The optics of focusing bent-crystal monochromators on X-ray powder diffractometers with application to lattice parameter determination and microstructure analysis

The use of an incident-beam monochromator (IBM) in an X-ray powder diffractometer modifies both the shape of the spectrum from the X-ray source and the relation between the apparent diffracted angle and the actual wavelength of the X-rays. For high-accuracy work, the traditional assumption of a narrow line of typically Gaussian shape does not suffice. Both the shape of the tails of peaks and their width can be described by a new model which couples the dispersion from the optic to the dispersion from the powder sample, and to its transport to a detector. This work presents such a model, and demonstrates that it produces excellent fits via the fundamental parameters approach and requires few free parameters to achieve this. Furthermore, the parameters used are directly relatable to physical characteristics of the diffractometer optics. This agreement is critical for the evaluation of high-precision lattice parameters and crystal microstructural parameters by powder diffraction.