Fine-shape analysis

A detailed analysis of the fine shapes of the spectra of single crystals of Mnl2,... 

In addition to the absorption maxima of the carotenoids, the shape of the spectra provides important information for identification of purified carotenoid extracts or pure standard (while the identity of the standard is generally not in question, it is a good idea to check the purity by fine structure analysis). Fine structure... 

In the most simplistic means of defining particle shape, measurements may be classified as either macroscopic or microscopic methods. Macroscopic methods typically determine particle shape using shape coefficients or shape factors, which are often calculated from characteristic properties of the particle such as volume, surface area, and mean particle diameter. Microscopic methods define particle texture using fractals or Fourier transforms. Additionally electron microscopy and X-ray diffraction analysis have proved useful for shape analysis of fine particles. 

Both mechanistic analysis and synthesis are gaining in complexity. There is much stereochemical detail to keep track of in many mechanistic analyses, for example. Perhaps the most complex mechanism considered so far is that for hydroboration. If you understand why it was necessary to modify the standard mechanism for the addition of Lewis acids to alkenes to accommodate the experimental observations, you are in fine shape so far. 

The nitroxide ESR fine shape is further influenced by interaction with other paramagnetic centers. Tfre simplest case is the interaction between two nitroxide radicals at a fixed distance r with further nitroxide radicals residing at distances much longer than r (isolated spin pair). In this case, distance r in the range between 0.8 and 2 nm can be determined by analysis of the dipole-dipole broadened fine shape, limitations and different approaches to data analysis have been discussed. ... 

If the experunental technique has sufficient resolution, and if the molecule is fairly light, the vibronic bands discussed above will be found to have a fine structure due to transitions among rotational levels in the two states. Even when the individual rotational lines caimot be resolved, the overall shape of the vibronic band will be related to the rotational structure and its analysis may help in identifying the vibronic symmetry. The analysis of the band appearance depends on calculation of the rotational energy levels and on the selection rules and relative intensity of different rotational transitions. These both come from the fonn of the rotational wavefunctions and are treated by angnlar momentum theory. It is not possible to do more than mention a simple example here. 

Cross-sectional shape. See also Shape of acrylic fibers, 11 189, 190 of fibers, 11 166-167 of inflated rayons, 11 262, 263 of solvent-spun fibers, 11 207-208 Cross-section analysis, in fine art... 

Particles come in all shapes and sizes and in large numbers. Data are presented graphically using histograms, fractional plots, or cumulative plots. These graphs are primarily useful as pictures of the size distribution of the mixture. Table 15.4 gives a typical screen analysis for a 900-g sample. The measured experimental data are the mesh sizes, and the masses of the particles on each of the sieves are the masses of the residuals or fines. The other quantities are calculated. 

On the average, the requirements for application of the statistical technique to filter data were met. Analysis of the 254 measured particle size distributions in 1979 indicates that the fine aerosol volume distribution preserved its shape. The measured sulfur mass distribution followed that of the total submicron volume. By difference, it was assumed that the organics did the same. The low relative humidity at China Lake minimized the formation of aqueous solutions due to water condensation on the particles. Therefore, it is expected that the statistical technique can be used with some success with the China Lake filter data. 

As can be seen in Fig. 4.14a, the metallic deposit obtained after application of a reductive electrodeposition step in Zr02 plus ZnO mixtures consists of large irregularly-shaped grains of Zn accompanied by fine Zn column-shaped grains—as indicated by the SEM/EDX analysis depicted in Figs. 4.14b and 4.14c [234]. 

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