The dynamical scattering amplitude of an imperfect crystal. II. A relation between Takagi's dynamical equation and a more exact dynamical equation

The importance of second-order partial derivatives in the theory of high-energy-electron diffraction from imperfect crystals

“…In this case one must use a more rigorous formulation of the dynamical theory (e.g. Kuriyama, 1972) to describe the diffraction process.…”

Dynamical effects in X-ray–thermal phonon interactions in symmetric Bragg reflections

“…This characterization becomes particularly important in the immediate neighborhood of the totally reflecting region. Since the distortions of an ideal crystal by thermal phonons are small, the more general treatment of scattering in distorted crystals by Kuriyama (1972) is not needed here.…”

On the asymmetric limits for the scattering of X-rays from imperfect crystals in the Bragg case

“…The rigorous treatment of X-ray dynamical scattering from an imperfect crystal is a difficult problem. Kuriyama (1970Kuriyama ( , 1972 and Kuriyama & Miyakawa (1970) have made valuable contributions to this field via a quantum-field-theoretical formulation of the problem. However, the numerical solution of Kuriyama's equations would seem to involve a large amount of computer time compared with the more approximate Takagi-Taupin equations (Takagi, 1962(Takagi, , 1969Taupin, 1964;Kuriyama, 1972) since his equations involve an extra angular variable describing the spreading out of the diffracted beams due to crystal imperfections.…”

“…Kuriyama (1970Kuriyama ( , 1972 and Kuriyama & Miyakawa (1970) have made valuable contributions to this field via a quantum-field-theoretical formulation of the problem. However, the numerical solution of Kuriyama's equations would seem to involve a large amount of computer time compared with the more approximate Takagi-Taupin equations (Takagi, 1962(Takagi, , 1969Taupin, 1964;Kuriyama, 1972) since his equations involve an extra angular variable describing the spreading out of the diffracted beams due to crystal imperfections. For certain classes of models of an imperfect crystal, and most particularly for a crystal consisting of local mosaic blocks, Kuriyama (1972) has indicated that one can expect the solution of the Takagi-Taupin equations to be very close to the solution of his more accurate equations.…”

“…However, the numerical solution of Kuriyama's equations would seem to involve a large amount of computer time compared with the more approximate Takagi-Taupin equations (Takagi, 1962(Takagi, , 1969Taupin, 1964;Kuriyama, 1972) since his equations involve an extra angular variable describing the spreading out of the diffracted beams due to crystal imperfections. For certain classes of models of an imperfect crystal, and most particularly for a crystal consisting of local mosaic blocks, Kuriyama (1972) has indicated that one can expect the solution of the Takagi-Taupin equations to be very close to the solution of his more accurate equations. In crude terms, one might understand this to be so because the Takagi-Taupin equations are essentially correct for a perfect crystal and so should correctly treat the scattering within perfect-crystal mosaic blocks, while the boundary conditions between blocks may be incorporated via, say, an appropriate numerical solution procedure for the equations, as in the present work.…”