X-ray diffraction under specular reflection conditions. Ideal crystals

The theory of X-ray diffraction by ideal crystals under the conditions when the incident and diffracted beams are directed at small angles to the entrance surface of a crystal has been developed. Besides the diffracted wave propagating inside the crystal (i.e. Laue-case diffraction) there are two specular reflected waves arising from incident and diffracted waves respectively. Such a diffraction scheme has been recently put into practice [Marra, Eisenberger & Cho (1979). J. Appl. Phys. 50, 6927-6933]. It is found that at small glancing angles of incidence there exist directions in which the intensity of the reflected diffracted wave is close to the incident wave intensity, while both the specular reflected wave and diffracted wave intensities are close to zero. The analytical expressions are obtained for the diffraction curve shape. It is shown that for diffraction curve measurements high collimation through the glancing angle of incidence of X-rays on the crystal, Φ, is sufficient. There is no need to provide collimation through parameter a denoting deviation from exact Bragg conditions. Owing to the rigid relation between α, Φ and the angle of emergence of the reflected diffracted wave from the entrance surface of the crystal, Φ′, Φ² = α + Φ′², when measuring the intensity of the reflected diffracted wave as a function of Φ, the intensity is obtained as a function of α. Measurement of Φ′ with the accuracy of about 30′′ corresponds to accuracy through α of about 0.1′′. These facts sufficiently simplify the performance of experiment and open wide prospects for studies of crystal structure of thin subsurface layers with unique accuracy.