I Directions of Diffracted Beams 3-2 Diffraction

Diffraction is due essentially to the existence of certain phase relations between two or more waves, and it is advisable, at the start, to get a clear notion of what is meant by phase relations. Consider a beam of x-rays, such as beam 1 in Fig. 3-1, proceeding from left to right. For convenience only, this beam is assumed to be plane-polarized in order that we may draw the electric field vector E always in one plane. We may imagine this beam to be composed of two equal parts, ray 2 and ray 3, each of half the amplitude of beam 1. These two rays, on the wave front AA, are said to be completely in phase or in step i.e., their electric-field vectors have the same magnitude and direction at the same instant at any point x measured along the direction of propagation of the wave. A wave front is a surface perpendicular to this direction of propagation. 

Now consider an imaginary experiment, in which ray 3 is allowed to continue in a straight line but ray 2 is diverted by some means into a curved path before 

Differences in the length of the path traveled lead to differences in phase. 

The introduction of phase differences produces a change in amplitude. 

We wish to know whether this incident beam of x-rays will be diffracted by the crystal and, if so, under what conditions, A diffracted beam may be defined as a beam composed of a large number of scattered rays mutually reinforcing one another. Diffraction is, therefore, essentially a scattering phenomenon and not one involving any new kind of interaction between x-rays and atoms. We saw in Sec. 1 -5 that atoms scatter incident x-rays in alt directions, and we shall see presently that in some of these directions the scattered beams will be completely in phase and so reinforce each other to form diffracted beams. 

---