X-Ray Diffraction and the Bragg Equation

Abstract

Typical derivations of the Bragg equation in introductory texts do not adequately explain why x-rays are reflected as if by a mirror by crystal planes, and often lead to the mistaken idea that lattice points can be identified with the centres of atoms or ions in the structure. The treatment offered here is a little more demanding, but to compensate for this also has the advantage that it can easily be extended to provide a basic understanding of the use of XRD in structure determination. Comparison of the x-ray powder diffraction patterns obtained from K Cl and K Br is used to illustrate how both the angles and the intensities of diffracted beams are determined by the structure of a solid. A brief discussion of the effects of crystal size on the broadening of diffraction lines is included both for its intrinsic interest, and because it emphasizes that the sharp diffracted beams which are often observed result from the cooperative effect of very large numbers of scattering centers.