Stacking sequence close-packed plane

Coarse-grained or single-crystalline (bulk) PbS possesses a rock salt structure (51 type). This phase is formed by the stacking of close-packed planes of lead and sulfur atoms and can be represented as the periodic stacking sequence ABC ABC... of either lead or sulfur planes. These structure features correspond to the octahedral coordination for lead and sulfur. 

Figure 2. The octahedral 13-atom cluster. A 3-atom triangular face is in the foreground of the figure, and the abc stacking of close-packed planes is most apparent for the three vertical planes in sequence from left to right across the figure.

Bulk CdS possesses wurtzite structure ( 4 type) or zincblende structure ( 3 type). Both phases are formed by stacking of close-packed planes of cadmium and sulfur atoms. Hexagonal wurtzite structure can be represented as the periodic sequence AB AB AB... of closed-packed planes. Cubic zincblende is a sequence ABCABC... of closed-packed planes. For both structures the tetrahedral surrounding of both elements, cadmium and sulfur, takes place. According to the available literature data X-ray diffraction patterns of nanostructured CdS films and powders synthesized by different methods have similar features. Analysis of these features shows that the atomic structure of CdS nanoparticles differs from that of the bulk material. 

For the face-centered crystal structure, the centers of the third plane are situated over the C sites of the first plane (Figure 3.18a). This yields an ABCABCABC. . . stacking sequence that is, the atomic alignment repeats every third plane. It is more difficult to correlate the stacking of close-packed planes to the FCC unit cell. However, this relationship is demonstrated in Figure 3.186. These planes are of the (111) type an FCC unit cell is outlined on the upper left-hand front face of Figure 3.186 to provide perspective. The significance of these FCC and HCP close-packed planes will become apparent in Chapter 7. 

Figure 2 Schematic representation of the structure of a-AbOs. (a) Pattern of occupancy by aluminum of the octahedral sites between the hexagonal close-packed planes of oxide ions and (b) stacking sequences of successive planes of aluminum atoms...

We now consider the sphere packings in which close-packed plane layers are stacked in the closest possible way. If we label the positions of the spheres in one layer as (Fig. 4.12) then an exactly similar layer can be placed above the first so that the centres of the spheres in the upper layer are vertically above the positions B. It is obviously immaterial whether we choose the positions B or the similar positions C, as may be seen by inverting Fig. 4.12. When the third layer is placed above the second (B) layer there are alternatives the centres of the spheres may lie above either the C ot A positions. The two simplest sequences of layers are evidently... 

Sm exhibits a rhombohedral crystal structure at low temperatures. In the nine layer sequence of close packed planes, two layers of atoms with a locally hexagonal environment alternate with one atomic layer in a locally cubic environment, so that the stacking pattern is of the form hhchhchhc. Hund s rules predict a ground state of the Sm ion with L = 5, 5 = and / = i with a small theoretical saturation moment of f / B/atom. 

There are plenty of natural examples The stacking sequence of the close-packed planes, that is, 111 sets of planes in face-centered lattice (fee) are... 

Fig. 10.2. Stacking sequence of close-packed plane 111 - The sHp occurs in <110> directions, which involves the sHding of one plane over other. A to B to C by the brnger vector b = V2[101]. Open circles, A Site light-shaded circles, B Site dark-shaded circles, C Site...

Figore 3.16 (a) A portion of a close-packed plane of atoms A, B, and C positions are indicated. (6) The AB stacking sequence for close-packed atomic planes. 

A second close-packed plane may be positioned with the centers of its atoms over either B or C sites at this point, both are equivalent. Suppose that the B positions are arbitrarily chosen the stacking sequence is termed AB, which is illustrated in Fignre 3.166. The real distinction between FCC and HCP lies in where the third close-packed layer is positioned. For HCP, the centers of this layer are aligned directly above the original A positions. This stacking sequence, ABABAB. . ., is repeated over and over. Of conrse, the A CACAC.. . arrangement would be equivalent. These close-packed planes for HCP are (OOOl)-type planes, and the correspondence between this and the nnit cell representation is shown in Figure 3.17. 

Figure 3.17 Close-packed plane stacking sequence for the hexagonal close-packed structure.

Hexagonal close packed and face-centered cubic crystals are both close-packed lattices having ABAB or ABCABC stacking sequences for atom planes. 

The difference between lillianite and heyrovskyite is in the width of the galenalike slabs. Counting the number of close-packed sulfur planes in each slab gives a stacking sequence of (6, 6) for lillianite and (9, 9) for heyrovskyite. Synthetic and mineral samples contain other members of the series in which the PbS slab regions have other... 

The difference between the fee and hep structures is best seen if one considers the sequence of close-packed layers. For fee lattices this is the (111) plane (see Fig. A.l), for hep lattices the (001) plane. The geometry of the atoms in these planes is exactly the same. Both lattices can now be built up by stacking close-packed layers on top of each other. If one places the atoms of the third layer directly above those of the first, one obtains the hep structure. The sequence of layers in the <001> direction is ababab, etc. In the fee structure, it is every atom of the fourth layer that is above an atom of the first layer. The sequence of layers in the <111> direction is abcab-cabc... 

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