A study on the limit of application of kinematical theory of X-ray diffraction

Author:

Dias Diego Felix1,Sasaki José Marcos1

Affiliation:

1. Physics Department , X-ray Laboratory, Federal University of Ceará , 60440-970, Fortaleza , Ceará , Brazil

Abstract

Abstract In this work, the limit of application of the kinematical theory of X-ray diffraction was calculate integrated intensities was evaluated as a function of perfect crystal thickness, when compared with the Ewald–Laue dynamical theory. The percentual difference between the dynamical and kinematical integrated intensities was calculated as a function of unit cell volume, Bragg angle, wavelength, module, and phase of structure factor and linear absorption coefficient. A critical thickness was defined to be the value for which the intensities differ 5%. We show that this critical thickness is 13.7% of the extinction length, which a specific combination of the parameters mentioned before. Also, we find a general expression, for any percentage of the difference between both theories, to determine the validity of the application of the kinematical theory. Finally, we also showed that the linear absorption decreases this critical thickness.

Publisher

Walter de Gruyter GmbH

Subject

Inorganic Chemistry,Condensed Matter Physics,General Materials Science

Reference28 articles.

1. Authier, A. Dynamical Theory of X-ray Diffraction; Oxford University Press: Oxford, 2001.

2. Chang, S. L. X-ray Multiple-Wave Diffraction: Theory and Application, Vol. 143; Springer Science & Business Media: Berlin, Germany, 2013.

3. Zachariasen, W. H. Theory of X-ray Diffraction in Crystals; Dover Publications, Inc.: New York, 1945.

4. Batterman, B. W., Cole, H. Dynamical diffraction of X rays by perfect crystals. Rev. Mod. Phys. 1964, 36, 681–717. https://doi.org/10.1103/revmodphys.36.681.

5. Borrmann, G. Physik. z. 1941, 43, 157.

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