Laue pattern

Laue pattern The symmetrical array of spots obtained on a photographic plate exposed to a non-homogeneous beam of X-rays after its passage through a crystal. The patterns constitute the earliest, although one of the most difficult, methods of investigating crystal structure by means of X-rays. 

The software required for the quantitative evaluation and wavelength normalisation of Laue data has been successfully developed at Daresbury since the feasibility of recording full white beam Laue patterns from protein crystals was established. The software and the method have been tested using Laue data from crystals of pea lectin. As an example of the statistical quality (to 3 A resolution) the mean fractional change on F between monochromatic and Laue pea lectin data was 11 % and the same quantity between conventional source monochromatic and SR monochromatic pea lectin data is 8% (Helliwell et al., 1986). 

Lateral interaction work of water adsoiption, 907 Lateral interactions of ionic adsoiption, 924, 944 Lateral interactions and Frumkin s isotherm, 938 Lattice gas models of adsorption, 965 Lattice spacing, 1276 Laue pattern, 793... 

If this is the case, the technique is then called X-ray diffraction. The wavelength of the X-rays is on the order of 0.1 nm and the diffraction pattern produced is also called a Laue pattern (see Section 5.2.3). 

You can see from Fig. 9.8 that a Laue diffraction pattern is much more complex than a diffraction pattern from monochromatic X rays. But modern software can index Laue patterns and thus allow accurate measurement of many diffraction intensities from a single brief pulse of X rays through a still crystal. If the crystal has high symmetry and is oriented properly, a full data set can in theory be collected in a single brief X-ray exposure. In practice, this approach usually does not provide sufficiently accurate intensities because the data lack the redundancy necessary for high accuracy. Multiple exposures at multiple orientations are the rule. 

Figure 18 X-ray monochromatic Laue pattern of TTF-TCNQ at 110 K. The horizontal direction is parallel to the one-dimensional i7-axis. (Reproduced from J. R Pouget et al., Rhys. Rev. Letters, 37 (1976) 437, Fig. 1(a))...

Fig. 3-6 (a) Transmission and (b) back-reflection Laue patterns of an aluminum crystal (cubic). Tungsten radiation, 30 kV, 19 mA,... 

A transmission Laue pattern is made of a cubic crystal having a lattice parameter of 4.00 A. The x-ray beam is horizontal. The [OTO] axis of the crystal points along the beam towards the x-ray tube, the [TOO] axis points vertically upward, and the [001 ] axis is horizontal and parallel to the photographic film. The film is 5.00 cm from the crystal. 

A transmission Laue pattern is made of a cubic crystal in the orientation of Prob. 3-1. By means of a stereographic projection similar to Fig. 3-8, show that the beams diffracted by the planes (2T0), (2T3), and (211), all of which belong to the zone [l20], lie on the surface of a cone whose axis is the zone axis. What is the angle between the zone axis and the transmitted beam ... 

The position of any Laue spot is unaltered by a change in plane spacing, since the only effect of such a change is to alter the wavelength of the diffracted beam. It follows that two crystals of the same orientation and crystal structure, but of different lattice parameter, will produce identical Laue patterns. 

A transmission Laue pattern is made of an aluminum crystal with 40-kV tungsten radiation. The film is 5 cm from the crystal. How close to the center of the pattern can Laue spots be formed by reflecting planes of maximum spacing, namely (111), and those of next largest spacing, namely (200) ... 

A transmission Laue pattern is made of an aluminum crystal with a specimen-to-film distance of 5 cm. The (111) planes of the crystal make an angle of 3° with the incident beam. What minimum tube voltage is required to produce a 111 reflection ... 

Diffraction of the continuous spectrum. Each crystal in a powder specimen forms a weak Laue pattern, because of the continuous radiation component of the incident beam. This is true whether or not that particular crystal has the correct orientation to reflect the characteristic component into the Debye ring. Many crystals in the specimen are therefore contributing only to the background of the photograph and not to the diffraction ring, and the totality of the Laue patterns from all the crystals is a continuous distribution of background radiation. If the incident radiation has been so chosen that very little fluorescent radiation is... 

As mentioned in Sec. 3-6, the Laue pattern of a single crystal consists of a set of diffraction spots on the film and the positions of these spots depend on the... 

Fig. 8-3 Greninger chart for the solution of back-reflection Laue patterns, reproduced in the correct size for a specimen-to-film distance D of 3 cm.

This procedure may be illustrated by determining the orientation of the aluminum crystal whose back-reflection Laue pattern is shown in Fig. 3-6(b). Fig. 8-5 is a tracing of this photograph, showing the more important spots numbered for reference. The poles of the planes causing these numbered spots are plotted stereographically in Fig. 8-6 by the method of Fig. 8-4 and are shown as solid circles. 

Fig. 8-5 Selected diffraction spots of back-reflection Laue pattern of an aluminum crystal, traced from Fig. 3-6(b).

However, a noncubic crystal may have such low symmetry and/or be so oriented that the Laue pattern shows only one spot, or none at all, from a low-index plane. Plane indexing can then be difficult. Methods of coping with this problem include the following ... 

The crystal is re-oriented, in a manner suggested by the Laue pattern, and examined in a diffractometer. See Sec. 8-5. 

Given a specimen of sufficiently low absorption, a transmission Laue pattern can be obtained and used, in much the same way as a back-reflection Laue pattern, to reveal the orientation of the crystal. 

Fig. 8-14 Leonhardt chart for the solution of transmission Laue patterns, reproduced in the correct size for a specimen-to-film distance of 3 cm. The dashed lines are lines of constant 0, and the solid lines are lines of constant 3. (Courtesy of C. G. Dunn [8.3].)...

The back-reflection Laue pattern of an aluminum crystal rotated into the orientation described above is shown in Fig. 8-22. Note that the arrangement of spots has 2-fold rotational symmetry about the primary beam, corresponding to the 2-fold rotational symmetry of cubic crystals about their <110> axes. (Conversely, the observed symmetry of the Laue pattern of a crystal of unknown structure is an indication of the kind of symmetry possessed by that crystal. Thus the Laue method can be used as an aid in the determination of crystal structure.)... 

The crystal-setting procedure illustrated in Fig. 8-21 can be carried out whether or not the indices of the various poles are known. If the Laue pattern of a crystal is difficult to solve, any spot on it can be indexed by using a Laue camera and a diffractometer in sequence [8.4]. In addition, a goniometer is required that fits both instruments. The procedure is as follows ... 

Make a Laue pattern and a stereographic projection of the poles corresponding to a few important spots. 

Fig. 8-22 Back-reflection Laue pattern of an aluminum crystal. The incident beam is parallel to [Oil], [Oil] points vertically upward, and [100] points horizontally to the left. Tungsten radiation, 30 kV, 19 mA, 40 min exposure, 5 cm specimen-to-film distance. (The light shadow at the bottom is that of the goniometer which holds the specimen.)...

Fig. 8-26 Formation of Debye arcs on Laue patterns of deformed crystals.

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