Determination of displacements from nanoprecipitates in a Cu–Ni–Fe single crystal using anomalous small-angle and large-angle X-ray scattering

Abstract

Single crystals of Cu±41.5 at.% Ni±16 at.% Fe have been studied by small-angle and large-angle X-ray scattering in order to determine the displacements induced by the disc-like precipitates formed during decomposition. The smallangle X-ray scattering (SAXS) patterns gave information on the size and the organization of the precipitates, while the scattering near Bragg peaks allows a determination of the distortions of the lattice created by these precipitates. The variations of the atomic scattering factors of Fe, Ni and Cu (for the large-angle measurements) were used to determine both the partial structure functions (`chemical' data) and the partial displacements. The precipitates were found to be enriched in Fe and Ni, which induced a contraction of the lattice, while the depleted matrix (mainly Cu) was dilated. This succession of compressed and dilated regions is very stable and prevents a single precipitate from growing much in this direction during coarsening. This can explain why a single precipitate tends to grow mainly in the orthogonal directions, where the extension of the displacements is smaller than the precipitated region.

Small-angle scattering in materials science - a short review of applications in alloys, ceramics and composite materials

“…The topological contribution, I t (Q) + I ct (Q), is negligible around the 0 th order Bragg-peak, that is, in the small-angle scattering region. Under some approximations (for details, see Lyon et al, 2000Lyon et al, , 2001, the asymmetric part of the intensity around a Bragg peak Q B is…”

“…Anomalous scattering may also be used in the combination of small angle and diffuse scattering described in the previous paragraph (equations (3) and (4)). Lyon et al (2001) have developed this approach for the study of Cu-Ni-Fe single crystalline alloys. Fig.…”

“…In this alloy, the SAXS pattern is practically independent of X-ray energy. (b-d) Two-dimensional large-angle scattering spectra (logarithmic scale) at different photon energies, appearing around a 200 Bragg peak of a similar sample aged for 3 h at 773 K (fromLyon et al, 2001).…”

Displacement measurements from nanoprecipitates in alloyed Cu single crystals using anomalous small- and wide-angle X-ray scattering

“…We have used a slightly different approach, which is summarized below, emphasizing the part that is particularly relevant to this study. The details can be found in papers by Lyon et al, (2000Lyon et al, ( , 2001.…”

“…Such effects can be studied only with single crystals. Their use is becoming quite frequent in the small-angle X-ray scattering (SAXS) field (see for example, Guilarducci et al, 1987 ;Sato et al, 1988 ;Fratzl et al, 1993 ;Lyon and Simon, 1994 ;Pedersen et al, 1997 ;Vyskocyl et al, 1997), but very few experiments have been attempted to determine the associated displacements (see, e.g., Lyon et al, 2000Lyon et al, , 2001. We have performed anomalous small-angle X-ray scattering (ASAXS) experiments in order to get information on the precipitates (dimension, mutual distance and chemical parameters like tie-line), while the elastic distortions of the lattice induced by these precipitates were obtained from anomalous wide-angle X-ray scattering (AWAXS) near a Bragg peak.…”