Unique axis

The orientation is defined by the distribution of a single unique axis (the OX3 axis) in the unit with respect to the sample axes. The v / variable therefore takes random values so the Plmn are non-zero only for n = 0. The coefficients up to fourth order are therefore P2oo and P400 as in (i) together with... 

In the latter type, the direction of the unique axis (b-axis) of the polymer coincides with that of the monomer while the directions of the other two axes do not. In the case of 3 OMe none of the directions of the axes of the polymer coincide with those of the monomer. However, the temperature effect on the reaction behaviour (see Section 3) and the continuous change of the X-ray diffraction pattern indicate a typical diffusionless crystal-lattice controlled mechanism (Hasegawa et al., 1981). 

Figure 2, A three-dimensional perspective of the structure of Ba1AhMo8016 as viewed down the unique axis parallel to the direction of chain growth and tunnel...

Monoclinic a — y — 90° (b is the unique axis for proteins this is a twofold axis or screw axis) or a = P = 90° (c is the unique axis for proteins this is a twofold axis or screw axis) 2... 

The unique axis in the monoclinic unit cell is mosdy taken as the b axis. Rhombohedral unit cells are often specified in terms of a bigger hexagonal unit cell. 

In the wurtzite form of ZnS the sulfur atoms are arranged in hexagonal close packing, with the metal atoms in one-half of the tetrahedral positions. There are two layers of tetrahedra in the repeat distance, c, and these point in the same direction. This gives the materials a unique axis, the c axis, and these compounds show piezoelectricity. 

Structures are described by the stBcking sequences of the sheet ataitg the unique axis like AABAtXC. Successive stack of fhc same type forms PUR and 8-ringst next to P6K at the same stacking ievet). 

The unique axis of this ellipsoid of revolution necessarily coincides with the unique (fourfold, sixfold, or threefold) symmetry axis of the crystal. 

The vibration directions and refractive indices of crystal fragments of mon ammonium phosphate lying on a microscope slide in any orientation are given by the indicatrix in the following way. A crystal fragment, oriented with its unique axis at any angle 6 to the line of vision, is mentally replaced by the indicatrix (Fig. 48). Perpendicular to the... 

When we are looking along the unique axis, both indices of the crystal or fragment are equal to 1 525 the crystal will therefore not show any interference colours when examined between crossed polarizers it will appear to be isotropic. This direction of apparent isotropy is called the optic axis there is only one such direction in the crystals we have hitherto dealt with—tetragonal, hexagonal, and trigonal crystals —and such crystals are therefore described as optically uniaxial. The optic axis necessarily coincides with the principal S3>mmetr3T axis. ... 

Crystals, except those belonging to the cubic system, are anisotropic in this respect the force of repulsion varies with the orientation of the crystal with respect to the direction of the field. The graph representing vectorialiy the diamagnetic susceptibility in all directions in a crystal is an ellipsoid, whose orientation with respect to the unit cell is restricted by symmetry in exactly the same way as that of the optical indicatrix. Thus, for uniaxial crystals the magnetic ellipsoid an ellipsoid of revolution whose unique axis coincides with the threefold, fourfold, or sixfold axis of the crystal for orthorhombic crystals the ellipsoid has three unequal axes which necessarily coincide with the three axes of the crystal for monoclinie crystals the only restriction is that one of the principal axes of the magnetic ellipsoid must coincide with the b axis of the crystal while for triclinic crystals the orientation of the ellipsoid is not restricted in any way. 

For a monoclinic lattice (primitive or centered) the unique axis, that is, the one perpendicular to both of the others is a twofold symmetry axis. When the inversion property is added to this, we have the point symmetry group Qyr... 

The list of alternate symbols arises because at an earlier stage in the history of X-ray crystallography, it was the accepted convention to call the unique axis b. The reader can easily see that if this is done, the alternate symbols become correct. Since in the other crystal systems with a unique direction (i.e., tetragonal and hexagonal) the unique direction is called c, the formally correct practice is now to do the same for the monoclinic system. However, the literature is still replete with the old choice of axes and it is necessary to be cognizant of both systems and of their relationship. 

Let us now see how these conditions for systematic absences are used. Suppose we have established from the X-ray diffraction data that a crystal is monoclinic. See Table 11.7 for the monoclinic space groups. We can next see if the unit cell is primitive or centered. If we choose the unique axis to be c, we look for absences indicative of A centering (hkl, k + 2 n) or B centering... 

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