Close-packing rule

Such a structure does not violate the close-packing rule. In fact, the individual benzene molecules are very closely associated, but not in one dimension as a stack of plates, but rather in three dimensions. 

The fourth principle is the Principle of close packing (Rule 11.4) which relates to the distribution of cations and anions ... 

The density of a syntactic foam is determined by the relative proportions (volume fractions) of microspheres, resin matrix, and dispersed air. The theoretical lower limit of the density in a two-phase system (without dispersed air) is determined by the close packing rules for spheres. Various packing possibilities in systems containing uniform-size spheres are summarized below 8> 8S) ... 

An important reason for the exceptions to the radius ratio predictions is that ions are not hard spheres but somewhat compressible, hence do not have a truly constant radius. Another reason for the inadequacy of the radius ratio rules, particularly when the anions are much larger than the cations, is that some structures are determined by the close packing of the anions, leaving the cations in holes between the anions. In such a case more anions may be packed around a cation of a given fixed radius than are predicted by the radius ratio, so that although the anions are touching each other, they are not touching the cation. However, if... 

Rule 11.4 (Principle of close packing). Like ions tend to lie on close packed lattices, since this arrangement minimizes their repulsive energy when they are confined to a fixed volume. 

Close packing, which is described in more detail in Section 11.2.1.2, gives not only the densest packing of spheres but also represents the arrangement of lowest energy when an array of like charges is confined to a fixed volume. This rule not only applies separately to the cations and the anions in ceramics, it also applies to the arrangement of the atoms in a metal. One consequence is that the same cation lattices are found in both metals and in ceramic materials (O Keeffe and Hyde 1985). 

In order to be able to describe the ideal crystal structure , it is important to bear in mind that there are two tetrahedral cavities and one octahedral one present for every sphere in a close-packed structure. With the help of Table 4.1 and the rules for octahedral and tetrahedral coordination the description of the following crystal structures are now easily understood when we bear in mind that in an ionic crystal lattice the larger negative ions form the close-packed structure and that the octahedral and tetrahedral cavities are filled with positive ions. 

The structure of p-quartz is unique and much different from those of tridymite and cristobalite. It does not follow the rules for the PTOT system, but the notation can be applied with some qualification. In general, for close-packed structures between packing layers there are two T layers, and half way between the P layers there is an O layer. The... 

Intermetallic compounds can be "valence compounds, with structures corresponding to those of NaCl, CaF2, etc., or compounds of various compositions with all atoms in close-packed layers. Because of the deficiencies of electrons and delocalized bonding, metals are not limited by the valence rules for ionic and covalent compounds. Some intermetallic compounds have structures found only for metals (Chapter 9). 

A second general rule specifies that soaps of monovalent metal cations tend to produce O/W emulsions, while those of polyvalent metal cations will tend to produce W/O emulsions. Figure 7.3 illustrates the concept. In the example shown, the calcium ions each coordinate to two surfactant molecules that are aligned with their polar groups near the metal ion. This forces the hydrocarbon tails into a wedge-like orientation. The hydrocarbon tails in a close-packed interfacial layer are most easily accommodated if the oil phase is the continuous phase. Thus, the oriented-wedge... 

---