One-dimensional disorder

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. 

On Pd(311) one-dimensional disordered structures with periodicities of 2a0 and 3a , respectively, in the [011] direction were observed (52). An interesting study was performed by Reed et al. (100) with a Ru(101) surface for which an ordered overlayer was detected whose proposed structure model is reproduced in Fig. 10. 

Substituted NH ions Whalley, 28> discussed the spectroscopic effects of orientional disorder about one axis (in contrast to the disorder about three axes as described by Whalley and Bertie 03) and Bertie and Whalley 129> in the a-phases of the methylammonium halides. In principle, all vibrations of an orientational disordered crystal are spectroscopically active, but if the disorder is only about one axis, some restrictions operate, the symmetric bands are sharp in the one-dimensional disordered case, but the bands due to asymmetric vibrations (E) are broad. Whalley use the infra-red results of Sandorfy et al. 130>131> 0f the CH3 -ammonium halides to illustrate the effect which is predicted from interionic coupling of the E-modes. No such effect is visible in the spectrum of the methoxyammonium ion CH3ONH3 reported by Nelson, 32>. 

Thermal Fluctuations in One-Dimensional Disordered Quantum Systems... 

The two Ni(omtbp)Ix materials isolated following oxidation with iodine have very different stoichiometries, x = 1.08 0.01 and 2.9 0.3, and represent the only case to date in which a porphyrinic metallomacrocycle has yielded crystals at different levels of partial oxidation. The crystal structure for the x = 1.08125 material exhibits columns of macrocycles, as illustrated in Fig. 2 a and 20. The iodine occurs as If chains which parallel the macrocyclic columns, and which exhibit an interesting one-dimensional disorder. The iodine disorder in Ni(omtbp)I1.08 is much more severe than that found in the Ni(pc)I2) or Ni(tbp) 132 1 systems (see below). In order to solve the structure of Ni(omtbp)Ii.08, the disordered iodine atom had to be treated as a statistical distribution of electron density, with the fit for both cosine and triangle-shaped distributions being comparable (Fig. 29). 

Fig. 6. One-dimensionally disordered sulfur chains adsorbed on Ni(l 11) at 0 = 0.22. Solid circles represent adsorbed sulfur atoms open circles, nickel atoms in the adsorbent surface layer (Ref. 47).

Figure 18 Synchrotron fixed-film fixed-crystal pattern obtained at LURE (France) on TTT2I3+b at 120 K. The sample has its b axis horizontal. The diffuse lines are due to a one-dimensional disorder of the I3 columns. Top left corner a magnified detail of a main Bragg reflection surrounded by two families of satellites. The latter are attributed to the existence of two families of iodine chains. (From Ref. 134.)...

Case study One-dimensional disorder in spinach ribulose bisphosphate carboxylase crystals (Pickersgill 1987)... 

ONE-DIMENSIONAL DISORDERED SYSTEMS 3.7.1 Review of Earlier Work... 

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