Germanium anode x-ray tube, Va = 20 KV, Ia = 100 μA. Exposure time of 1 h
Laue pattern obtained with grains of sodium chloride. The images below show the crystals and the diffractogram with some diffraction spots. The crystals were obtained by evaporation from a supersaturated solution. Given the low intensity of radiation X it is necessary to expose the plate for a long time (for example 1 – 3 hours).Īs done in 1912 by Max von Laue, Paul Knipping and Walter Friedrich, we at PhysicsOpenLab did the first diffraction tests using copper sulphate. It is important that the sample under analysis is very thin (for example 0.5 mm) so as to reduce the absorption of the beam inside the sample. The sample under analysis is positioned at the exit of the collimator, the photographic plate is placed at a distance of 1 – 2 cm to collect the diffraction spots. In both cases a Φ 1mm collimator is used in order to produce a collimated X-ray beam. The Laue diffraction tests were carried out both with the Teltron diffractometer and with the DIY diffractometer. The symmetry of the figure is evident for rotations of angles of 2π / 4 around the axis perpendicular to the plane of the image.
The image below is the computer simulation of the diffraction pattern that is obtained from an fcc cubic crystal in which the beam is parallel to an axis of symmetry of the crystal. Usually the spots are arranged along the ellipses which are the intersection of the diffraction cones with the plane of the photographic plate. The image obtained is linked to the structure of the crystal lattice and its symmetry properties. The image below shows the basic scheme of the two methods. The ways in which Laue diffraction is performed are essentially two : The Laue image is therefore a direct representation of the reciprocal lattice and each spot corresponds to a point of the reciprocal lattice, corresponding in turn to a set of crystallographic planes.įor the occurrence of the von Laue condition it is necessary that the incident beam is polychromatic, that is, it contains all the wavelengths that potentially satisfy the constructive interference condition. The spots present in a Laue diffractogram correspond therefore to the reflections (constructive interferences) produced by a set of crystallographic planes. In this way the Laue condition indicates that, in an elastic collision, the moment transferred to a crystalline lattice is equal to a vector of the reciprocal lattice. This condition can be expressed wit the concept of reciprocal lattice vectors, so it becomes : Where is the inter-atomic distance and is the difference between the incident and the diffracted wave vector (the interaction is elastic scattering so the incident and diffracted radiation have the same energy so the module is constant). The condition is expressed by the formula: The von Laue condition establishes the relationship that exists between the occurrence of constructive interference and the distance of the atoms within a crystal. Laue patterns, first detected by Max von Laue, a German physicist, are invaluable for crystal analysis. When a thin, pencil-like beam of X rays is allowed to impinge on a crystal, those of certain wavelengths will be oriented at just the proper angle to a group of atomic planes so that they will combine in phase to produce intense, regularly spaced spots on a film or plate centered around the central image from the beam, which passes through undeviated. Laue diffraction pattern, in X rays, a regular array of spots on a photographic emulsion resulting from X rays scattered by certain groups of parallel atomic planes within a crystal.
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