On the treatment of primary extinction in diffraction theories based on intensity coupling

Abstract

Czochralski-grown silicon crystals of approximately 10 cm diameter and 1 cm thickness have been annealed at 1470 K in order to create a homogeneous defect structure, which is a basic condition for all statistical treatments of extinction. Absolute values of the integrated reflecting power of the 220, 440 and 660 reflections have been measured with 0.0392 A γ-radiation in symmetrical Laue geometry for sample thicknesses between 1 and 3 cm. The amount of extinction in the experimental data varies between y ≃ 0.95 and y ≃ 0.05. Darwin's extinction theory has been used to describe the thickness dependence of the data sets. Despite some shortcomings of the model, it is shown that the assumption of a physically unrealistic Lorentzian mosaic distribution models the effect of primary extinction in an extinction theory based on the energy-transfer model. The sharp central part of the Lorentzian distribution produces a reduction of the effective sample thickness due to primary extinction, whereas the wings of the distribution dominate the correction for secondary extinction in the remaining part of the sample. A more flexible mosaic distribution function is proposed, which should be useful in cases of severe extinction.