Analysis of X‐ray extinction in crystals with inhomogeniously distributed dislocations

Abstract

The secondary extinction theory of Zachariasen for mosaic crystals as well as the formalism of Becker&Coppens have been used for substructure analysis (lattice disorientations, block size, density of excess dislocations, etc.) in crystals with inhomogeniously distributed dislocations in the Bragg case of diffraction geometry. In the case of large crystals D S >>Λ hkl the mean total density ρ D of randomly distributed dislocations was also estimated taking into account additionally the primary X-ray extinction treatment. In this connection two cases are considered: I) pure secondary extinction related to arrangement of dislocation walls and II) mixed extinction in crystals with large subgrains related to randomly distributed dislocations and arrangement of dislocation walls. In order to check the considerations, the experimental and calculated data were compared for Be (model I) and Cu (model II) single crystals. The weakly distorted single crystals of Be and Cu were experimentally investigated in the Bragg case of diffraction geometry using Cu Kα 1 radiation by means of double crystal diffractometer. A new experimental procedure was proposed. Using alternative technique for substructure analysis (for instance EBSD) the reliability of analysis based on extinction phenomenon in weakly distorted single crystals has been checked.

Point Contact Spectroscopy of Nb3Sn Crystals: Evidence of a CDW Gap Related to the Martensitic Transition

“…A characteristic parameter in a crystal is the high value of the extinction coefficient, which converges to identical values for both samples: so in those crystals we found 0.82 (18) for NS1 and 0.8(2) for NS4 [18]. Assuming that applied correction covers mixed primary and secondary extinctions, this result suggests that samples should have similar block sizes and similar concentrations of randomly distributed dislocations [19].…”

Point contact spectroscopy of crystals: Evidence of a CDW gap related to the martensitic transition

“…A characteristic parameter in a crystal is the high value of the extinction coefficient, which converges to identical values for both samples: so in those crystals we found 0.82(18) for NS1 and 0.8(2) for NS4 [18]. Assuming that applied correction covers mixed primary and secondary extinctions, this result suggests that samples should (7) Nb-Nb (Å) 2.6350 (5) 2.6266 (6) Nb...Nb (Å) 3.2272 (5) 3.2169 (8) have similar block sizes and similar concentrations of randomly distributed dislocations [19].…”

X-ray extinction changes due to dislocations

“…The procedure was applied to Cu and Be single crystals in the Bragg case, but yields reliable results in combination with alternative techniques, e.g. electron backscatter diffraction, transmission electron microscopy (for more details, see Masimov, 2007a).…”

“…It was proposed that the primary extinction can be calculated according to the IKS procedure. Such a procedure enables the calculation of the block size, and the densities of excess dislocations in walls and chaotically distributed dislocations in subgrains (for more details see Masimov, 2007a).…”

“…where a is the lattice parameter; D ' 1 is a coefficient taking into account dynamical effects and depends on the reflections. Masimov (2007a) used the radius of a heavily distorted region calculated from condition (3) given by Authier & Balibar (1970) as the cut-off radius for a correct determination of the static Debye-Waller factor as…”