Acta Crystallographica Section A

Foundations of Crystallography

Volume 58, Part 1 (January 2002)

research papers

Acta Cryst. (2002). A58, 54-59 [ doi:10.1107/S0108767301016221 ]

Experimental study on the correlation lengths of the statistical dynamical theory of X-ray diffraction by measurements of integrated intensities from silicon crystals with dislocations

D. Sakaki and T. Takama

Abstract: X-ray integrated intensities J were measured from Si single crystals containing dislocations as a function of crystal thickness using Mo K [alpha] radiation. The thickness dependence of J was compared with the statistical dynamical theory of Kato [Acta Cryst. (1980), A36, 763-769, 770-778], which contains three parameters: the static Debye-Waller factor E, the correlation length [tau] for the phase factor and the correlation length [Gamma] for the wave-field amplitudes. These three parameters are absolutely required to interpret the experimental data in contrast to the case of [gamma] -ray experiments in which J can be described by the parameter E alone. For our specimens, the ranges of the fitted values of [tau] and [Gamma] are 0.003-0.108 µm and 2.4-7.3 µm, respectively, depending on the reflection plane and the crystal perfection. This fact indicates that the assumption made in Kato's original theory, that [Gamma] is proportional to the extinction distance, should be abandoned. The reason for which the two correlation lengths can be neglected in the [gamma] -ray experiments is clarified.

Keywords: correlation lengths; dynamical diffraction; dislocations.