Uniaxial birefringence

Fig.7.32. (a) Index ellipsoid and refraction indices n and n for two modes of polarization in a plane perpendicular to the wave propagation, (b) Dependence of ng and ne on the angle e between optical xis and wave-vector k, for a positive birefringent uniaxial crystal... 

Biaxial Orientation. Many polymer films require orientation to achieve commercially acceptable performance (10). Orientation may be uniaxial (generally in the machine direction [MD]) or biaxial where the web is stretched or oriented in the two perpendicular planar axes. The biaxial orientation may be balanced or unbalanced depending on use, but most preferably is balanced. Further, this balance of properties may relate particularly to tensile properties, tear properties, optical birefringence, thermal shrinkage, or a combination of properties. A balanced film should be anisotropic, although this is difficult to achieve across the web of a flat oriented film. 

In thin sections natural graphite is translucent, strongly pleochroic, and uniaxial. It has a negative sign of birefringence and two extinctions per revolution under crossed Nicol prisms. The atomic number of carbon accounts for its low absorption coefficient for x-rays and electrons. 

Only two birefringence indices are independent and necessary to describe the anisotropy of a biaxial system, while a single birefringence measurement is required for uniaxial samples because nx — ny. 

The uniaxial orientation parameter related to the orientation of polymer chains gains particular importance, because it can also be determined by measurement of birefringence [250,252],... 

The pyrazine LB films was expected to show uniaxial birefringence because the LB film possess uniaxial molecular orientation. Accordingly, the refractive index in the film plane no and film thickness W was determined by the analysis of TE modes. Then, the refractive index perpendicular to the film plane ne was obtained form the analysis of the TM modes. 

Simulation of the Birefringence of Uniaxially Stretched Polyethylene Melts. 

The optical character of chalcedony is distinct from that expected for the normally uniaxial mineral, quartz, and signals the fibrous nature of a particular sample. The direction of fiber elongation is often parallel to the [1120] crystallographic direction of the quartz structure (Fig. 2.19A), but other fiber directions have also been determined within a single sample (Frondel, 1985). The presence of helically twisted fibers are suspected from the variations in extinction and birefringence noted along the fiber length (Fig. 2.19C). More detailed information on the optical or other physical and chemical properties of quartz and its many varieties can be found in volume 3 of Palache et al. (1962) and in Frondel (1985). 

In the same way that close-packed directions in a crystal have larger refractive indices, so too can the application of a tensile stress to an isotropic glass increase the index of refraction normal to the direction of the applied stress. Uniaxial compression has the reverse effect. The resulting variation in refractive index with direction is called birefringence, which can be used as a method of measuring stress. 

A detailed insight into the freezing-in process is given by optical investigations. As described in 2.3.1.4 for nematics, 2.3.2.3 for cholesterics and 2.3.3.3 for smectics, the optical uniaxial character of the polymers in the liquid crystalline state has been proved by birefringence measurements and the state of order was calculated from these measurements. This method also provides information about the glassy state. For conventional l.c s it has been demonstrated, that the temperature dependence of... 

Such polymers adopt, when affected by a mechanical field, an optically uniaxial homeotropic structure polymers B.1.2, B.1.7, B.1.8 (Table 8) have positive birefringence polymers B.1.1, B.1.8. (Table 9) have negative birefringence, which has not been reported to our knowledge, for low-molecular nematic liquid crystals. Although the authors do not comment on the cause for the observed phenomenon, the fact in itself is sufficiently uncommon. 

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