Section 9.1.6.1. Rotation geometry

The physical process of diffraction from a crystal involves the interference of X-rays scattered from the electron clouds around the atomic centres. The ordered repetition of atomic positions in all unit cells leads to discrete peaks in the diffraction pattern. The geometry of this process can alternatively be described as resulting from the reflection of X-rays from a set of hypothetical planes in the crystal. This is explained by the Ewald construction (Fig. 9.1.6.1), which provides a visualization of Bragg's law. Monochromatic radiation is represented by a sphere of radius , and the crystal by a reciprocal lattice. The lattice consists of points lying at the end of vectors normal to reflecting planes, with a length inversely proportional to the interplanar spacing, . In the rotation method, the crystal is rotated about a single axis, with the rotation angle defined as φ. A seminal work giving an excellent background to this field by a number of contributors was edited by Arndt & Wonacott (1977).

Figure 9.1.6.1| top | pdf | The Ewald-sphere construction. A reciprocal-lattice point lies on the surface of the sphere, if the following trigonometric condition is fulfilled: . After a simple rearrangement, it takes the form of Bragg's law: . Therefore, when a reciprocal-lattice point with indices hkl lies on the surface of the Ewald sphere, the interference condition for that particular reflection is fulfilled and it gives rise to a diffracted beam directed along the line joining the centre of the sphere to the reciprocal-lattice point on the surface.