Anomalous X-ray diffraction from ω nanoparticles in β-Ti(Mo) single crystals

Abstract

Anomalous X-ray diffraction (AXRD) is a technique which makes use of effects occurring near the energy of an absorption edge of an element present in the studied sample. The intensity of the diffracted radiation exhibits an anomalous decrease when the primary beam energy matches the energy needed to excite an electron from an atomic orbital. The characteristics of this step are sensitive to the concentration of the 'anomalous' element and its spatial distribution in the sample. In the present investigation, AXRD was employed to study ! particles in a metastable titanium alloy Ti-15Mo (in wt%). The experiments were done in an energy range around the Mo K edge at 20.0 keV, allowing investigation of the distribution of Mo in the material, which is rejected from the volume of ! particles during their diffusion-driven growth. This paper deals with diffuse scattering patterns around the (006) diffraction maximum. It was observed that different regions of the diffuse scattering exhibited different variations of diffracted intensity with the incident photon energy near the absorption edge. Numerical simulations of diffuse scattering patterns as well as of energy dependences of the scattered intensity were performed. It was found that the observed patterns and their dependence on the primary beam energy can be explained by taking into account (a) elastic deformation of the matrix arising from the presence of slightly misfitting ! particles and (b) the presence of a 'cloud' of a higher Mo concentration around ! particles.

Composition of ω-Phase Particles in Ti(Mo) Alloys Studied by Anomalous X-ray Diffraction

“…The particle radii are between 2 and 8 nm; these data are in agreement with the results of X-ray small-angle scattering in Refs. [7,20], as well as with transmission electron microscopy [22]. From the shape of the diffraction maximum, we were also able to roughly estimate the relative rms deviation of the radii to R = (30 ± 15)%; however, this parameter has almost no influence on the resulting values of R L,V .…”

“…parallel to the detector plane, K i,f are the wave vectors of the primary and scattered X-rays, h is the reciprocal-lattice vector (diffraction vector). The elliptical shape of the maximum is caused by the ellipsoidal particle shapes, the half-axes of the iso-intensity ellipses are inversely proportional to the half-axes of the particle ellipsoids and depend also on the orientation of the ellipsoid axes with respect to the detector plane [21,22].…”

“…Since the heoretical description of AXRD effect in ω-Ti nanoparticles is presented in detail in our previous paper [22], here we show only a short overview. In contrast to the previous study, where we investigated the AXRD in the β-Ti matrix, here we completely neglect inhomogeneous deformation in the very small volumes of the ω-Ti nanoparticles, which makes the whole theoretical description much simpler.…”

“…[21], we showed that the ω-Ti nanoparticles contain thin shell layers, in which the phase transformation β → ω is not complete, and estimated the shell layer thickness to about 1 nm. In our previous paper [22], we used anomalous X-ray diffraction (AXRD) for the study of Mo-rich "clouds" around the growing ω-Ti nanoparticles [23]. The method consists in measuring the energy dependence of the reciprocal-space distribution of X-ray intensity diffracted from the β-Ti matrix for the energies E of the primary photons slightly below and above the MoK absorption edge E K ≈ 20.0 keV.…”