X-ray diffuse scattering of a decomposing hexagonal alloy

Abstract

A new type of X-ray diffuse scattering has been found in the early stages of decomposition of the hexagonal phase of Mn-44at.% A1. The diffuse scattering is observed mainly within the basal plane of the reciprocal lattice and differs for the 10T/and l l~l points. Theoretical calculations of the X-ray diffuse scattering according to the kinematic scattering theory have been performed for the elastically isotropic and anisotropic cases and for precipitates of various forms and orientations with and without a depleted layer surrounding them. In the latter case, a zero-intensity region near the reciprocal-lattice points occurs. There are cases of good agreement between the experimental results and calculations for the precipitates with a depleted layer.

Diffraction Analysis of Defects: State of the Art

“…Characterization of orientation space may be performed by white-beam techniques Larson et al, 2002;Barabash et al, 2003a;Levine, 2006), rocking curve analysis (Hirsch, 1956;Wilkens et al, 1987;May et al, 1995;Breuer et al, 2000;Barabash, 2001), reciprocal space mapping (Barabash et al, 1990) and/or orientation mapping (Laurisden et al, 2000;Margulies et al, 2001;Jakobsen et al, 2006). Generally, the radial intensity distributions, I(2θ), and orientation space distributions, I(q ⊥ ), have quite different characters correlating with distinct parameters of the dislocation ensemble.…”

Lattice and continuum theories of Huang scattering

“…The continuum theory of diffuse scattering from isolated defects [2][3][4][5][13][14][15][16] gives a detailed analysis of isodiffuse surfaces in the vicinity of reciprocal-lattice sites for cubic crystals. This theory has been worked out for a wide variety of geometries and defect types and is summarized in a recent book [3].…”

“…Note that the bulk modulus K is associated with the inner material and the shear modulus µ with the outer material, although here we do not make any distinction as the two materials are assumed to be the same elastically. We can rewrite the result (9) in a more convenient form if we use the fact that the difference R = R 1 − R 2 is small, and also use the Poisson ratio ν as given by K/µ = 2 3 (1 + ν)/(1 − 2ν) so that (9) becomes…”

“…In the case when all of the scattering factors f i in (4) are not all set equal, the separation into Bragg and Huang scattering in (12) must be done with more care [2][3][4]. In particular there are the strong Bragg peaks that we have been discussing, with their associated diffuse scattering I D ( Q) given by…”

“…The theory of diffuse scattering from random alloys was developed many years ago. After the very important early work of Huang [1], a rather complete theory of the diffuse scattering from alloys was developed by Krivoglaz and co-workers [2][3][4] in the Ukraine. This pioneering work contains most of the formalism necessary to understand diffuse scattering in the continuum limit.…”