Laue Pattern

a diffraction pattern of a stationary single crystal, obtained by X ray; named after M. Laue, who proposed the method by which W. Friedrich and P. Knipping obtained the first such pattern (1912).

The Laue method consists of the following: a narrow X-ray beam with a continuous spectrum is directed at a stationary single crystal, which serves as a diffraction grating. The diffraction pattern produced by the crystal is recorded on a photographic film located behind the crystal. In addition to the center spot formed by the undeflected X-ray beam, various additional spots also appear in the Laue pattern. The number and arrangement of these spots depend on the type of crystal and on its orientation relative to the beam.

The X-ray beam strikes the crystallographic planes and is reflected (X-ray diffraction); the direction of the reflected beam, in accordance with the Bragg-Vul’f condition, corresponds to the direction of the diffraction maximum, to which all of the atoms on the crystallographic plane contribute. Each set of parallel crystallographic planes accounts for one spot on the Laue pattern.

A set of crystallographic planes (a zone, or belt) parallel to a given spatial direction (zone axis) gives reflections along the directrix of a cone whose axis coincides with the zone axis. The spots on the Laue pattern produced by such families are arranged on a cross section of this cone corresponding to the film plane (zone curves). If the primary beam coincides with the axis of symmetry of the crystal, the spots of the Laue pattern will be arranged symmetrically in relation to the central spot, in accordance with the symmetry of the given direction in the crystal. The number of spots increases as the distance between the atoms along the zone axis decreases.

The Laue pattern makes it possible to determine the direction of the axes of symmetry of a crystal (that is, to perform its “orientation”; this is especially important for unfaceted crystals). Furthermore, it is possible to evaluate the degree of a crystal’s perfection and to determine certain defects, such as block structure, mosaic structure, and the presence of internal deformations (asterism, X-ray topography), from the distribution of intensity in the spots.

Laue patterns contain information on the symmetry of a crystal. However, it is impossible without additional data to establish unequivocally to which of the 32 crystal groups a crystal belongs.

When the dimensions of a monocrystal are too large for radiation to pass through to the film, the X rays reflected by the crystal faces are recorded on a film plate placed in front of the crystal. The pattern obtained, called an epigram, serves the same purposes as does the Laue pattern.