Bragg Diffraction of X-Rays by Single Crystals with Large Microdefects

Abstract

Dynamical wave fields formed in imperfect single crystals by diffusely scattered waves have been considered in the two-beam case of diffraction for the homogeneous distribution of microdefects with large sizes. Wave vectors of the constituent plane waves include the complex dispersion corrections accounting for multiple diffuse scattering processes. The corresponding dynamical diffuse scattering amplitudes and cross-sections in vacuum have been derived for both reflection and transmission directions. The diffuse component of crystal reflectivity has been calculated in the approximation of semiinfinite crystal and has been integrated over exit angles for two microdefect types: spherical clusters and prismatic dislocation loops. The obtained formula for the diffuse reflectivity has been analyzed and compared with the known kinematical one.Dinamiqeskie volnovye pol¾, obrazuemye v nesoverxennyh monokristallah diffuzno rasse¾nnymi volnami, rassmotreny v dvuhvolnovom sluqae difrakcii dl¾ odnorodnogo raspredeleni¾ mikrodefektov bol#xih razmerov. Volnovye vektory sostavl¾ˇ §ih ih ploskih voln soderwat kompleksnye dispersionnye popravki, uqityvaˇ §ie processy mnogokratnogo diffuznogo rasse¾ni¾. Sootvetstvuˇ §ie amplitudy i seqeni¾ dinamiqeskogo diffuznogo rasse¾ni¾ v vakuume vyvedeny dl¾ napravlenij otraweni¾ i prohowdeni¾. Diffuzna¾ komponenta otrawatel#noj sposobnosti kristalla vyqislena v pribliwenii polubeskoneqnogo kristalla i prointegrirovana po uglam vyhoda dl¾ mikrodefektov dvuh tipov: sferiqeskih klasterov i prizmatiqeskih dislokacionnyh petel#. Vypolnen analiz poluqennoj formuly dl¾ diffuznoj otrawatel#noj sposobnosti i provedeno ee sravnenie s izvestnym kinematiqeskim vyraweniem.

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

“…[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:…”

“…The diffuse component of the dynamical differential reflection coefficient of imperfect crystal with randomly distributed microdefects has the form [22]:…”

“…Function F(q) in Eq. (40) for momentum transfers in Huang scattering region, i.e., at k  k m  1/R eff , where R eff is an effective radius of defect [22], can approximately be written 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].…”