Diffraction by a randomly distorted crystal. I. The case of short-range order

Abstract

Kato's statistical theory of diffraction [Kato (1980). Acta Cryst. A 36 , 763-769, 770-778] is reformulated in a self-consistent manner. The local displacement field u ( r ) occurs through the phase factor φ ( r ) = exp [2 πi h . u ( r )]. The present paper is concerned with the limiting case where ( φ ~( r )) = E = 0: this corresponds to the situation where only secondary extinction is present. There are two correlation lengths in the problem, the first one τ for the phase factor φ , the second one Γ for the wave-field amplitudes. Kato assumed Γ » τ . It is shown in the present paper that Γ ≃ τ , a property which has important consequences for the general theory, where E ≠ 0, to be discussed in the second paper of this series.