Mosaic-block structure

Fig. 4. Model of local plastic deformation of lamellae beneath the stress field of the indenter. The mosaic block structure introduces a weakness element allowing faster slip at block boundaries leading to fracture (right)...

The crystallization temperature of 2GT has been investigated in relation to fibre spinning, as has the melting behaviour and the mosaic block structure of the crystalline layers in 2GT crystallized by annealing in the highly oriented state. DTA studies have also been made on 2GT fibres, and the relationship between peak area of drawn fibres and the crystalline, intermediate, and amorphous phase indices, obtained by X-ray analysis, have been evaluated. ... 

Part 2. Melting behavior and the mosaic block structure of the crystalline layers, Polymer 18 1121-1129. 

The authors analyzed the effect of quenching, annealing, and cold-drawing on the mosaic-block structure of their films. 

Whereas Wendorff states that fatigue does not affect the crystalline regions of POM Nagamura et al. [146] report a change of the crystalline mosaic block structure of HOPE. They arrived at this conclusion by analysis of the trapping and decay behavior of 7-ray induced free radicals. 

Studies of the micromechanics of deformation in semicrystalline polyethylene in environmental stress cracking agents [107, 154, 170, 171, 204] have elucidated the role of spherulites and of the mosaic block structure and its disintegration into independent nonuniform fibrils. The morphology of crazes in amorphous PVC in liquid and vapor environment was examined by Driesen [122] and Martin et al. [198]. 

Kinematical diffraction Diffraction theory in which it is assumed that the incident beam only undergoes simple diffraction on its passage through the crystal. No further diffraction occurs that would change the beam direction after the first diffraction event. This type of diffraction is assumed in most crystal structure determinations by X-ray diffraction. Kinematical theory is well applicable to highly imperfect crystals made up of small mosaic blocks. 

Mosaic blocks (mosaic spread) Tiny blocks within a crystal structure that are slightly misoriented with respect to each other. As a result of such mosaic spread, Bragg reflections have a finite width. Extinction is weaker in a mosaic crystal than in a perfect crystal, and therefore the intensities can be predicted by the rules of kinematical diffraction. 

For a typical slit with / = 10 cm and s = 0.025 cm, a = 0.3°. But further divergence is produced by the mosaic structure of the analyzing crystal this divergence is related to the extent of disorientation of the mosaic blocks, and has a value of about 0.2° for the crystals normally used. The line width B is the sum of these two effects and is typically of the order of 0.5°. The line width can be decreased by increasing the degree of collimation, but the intensity will also be decreased. Conversely, if the problem at hand does not require fine resolution, a more open collimator is used in order to increase intensity. Normally, the collimation is designed to produce a line width of about 0.5°, which will provide adequate resolution for most work. 

The Aral Sea is positioned in the zone where geological structures of the Urals join those of Tien-Shan. The Aral depression is bordered on the west by Precambrian crystalline basement, and on the northeast - by the Central Kazakhstan massif [9]. Pre-Mesozoic rocks are highly metamorphosed, heavily distorted and broken by faults into mosaic block systems of varying altitudes. 

As a preface to a simple mathematical description of the model, let us review with a few equations the relation between the crystal structure and the diffraction experiment. The crystal structure is defined in terms of direct space, while the diffraction experiment is basically concerned with reciprocal space. In the equations below, applicable to a single tiny perfect crystallite (i.e., one mosaic block isolated from the real crystal), the equations concerned with direct space (for which the positional vector is r, expressed in Eq. (la) with base vectors a, b, c and... 

Fig. 4. Molecular model of a stack of parallel lamellae of the spherulitic structure A, interlamellar tie molecule B, boundary layer between two mosaic blocks C, chain end in the amorphous surface layer (c ilium) D, thickness of the crystalline core of the lamella E, linear vacancy caused by the chain end in the crystal lattice L. long period I, thickness of the amorphous layer (Peterlir ).

There has been discussion as to the size and distribution of the Smekal blocks in a mosaic crystal. Zwicky(i8) suggested that a lattice is subdivided into a periodic block structure with definite spacings, basing his theory in part upon the appearance... 

Even if one solves the indexing problem and then proceeds with the analysis by an evaluation of measured reflection intensities, one cannot expect to achieve an accuracy in the crystal structure data which would be comparable to those of low molar mass compounds. This is not only a result of the lack of single crystals, but represents also a principal property In small crystallites, as they are found in partially crystalline polymers, lattice constants can be affected by their size. In many cases crystallites are not only limited in chain direction by the finite thickness of the crystalline lamellae but also laterally since polymer crystallites are often composed of mosaic blocks. Existence of these blocks is indicated in electron microscopic investigations on... 

The second type includes various lamellar models which describe the fibre structure in terms of alternating layers of crystalline and noncrystalline material. Considerations of shape and intensity of SAXS patterns and crystallinity rule out any regular lamellar structure. According to Fischer and Fakirov, the crystalline lamellae consist of mosaic blocks whose size and mutual packing depend on crystallization conditions. 

For density values g > 0.92 g/cm3 the deformation modes of the crystals predominate. The hard elements are the lamellae. The mechanical properties are primarily determined by the large anisotropy of molecular forces. The mosaic structure of blocks introduces a specific weakness element which permits chain slip to proceed faster at the block boundaries than inside the blocks. The weakest element of the solid is the surface layer between adjacent lamellae, containing chain folds, free chain ends, tie molecules, etc. 

Many other examples of outwardly complex molecular structures, whose salient architectural features appear to self-assemble from their constituent building blocks, have been documented [16]. The formation of the DNA double helix from its constituent chains is perhaps the quintessential example, whilst the perfect reconstitution of the intact tobacco mosaic virus from its constituent RNA and protein monomers also exhibits all the hallmarks of a cooperative self-assembly process [17]. The same is true of ribonuclease. Reconstitution of this enzyme in the presence of mercaptoethanol, to allow reversible exchange of the four disulfide bridges, proceeds smoothly to generate eventually only the active conformation from many possible isomeric states [18], In each of these cases, the thermodynamic stability of the product is vital in directing its synthesis. These syntheses could therefore be termed product-directed. 

Another attempt to overcome the phenomenological character of nonequilibrium thermodynamics is called mosaic nonequilibrium thermodynamics. In the formulation of mosaic nonequilibrium thermodynamics, a complex system is considered a mosaic of a number of independent building blocks. The species and each process are separately described and hence the biochemical and biophysical structures of the system are included in the description. The mosaic nonequilibrium thermodynamics model can be expanded to complex physical and biological systems by adding the well-characterized steps. These steps obey the thermodynamic laws and kinetic principles. 

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