Monoclinic and Triclinic Systems

For biaxial crystals, similar results are obtained as with uniaxial crystals. The exception to this rule is that in monoclinic and triclinic systems, the polarization directions need not be parallel to faces or to the bisectors of face angles. If the prominent faces or edges of an extinguished crystal are not parallel to the axes of the initial polarizer, the extinction is said to be oblique (Fig. 3d). 

Merten 14> has extended the theory for the general case of a biaxial, polyatomic crystal. His theory is worked out in detail for crystals of the orthorhombic system and all crystal classes of higher symmetry, but not yet for crystals of the monoclinic and triclinic systems. 

Six types of spectra are theoretically possible in minerals of the orthorhombic, monoclinic and triclinic systems (McClure, 1959). However, for electric dipole transitions only three spectra are usually distinguished. These are the a, P and y spectra obtained when light is polarized along each of the three indicatrix axes, which in orthorhombic minerals such as olivine and orthopyroxene correspond to the three crystallographic axes. The majority of the spectra of minerals described in chapters 4 and 5 consist of polarized spectra measured in the three mutually perpendicular directions corresponding to a, P and y polarized light... 

The correct unit cell may be identified by associating indices to n inter-planar distances, where n depends on the lattice symmetry. In accordance with Table 7.3, the minimum values of n are n=l for the cubic system, n = 2 for tetragonal and hexagonal crystals, = 3, 4, 6 for orthorhombic, monoclinic and triclinic systems, respectively. 

The use of a systematic reduced-cell analysis in monoclinic and triclinic systems to choose among equivalent (having the same reduced cell) solutions. 

Biaxial crystals n. Anisotropic crystals in the orthorhombic, monoclinic and triclinic systems. They have three principal refractive indices, a, and y. 

In X-ray crystallography atomic coordinates are usually given as fractions of the unit cell parameters in a reference system that coincides with the cell axes system. This choice has the disadvantage of accepting an oblique reference frame, at least in monoclinic and triclinic systems. The advantages will soon become clear. 

The original work was on polyethylene which possesses an orthorhombic unit cell. The problem of obtaining fa, fb, andfc with nonorthorhombic monoclinic and triclinic systems was more difficult. Wilchinsky (61) described a method for using wax diffraction to determine the orientation of all crystallographic axes from available diffraction planes (62,63). 

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