Unit-cell twinning

Many structures can be thought of as built from twinned fragments within the unit cell. The phenomenon is referred to as chemical twinning (CT), or unit cell twinning. As the size of the twin fragments increases, different structure types arise, all related as in homologous series. 

IR-11.4.5 Defect clusters and use of quasi-chemical equations IR-11.5 Phase nomenclature IR-11.5.1 Introduction IR-11.5.2 Recommended notation IR-11.6 Non-stoichiometric phases IR-11.6.1 Introduction IR-11.6.2 Modulated structures IR-11.6.3 Crystallographic shear structures IR-11.6.4 Unit cell twinning or chemical twinning IR-11.6.5 Infinitely adaptive structures IR-11.6.6 Intercalation compounds IR-11.7 Polymorphism IR-11.7.1 Introduction IR-11.7.2 Use of crystal systems IR-11.8 Final remarks IR-11.9 References... 

Theta-1 and ZSM-23, for example (Figure 2.10), contain the same sheets related either by translation or by mirror planes ( unit cell twinning ), as do RUB-13 and ITQ-3. ... 

Figure 2.10 Comparison of the structures of the lOMR zeolites Theta-1 and ZSM-23 shows that ZSM-23 is related to Theta-1 by unit cell twinning. The photograph illustrates the unit cells of the two related structures.

Crystal structures of a large number of complex sulfides can be described as composed of rods, blocks or layers of simple, archetypal structures that are joined (recombined) in various ways by the action of one or more structure-building operators, such as the various kinds of unit-cell twinning. The resulting structures were denoted as the recombination structures by the Subcommittee on the Nomenclature of Inorganic Structure Types (Lima-de Faria et al., 1990). It is this kind of complex sulfides we deal with in the present review those with complex chemistry but simple structural principles (e.g., the substitution-, interstitial- or omission derivatives of archetypal stmctures) are not included. 

It is well known that in rutile-like structures the planes [Oil] and [0 3 1] are twinning planes. Hence, Chabre and Pannetier concluded that twinning faults in the planes [0 2 1] and [0 6 1] (the equivalent planes in the ramsdel-lite doubled unit cell) are the explanation for some features in the diffraction patterns of y — Mn02 e.g., the lineshift of the (1 1 0) reflection toward lower angles or the merging of the reflection groups (h 2 1 )/(h 4 0) and (h 6 1 )/(h 0 2). 

In the paramagnetic regime, the evolution of the EPR line width and g value show the presence of two transitions, observed at 142 and 61 K in the Mo salt, and at 222 and 46 K in the W salt. Based on detailed X-ray diffraction experiments performed on the Mo salt, the high temperature transition has been attributed to a structural second-order phase transition to a triclinic unit cell with apparition of a superstructure with a modulation vector q = (0,1/2, 1/2). Because of a twinning of the crystals at this transition, it has not been possible to determine the microscopic features of the transition, which is probably associated to an ordering of the anions, which are disordered at room temperature, an original feature for such centrosymmetric anions. This superstructure remains present down to the Neel... 

Figure 3.22 A (101) twin plane in rutile, Ti02. The two parts of the crystal are related by mirror symmetry. The unit cells in the two parts are shaded.

Figure 8.12 Basal (001) plane of YBa2Cu307 containing a [110] twin boundary. The projection of the unit cell is outlined. The dopant oxygen atoms run along the b axis in each twin.

The water and A1 contents decrease while the amount of M cations per unit cell of zeolite increases. For Li and Na,the morphology consists of clusters of polycrystalline aggregates. Better outlined single crystals are observed for K and Rb and additional pronounced twinning appears for (Cs)ZSM-5 (Figure 10). 

The introduction to this chapter mentions that crystals often contain extended defects as well as point defects. The simplest linear defect is a dislocation where there is a fault in the arrangement of the atoms in a line through the crystal lattice. There are many different types of planar defects, most of which we are not able to discuss here either for reasons of space or of complexity, such as grain boundaries, which are of more relevance to materials scientists, and chemical twinning, which can contain unit cells mirrored about the twin plane through the crystal. However,... 

Before interface energy was understood, the concept was explained by Friedel [2] in terms of a compound or twin lattice. This may be explained as follows (see Fig. 7.2). If the lattice of one individual crystal is extended to superpose that of the other, where both are projected onto the same plane, a new lattice consisting of common lattice points results. This lattice is called a twin lattice or compound lattice, and the twin index is defined by the number of multiples of the unit cell size of a single crystal. The smaller the twin index, the higher the probability that twinning will occur. 

Fig. 2.58 Structure of FcjC (cementite)-type, (3, 3)hcp Fej C , projected on (001). Large circles are metal atoms and small ones are carbon atoms. Heights are in units of c/100. On the left are drawn the M C prisms and on the right the empty Mg octahedra. The arrows indicate the twin planes. The unit cell is outlined.

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