Dynamical disorder

The term exp(-2k2c ) in (6-9) accounts for the disorder of the solid. Static disorder arises if atoms of the same coordination shell have slightly different distances to the central atom. Amorphous solids, for instance, possess large static disorder. Dynamic disorder, on the other hand, is caused by lattice vibrations of the atoms, as explained in Appendix 1. Dynamic disorder becomes much less important at lower temperatures, and it is therefore an important advantage to measure spectra at cryogenic temperatures, especially if a sample consists of highly dispersed particles. The same argument holds in X-ray and electron diffraction, as well as in Mossbauer spectroscopy. 

The preparation of single crystals is difficult, but is successful in some case, so that we are well informed about the structures (1,6,17,21,22,23). The structures of the plastic phases are related to the well-known intermetallic phase Li3Bi, where the centres of the polycyclic P7 or Pn anions surround the positions of the Bi atoms in LisBi. The orientation of the polyanions is disordered (dynamically ). For these structures this orientation leads to a typical electron density distribution of a seemingly octahedral unit. In contrast the orientation of the anions is fixed for the crystalline phases. The symmetry of the unit cells as well as the distribution of cations and anions in these M3P7 and M3P11 type structures reflect the direct relationship to the structures of the plastic phases. 

Vulnerability of the liver to injury necessitates routine evaluation of hepatic function in patients and asymptomatic individuals to avert or control adverse clinical conditions. Thus, a plethora of methods has been developed for the diagnosis of liver diseases and dysfunctions. One such method uses physical palpation to determine alterations or changes in the orientation of the liver, which provides valuable information about the organ status but the quality of information is subjective and imprecise [3]. Another common method for the diagnosis of more serious hepatic injuries involves liver biopsies coupled with biochemical tests to determine the extent of liver injury and prognosis [4-7]. However, in acute and some chronic hepatic disorders, dynamic and continuous hepatic function monitoring would be advantageous. 

Fig. 4.19 is a cross-section the actual micelle structure is three-dimensional. The assembled structure is completely nonregular rapid exchange between micelle molecules and monomeric soluble molecules occurs. Therefore, a micelle can be regarded as a disordered dynamic supramolecular assembly. In a micellar structure, the hydrophilic part of the component molecule is located on the outer surface of the micelle, in contact with the aqueous phase, which minimizes the unfavorable contact of the hydrophobic part with water. Micelles can trap organic materials hke oils in the inner hydrophobic core, so micelle formation is used in many cleaning agents. 

The displacements of atoms may take several forms (Figure 13.2). These have been described by Jack Dunitz, Verner Schomaker, and Kenneth N. Trueblood as follows The perfectly ordered crystal would have every atom firmly fixed to its own perfectly defined site in each unit cell for the entire period of observation. There are, however, various types of disorder from unit cell to unit cell. If the atom jumps to a different site, that is one kind of disorder [a mixture of static and dynamic disorder ] if it moves to and fro, that is another kind of disorder [ dynamic disorder] if it is forever in one site in a certain unit cell and in a different site in another cell, that is still another kind [static disorder]. Each of these types of vibrations, displacements, and disorder has somewhat similar effects on the intensities of Bragg reflections the effect they have in common is that they reduce these intensities by an amount that increases with increasing scattering angle, 26, as shown in Figure 13.1. 

Now that fairly precise measures of electron density can be made, atomic displacement parameters can be refined so that the best possible fit to the experimental electron-density profiles of each atom is obtained. This is done by the introduction of additional atomic parameters, one parameter if the displacements are isotropic, six if they are anisotropic. When this least-squares refinement of displacement parameters is completed, the crystallographer is then left with the problem of explaining the atomic displacement parameters so obtained in terms of vibration, static disorder, dynamic disorder, or a combination of these. 

In this work the main aspect has been concerned with the problem of electronic energy relaxation in polychro-mophoric ensembles of aromatic horaopolymers in dilute, fluid solution of a "good" solvent. In this morphological situation microscopic EET and trapping along the contour of an expanded and mobile coil must be expected to induce rather complex rate processes, as they proceed in typically low-dimensional, nonuniform, and finite-size disordered matter. A macroscopic transport observable, i.e., excimer fluorescence, must be interpreted, therefore, as an ensemble and configurational average over a convolute of individual disordered dynamical systems in a series of sequential relaxation steps. As a consequence, transient fluorescence profiles should exhibit a more complicated behavior, as it can be modelled, on the other hand, on the basis of linear rate equations and multiexponential reconvolution analysis. 

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