Crystals and Superlattices

The concept of a crystal as a three-dimensional lattice consisting of periodically repeating units provides no information, per se, on the structure or size of these units or of the periodicity of their repetition. With substances of low molar mass, these units are often identical to the molecules themselves, and the intermolecular distance determines the periodicity of these molecular crystals. 

Similar molecular crystals can also occur with macromolecular substances. Spherically shaped and ellipsoidal proteins produce, for example, protein crystals, with protein molecules occupying the lattice positions. The quite large voids between the lattice points and the vacant spaces within the protein molecules are filled with water or aqueous salt solution. Protein crystals consist of up to 95% water or salt solution. The channels and holes so produced are often so large that low-molar-mass substrates can penetrate and enzymatically react in these spaces. Heavy metals can also diffuse into these spaces. This effect is made use of in X-ray crystallography, since the phases of the X-ray scattering distribution can then be evaluated, and this aids the determination of the internal structure of the protein molecule (see also Section 4.4.2). 

Long-chain macromolecules only seldom form large crystals. One of the few examples is poly(oxy-2,6-diphenyl-l,4-phenylene), for which crystals up to centimeter size can be obtained from solutions in tetrachloroethane. These crystals also contain large amounts of solvent, in this case, up to 35%. 

Another special case is what are known as superlattices of certain block polymers. In the solid state, like blocks of different molecules arrange themselves into certain shapes—for example, as spherical domains of one kind of block in a continuous matrix of the other kind of block (see also Section 5.6.3). If the blocks are of approximately the same size, the spherical domains recur at regular distances. In this way, they form a lattice, which is called a superlattice because of the magnitude of the interdomain distances in comparison with atomic dimensions. 

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Yet another development of remarkable nanostmctured materials yields superlattices of nanosized objects. As there is no dear distinction between molecular crystals and superlattices formed from nanopartides, at this point reference will be made to structures composed of very similar (but most likely not exactly identical) nanopartides, namely colloidal partides in the size range 2 to 10 nm. Two excellent reviews by leading experts in the field were produced in 1998 and 2000 [19, 20], the titles of which contained the terms nanocrystal superlattices and close-packed nanociystal assemblies. These are in line with the above-outlined delimitation, although Collier et al. have also reported on molecular crystals (as above). The two reviews comprised approximately 100 pages with some 300 references, and summarized the state of the art at that time in exemplary fashion. The topics induded preparative aspects of the formation of monodisperse nanopartides of various compositions including metals, the superlattice formation itself with some theoretical background, covalent linking of nanocrystals (see below), and an appropriate description of the physical properties and characterization of the nanocrystal superlattices. 

Studying the temperature evolution of UV Raman spectra was demonstrated to be an effective approach to determine the ferroelectric phase transition temperature in ferroelectric ultrathin films and superlattices, which is a critical but challenging step for understanding ferroelectricity in nanoscale systems. The T. determination from Raman data is based on the above mentioned fact that perovskite-type crystals have no first order Raman active modes in paraelectric phase. Therefore, Raman intensities of the ferroelectric superlattice or thin film phonons decrease as the temperature approaches Tc from below and disappear upon ti ansition into paraelectric phase. Above Tc, the spectra contain only the second-order features, as expected from the symmetry selection rules. This method was applied to study phase transitions in BaTiOs/SrTiOs superlattices. Figure 21.3 shows the temperature evolution of Raman spectra for two BaTiOs/SrTiOa superlattices. From the shapes and positions of the BaTiOs lines it follows that the BaTiOs layers remain in ferroelectric tetragonal... 

The distance between metal ion clusters and the orientation of the clusters in zeolite cages depends on the zeolite hosts, and as a result the three-dimensional arrays can be described in different ways. They can be called cluster crystals or superlattices. The Na/ Na-Y cluster crystal formed by accommodation of one Na43+ cluster in each sodalite cage is written as in Equation (9.2) ... 

Clearly hydrogen is useful in decorating surfaces within crystals, and has been used in amorphous silicon in coiiparable ways [88,89,97,98] (albeit with less structural resolution), including exciting recent work on multilayered amorphous superlattices [99] the prospect of con )arable work on crystalline superlattices we also find exciting. 

An ordered arrangement of particles, colloidal crystals, is found in a wide range of scales. Opal is a typical colloidal crystal with an ordered arrangement of silica particles." Photonic crystals have been developed for the control of optical properties." A variety of supercrystals and superlattices consisting of nanoparticles are fabricated through self-assembly." When the unit particles are an amorphous material and the crystal lattices of each unit particle are not oriented, the colloidal assembly is not regarded as a mesocrystal (Fig. Ig). In contrast, colloidal crystals... 

The topic of magnetic properties of surfaces, thin films, and thin film systems (such as multilayers and superlattices) is of tremendous scientific and economic importance, not only for well-known data storage devices but also for future electronics, which may utilize the electrons spin in addition to their charge. Surfaces, interfaces, thin films, and nanostractures often display magnetic properties fundamentally different from the properties of bulk crystals, which are thus important to understand principles of magnetism. Recent experiments probed local magnetic moments (and their temperature dependencies) of films and their sur-faces/interfaces, small clusters, as well as nanowires, nanodots, and single atoms deposited on solid surfaces. 

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