A general approach for determining the diffraction contrast factor of straight-line dislocations

Abstract

Dislocations alter perfect crystalline order and produce anisotropic broadening of the X-ray diffraction profiles, which is described by the dislocation contrast factor. Owing to the lack of suitable mathematical tools to deal with dislocations in crystals of any symmetry, contrast factors are so far only known for a few slip systems in high-symmetry phases and little detail is given in the literature on the calculation procedure. In the present paper a general approach is presented for the calculation of contrast factors for any dislocation configuration and any lattice symmetry. The new procedure is illustrated with practical examples of hexagonal metals and some low-symmetry mineral phases.

Characterization of dislocations in germanium layers grown on (011)- and (111)-oriented silicon by coplanar and noncoplanar X-ray diffraction

“…It has two contributions: the elastic due to the tensor E and the geometric due to the tensor G, which describes the dependence on the used reflection. Comparing to the similar expressions used in the powder diffraction case (Klimanek et al, 1988;Martinez-Garcia et al, 2009;Ungá r et al, 2001;Scardi & Leoni, 2002) one can see that w ðzÞ is the analog of the dislocation contrast factor, but it has two significant distinctions: (i) it is not a factor but a 2 Â 2 matrix and (ii) in the case of misfit dislocations it is z dependent owing to the effect of the boundary. 3.2.2.…”

“…The tensor E in equation (5) is a fourth-rank tensor describing strain fluctuation. In analogy to the approach used in powder X-ray diffraction, this tensor is the elastic component of the dislocation contrast factor (Klimanek et al, 1988;Martinez-Garcia et al, 2009). In the case of epitaxial layers, this tensor becomes z dependent (which is not the case for powder X-ray diffraction), its components in the Dm coordinate system being equal to …”

On the Modeling of the Diffraction Pattern from Metal Nanocrystals

“…As of the most recent developments, [24] WPPM can use virtually any crystalline domain shape and strain models for dislocations in any crystal system. [25] Nanocrystals can then be studied down to small sizes, with the highest precision for the spherical domain shape. [26] Less accurate is the description of the complex effects caused by the nanocrystal surface, which displaces atoms from the expected perfect crystal positions: so far only simplified models for this surface relaxation effect could be implemented in a WPPM procedure.…”

Diffraction peaks from correlated dislocations

“…For screw dislocations considered here, c ¼ p. For general expressions of c that take into account crystal symmetry, elastic anisotropy, and dislocation arrangements we refer to a recent paper [22] that also reviews previous works. Calculation of the correlation function GðxÞ for positionally uncorrelated dislocations [1,2] gives f ðhÞ ¼ Àln h. If this formula is used in the whole range of x from 0 to R in the Fourier integral (3), the calculated structure factor SðqÞ reveals unphysical oscillations caused by an abrupt truncation of the integrand.…”