Journal of the Physical Society of Japan
Online ISSN : 1347-4073
Print ISSN : 0031-9015
ISSN-L : 0031-9015
Pendellösung Fringes in Distorted Crystals II. Application to Two-Beam Cases
Norio Kato
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1964 Volume 19 Issue 1 Pages 67-77

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Abstract
Wave-optical principles of electron and X-ray diffraction in distorted crystals developed in Part I are applied to Laue cases where only one diffracted wave is excited appreciably. Using the two-beam approximations, it can be shown that the trajectory of a “modified Bloch-wave” is determined by a differential equation which has an analogous form to a special-relativistic equation of motion for a charged particle in an electric field. The apparent force which changes the direction of motion is caused by lattice distortions. The phase change along the trajectory is obtainable by the phase integral given in Part I. The amplitudes of the direct and the diffracted waves are given by considering the compatibility of crystal and vacuum waves as to the energy flows on the crystal boundaries. The boundary conditions are discussed for electron and X-ray cases separately. Pendellösung fringes are expected for both cases from an interference between two modified Bloch-waves corresponding to the different branches of the dispersion surface.
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