ABC Packing

The closest packing arrangement of uniform spheres. In each layer a given sphere is surrounded by six others, (a) aba packing The second layer is like the first, but it is displaced so that each sphere in the second layer occupies a dimple in the first layer. The spheres in the third layer occupy dimples in the second layer so that the spheres in the third layer lie directly over those in the first layer (aba), (b) abc packing The spheres in the third layer occupy dimples in the second layer so that no spheres in the third layer lie above any in the first layer (abc). The fourth layer is like the first. 

For the face-centred cubic [Al, copper structure], the atoms are in ABC ABC packing, and in contact along a cube face diagonal, so that... 

The first sequence of layers (Figure 13) is sometimes referred to as AB packing, which indicates that every third layer has exactly the same orientation as the first layer. Of course, as the three-dimensional solid is built up the layers repeat ABABAB. .. The second sequence of layers (Figure 14) is referred to as ABC packing to indicate that every fourth layer is the same as the first. So the solid has the sequence ABCABC. .. 

Figure 33 The ABC packing of spheres. The more intense the color of the sphere the closer in space to the reader. Unlike figure 31, this is a side view of four layers.

Figure 8. Structure of the crystal B phase showing ABC packing.

Are emergency self-contained breathing apparatus (SCBA) or escape air packs available in the work areas involved m the ABC Co. processing ... 

Fig. 5.1. The close packing of hard-sphere atoms. The ABC slacking gives the face-centred cubic (f.c.c.) structure.

Fig. 20.26 (a) Single close-packed sheet of atoms, with the close-packed directions arrowed and (b) stacking of three close-packed planes of atoms, showing aba and abc positions... 

Cl 6c +(u,u,u +m, + m, + m + w, + w, +m) w= This structure has a rhombohedral symmetry but is usually described in terms of a triple-volume hexagonal cell, which makes comparison with the idealized Cdl2 structure simpler. The idealized unit cell is adequate for the purposes of this book. In this representation the anion layers are in cubic closest packing. .. ABC ABC ABC... The metal and nonmetal stacking sequence is... 

The simplest of structures is the rock salt structure, depicted in Figure 2.2a. Magnesium oxide is considered to be the simplest oxide for a number of reasons. It is an ionic oxide with a 6 6 octahedral coordination and it has a very simple structure — the cubic NaCl structure. The structure is generally described as a cubic close packing (ABC-type packing) of oxygen atoms in the (111) direction forming octahedral cavities. This structure is exhibited by other alkaline earth metal oxides such as BaO, CaO, and monoxides of 3d transition metals as well as lanthanides and actinides such as TiO, NiO, EuO, and NpO. 

Figure 3.20. A lateral view of different stacking sequences of triangular nets. They correspond to some typical close-packed structures. The first layer sequence shown corresponds to a superimposition according to the scheme ABABAB... (equivalent to BCBCBC... or CACACA... descriptions) characteristic of the hexagonal close-packed, Mg-type, structure. With reference to the usual description of its unit cell, the full stacking symbol indicating the element, the relative position of the superimposed layers and their distance is Mg Mg. The other sequences correspond to the schemes ABC.ABC. (Cu, cubic), ABAC.ABAC. (La, hexagonal), ACACBCBAB. (Sm, hexagonal). For Cu the constant ch of the (equivalent, non-conventional) hexagonal cell is shown which may be obtained by a convenient re-description of the standard cubic cell (see 3.6.1.3). ch = cV 3, body diagonal of the cubic cell.

The atoms are arranged in close-packed layers stacked in the ABC sequence (see the triangular net stacking symbol). 

It is a close-packed superstructure based on a face-centred cubic pseudo-cell. Distorted close-packed triangular layers are stacked in close-packed ABC sequence. 

In P", (a), the oxide packing arrangement comprises close packed layers in a cubic close packed,. .. ABC. .., stacking sequence, which continues throughout the structure. The spinel blocks are four oxide layers thick and contain AP" ions (and stabilising Li, Mg ions) distributed over tetrahedral and octahedral sites, as in spinel, MgAl204. These sites... 

The structure of layered compounds often can be described by the ABC notation, shown in conjunction with the sites between close-packed layers in Fig. 7.1. Given a close-packed layer of atoms, with atoms at positions we call A, there are three possible places to put the atoms of the next layer directly above the first layer (also in the A positions), or fitted into the interstices of the first layer, either in B or C positions. In this notation, a trigonal prism sandwich is denoted AbA, and an octahedral sandwich is AbC, where the uppercase letters denote the layers of chalcogen or oxygen, and the lowercase letters the layers of transition metal atoms. 

The layered oxides LiNiOj and LiCoOj also have the 3R form AbC(a)BcA(b)CaB. In this structure, the oxygen lattice considered alone has cubic close packing ACBACB (or equivalently ABCABC). As a result, these compounds are closely related to cubic compounds. To visualise the structure of LiNiOj or LiCoOj, for example, start from cubic NiO or CoO (AbCaBcAbCaB), and replace every second layer of Ni or Co by Li. In the case of Ni this replacement may be incomplete, and the Li layers may contain residual Ni (Dahn, von Sacken and Michal, 1990b). 

---