Experimental verification of the statistical dynamical theories of diffraction

The influences of crystal imperfection on dynamical diffraction have been studied by measuring integrated intensities in the Laue case as a function of X-ray wavelength. SiO₂-precipitate microdefects were introduced into Czochralski-grown silicon wafers by heating at 1223 K for five different periods of time varying from 25 to 145 h. The X-ray intensities were measured by the energy-dispersive diffraction method over the wavelength range 0.15 to 0.78 Å. The measurements revealed that increases in both the integrated intensity and the Pendellösung beat spacing were accompanied by a decrease of the beat amplitude with increasing heating period. The data were compared quantitatively with those obtained using the theories of Kato [Acta Cryst. (1980), A36, 763–769, 770–778] and Becker & Al Haddad [Acta Cryst. (1992), A48, 121–134). The former theory, where the correlation length Γ for the wavefield amplitudes is assumed to be close to the extinction distance, did not describe the data. The latter theory fitted only the specimen heated for 25 h. A model assuming that Γ is independent of wavelength and varies with crystal perfection and reflection plane was proposed in lieu of Kato's assumption. The application of the model led to an excellent agreement for the specimens studied. The best fitted values of Γ, from 0.07 to 1.6 μm, were much the same as the correlation lengths of the phase factor, from 0.04 to 2.6 μm.