Crystal stacking sequence

There are three possible arrangements of atoms in a layer of SiC crystal, and each type has the same layers but a different stacking sequence (29). Designation (30) is by the number of layers in the sequence, followed by H, R, or C to indicate whether the type belongs to the hexagonal, rhombohedral, or cubic class. 

Fig. 1. Crystal structures of (a) cubic diamond and (b) lonsdaleite. A, B, and C indicate the stacking sequence of sheets of atoms.

On silicon carbide, it is easier to see and measure step heights than in crystals like beryl, because SiC has polytypes, first discovered by the German crystallog-rapher Baumhauer (1912). The crystal structure is built up of a succession of close-packed layers of identical structure, but stacked on top of each other in alternative ways (Figure 3.24). The simplest kind of SiC simply repeats steps ABCABC, etc., and the step height corresponds to three layers only. Many other stacking sequences... 

This is achieved by coupling the system to a suitably defined order parameter that is sensitive to the crystal order (the stacking sequence of 111 planes in this case), and doing umbrella sampling with this quantity. The result of the simulation is the free energy difference between both candidate structures—and the winner is fed... 

Zeolite structures sometimes remain unsolved for a long time, because of either their complexity, the minute size of the crystallites or the presence of defects or impurities. One extreme example of stacking disorder is provided by zeolite beta [1,2], Different stacking sequences give rise to two polymorphs (A and B) in zeolite beta that always coexist in very small domains in the same crystal. Not only do the small domains make the peaks in the powder X-ray diffraction pattern broad and thereby exacerbate the reflection overlap problem, but the presence of stacking faults also gives rise to other features in the diffraction pattern that further complicate structure solution. 

Because the cubic ZB and hexagonal WZ crystal structures described in Sect. 2.2 are energetically very similar and differ only in their stacking sequence, in a number of semiconductors either or both forms may be present depending upon growth conditions. Figure 7 shows how MAS-NMR on nuclei of both elements in GaN can clearly distinguish the more stable WZ form from the less common ZB form. 

A table of crystal structures for the elements can be found in Table 1.11 (excluding the Lanthanide and Actinide series). Some elements can have multiple crystal structures, depending on temperature and pressure. This phenomenon is called allotropy and is very common in elemental metals (see Table 1.12). It is not unusual for close-packed crystals to transform from one stacking sequence to the other, simply through a shift in one of the layers of atoms. Other common allotropes include carbon (graphite at ambient conditions, diamond at high pressures and temperature), pure iron (BCC at room temperature, FCC at 912°C and back to BCC at 1394°C), and titanium (HCP to BCC at 882°C). 

Fig. 8. Crystal structure of M0S2. (a) Side view of a single-layer S-Mo S slab of M0S2. The molybdenum atoms (dark) are coordinated to six sulfur atoms (bright) in a trigonal prismatic coordination, (b) Within each layer, the sulfur lattice (and the molybdenum lattice) are hexagonal ly arranged with inplane interatomic distances tZs s or i/m., no equal to 3.15A. (c) Illustration of the 2II-M0S2 stacking sequence of successive layers in bulk M0S2. The distance between the molybdenum layers is 6.15 A.

If a (full) dislocation has passed through a crystal, its surface shape is affected. If a partial dislocation has passed through a crystal, the stacking sequence is disturbed across the glide plane. If bundles of partial dislocations pass through a crystal in a certain order, they may change the crystal structure by correlated atomic displacements, for example, from fee to hep. 

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