Diffraction by a randomly distorted crystal. II. General theory

Abstract

A method is presented to deal with the propagation of X-rays or neutrons in a statistically distorted crystal in the general case where both short-range and long-range order are present: it is the generalization of a theory presented in a previous paper [Becker & Al Haddad (1990). Acta Cryst. A46, 123–129]. The main difference from Kato's formulation is concerned with the correlation length Γ of the incoherent part of the beams [Kato (1980). Acta Cryst. A36, 763–769, 770–778; Al Haddad & Becker (1988). Acta Cryst. A44, 262–270; Becker & Al Haddad (1990)]. The present formulation shows that Γ is variable within the sample under study, and is of the same order of magnitude as the correlation length τ of the phase factor [exp (27πih ˙ u) where u is the distortion field]. This is the main difference from Kato's approach where Γ was considered as >> τ. A detailed solution of the propagation equations is proposed and is applied to the case of silicon crystals containing a variable amount of oxygen, using measurements by Schneider, Goncalves, Rollason, Bonse, Lauer & Zulehner [Nucl. Instrum. Methods Phys. Res. (1988), B29, 661–674] using γ-ray diffraction. The present theory is in fair agreement with the observed intensities, although Kato's original proposition does not work.