Analytical expressions for the transmission factor and peak shift in absorbing cylindrical specimens

Analytical expressions for the transmission factor and peak shift for absorbing cylindrical specimens or crystals are given. These expressions can be used over a range of mu R useful in X-ray scattering experiments, typically mu R < 10. Comparison with tabulated values of the transmission factor obtained by numerical calculation shows that the maximum difference occurs at theta = 45 degrees and ranges from 1% at mu R = 1 to 20% at mu R = 20. The analytical expressions were tested on synchrotron data from rutile at four wavelengths (0.628, 1.100, 1.536 and 1.895 Angstrom) using the Rietveld method. Separate mu R values were obtained at each wavelength, as well as a single mu R value from a combined refinement of all wavelengths. The results confirmed that the absorption can be modelled using these expressions.