Two-dimensional crystal structures

To determine the plane group of a pattern, write down a list of all of the symmetry elements that it posses, (not always easy), order them and then compare the list to the symmetry elements associated with the point groups given in Table 3.3. 

In describing a crystal structure, it is necessary to list the positions of all the atoms in the unit cell, and even in two-dimensional cases this can be a considerable chore. However, all structures must be equivalent to one of the 17 patterns described by the plane groups, and the task of listing atom positions can be reduced greatly by making use of the symmetry elements apparent in the appropriate plane group. To aid in this, each plane group is described in terms of a pair of standard dia- 

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Grazing incidence x-ray diffraction (GID) measurements have indicated that both precollapse and collapsed state monolayers at the air-water interface can be crystalline (Birdi, 1989). A general procedure was delineated that could provide near-atomic resolution of two-dimensional crystal structures of -triacontanoic acid (C29H59COOH). A monolayer composed of rod-like molecules would generally pack in such a way that each molecule has six nearest neighbors, that is, hexagonal cell. 

The topography of Complex IV with respect to the membrane has been studied both by the aid of several kinds of labelling and cross-linking techniques (see Refs. 85, 92, 95, 96, 99), and by image reconstruction of two-dimensional crystal structures [102-106]. The wealth of this information may be summarised as the model in Fig. 

From the forgoing, it is seen that in order to specify a two-dimensional crystal structure, all that needs to be specified are (i), the lattice parameters, (ii), the plane group symbol, (iii), a list of atom types together with the Wyckoff letter and the atomic coordinates. For complex crystals, it simplifies the amount of information to be recorded enormously. 

LeveiUer, R, Jacquemain, D., Leiserowitz, L., Kjaer, K., and Als-Nielsen, J., Toward a determination at near atomic resolution of two-dimensional crystal structures of amphiphihc molecules on the water surface A study based on grazing incidence synchrotron x-ray diffraction and lattice energy calculations, J. Phys. Chem. 96,10380,1992. Als-Nielsen, J., Jacquemain, D., Kjaer, K. et al.. Principles and applications of grazing incidence x-ray and neutron scattering from ordered monolayers at the air-water interface, Phys. Rep. 246, 251, 1994. 

Kautksy, H. 1952. Two-dimensional crystal structures in compounds of silicon. Z. Naturforsch. 7b 174-183. 

If molecules are consirained in two dimensions at a substrate surface, then other phenomena can be observed in the formation of supramolecular structures, sometimes referred to as two-dimensional crystal structures. Porphyrins were... 

CS. The true two-dimensional crystal with chains oriented vertically exists at low T and high ir in the CS phase. This structure exhibits long-range translational order. 

Figure 12.3 Two-dimensional crystals of the protein bacteriorhodopsin were used to pioneer three-dimensional high-resolution structure determination from electron micrographs. An electron density map to 7 A resolution (a) was obtained and interpreted in terms of seven transmembrane helices (b).

The three-dimensional structure of the bacterial membrane protein, bac-teriorhodopsin, was the first to be obtained from electron microscopy of two-dimensional crystals. This method is now being successfully applied to several other membrane-bound proteins. 

Another example is dendritic crystal growth under diffusion-limited conditions accompanied by potential or current oscillations. Wang et al. reported that electrodeposition of Cu and Zn in ultra-thin electrolyte showed electrochemical oscillation, giving beautiful nanostmctured filaments of the deposits [27,28]. Saliba et al. found a potential oscillation in the electrodeposition of Au at a liquid/air interface, in which the Au electrodeposition proceeds specifically along the liquid/air interface, producing thin films with concentric-circle patterns at the interface [29, 30]. Although only two-dimensional ordered structures are formed in these examples because of the quasi-two-dimensional field for electrodeposition, very recently, we found that... 

The presence of triethylenetetramine in the hydrothermal synthesis of open-framework zinc phosphates results in a number of frameworks with one- to three-dimensional structures. The structures include one-dimensional ladders, two-dimensional layer structures, and one structure where the tetramine is bound to the zinc center. The structural type was highly sensitive to the relative concentration of the amine and phosphoric acid.411 Piperazine and 2-methylpiperazine can be used as templating molecules in solvothermal syntheses of zinc phosphates. The crystallization processes of the zinc compounds were investigated by real time in situ measurements of synchrotron X-ray powder diffraction patterns.412... 

Lyotropic lamellar (La) liquid crystals (LC), in a form of vesicle or planar membrane, are important for membrane research to elucidate both functional and structural aspects of membrane proteins. Membrane proteins so far investigated are receptors, substrate carriers, energy-transducting proteins, channels, and ion-motivated ATPases [1-11], The L liquid crystals have also been proved useful in the two-dimensional crystallization of membrane proteins[12, 13], in the fabrication of protein micro-arrays[14], and biomolecular devices[15]. Usefulness of an inverted cubic LC in the three-dimensional crystallization of membrane proteins has also been recognized[16]. 

Photosystem I is a membrane pigment-protein complex in green plants, algae as well as cyanobacteria, and undergoes redox reactions by using the electrons transferred from photosystem II (PS II) [1], These membrane proteins are considered to be especially interesting in the study of monomolecular assemblies, because their structure contains hydrophilic area that can interact with the subphase as well as hydrophobic domains that can interact either with each other or with detergent and lipids [2], Moreover, studies with such proteins directly at the air-water interface are expected to be a valuable approach for their two-dimensional crystallization. 

A series of aggregation structures of bilayer forming azobenzene amphiphiles, CnAzoCmN+Br, both in single crystals and cast films was determined by the X-ray diffraction method and uv-visible absorption spectroscopy. From the relationship between chemical structures and their two-dimensional supramolecular structure, factors determining the molecular orientation in bilayer structure were discussed. Some unique properties based on two-dimensional molecular ordering were also discussed. 

Based on structural analyses obtained by the electron diffraction technique, the deposited films are known to be monocrystalline in nature, and thus, can be regarded as a special case of a layer-bilayer mechanical growth forming almost two-dimensional crystals. However, there is evidence that Ba-behenate multilayers do in fact show absence of crystallization, as demonstrated by electron micrographic studies. 

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