Bragg Diffraction of X-Rays by Single Crystals with Large Microdefects I. Generalized Dynamical Theory

Abstract

Basic equations of the dynamical scattering theory in momentum space have been considered in the two-beam approximation for single crystals containing randomly distributed microdefects commensurable with extinction length. The amplitudes of coherent and diffusely scattered waves inside the crystal have been found by using the perturbation theory with average and fluctuating parts of crystal polarizability as small parameters. In the complex dispersion corrections to the wave vectors of coherent and diffuse waves, the imaginary parts of which describe the attenuation of these waves due to diffuse scattering, the dynamical effects in diffuse scattering and their dependences on the incidence angle have been taken into account. These corrections also take account of the influence of any multiple diffuse scattering processes. The coherent component of crystal reflectivity has been calculated in the approximation of semiinfinite crystal for an arbitrary diffraction geometry.Osnovnye uravneni¾ dinamiqeskoj teorii rasse¾ni¾ v impul#snom prostranstve rassmotreny v dvuhvolnovom pribliwenii dl¾ monokristallov, soderwa §ih sluqajno raspredelennye mikrodefekty s radiusami por¾dka +kstinkcionnoj dliny. Amplitudy kogerentnyh i diffuzno rasse¾nnyh voln vnutri kristalla najdeny s ispol#zovaniem teorii vozmu §enij so srednej i fluktuacionnoj qast¾mi pol¾rizuemosti krustalla v kaqestve malyh parametrov. V kompleksnyh dispersionnyh popravkah k volnovym vektoram kogerentnyh i diffuznyh voln, mnimye qasti kotoryh opisyvaˇt zatuhanie +tih voln iz-za diffiznogo rasse¾ni¾, uqteny dinamiqeskie +ffekty v diffuznom rasse¾nii i ih zavisimost# ot ugla padeni¾. *ti popravki uqityvaˇt takwe vli¾nie lˇbyh mnogokratnyh processov diffuznogo rasse¾ni¾. Kogerentna¾ komponenta otrawatel#noj sposobnosti kristalla vyqislena v pribliwenii polubeskoneqnogo kristalla dl¾ proizvol#noj geometrii difrakcii.

Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

“…Then, from Maxwell's equations after the Fourier transformation at ||  1, the set of basic equations of dynamical theory for the imperfect crystal in momentum space can be derived [21]:…”

“…[21,22] if inequalities hold for the dispersion corrections to the wave vectors of coherent and diffusely scattered waves, respectively, which describe the attenuation of these waves due to diffuse scattering:…”

“…According to the generalized dynamical theory of the X-ray scattering in imperfect single crystals [21,22], the amplitude reflection coefficient in Eq. (14) can be written for each polarization state ( and ) in the form:…”

“…This implies also the account for dynamical effects in diffuse scattering intensity and diffuse scattering effects in coherent intensity distributions. Such self-consistent approach in the triple-crystal X-ray diffractometry [15][16][17][18][19], which is necessary for the reliable quantitative characterization of defects and strains in crystals, was consequently developed on the base of the generalized dynamical theory of X-ray scattering by imperfect crystals with randomly distributed microdefects [20][21][22].…”

Unique Informativity of the Diffuse Dynamical Combined Diffractometry of Materials and Products of Nanotechnologies

“…Указанная динамическая теория рассеяния в кристаллах с де-фектами была построена впервые сорок лет назад для кристаллов со слабыми отклонениями от периодичности [15][16][17] и двадцать пять лет назад -обобщена на случаи произвольных отклонений, что по-зволило провести в рамках динамической теории классификацию дефектов [18][19][20][21][22][23], а пять-десять лет назад -обобщена на случаи дефектов, размеры которых соизмеримы с длиной экстинкции, и кристаллов с упругим изгибом и дефектами [38][39][40][41][42][43][44][45][46][47][48][49].…”