Definitions, Anisotropy, Theory

If one of the media is vacuum, where the speed of light is constant (c), we measure 

Rl is routinely used in laboratory practice as a fingerprint of a substance. Usually it is measured in relation to atmospheric air, but since the latter has n = 1.0(X)27 1, 

The optical properties of an anisotropic crystal can be conveniently described by the optical indicatrix (Fig. 11.2), which is derived from the optical surfaces by 

An important corollary is that measurements of RI can distinguish between three major types of crystal symmetry high—cubic (optically isotropic crystals), medium—tetragonal, trigonal or hexagonal (anisotropic crystals with o and e), and lower—orthorhombic, monoclinic or triclinic (crystals with three indices of refraction). 

The average RI of an anisotropic crystal can be calculated by converting the ellipsoid into a sphere of equal volume. 

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Hardness determination methods find wide uses in basic research on the mechanical properties of minerals and their deformation. In the face of the rapid development of industrial uses of natural minerals, as well as manmade, in monocrystal or grain form or as polymineral materials, there is a definite need for more comprehensive crystallomechanical investigations. Apart from the above aspects, hardness determination should furnish valuable information on the genesis of minerals. These authors consider that it would well serve the purpose to examine the mechanical properties of all minerals so as to obtain their allround crystallomechanical characterization and to investigate into their anisotropy and relationship to the structure and composition of minerals. By determining the typomorphism of the mechanical parameters of minerals and its involvement in the conditions of their formation, and also by investigating the specificity of occurrence of deformations in minerals under natural conditions and of the deformative mechanism, it should be possible to develop a general theory of mechanical properties of crystals. 

Figure 5.2 i Anisotropy of various contributions to the 3-body forces for the cyclic water trimer . See Fig. 5.19 for definition of a. HL refers to Heitler-London term which prohibits modification of the charge clouds of each molecule in the presence of the others, and SCF-def to the result of such deformation, both at the SCF level. Three-body induction is computed directly via perturbation theory. 

For a more definitive test of the theory, Irvine has determined the optical anisotropies of nematogens and analogous compounds from depolarized Rayleigh... 

The conventional, and very convenient, index to describe the random motion associated with thermal processes is the correlation time, r. This index measures the time scale over which noticeable motion occurs. In the limit of fast motion, i.e., short correlation times, such as occur in normal motionally averaged liquids, the well known theory of Bloembergen, Purcell and Pound (BPP) allows calculation of the correlation time when a minimum is observed in a plot of relaxation time (inverse) temperature. However, the motions relevant to the region of a glass-to-rubber transition are definitely not of the fast or motionally averaged variety, so that BPP-type theories are not applicable. Recently, Lee and Tang developed an analytical theory for the slow orientational dynamic behavior of anisotropic ESR hyperfine and fine-structure centers. The theory holds for slow correlation times and is therefore applicable to the onset of polymer chain motions. Lee s theory was generalized to enable calculation of slow motion orientational correlation times from resolved NMR quadrupole spectra, as reported by Lee and Shet and it has now been expressed in terms of resolved NMR chemical shift anisotropy. It is this latter formulation of Lee s theory that shall be used to analyze our experimental results in what follows. The results of the theory are summarized below for the case of axially symmetric chemical shift anisotropy. 

TDI and, in some cases, a diamine.) According to both this classical definition and the simple Kuhn-Griin molectilar theory of birefringence of rubberlike material (H,5) K should be directly proportional to the modulus, while the latter shows that the elope should be a measure of the optical anisotropy of a chain segment. (See Chapter I5). 15ie linearity of the response shows that the birefrigence can be described in conventional terms, in spite of the fact that some of the systems are rather highly crosslinked. 

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