Stacking fault disorder

Stacking fault disorder and fragmentation of structures into multiplicity of layered nanocrystals (viz. in oxides, hydroxides, and graphites)... 

Fig. 4.9 Stacking of hexagonal basal planes in graphite left). Mechanical activation results in a structure with prohferation of faults in the plane stacking right). The change of stacking sequences in nearby subgrains is marked by arrows. The stacking fault disorder is corroborated from the nonuniform peak broadening or absence of hk indexed peaks in XRD pattern (see Sect. 1.3.3.3)...

Disorder in the Stacking of Ordered Layers (Stacking Fault Disorder), 58... 

Figure 1 Intrinsic stacking fault energy for chemically disordered solid solution Al-X (where X=Cu or Mg) as a function of composition.

Among crystals with stacking faults the lack of a periodic order is restricted to one dimension this is called a one-dimensional disorder. If only a few layer positions occur and all of them are projected into one layer, we obtain an averaged structure. Its symmetry can be described with a space group, albeit with partially occupied atomic positions. The real symmetry is restricted to the symmetry of an individual layer. The layer is a three-dimensional object, but it only has translational symmetry in two dimensions. Its symmetry is that of a layer group there exist 80 layer-group types. 

Aside from the ordered stacking sequences we have considered so far, a more or less statistical sequence of hexagonal layers can also occur. Since there is some kind of an ordering principle on the one hand, but on the other hand the periodical order is missing in the stacking direction, this is called an order-disorder (OD) structure with stacking faults. In this particular case, it is a one-dimensionally disordered structure, since the order is missing only in one dimension. When cobalt is cooled from 500 °C it exhibits this kind of disorder. 

We attributed the sudden increase in entropy at x 0.5 where stage 1 should begin to form to combined contributions from configurational and vibrational entropy [22], Configurational entropy goes with in-plane or the out-of-plane lithium vacancy disorder . This translates into either the formation of lower Li density layers or the presence of Li stacking faults. Indeed a possible mechanism of the stage 1 phase formation may involve a... 

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. 

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