Crystalline solids packing efficiency

Crystalline solids consist of periodically repeating arrays of atoms, ions or molecules. Many catalytic metals adopt cubic close-packed (also called face-centred cubic) (Co, Ni, Cu, Pd, Ag, Pt) or hexagonal close-packed (Ti, Co, Zn) structures. Others (e.g. Fe, W) adopt the slightly less efficiently packed body-centred cubic structure. The different crystal faces which are possible are conveniently described in terms of their Miller indices. It is customary to describe the geometry of a crystal in terms of its unit cell. This is a parallelepiped of characteristic shape which generates the crystal lattice when many of them are packed together. 

Linear and branched polymers do not form crystalline solids because their long chains prevent efficient packing in a crystal lattice. Most polymer chains have crystalline regions and amorphous regions ... 

Crystalline solids consist of particles tightly packed into a regular array called a crystal lattice. The unit cell is the simplest portion of the crystal that, when repeated, gives the crystal. Many substances crystallize in one of three types of cubic unit cells, which differ in the arrangement of the particles and, therefore, in the number of particles per unit cell and how efficiently they are packed. 

Previously known as cyclopolyphosphates, these rings may contain up to 12 tetrahedra, but those with three, four, and six units are most common (see Table 1). The cyclotri- and cyclotetraphosphate rings adopt puckered geometries typical of saturated six and eight atom rings. The predominance of even membered cyciophosphates reflects their ability to pack efficiently in the solid state, rather than any inherent stability over odd membered ones. This is often reflected by a high internal symmetry in the crystalline state an analysis of thirty reliably determined cyclohexaphosphate structures shows that 18 have inversion symmetry and a further seven have threefold (Dsd) internal symmetry. ... 

For solid materials, the packing of the constiment particles into a regular array, or lattice, often provides the first sim-pUfying component for building a model. There are important disordered, or amorphous, solids, but the order in crystalline solids makes them much easier to understand. A crystalline solid can be described at the atomic/molecular level in terms of its packing efficiency or coordination number. 

The structures adopted by crystalline solids are those that bring particles in closest contact to maximize the attractive forces between them. In many cases the particles that make up the solids are spherical or approximately so. Such is the case for atoms in metallic solids. It is therefore instructive to consider how equal-sized spheres can pack most efficiently (that is, with the minimum amount of empty space). 

The barrier efficiency of lipids also depends on their physical state (solid fat content at the temperature of use, crystalline form, etc.). Indeed, many lipids exist in a crystalline form and each individual crystal is impervious to water vapour. Water flow permeates mainly between crystals and the intercrystalline packing arrangement has major consequences on the barrier properties of the material (Martini et al. 2006). 

Desiraju has reported a crystalline supramolecular wheel-and-axle compound with a structure based on a carboxylic acid dimer.33 Specifically, the group predicted that 4-(triphenylmethyl)benzoic acid would self-assemble to give a homodimer. The dimer was expected, owing to an inability to efficiently pack, to form inclusion compounds that host solvent molecules as guests. Such inclusion would be reminiscent of structurally similar organic molecules that serve as wheel-and-axle compounds in the solid state. The homodimer would, thus, circumvent a covalent synthesis. As predicted, the carboxylic acid formed a homodimer that produced solids that exhibited solvent inclusion (Fig. 15). The packing was dominated by... 

---