The Enigma of Bragg's Law

Authors: Sosale Chandrasekhar

It is argued that the fundamental theory of X-ray diffraction is based on a flawed model of wave interference. This is because the macroscopic distances between the crystalline sample on the one hand, and the X-ray source and the detector on the other, cannot be defined to the accuracy of a fractional wave-length. Thus, the inherent ‘graininess’ of the detector surface does not support the idea of constructive or destructive interference of electromagnetic radiation. This critique then applies equally to the presumed extensions of ‘Bragg’s Law’, particularly the so-called phase problem. The phase problem is thus a theoretical construct that is, practically, an artefact of the Bragg derivation. The Bragg approach, however, has been ingeniously adapted to make contact with the structural theory of chemistry by various guises and protocols. These are, inter alia, based on ideas about crystal morphology and internal structure that preceded the Bragg approach. An alternative theory of X-ray scattering, however, needs also to be compatible with the structural theory to be practically meaningful. A model of scattering is proposed herein, that is based on absorption and emission by groups of atoms that are defined by a conventional lattice plane. The Bragg equation is thus re-interpreted as relating the energy of the emitted radiation and the angle of ‘reflection’. It is argued that the Bragg approach is essentially empirical, and that its apparent consistency with the structural theory is based on a synergistic evolution of theoretical ideas and experimental observation. In this, therefore, it is not unlike other spectroscopic techniques in common use for structure determination.

Comments: 10 Pages.

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[v1] 2014-01-01 05:28:21

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