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' pl ane parallel plate. The solution of energy-transfer equations contains a 't hickness-dependent term' which enables further extension of the problem to the 'thin' film case. The new formulae are derived assuming a rectangular o r triangular crystalline block distribution, which leads to exact integrati on of the diffracted intensity. In addition, a general term for Zachariasen [Acta Cryst. (1963), 16, 1139-1147] series expansion, assuming Gaussian do main distribution, is deduced. In fact, the new analytical results represen t a variety of improved approximations which are simultaneously valid both for weak and for strong extinction effects usually observed in textured fil ms. The formulae are used for computing the pole density and secondary exti nction in electrodeposited nickel films having different texture sharpnesse s. It may be anticipated that the precision in any X-ray diffraction charac terization of films could be enhanced using the improved secondary-extincti on corrections.