EXPANSION OF THE X-RAY STATISTICAL DYNAMICAL SCATTERING THEORY TOWARDS PRACTICAL APPLICATIONS.
A. M. Poliakov
Moscow State Steel and
Alloys Institute, 117936, Moscow, Leninsky pr. 4,
X-ray and Metal Physics Department.
Statistical description of x-ray scattering in crystals with defects is one of the most physically interesting and practically important problems of x-ray optics because it is a key to the new method development of defects control. In most of the practical applications defect distribution in the sample under investigation may be assumed to be random, therefore x-ray scattering amplitudes are also random, and the observed intensities should be statistically averaged. The valuable example of a statistical x-ray scattering theory is well-known Krivoglaz's scattering theory [1], developed in the kinematical (or single-scattering) approximation of scattering process.
Kato [2] applied statistical principles to dynamical (multiple-scattering) theory. Mathematical difficulties allow considering the case t << L only, where t- correlation length of e+-ihu random field, L-extinction length. Rigorous statistical dynamical treatment was performed by Kato [3] for Gaussian random field e+-ihu and by Polyakov, Chuchovskii & Piskunov [4] without any statistical assumptions. Final equations in both treatments were too complicated for practical calculations, but the simplifications lead to the already known case t << L.
The polarisation and intensity operators in the case 
(see [4] for definitions)
are presented now. The calculations of these operators were
performed on the basis of thorough treatment of coherent and
diffuse scattering process. These calculations allow to compose
the approximate expressions for polarisation and intensity
operators, which lead to correct solution of coherent and diffuse
scattering problem in both cases t << L
and . It is assumed
that these approximate expressions are close enough to the exact
ones.
The proposed approximation is especially interesting for the investigations of statistically distributed dislocations because the value t ~ nd ~ L (nd-dislocation density) exhibits main extinction effects. The case of the II -class defects (dislocations in particular) is discussed in details. It allows practically valuable intensity calculations for the crystals with dislocations density.