3D crystals

The arrangement of lattice points in a 2D lattice can be visualized as sets of parallel rows. The orientation of these rows can be defined by 2D Miller indices (hksee Figure lb). Inter-row distances can be expressed in terms of 2D Miller indices, analogous to the notation for 3D crystals. 

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

The 3D crystal structure of Dsm. baculatum [NiSeFe] hydrogenase has been solved 185), and it was indicated that the enzyme contains three [4Fe-4S] centers. A cysteine (replacing a proline usually found near the [3Fe-4S] core) provides an extra ligand, enabling the acceptance of a fourth iron site at this cluster. 

Indeed, hydrophilic N- or C-terminal ends and loop domains of these membrane proteins exposed to aqueous phases are able to undergo rapid or intermediate motional fluctuations, respectively, as shown in the 3D pictures of transmembrane (TM) moieties of bacteriorhodopsin (bR) as a typical membrane protein in the purple membrane (PM) of Halobacterium salinarum.176 178 Structural information about protein surfaces, including the interhelical loops and N- and C-terminal ends, is completely missing from X-ray data. It is also conceivable that such pictures should be further modified, when membrane proteins in biologically active states are not always present as oligomers such as dimer or trimer as in 2D or 3D crystals but as monomers in lipid bilayers. 

As a final comment, we would like to add that the tapered shape of the growing lamella observed in our simulation of 3D crystallization from the melt can be a transient form of the growing lamellae. The advancing tapered... 

Within the present model, we have many unsolved problems. Most of the present studies on 3D crystallization from the melt deal with the relatively short Cioo chain. The study of the much longer Ciooo chain is still preliminary we want to clarify more polymer-like behavior such as the reeling-in process of the chains. Since the polymers in the ideal melt are the ideal Gaussian and highly entangled, we need a much larger MD cell to accommodate such large polymers. 

D CRYSTAL STRUCTURES HOMOLOGY MODELLING MOLECULAR SIMILARITY ... 

Another characteristic point is the special attention that in intermetallic science, as in several fields of chemistry, needs to be dedicated to the structural aspects and to the description of the phases. The structure of intermetallic alloys in their different states, liquid, amorphous (glassy), quasi-crystalline and fully, three-dimensionally (3D) periodic crystalline are closely related to the different properties shown by these substances. Two chapters are therefore dedicated to selected aspects of intermetallic structural chemistry. Particular attention is dedicated to the solid state, in which a very large variety of properties and structures can be found. Solid intermetallic phases, generally non-molecular by nature, are characterized by their 3D crystal (or quasicrystal) structure. A great many crystal structures (often complex or very complex) have been elucidated, and intermetallic crystallochemistry is a fundamental topic of reference. A great number of papers have been published containing results obtained by powder and single crystal X-ray diffractometry and by neutron and electron diffraction methods. A characteristic nomenclature and several symbols and representations have been developed for the description, classification and identification of these phases. 

Crystallization and reactivity in two-dimensional (2D) and 3D crystals provide a simple route for mirror-symmetry breaking. Of particular importance are the processes of the self assembly of non-chiral molecules or a racemate that undergo fast racemization prior to crystallization, into a single crystal or small number of enantiomorphous crystals of the same handedness. Such spontaneous asymmetric transformation processes are particularly efficient in systems where the nucleation of the crystals is a slow event in comparison to the sequential step of crystal growth (Havinga, 1954 Penzien and Schmidt, 1969 Kirstein et al, 2000 Ribo et al 2001 Lauceri et al, 2002 De Feyter et al, 2001). The chiral crystals of quartz, which are composed from non-chiral Si02 molecules is an exemplary system that displays such phenomenon. 

Five amino acid residues were picked for mutation, based on the 3D crystal structure of DERA complexed with its natural substrate. 

The new aldolase differs from all other existing ones with respect to the location of its active site in relation to its secondary structure and still displays enantiofacial discrimination during aldol addition. Modification of substrate specificity is achieved by altering the position of the active site lysine from one /3-strand to a neighboring strand rather than by modification of the substrate recognition site. Determination of the 3D crystal structure of the wild type and the double mutant demonstrated how catalytic competency is maintained despite spatial reorganization of the active site with respect to substrate. It is possible to perturb the active site residues themselves as well as surrounding loops to alter specificity. 

A 3D crystal has its atoms arranged such that many different planes can be drawn through them. It is convenient to be able to describe these planes in a systematic way and Fig. 4 shows how this is done. It illustrates a 2D example, but the same principle applies to the third dimension. The crystal lattice can be defined in terms of vectors a and b, which have a defined length and angle between them (it is c in the third dimension). The box defined by a and b (and c for 3D) is known as the unit cell. The dashed lines in Fig. 4A show one set of lines that can be drawn through the 2D lattice (they would be planes in 3D). It can be seen that these lines chop a into 1 piece and b into 1 piece, so these are called the 11 lines. The lines in B, however, chop a into 2 pieces, but still chop b into 1 piece, so these are the 21 lines. If the lines are parallel to an axis as in C, then they do not chop that axis into any pieces so, in C, the lines chopping a into 1 piece and which are parallel to b are the 10 lines. This is a simple rule. The numbers that are generated are known as the Miller indices of the plane. Note that if the structure in Fig. 6.4 was a 3D crystal viewed down the c axis, the lines would be planes. In these cases, the third Miller index would be zero (i.e., the planes would be the 110 planes in A, the 210 planes in B, and the 100... 

The buried QDs form a 3D crystal where the lattice constant can be tuned continuously over several tens of nanometers by the thickness of the spacers, and the size and spacing uniformities increase with number of stacking sequences. For the size uniformity it is essential to distinguish diameter, area, and volume since they typically differ by factors of 2, respectively, 3. Some physical properties may depend on volume, some on area, and some on diameter, thus reflecting the polydispersity in a different way. For instance, the quantization energies are dominated by the smallest dimension of the QDs, which is the height in the cases discussed above. 

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