Three-dimensional anisotropy

Figure 39 (a) Schematic representation of an experimental setup for measuring of three-dimensional anisotropy of the magnetic field effect on photoconductivity (C—crystal, M—mirror), (b) Orientation of the magnetic field B with respect to the crystal axes (a, b, c ). From Ref. 248. 

Figure 40 Three-dimensional anisotropy of the magnetic field effect on photoconduction of a 7 um-thick tetracene single crystal illuminated through a semitransparent gold evaporated anode (cf. Fig. 39a). (a) Relative increase of the photocurrent (iph) when a magnetic field B = 0.5T is rotated perpendicular to the a 6-plane for different orientations of the crystal

An important consequence of the dynamic conditions used in the papermaking process is the introduction into the paper sheet of a three dimensional anisotropy. During the papermaking process as the fibers are much longer than the paper thickness, they undergo an in-plane orientation. Futhermore, the dynamic conditions cause the fibers to orient themselves, not only in the plane of the sheet, but also in the direction of the moving wire. This direction is called the Machine Direction (MD) and the direction perpendicular to it is the Cross-Direction (CD). Paper anisotropy is one of its more important characteristics, since it influences all its mechanical properties. A schematic illustration of the distribution of the fibers in a paper sheet is shown in Fig. 3- In this article, it will be demonstrated that, the anisotropy also influences the electrical conductivity of the paper. 

Watanabe, T., et al., Three-dimensional anisotropy contrast magnetic resonance axonography to predict the prognosis for motor function in patients suffering from stroke. J Neurosurg, 2001. 94(6) p. 955-60. 

This equation has the same form as that for three-dimensional diffusion (see Table 8.2). The Jander equation was found to model the process shown in Eq. (8.27) quite well. The reaction between two solids requires the reaction to begin on the surface of the particles and progress inward. For solids in which there is no anisotropy in the structures, diffusion should take place equally in all directions, so a three-dimensional diffusion model would seem to be appropriate. 

As another example, the three-dimensional structure of Cytochrome c has been determined on the basis of structural information from pseudocontact paramagnetic chemical shifts, Curie-Dipolar cross-correlation, secondary structure constraints, dipolar couplings and 15N relaxation data [103]. This protein has a paramagnetic center, and therefore the above-mentioned conformational restraints can be derived from this feature. Dipolar couplings do not average to zero because of the susceptibility tensor anisotropy of the protein. The structure determination of this protein without NOE data gives an RMSD (root... 

Although the anisotropy of the complexes electrical conductivity was not mentioned, the three-dimensional nature of the complex facilitates a metal-like temperature dependence of its conductivity down to 4K where a = 105 2 lcm l (room-temperature a is a respectable 300 2 1cm 1). The absence of a metal-insulator transition down to 4K shows that the Peierls instability has been successfully avoided by increasing the interstack coupling. 

Often, we want to achieve a high selectivity and a high anisotropy. Practically these exclude each other and we have to compromize. To illustrate this we show different possible combinations for dry and wet etching below, leading to different anisotropy and selectivity. Figure 10.12 shows a bilayer system with different materials to which a certain selectivity must be applied. Such layered systems are etched through a mask to inscribe a certain desired three-dimensional structure for which a certain anisotropy must be maintained. 

The same effect is produced if, instead of physical rotation of the chromophore, energy transfer takes place among them. A randomization of the emitting dipoles in a three-dimensional space results to a limiting value of r equal to zero. If the transport process involves transition dipoles orthogonal to an axis, the limiting value of r is equal to 0.137. The loss of anisotropy... 

The electronic properties are also modified by polymerization. Experimentally, the band gap decreases to less than 1.2 eV in the low-pressure orthorhombic phase [65], and experiments [66,88,108] and calculations [80,109-111] agree that the band gap should decrease with an increasing number of intermolecular bonds. (We note the possible exception of the high-pressure polymerized orthorhombic phase, as discussed above.) Calculations [85, 111] show that the rhombohedral phase should have a more three-dimensional band structure than the orthorhombic phase but still be a semiconductor. However, recent measurements by Makarova et al. [88] showed that oriented samples of the rhombohedral phase had an extremely large electrical anisotropy, larger than that of single-crys-... 

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