Subject shape anisotropy

Shape Change of Structural Entities. In many cases the growing anisotropy is not only a phenomenon of rotating structural entities, but also goes along with a deformation of the structural entities themselves. This case will be studied here. Only affine deformations shall be discussed. In practice, such processes are observed while thermoplastic elastomers are subjected to mechanical load, but also while fibers are spun. 

FIGURE 12. Bottom 13C NMR line shapes of 7Li bound 13C, 1./ (13C,7 Li) = 43.3 Hz, subject to relaxation via anisotropy of the chemical shift, csa, at different rates, jc Top as above, but calculated as a function of the dipole-dipole (dd) relaxation rate, vi- Reprinted with permission from Reference 14. Copyright (1995) American Chemical Society... 

Single crystals are the most valuable subjects for investigating the bulk properties of materials. In particular, they clearly demonstrate the conduction anisotropy (if any), and are free from grain-boundary effects. For technical utilization, however, they are usually impractical due to their unsuitable shape and size, and high cost of production. 

More detailed aspects of transport in heterogeneous media have been given in the excellent reviews of the subject by Barrer (55) and Petropolus (51) The models described by these authors and others include the effects of size, shape, and anisotropy of the crystalline phase on the tortuosity. Models of highly ordered anisotropic media have been demonstrated to have tortuosities in the range of 30, which reflects the rather dramatic role that orientation can have on the barrier properties of semicrystalline polymers. 

The amount of strain in various parts of a transparent plastic model of a machine part, subjected to loads simulating those in actual operation, is determined by measuring the anisotropy with polarized light therefore from this measurement the distribution of stress and strain in the actual metal part can be deduced. Very complicated shapes, including complete structures such as bridges or aircraft wings, have been successfully analyzed in this manner, employing plastic models. 

The anisotropy of the oxide formation rate was used to convert the cross-sectional shape of macropores in (lOO)-oriented Si wafers from rounded square to circular upon an increase in their diameter via removal of the sacrificial Si02 layers (Trifonov et al. 2007). Figure 2 presents the results for a sample subjected to 11 cycles of oxidation in dry oxygen at 1,100 °C for 1 h. Note that the tendency toward pore rounding due to the oxidation rate anisotropy is enhanced by the oxidation retardation on the concave surface at square comers. 

In a system that enables rotational diffusion of paramagnetic species, the anisotropy of magnetic interactions is subject to a partial or complete averaging, and this results in changes of the EPR line shape. The correlation time of rotational movements, Tr, is related to the viscosity and temperature of the medium in the case of isotropic Brownian diffusion of a spherical molecule, it is given by the equation ... 

The Gibbs surface free energy will usually be different for different facets of a crystal. Such variations, often referred to as surface free energy anisotropies, are key to determining the equilibrium crystal shape (as well as many other properties) of materials because at equilibrium, a crystal seeks to minimize its total surface free energy subject to the constraint of constant volume. 

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