Intensity of secondary scattering of X-rays by non-crystalline materials. Transmission gemoetry with an incident-beam monochromator

Equations are derived for the intensity ratio R of secondary to primary scattering in the fixed-sample transmission case with an incident-beam monochromator crystal that results in a polarization ratio K_m for unpolarized incident radiation. A table allows R to be calculated for K_m = 0. This table, along with the one for K_m = 1 published previously for the case without a monochromator, allows R to be estimated before an experiment is done and thus an optimum experiment can be designed. A simple computer program allows direct calculation of R once experimental data are obtained if it is desired to avoid interpolation. Determination of R involves some approximation, but the values obtained are sufficiently accurate for most purposes. However, R can be improved using exact equations, if desired. If synchrotron radiation polarized normal to the plane of scattering of the monochromator is used, R does not depend on K_m, and the value of R for K_m = 0 applies despite the true value of K_m. As is expected from symmetry considerations, R is independent of K_m in the small-angle scattering limit.