Journal of Applied Crystallography

Volume 31, Part 1 (February 1998)

research papers

J. Appl. Cryst. (1998). 31, 47-51 [ doi:10.1107/S0021889897006961 ]

Analytical Expressions for the Transmission Factor and Peak Shift in Absorbing Cylindrical Specimens

T. M. Sabine, B. A. Hunter, W. R. Sabine and C. J. Ball

Abstract: 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° 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 Å) 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.