Laue geometry

The universal spectral curve of SR, however, ideally lends itself to Laue geometry since a broad band of wavelengths of high intensity is emitted by the synchrotron electron beam. As a result, a very large number of reflections can be recorded in a remarkably short exposure time in a Laue experiment this has led to a revival of the Laue method as a means for quantitative structure analysis, especially for kinetic studies and the analysis of structural perturbations. Time resolved investigations include the study of enzyme or zeolite catalysis in crystals. The perturbations which are of interest include the effects of electric fields, pressure and temperature on various materials. 

Additionally, in Laue geometry only cell ratios can be determined from the angular coordinates of spots. The absolute cell parameters therefore have to be provided from a monochromatic study. However, if the intensities of spots are also considered, then there appears to be scope to solve the problem by using knowledge of Amin (section 7.2.3) and the bromine K edge in the photographic film as wavelength markers. 

Fig. 6.7. Schematic cell designs for X-ray scattering experiments (a) reflection (Bragg) geometry (b) transmission (Laue) geometry...

Melone, S., Ftancescangeli, O., and Caciuffo, R. Gamma-ray focusing concentrators for astrophysical observations by crystal diffraction in Laue geometry . Rev. Sci. Instrum., 64, 3467. 

This study clearly demonstrates that by using the differencing technique, sufficient sensitivity is achieved to permit the study of electrochemically induced structural changes in thin surface films. The results obtained indicate that it should be possible to study films of about 100-A thickness fairly easily with a small, fixed anode X-ray source, with such a system probably requiring less than 24 hours of data acquisition time. The study of adsorbed monolayers clearly will be more difficult. Such investigations will benefit from the use of high-surface-area electrodes, e.g., platinum black, and/or the use of the Laue geometry. 

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

Electrons diffract from a crystal under the Laue condition k — kg=G, with G = ha +kb +lc. Each diffracted beam is defined by a reciprocal lattice vector. Diffracted beams seen in an electron diffraction pattern are these close to the intersection of the Ewald sphere and the reciprocal lattice. A quantitative understanding of electron diffraction geometry can be obtained based on these two principles. 

Another approach to these experiments is also being followed, which involves the use of the full white beam from the SRS wiggler. The geometry of the Laue method is advantageous since a single exposure (Fig. 8) yields 30% of all data to 3 A resolution for the tetragonal crystal form of phosphoryla% and exposure times in the millisecond time scale. 

Fig. 7) was operated routinely for many years on the neutron diffractometer DIO at the Institut Laue Langevin and was used for studies on, for example, Bechgaard salts at temperatures close to the superconducting transition [87,88]. Since 1990, 1.6 K can be reached routinely with an improved design and a dilution cryostat has been tested successfully in the laboratory which fits the Euierian cradle and is capable of 70 mK (C. M. E. Zeyen and S. Pujol, private communication, 1993). The helium flow cryostat of Argoud and Muller [80] is also well adapted to four-circle geometry and can be installed even on a small Euierian cradle. 

The geometry of diffraction from a lattice, or in other words the relationships between the directions of the incident and diffracted beams, was first given by Laue (see the footnote on page 31) in a form of three simultaneous equations, which are commonly known as Laue equations ... 

Laue equations once again indicate that a periodic lattice produces diffraction maxima at specific angles, which are defined by both the lattice repeat distances (a, b, c) and the wavelength (A,). Laue equations give the most general representation of a three-dimensional diffraction pattern and they may be used in the form of Eq. 2.20 to describe the geometry of diffraction from a single crystal. 

Fig. 3.30 Schematic of the direct geometry spectrometer IN4 at the ILL. Reproduced from [32] with permission from the Institut Laue Langevin.

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