Simultaneous Diffraction and Borrmann Effect

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Abstract
Simultaneous diffraction of X-ray is theoretically studied for four cases in which the relevant reciprocal points form an isosceles triangle, an equilateral triangle, a square, or a regular hexagon. Explicit expressions are derived for the X-ray wave-field in the crystal when all sets of the diffracting planes concerned satisfy the Bragg condition simultaneously. These expressions give the absorption coefficient characteristic of each polarization-type and eventually explain the anomalous transmission owing to the simultaneous diffraction for the particular configurations. In the case of the equilateral-triangle configuration, the smallest absorption coefficient is the same as in the case of a single diffraction corresponding to a side of the triangle. In all the other cases enhancements of the anomalous transmission are predicted. Some of the results are compared with the experiment by G. Borrmann (Z. Krist. 121 (1965) 6).

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