Phenomenon of primary and secondary extinction in textured material

Abstract

A new X-ray diffraction method is proposed for a more exact calculation of pole figures to determine the crystallite orientation distribution function (CODF) in textured materials, by the introduction of a correction of the integrated intensity of the diffracted beam due to the phenomenon of extinction. Besides, for the case of a symmetrical Bragg reflection from an ``infinitely thick'' flat parallel plate textured sample a simple solution is developed for the problem of separation and determination of primary and secondary extinction parameters, which can be present simultaneously. The determination of these parameters gives additional information about crystallite structure and allows us to evaluate the average subgrains size and their disorientation, respectively [1]. In this work, according to the dynamic diffraction theory, it is shown that the extinction length, which is directly connected with the phenomenon of primary extinction, in the Bragg geometry for $\sigma $ polarization (perpendicular) is independent on the wavelength used for a given reflection. On the other hand, the additional contribution from secondary extinction depends on X-rays wavelength due to the change of effective absorption coefficient. Considering this fact, the calculations of pole density and the parameters of primary and secondary extinction are performed using the same strong reflection for two different wavelengths and, for one of these wavelengths, a second order of reflection. For confirmation of the proposed method a partially cold rolled aluminum sample and an aluminum powder standard sample were measured. The corrected pole densities, the values of primary and secondary extinction and the average sizes of perfect coherent areas and average angle of disorientation of subgrains in the selected directions were obtained. The obtained results show that the precise X-ray diffraction characterization of textured materials requires the consideration, in general, of primary as well as secondary extinction phenomenon.