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In recent years, with the advent of nearly perfect crystals, double-crystal topography has become very useful. For applications with such crystals the diffraction geometry in the double-crystal arrangement in three dimensions should be taken into account. Detailed studies of this problem are presented in this paper. Formulas for calculating the image height and displacement as the crystal is rotated are reported for various conditions. In the equispacing case, the image height is not limited provided the sample crystal is untilted with respect to the first crystal. However, if the crystal is tilted even a small amount then the image is limited and depends not only on the tilt angle φ but also on the distance between the X-ray source and the crystal L and on the degree of crystal perfection β. In general, the tilt angle should not exceed 1′ to obtain a large-area topograph and to measure the correct rocking curve in the asymmetric mode. In the unequispacing case, the image height is always limited. In this case, even when the crystal is not tilted, the image height is a function of L, φ and the difference in Bragg angle, Δθ, between the diffraction planes of the two crystals. The image height is directly proportional to β and inversely related to Δθ. In this case, in order to obtain a large-area topograph of a nearly perfect crystal L must be large or Δθ must be small. The different experimental conditions are explored for various types of first and second crystals to verify the analytical formulas that have been derived. The experimental data were found to be in good agreement qualitatively and quantitatively with the analysis.

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