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.

Abstract

X-ray integrated intensities J were measured from Si single crystals containing dislocations as a function of crystal thickness using Mo Kalpha 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 microm and 2.4-7.3 microm, 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.