shows in successive steps (1) the generation of a circular set of waves from a 

 series of parallel wave fronts by a post (or other small object) in a quiet body 

 of water; (2) the interaction of these newly generated circular waves from a row 

 of equally spaced posts produced new diffracted wave fronts; (3) the interaction 

 of these generated circular waves from two rows of posts (two planes) under 

 conditions where Bragg's law is not satisfied; and finally, (4) the interaction 

 of these waves where the angle has been so chosen that all conditions for the 

 observance of diffraction effects by this particular family of planes have been 

 satisfied. The fact that the diffracted wave fronts from each row of posts are 

 one-quarter of a wave length out of phase with those diffracted by the adjacent 

 rows, under the conditions where Bragg's law is not satisfied, immediately shows 

 that we cannot observe any diffraction from this family of planes under the 

 selected conditions. On the other hand, when the angle 9 has been so adjusted 

 that Bragg's law is satisfied, all these wave fronts coincide: that is, they are in 

 phase, and diffraction effects from this particular family of planes are observed. 

 A sketch set into the figure shows how this phenomenon is related to conditions in 

 the X-ray camera. The directions of the original and diffracted beams are shown 

 by arrows and have the same directions as the labels in part 2 of Figure 9-2. 



This simple two-dimensional analogy can be applied to the three-dimensional 

 diffraction of X-rays by crystalline matter if the posts are replaced by a regular 

 assemblage of points (atoms or ions) distributed in space at a distance that is of 

 the same order of magnitude as the wave lengths of X-rays. Spherical waves are 

 created when X-rays, which are electromagnetic waves, cause forced oscillations 

 of the planetary electrons of the atoms which they traverse, the electrons ab- 

 sorbing energy from the X-rays when moving away from the nucleus and 

 radiating energy in all directions when moving toward the nucleus. Inspection 

 reveals that this three-dimensional point system will produce very narrow pencils 

 of rays only in those directions in which these spherical waves are in phase. 

 These reinforced waves are the rays that produce the individual spots in X-ray 

 patterns (Laue, rotation, Weissenberg, etc.) obtained from single crystals. If 

 the single crystal is replaced by a large number of smaller crystals, that is a 

 powder, the 20 angle with the undiffracted beam must remain constant since, in 

 Bragg's equation, d for the particular set of planes and the wave length, A, of 

 the X-rays from a particular target material are fixed. The crystals of the 

 powder with their statistical orientation, unless preferred orientation effects 

 result owing to peculiar crystal shapes, then must produce a whole series of such 

 discrete pencils, so that as a result a continuous diffraction cone with an apex 

 angle of 40 is obtained. If this cone is now recorded on a photographic film 

 placed perpendicular to the cone axis, the diffraction effect is obtained as a line 

 which is in the form of a ring. A pattern on which the diffraction rings from all 

 families of planes have been recorded is usually referred to as a powder pattern 



152 



