Common Solid Structures

Noteworthy also is the extensive compilation of early data on layered MX2 given by Wilson and Yoffe [37], who worked out a group-by-group correlation of transmission spectra of the compounds to available electrical and structural data and produced band models in accord with a molecular orbital approach. 

---

Solid solutions are very common among structurally related compounds. Just as metallic elements of similar structure and atomic properties form alloys, certain chemical compounds can be combined to produce derivative solid solutions, which may permit realization of properties not found in either of the precursors. The combinations of binary compounds with common anion or common cation element, such as the isovalent alloys of IV-VI, III-V, II-VI, or I-VII members, are of considerable scientific and technological interest as their solid-state properties (e.g., electric and optical such as type of conductivity, current carrier density, band gap) modulate regularly over a wide range through variations in composition. A general descriptive scheme for such alloys is as follows [41]. 

A second product is the ICE Solid-State Model Kit, developed by L. A. Mayer and G. C. Lisensky, which makes it possible to build extended three-dimensional structures Using a base with holes, templates for some 60 different structures, rods, and four sizes of spheres in radius ratios, common crystal structures can be assembled in a matter of minutes (3). Furthermore, many structures can be assembled from different perspectives by teams of students For example, the cubic NaCl unit cell can be assembled with its orientation on the face of the cube or on the body diagonal. Natural cleavage planes can be found with the kit Lifting one sphere will separate atomic planes from one another. (Contact ICE for ordering information.)... 

Vauquelin (14), A. Klaproth (6), and R. Jameson (5), alkali soluble organic constituents of soil and coal are designated as humic acids/ Collectively, these substances make up an ill-defined series of dark colored, weakly acidic solids which form whenever plant components (such as lignin) are exposed to fungal oxidases, or when coal is allowed to weather or otherwise oxidize. Some evidence now exists that humic acids isolated from these varied sources do indeed contain several common peripheral structures (2, II, 16), but by any more discriminating test, the term possesses little chemical significance or fixed meaning. 

The most common solid form of water is known as ice Ih (hexagonal ice), with the molecular structure as shown in Figure 2.1 from Durrant and Durrant (1962). In ice each water molecule (shown as a circle) is hydrogen bonded (solid lines) to four others in essentially tetrahedral angles (Lonsdale, 1958). A description of... 

It is of extreme interest to note that the calculated Tm for Nb and Ta are lower than the observed and conversely, the calculated Tm for Mo and W are higher than the observed. This fact is rather puzzling in view of the fact that all four elements have a common crystal structure of bcc. Furthermore, the four elements, Nb (sometime called Cb) Mo, Ta and W all have 4d, 5d atomic orbital and they all form continuous solid solutions with one another. Therefore, metallurgically, the four elements are totally compatible with one another which contradicts the sharp differences in their observed vs. calculated melting temperatures. To understand these differences we first look at the differences (or similarities) in their phonon dispersion curves (Fig. 1) along the three principal axes. A distinct difference is observed between the dispersion curves for Mo and W, on one hand, and those for Nb and Ta on the other in the [ 0] and [i 00] directions. 

Other amorphous solids such as polymers, being rigid and brittle below. Tg, and elastic above it, also exhibit this behavior. Table 2.1 lists the glass transition temperatures of common solid materials. Although most solid-state textbooks deal almost exclusively with crystalline materials, this text will attempt to address both the crystalline and amorphous states, describing the structure/property relationships of major amorphous classes such as polymers and glasses. 

A three-dimensional mass fractal dimension. Dm, describes the packing of particles forming an aggregate. Its value varies from 1 to 3. Unlike the Ds, which ascribes a low value to a smooth surface, the higher the value of Dm, the more densely packed is the aggregate. Mass fractal dimension of 3 corresponds to a solid structure. A lower Dm shows a loose and commonly branchier structure of the fractal aggregate (Fig. 3). 

Most salts crystallize as ionic solids with ions occupying the unit cell. Sodium chloride (Figure 13-28) is an example. Many other salts crystallize in the sodium chloride (face-centered cubic) arrangement. Examples are the halides of Li+, K+, and Rb+, and M2+X2 oxides and sulfides such as MgO, CaO, CaS, and MnO. Two other common ionic structures are those of cesium chloride, CsCl (simple cubic lattice), and zincblende, ZnS (face-centered cubic lattice), shown in Figure 13-29. Salts that are isomorphous with the CsCl structure include CsBr, Csl, NH4CI, TlCl, TlBr, and TIL The sulfides of Be2+, Cd2+, and Hg2+, together with CuBr, Cul, Agl, and ZnO, are isomorphous with the zincblende structure (Figure 13-29c). 

The definition of the term nanoparticles varies significantly depending on the scientific community where it is used. While in material sciences, the prefix nano is generally restricted to structures smaller than 10 nm or, at the most, 100 nm, the same term in pharmaceutical sciences may refer to particles with up to 1000 nm in diameter. However, when dealing with nanoparticles, there is general agreement on the phase state of the particles themselves which are supposed to be solid and dispersed in a continuous solid or fluid medium. In the following, we stick to a nomenclature that is common in pharmaceutical applications and has been proposed by Kreuter spherical nanoparticles with a compact solid structure are referred to as nanospheres, while hollow nanoparticles with a fluid content are named nanocapsules. 

The method of piperazinedione synthesis [119] illustrated above (Scheme 22) is an example of scaffold proliferation by branching out from common intermediate structures ( divergent library design ). Resin-bound bromides such as 97 are suitable for bromine displacement with primary amines to obtain acyclic precursors of piperazinediones, but direct treatment with TFA also induces cycliza-tion, providing an efficient route to analogous morpholine derivatives. The intramolecular displacement of bromine by the carboxylate seems to occur in the cleavage solution, once the acyclic intermediate has been released from the solid support. 

This section draws attention to some of the common structure types adopted by semiconductors. The diamond-type network (often referred to an adamantine solid structure) is adopted by Si and Ge the addition of dopants occurs without structural change. Related to this network is the zinc blende lattice and among compounds adopting this structure are GaAs, InAs, GaP, ZnSe, ZnTe, CdS, CdSe,... 

---