimensional lattices such as quantum dots and quantum wires have been fabricated by a subtractive approach that removes bulk fractions of the material leaving nanosized wires and dots. These nanostructures are discussed in Chapter 9.

6.2.5. Nanoparticle Lattices In Colloidal Suspensions

Colloidal suspensions consist of small spherical particles 10-100 nm in size suspended in a liquid. The interaction between d» particles is hard-sphere repulsion, meaning that the center of the particles cannot get closer than the diameters of the particles. However it is possible to increase the range of die repulsive force between the particles in order to prevent them from aggregating. This can be done by putting an electrostatic charge on die particles. Another method is to attach soluble polymer chains to the particles, in effect producing a dense brush with flexible bristles around the particle. When the particles with these brush polymers about them approach each other, the brushes compress and generate a repulsion between the particles. In both charge and polymer brush suspensions the repulsion extends over a range that can be comparable to the size of the particles. This is called "soft repulsion." When such particles occupy over 50% of the volume of the material, the particles begin to order into lattices. The structure of the lattices is generally hexagonal close-packed, face-centered cubic, or body-centered cubic. Figure 6.27 shows X-ray densitometry measurements on a 3-mM salt solution containing 720-nm polystyrene spheres. The dashed-line plots are for the equations of state of the material, where the pressure P is normalized to the thermal energy kBT, versus the fraction of particles in the fluid. The data show a gradual transition from a phase where the particles are disordered in the liquid to a phase where there is lattice ordering. In between there is a mixed region where there is both a fluid phase and a crystal phase. This transition is called the Kirhvood-Alder transition, and it can be altered by changing the concentration of the particles or the charge on them. At high concentrations or for short-range

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