X-ray diffraction line broadening due to dislocations in non-cubic materials. I. General considerations and the case of elastic isotropy applied to hexagonal crystals

Abstract

Use is made of the theory of dislocation-induced Xray diffraction line broadening in the form presented by Krivoglaz, Martynenko & Ryaboshapka [Fiz. Metall. Metalloved. (1983), 55, to express the socalled orientation factors occurring in the relations of diffraction profile parameters (e.g. Fourier coefficients, line widths) in a form which systematically takes into account both the lattice geometry and the elastic behaviour of the scattering crystals. The formalism can be used, in principle, for any materials and types of dislocations. In the case of elastically isotropic media the orientation factors can be described by analytical expressions. The application of the formalism is demonstrated in some detail for various slip systems in hexagonal polycrystals with random orientation of grains.

Nanocrystalline materials studied by powder diffraction line profile analysis

“…There are 4, 2 and 5 slip systems in the hai, hci and hc þ ai Burgers vector groups, respectively [47,93]. A computer program was elaborated to determine the Burgers vector population from the measured values of q1 and q2.…”

The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice

“…A more comprehensive compilation of the dislocation contrast factors for copper taking into account elastic anisotropy has been presented by Wilkens (1987). A general formalism for the calculation of the contrast factors, especially for hexagonal crystals, has been given by Kuzel, 1988, 1989;.…”

Microstructure et profil des raies de diffraction des rayons X

“…Ces calculs sont rapportés pour des matériaux cubiques [26] et hexagonaux [27]. Pour des cristaux de symétrie cubique, les facteurs moyens de contraste des dislocations peuvent être écrits de la façon suivante [26] :…”