Laues idea

Crystals result when a solid substance is precipitated, under appropriate conditions, from a vapour or solution. It was suspected for a long time that the geometrical forms of crystals were due to a regular arrangement of atoms or molecules. Experimental verification of this idea was provided in 1912 by von Laue, who demonstrated that crystals showed interference phenomena with x-rays and, further, that it was possible to determine the structure of the crystal so accurately that sometimes the positions of atoms in the crystal could be given in one part in 100,000. It thus became possible to find the distance between the atoms in crystals, and it is important that it is not necessary to have well-formed crystals for this purpose. Nearly all substances are crystalline, even the silver chloride flocculent precipitate which is obtained when Cl" and Ag+ ions are brought together. 

It was only in 1927 from the experiments of Davisson and Germer and slightly later from those of G. P. Thomson that it was found that these electron beams exhibit exactly the same diffraction phenomena as those which Von Laue, Friedrich and Knipping had observed with X-rays in 1912. For X-rays this result was in agreement with the prevailing conception of the nature of these rays. With electrons, however, this wave character appeared to be completely in conflict with the ideas which had been supported for more than 50 years, nevertheless only three years before De Broglie had published his fundamental hypothesis on the wave nature of electrons in his thesis (1924). 

These experimental results and their interpretations clearly showed that the study of the diffracted intensity makes it possible to accurately determine the nature and the positions of the atoms inside the crystal cell. Nevertheless, the link between stmctural arrangement and the value of the total diffracted intensity was not proven. This aspect will be studied in detail by Darwin, who showed in two famous articles [DAR 14a, DAR 14b] that, on the one hand, the intensity is not concentrated in one point (defined by the Laue relations), but that there is a certain intensity distribution around this maximum (referred to as the Darwin width) and, on the other hand, that real crystals show a certain mosaicity that can account for the values of the diffracted intensity measured experimentally. These considerations were based on a description similar to that used for visible light in optics and constituted a preamble to the dynamic theory of X-ray diffractiort, the core ideas of which were later established by Ewald [EWA 16a, EWA 16b]. 

The original X-ray diffraction experiment was based on an idea of von Laue and conducted by Friedrich and Knipping (Friedrich et al 1912). It earned von Laue the Nobel Prize for Physics in 1914. The basis of the idea was that if X-rays were electromagnetic waves then their wavelengths might be of the same order as the interatomic separation in crystals and diffraction would be observed. The original diffraction photograph was from a crystal of copper sulphate. 

Before we follow out these ideas in detail, we shall give a brief summary of some of the results of observations on X-ray spectra. Since the discovery of v. Laue, the natural gratings of crystals have been available for the analysis of these spectra. Each X-ray spectrum consists of a continuous band and a series of lines. 

In 1912, Von Laue, Friedrichs, and Knipping had detected the scattering of X-rays by crystals. Between 1912 and 1914, the Braggs had applied those ideas to describe the crystal structure of solids, They d made it clear that the atoms of a crystal are arranged in an orderly lattice of dimensions comparable to the wave length of X-rays, If so, the atoms on the surface of that lattice must present unsaturated surface chemical bonds, ready to combine with unsaturated bonds of species that alight on the surface. 

Following such an idea, Tanaka et al. [2009) performed X-ray diffraction and Raman scattering spectroscopy, but no signatures of crystallization have been obtained. We may also envisage some oriented amorphous structures [as in Fig. 3.10), but experiments using a Laue camera, which took two-dimensional diffraction patterns for transmitted X-ray beams, could not detect any anisotropy. [Some oriented structure may exist, but the degree of orientation seems to be smaller than 10%, which is an experimental limit of the X-ray measurement for small samples.) For wrinkled a-Se films... 

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