Data analysis disordered systems

The basic modem data describing the atomic stmcture of matter have been obtained by the using of diffraction methods - X-ray, neutron and electron diffraction. All three radiations are used not only for the stmcture analysis of various natural and synthetic crystals - inorganic, metallic, organic, biological crystals but also for the analysis of other condensed states of matter - quasicrystals, incommensurate phases, and partly disordered system, namely, for high-molecular polymers, liquid crystals, amorphous substances and liquids, and isolated molecules in vapours or gases. This tremendous... 

The fundamental vibrations have been assigned for the M-H-M backbone of HM COho, M = Cr, Mo, and W. When it is observable, the asymmetric M-H-M stretch occurs around 1700 cm-1 in low temperature ir spectra. One or possibly two deformation modes occur around 850 cm l in conjunction with overtones that are enhanced in intensity by Fermi resonance. The symmetric stretch, which involves predominantly metal motion, is expected below 150 cm l. For the molybdenum and tungsten compounds, this band is obscured by other low frequency features. Vibrational spectroscopic evidence is presented for a bent Cr-H-Cr array in [PPN][(OC)5Cr-H-Cr(CO)5], This structural inference is a good example of the way in which vibrational data can supplement diffraction data in the structural analysis of disordered systems. Implications of the bent Cr-H-Cr array are discussed in terms of a simple bonding model which involves a balance between nuclear repulsion, M-M overlap, and M-H overlap. The literature on M-H -M frequencies is summarized. 

See, for instance, M. Lax, in Multiple Scattering and Waves in Random Media, P. L. Chow, W. E. Kohler, and G. C. Papanicolaou, Eds., North Holland, 1981, and references therein J. Klafter and M. S. Schlesinger, Proc. Nat. Acad. Sci. U.S.A. 83, 848 (February 1986), and references therein R. Brown, Thesis, University of Bordeaux 1,1987 R. Brown et al. J. Phys. C20, L649 (1987) 21 (1988) in press. (This last work thoroughly discusses the applicability of fractal theory to isotopically mixed crystals as disordered system. Serious criticism is presented both of the analysis of the experimental data and of the fundementals of their description in the present theory of fractals. For this reason we omit all works treated there. 

For most systems, EXAFS spectra can be analyzed to yield average interatomic distances accurate to 2 pm and average coordination numbers accurate to 10-20%, if systematic errors have been minimized in both the experiment and data analysis, and if static and thermal disorder are both small. 

Single crystal ENDOR measurement is an informative but not always applicable method to identify paramagnetic species in solids. It is for instance difficult to obtain single crystals of biochemical materials. In other cases the paramagnetic species are intentionally trapped in a disordered matrix or in a frozen solution. The ENDOR lines are then usually broadened by the anisotropy of the magnetic couplings. Some data that a single crystal analysis can provide are difficult to extract from a powder sample. However, a considerable amount of information can often be obtained from ENDOR spectra of disordered systems. 

Abstract The analysis of ESR, ENDOR, and ESEEM data to extract the resonance parameters is treated. Free radicals in solution are mainly identified by their hyper-fine couplings (hfc). The analysis of ESR and ENDOR spectra by visual inspection and by computer simulation is discussed. The Schonland method to obtain the principal values and directions of the anisotropic g- and hfc- tensors from single crystal ESR and ENDOR data is presented. The modifications needed when 5 > A or / > A to obtain zero-field splitting ( i) or nuclear quadrupole coupling (nqc) tensors are considered. Examples of simulations to extract g-, hfc-, Tfs-, and n c-tensors from ESR and ENDOR spectra of disordered systems are presented. Simulation methods in pulsed ESR (1- and 2-dimensional ESEEM) studies are exemplified. Internet addresses for down-loading software for the simulation of ESR, ENDOR, and ESEEM spectra are provided. Software for the analysis of single crystal data by the Schonland method is also available. 

Nearly all experimental eoexistenee eurves, whether from liquid-gas equilibrium, liquid mixtures, order-disorder in alloys, or in ferromagnetie materials, are far from parabolie, and more nearly eubie, even far below the eritieal temperature. This was known for fluid systems, at least to some experimentalists, more than one hundred years ago. Versehaflfelt (1900), from a eareflil analysis of data (pressure-volume and densities) on isopentane, eoneluded that the best fit was with p = 0.34 and 8 = 4.26, far from the elassieal values. Van Laar apparently rejeeted this eonelusion, believing that, at least very elose to the eritieal temperature, the eoexistenee eurve must beeome parabolie. Even earlier, van der Waals, who had derived a elassieal theory of eapillarity with a surfaee-tension exponent of 3/2, found (1893)... 

For further progress towards mechanisms based models, such phenomenological descriptions shall also be examined in context with disease-related disturbances of autonomous functions. This mainly concerns disturbances of sleep-wake cycles and cortisol release which are the most reliable biological markers of mental diseases, especially major depression, and can provide objective and quantifiable parameters (e.g. EEG frequency components, cortisol blood level) for the estimation of an otherwise mainly subjective and only behaviorally manifested illness. Moreover, there is a manifold of data which interlink the alterations of the autonomous system parameters (sleep states, cortisol release) with alterations of neural dynamics. Therefore, the most promising approach also to understand the interrelations between neural dynamics and affective disorders probably goes via the analysis of mood related disturbances of autonomous functions. 

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