Anomalous small-angle x-ray scattering determination of the partial structure factors and kinetic study of unmixed Cu-Ni-Fe alloys

Abstract

Different unmixed states of a Cu-Ni-Fe alloy have been studied by anomalous small-angle x-ray scattering (ASAXS). The data were obtained at different x-ray energies near the Fe and Ni absorption edges: ASAXS intensities increase by a factor of 3, varying with the atomic contrast (with respect to Cu). Various methods for the determination of partial structure factors (PSF) have been tested and results are found reliable if we use the intensity data in the proximity of at least two edges. The homoatomic PSF curves have similar shapes with a maximum I which increases and shifts towards lower q values as the power laws I -t ' and q -t, and the scaling behavior is obeyed. These features are very similar to the ones observed during late stages of aging of concentrated binary systems. On the other hand, there is evidence that the phase separation of Cu-Ni-Feo l& at 500'C cannot be modeled by a two-phase system, and different possible partitioning of Cu, Ni, and Fe are discussed.

Small-angle scattering studies of phase separation and defects in inorganic materials

“…For Cu-42 at.% Ni-15 at.% Fe aged at temperatures between 733 and 823 K, anomalous SAXS experiments have shown deviations from a quasibinary behaviour (Lyon & Simon, 1987, 1988. Although the partial structure functions S 0 all look very similar, the peak position, Q,,, for Scat, clearly appears at smaller values than Q,,, for SNiNi or Sveve and S2veNi is not equal to SvcveSN~N~-there are thus two independent structure functions in this system.…”

“…A three-phase model (i.e. a second precipitate phase) can be ruled out (Lyon & Simon, 1987). Inhomogeneities in the matrix or the precipitate and segregation at interfaces may of course also occur in binary systems with a well defined precipitate phase.…”

The nature of the scattering tail in Cu–Ni–Fe and Invar alloys investigated by anomalous small-angle X-ray scattering

“…They have been intensively studied by SANS (Aadlers, Van Dijck & Radelaar, 1984;P6erschke, Wagner, Wollenberger & Fratzl, 1986) and by ASAXS (Lyon & Simon, 1987, 1988. The intensity displays a maximum which increases and shifts towards low q values (q = 4-n-/,~ sin0) as ageing goes on: it was shown that it corresponds to an orderly pattern of two phases whose growth is driven by coarsening.…”

Structure analysis of multiphase systems by anomalous small-angle X-ray scattering

“…Two of them borrow the partial structure factors (PSFs) formalism that is used in wide angle x-ray scattering (WAXS) [24]. De Fontaine, Lyon, and Simon and Regan and Bienenstock applied the partial structure factors, that are Fourier transforms of the atomic pair correlation functions, to the ASAXS data analysis [25][26][27][28][29][30][31][32][33]. The second method was proposed by Haubold [34,35], and is often referred as the "BhatiaThornton" method.…”

“…The coefficients of the equations are being calculated from the atomic scattering factors of the resonant atoms. However, the system is often ill-conditioned [26,28], and a number of methods were proposed to solve it, including overdetermination by measuring at more then three energies, or omitting the smallest term in the system.…”