Anisotropy, local

Figure 6.6 (a) Calculated local anisotropy axes on Dy(lll) sites (dashed lines) and the local magnetic moments in the ground state (arrows), (b) Temperature dependence of the /T product for Dy3-isoscelles complex. 

Figure 6.8 (a) Direction of local anisotropy axes (dashed lines) and the low-temperature alignment of magnetic moments (blue arrows) on dysprosium ions along the chain in crystal [(CuUjDyKMotCNlg] ... 

The interplay between the local Pb polarization and B-site ions may be described by a simple model. As discussed above the magnitude of the local off-centering of Pb " ions is always about 0.5 A, and does not depend on the environment. Thus it could be described as a pseudo-spin, and justifies the pseudo-spin model with the dipolar-dipolar interaction and the local anisotropy energy ... 

On the epoxy side of the interface, high fracture toughness and low residual stresses 72,73) are a requirement for optimum transverse strength in graphite and glass-epoxy 1A) composites. Since the adsorption of epoxy components has been shown to be probable, the local structure of the epoxy at the interphase will most likely not be the same as in the bulk. This local anisotropy caused by the interphase is a limitation in the predictive capability of micromechanical models which do not include the interphase as a component. 

We conclude this subsection with several remarks on the interpretation of the anisotropy of Hc2. The largest in-plane anisotropy reported by Metlushko et al. (1997) coincides with the direction of the nesting vector (0.55,0,0). Another manifestation of strong local anisotropy effects is provided by deviations from the 9 (angular) dependence due to anisotropic effective masses (Fermi velocities)... 

So far, speculations which attribute the observed upfield shifts of the NMR signals of 1 to a ring current of the cr-electrons199 (in line with the idea of cr-aromaticity8) have not been refuted. However, a less spectacular rationalization of the NMR chemical shifts in terms of local anisotropy contributions caused by the unique electron distribution of 1 (see Section IV) may also be possible200. 

Neutral homoantiaromaticity has also been invoked for 117 by Wilcox and cowork-ers251. A shift difference of 2.25 ppm was found for the methylene protons of 117 which was interpreted as arising from a paratropic ring current and local anisotropies. Support for the importance of the homoantiaromaticity in describing 117 was also suggested from a consideration of its UV and PE spectra. However, we note our earlier caution about the use of PE as a criterion for homoaromaticity. 

Munera [57] took into account both earth rotation and orbital motion, as a function of the local latitude and longitude. Prediction of the variation of speed difference as function of time of day are given in Munera [57] for the locations of Miller s experiment. The qualitative shape of the variations is of the same sort observed by Miller in the 1930s. However, the magnitudes are not correct because solar motion was not included.2 Selleri [58] allowed for small violations of Lorentz invariance a correction factor around 10-3 reproduces Miller s observations. Also independently, Allais [59] revisited Miller s work. He argues that Miller s seasonal variations are strong proof for a local anisotropy of space. 

In summary, the only direct evidence against the existence of a preferred frame E is the interpretation of Michelson-Morley experiments as being a nullresult. To put it mildly, this evidence is fairly weak. On the contrary, there is mounting evidence for the existence of local anisotropies [49,59,60], which can be interpreted as motion of the earth relative to E. Additionally, a replication of Faraday induction experiments with a rotating permanent magnet yielded a positive outcome [61]. Such results may be interpreted as an indication of the existence of absolute motion, and hence of E. As usual, the final referee will be empirical evidence. Hence, there is a pressing need to carry out new... 

In subsequent sections we shall consider a few phenomenological axisymmetric potentials that determine the steady-state law of motion of a dipole. A polar fluid considered in most of our models is characterized by a local anisotropy—that is, by that in a short-range space scale. Correspondingly, we represent polar fluid as... 

These atomic charges are usually capable of reproducing the calculated dipole moment and the quantum chemical MEP map of the molecule outside the van der Waals surface. The MEP map of the classical EP system is not so rich in information, however, and there are problems, e.g., with the lone pairs. The local anisotropies due to the lone pairs largely disappear. In order to obtain a more accurate description further point charges, situated in appropriate sites, are usually taken into account during optimization [68],... 

The magnetoelastic energy, simply related to the magnetostriction constants, can be written in the following form in the coordinate axes connected to the local anisotropy ... 

In multilayered lattices, even in such ones, for which the macroscopic characteristics are not distinguished by an appreciable anisotropy (as, for example, HTSC type 1-2-3), the interaction between separate atoms or atomic groups can be strongly anisotropic. The "damping" interaction propagation between layers inherent in substances of the specified class may result in appreciable manifestation of such local anisotropy both in the phonon spectrum [15] and in the behaviour of some vibrationary characteristics, in particular the root-mean-square displacement of atoms from separate layers along various crystal directions. 

Some multilayered HTSC, for example Bi2Sr2CaCu20x, show an anisotropy of the elastic moduli inherent for layered crystals, and negative thermal expansion in a direction within the layer [16], which can be described by formula (2). At the same time for multilayered structures such as HTSC 1-2-3, where the interlayer interaction between all layers is of the same order, the intralayer interaction essentially varies from one layer to another layer. Local anisotropy of chain type is characteristic for layers with weak intralayer interaction (a layer of the rare earth and a layer of chains Cu-O). In these layers the root-mean-square displacement of atoms in a direction within the plane is beyond the classical limit at lower temperatures, and is appreciably higher than the root-mean-square... 

In the simplest case, one can assume that there is neither global nor local anisotropy, which means that... 

For the case, when the local anisotropy is taken into account, the relations (3.9) ought to be generalised as... 

Introduction of the local anisotropy of mobility allows us to specify the matrixes of the extra forces of external and internal resistance and to formulate dynamic equations, which will be discussed in Section 3.4. One can expect that, as a result of the introduction of the local anisotropy, mobility of a particle along the axis of a macromolecule appears to be bigger than mobility in the perpendicular direction, so that the entire macromolecule can move more easily along its contour. The local anisotropy hinders also change of the form of the macromolecular coil, and, by this way, plays a role similar to the role of the term with internal resistance in linear version of the model. 

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