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Zeitschrift für Kristallographie - Crystalline Materials

Ed. by Antipov, Evgeny / Bismayer, Ulrich / Huppertz, Hubert / Petrícek, Václav / Pöttgen, Rainer / Schmahl, Wolfgang / Tiekink, E. R. T. / Zou, Xiaodong

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Corrections for x-ray absorption by a crystal of arbitrary shape1

Bernhardt J. Wuensch / C. T. Prewitt

Citation Information: Zeitschrift für Kristallographie. Volume 122, Issue 1-2, Pages 24–59, ISSN (Online) 0044-2968, ISSN (Print) 1433-7266, DOI: 10.1524/zkri.1965.122.1-2.24, July 2010

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A direct procedure, designed for application in high-speed computation, is described for the determination of x-ray absorption corrections in the equi-inclination Weissenberg, Eulerian orienter, and precession geometries. Crystal shapes with re-entrant angles may be treated. The main restriction on the specimen shape is that it be representable by a combination of functions which may be expressed analytically.

The crystal volume is subdivided into volume elements which are represented by a collection of grid points. The grid points are established as submultiples of the maximum dimensions of the crystal and are tested to reject those which lie outside the crystal volume. Only half of the grid points which are contained within the crystal need be considered explicitly when the crystal has a centrosymmetric shape.

Unit vectors are established, relative to the crystal, in the directions of both the incident and diffracted beams for each reflection. These vectors are expressed in terms of reciprocal-cell dimensions in a form which may be evaluated by a computer. Distances from each grid point to the surface of the crystal are determined as multiples of these vectors and are summed to evaluate the transmission factor. If the crystal has re-entrant angles, the path lengths are tested to take account of portions of the beam paths which lie outside the crystal.

Application of the procedure in a program written in FORTRAN and the speed and accuracy of the program will be evaluated in a later paper.

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