SYSTEMATIC CORRECTIONS IN BRAGG X-RAY-DIFFRACTION OF FLAT AND CURVED CRYSTALS

Measurements of spectral wavelengths in Bragg diffraction from crystal s often require refractive index corrections to allow a detailed compa rison of experiment with theory. These corrections are typically 100-3 00 ppm in the x-ray regime, and simple estimates may sometimes be accu rate to 5% or better. The inadequacies of these estimates are discusse d. Even with a possibly improved index of refraction estimate, this co rrection is insufficient since additional systematics in the diffracti on process occur at or above this level. For example, asymmetries of d iffraction profiles with ir-polarized radiation or due to three-beam d iffraction can approach the magnitude of refractive index corrections for flat or curved crystals. The depth of penetration of the x-ray fie ld inside curved crystals, the shift of the mean angle to the diffract ing planes, and lateral shifts around the crystal surface are rarely c onsidered but can dominate over:refractive index corrections, particul arly for high-order diffraction or medium-energy x rays. Shifts and no nlinearities arise when diffracting surfaces lie off the Rowland circl e, and exhibit strong and rapidly varying angular dependencies. Johann geometries with the source located on the Rowland circle should be av oided to minimize profile truncation shifts from crystal ranges or min imum grazing angles, and to avoid extreme scaling corrections. Other s ignificant shifts are identified and illustrated, with functional rela tions provided to allow an estimation of related magnitudes. The centr al concerns of this paper are the effects on flat crystal diffraction and curved crystal diffraction in the Johann geometry, with a source a nd crystal of variable dimensions and location. Experiments often inte rpolate or extrapolate from calibration lines, so dependencies upon th e diffracting angle are as important as the magnitude of the correctio ns. These dependencies are presented in formulas and graphs. (C) 1995 American Institute of Physics.