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 expressio ns can be used over a range of mu R useful in X-ray scattering experim ents, typically mu R < 10. Comparison with tabulated values of the tra nsmission factor obtained by numerical calculation shows that the maxi mum 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 sy nchrotron data from rutile at four wavelengths (0.628, 1.100, 1.536 an d 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 co mbined refinement of all wavelengths. The results confirmed that the a bsorption can be modelled using these expressions.