Toward a secondary-extinction correction

The treatment of secondary extinction currently in general use by crystallographers is due to Becker & Coppens [Acta Cryst. (1974), A30, 129-147]. It is derived from approximate solutions to the Darwin transfer equations developed by Zachariasen [Acta Cryst. (1967), 23, 558-564]. Among the approximations invoked by Zachariasen is that the effects of scattering and absorption are to be treated separately. A scheme is here proposed which makes that unnecessary. It is further suggested that progress in the correction of experimental data for secondary- extinction effects is more likely if one begins with the exact solution to the transfer equations due to Werner [J. Appl. Phys. (1974), 45, 3246-3254]. That solution has so far not penetrated the diffraction literature, probably because it is in the form of a difficult infinite series of Bessel functions. In one special case, which nevertheless has attracted the general attention of those interested in this subject, it is shown that the Werner series may be summed, yielding an integral equation involving only the zero-order Bessel function. Excellent closed-form approximations to this integral, accurate to about 1% or less, are displayed.