Secondary extinction in textured films

A simple solution accounting for the secondary-extinction correction of the integrated intensity of the diffracted beam in a mosaic crystal is derived for the case of symmetrical Bragg reflection from an `infinitely thick' plane parallel plate. The solution of energy-transfer equations contains a `thickness-dependent term' which enables further extension of the problem to the `thin' film case. The new formulae are derived assuming a rectangular or triangular crystalline block distribution, which leads to exact integration of the diffracted intensity. In addition, a general term for Zachariasen [Acta Cryst. (1963), 16, 1139-1147] series expansion, assuming Gaussian domain distribution, is deduced. In fact, the new analytical results represent a variety of improved approximations which are simultaneously valid both for weak and for strong extinction effects usually observed in textured films. The formulae are used for computing the pole density and secondary extinction in electrodeposited nickel films having different texture sharpnesses. It may be anticipated that the precision in any X-ray diffraction characterization of films could be enhanced using the improved secondary-extinction corrections.