Fibre patterns and the unit cell

In order to determine the crystal structure it is necessary to determine the positions and intensities of all the spots in the fibre pattern. The positions of the spots provide information from which the shape and dimensions of the unit cell can be calculated and the intensities provide information about the contents of the unit cell. The following section considers the relationship between the fibre pattern and the unit cell. 

Imagine a particular set of planes in such a single erystal and consider what happens as the crystal is rotated about the c-axis, which is assumed to be vertical. During the rotation the angle 6 changes eontinuously. Imagine 

8 Formation of a powder ring from a particular set of planes. 

The conclusion is that, for a rotating crystal, most sets of crystal planes give rise to four spots lying at particular points on the imaginary circle where the corresponding powder-pattern circle would have been. These points are symmetrically placed with respect to the plane that contains the incident X-ray beam and the rotation axis and to the plane that contains the incident X-ray beam and is normal to the rotation axis, as shown in fig. 4.9. A similar conclusion can be drawn for a stationary, highly oriented polymer fibre. Planes parallel to the rotation or fibre axis give rise to only two diffraction spots. 

The radius of the (imaginary) powder circle and the positions of the four spots on it for a particular type of crystal plane depend on the indices of the planes, which are also the diffraction indices for the spots, as explained in section 2.5.1. The diffraction indices h, k and I are the numbers of 

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