Stacking, one-dimensional

In columnar stacked one-dimensional complexes, such as the tetracyanoplatinates, with relatively short intrachain Pt—Pt separations, it is possible to postulate a simple band model by considering overlap of the filled 5dzi orbitals on individual atoms in the chain to produce a full 5dp band, and overlap of the empty 6pz orbitals to produce an empty 6pz band (Figure 1). 

It is, however, important to note tliat individual columns are one-dimensional stacks of molecules and long-range positional order is not possible in a one-dimensional system, due to tlieniial fluctuations and, therefore, a sliarji distinction between colj. and colj. g is not possible [20]. Phases where tlie columns have a rectangular (col. ) or oblique packing (col j of columns witli a disordered stacking of mesogens have also been observed [9, 20, 25,... 

Many references can be found reporting on the mathematical/empirical models used to relate individual tolerances in an assembly stack to the functional assembly tolerance. See the following references for a discussion of some of the various models developed (Chase and Parkinson, 1991 Gilson, 1951 Harry and Stewart, 1988 Henzold, 1995 Vasseur et al., 1992 Wu et al., 1988 Zhang, 1997). The two most well-known models are highlighted below. In all cases, the linear one-dimensional situation is examined for simplicity. 

Now consider an entire temporal history of this PCA. That is, consider the effective two-dimensional lattice that is formed by stacking successive one-dimensional layers on top of one another (see figure 7.4). Because of the Markovian nature of the evolution, the probability of this temporal history is given simply by... 

Unsubstituted phthalocyanines and also halogenated phthalocyanines show very poor solubility in organic solvents. In the solid state, unsubstituted phthalocyanines exhibit, in most cases, inclined one-dimensional stacking of the planar molecules. Besides other polymorphous modifications PcCu shows an x- and / -arrangement.74-75... 

Point defects are changes at atomistic levels, while line and volume defects are changes in stacking of planes or groups of atoms (molecules) m the structure. Note that the curangement (structure) of the individual atoms (ions) are not affected, only the method in which the structure units are assembled. Let us now examine each of these three types of defects in more detail, starting with the one-dimensional lattice defect amd then with the multi-dimensional defects. We will find that specific types have been found to be associated with each t3rpe of dimensional defect which have specific effects upon the stability of the solid structure. 

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. 

Equation (8.59) defines the ID interference function of a layer stack material. G (s) is one-dimensional, because p has been chosen in such a way that it extinguishes the decay of the Porod law. Its application is restricted to a layer system, because misorientation has been extinguished by Lorentz correction. If the intensity were isotropic but the scattering entities were no layer stacks, one would first project the isotropic intensity on a line and then proceed with a Porod analysis based on p = 2. For the computation of multidimensional anisotropic interference functions one would choose p = 2 in any case, and misorientation would be kept in the state as it is found. If one did not intend to keep the state of misorientation, one would first desmear the anisotropic scattering data from the orientation distribution of the scattering entities (Sect. 9.7). 

D Intensity. As already mentioned (cf. p. 126 and Fig. 8.12), the isotropic scattering of a layer-stack structure is easily desmeared from the random orientation of its entities by Lorentz correction (Eq. 8.44). For materials with microfibrillar structure this is more difficult. Fortunately microfibrils are, in general, found in highly oriented fiber materials where they are oriented in fiber direction. In this case the one-dimensional intensity in fiber direction,... 

Figure 4. Electron diffraction pattern (bottom left) of a typical disordered wol-lastonite specimen. Evidence of the disorder comes from the streaked (Tc odd) diffraction spots. The fringes shown in the dark-field image (a) are 7 A apart. Dark-field image b, taken from the streaked diffraction spots, shows a one-dimensional image of the disordered wollastonite. Dark-field image c shows a two-dimensional image which shows the haphazard stacking of the triclinic and monoclinic...

In the early stage of the development of molecular conductors based on metal complexes, partially oxidized tetracyanoplatinate salts (for example, KCP K2 [Pt(CN)4]Br0.30-3H2O) and related materials were intensively studied [6], In this system, the square-planar platinum complexes are stacked to form a linear Pt-atom chain. The conduction band originates from the overlap of 5dz2 orbitals of the central platinum atom and exhibits the one-dimensional character. 

The crystal structures of (EDT-TTFBr2)2MX4 and (EDO-TTFBr2)2MX4 are quite similar, although the space group symmetry is different in these two systems. However, this difference comes only from the conformation of terminal six-membered rings of the donor molecules, which plays no important role in the physical properties of the present salts. The donor molecules are stacked in a head-to-tail manner to form quasi-one-dimensional columns as shown in Fig. 6a. 

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