F. Bley

The Samson phase, β-Mg2Al3, revisited

Co-Authors: Michael Feuerbacher, Carsten Thomas, Julien P. A. Makongo, Stefan Hoffmann, Wilder Carrillo-Cabrera, Raul Cardoso, Yuri Grin, Guido Kreiner, Jean-Marc Joubert, Thomas Schenk, Joseph Gastaldi, Henri Nguyen-Thi, Nathalie Mangelinck-Noël, Bernard Billia, Patricia Donnadieu, Aleksandra Czyrska-Filemonowicz, Anna Zielinska-Lipiec, Beata Dubiel, Thomas Weber, Philippe Schaub, Günter Krauss, Volker Gramlich, Jeppe Christensen, Sven Lidin, Daniel Fredrickson, Marek Mihalkovic, Wieslawa Sikora, Janusz Malinowski, Stefan Brühne, Thomas Proffen, Wolf Assmus, Marc de Boissieu, Francoise Bley, Jean-Luis Chemin, Jürgen Schreuer Abstract. The Al−Mg phase diagram has been reinvestigated in the vicinity of the stability range of the Samson phase, β-Mg2Al3 (cF1168). For the composition Mg 38.5 Al 61.5, this cubic phase, space group Fd-3m (no 227), a = 28.242(1) Å, V = 22526(2) Å3, undergoes at 214 °C a first-order phase transition to rhombohedral β′-Mg2Al3(hR293), a = 19.968(1) Å, c = 48.9114(8) Å, V = 16889(2) Å3, (i.e. 22519 Å3 for the equivalent cubic unit cell) space group R3m (no 160), a subgroup of index four of Fd-3m. The structure of the β-phase has been redetermined at ambient temperature as well as in situ at 400 °C. It essentially agrees with Samsons model, even in most of the many partially occupied and split positions. The structure of β′-Mg2Al3is closely related to that of the β-phase. Its atomic sites can be derived from those of the β-phase by group-theoretical considerations. The main difference between the two structures is that all atomic sites are fully occupied in case of the β′-phase. The reciprocal space, Bragg as well as diffuse scattering, has been explored as function of temperature and the β- to β′-phase transition was studied in detail. The microstructures of both phases have been analyzed by electron microscopy and X-ray topography showing them highly defective. Finally, the thermal expansion coefficients and elastic parameters have been determined. Their values are somewhere in between those of Al and Mg.

Using direct illumination CCDs as high-resolution area detectors for X-ray scattering

Abstract The use of charge-coupled devices (CCDs) under direct illumination of X-rays for two-dimensional position-sensitive detectors in high-resolution diffraction experiments is discussed. Two detectors are compared: a standard CCD and a “deep depletion” CCD. These give position resolution close to the pixel size ( ∼22 μm ), and energy resolution close to the theoretical resolution of a Si detector. These detectors can be used for photon-counting and an algorithm for electronic noise suppression is presented. This algorithm is useful for experiments with frequent readouts and low intensity. Examples demonstrating the advantages of this algorithm for diffraction experiments are given.

A small‐angle neutron scattering study of fine‐scale NbC precipitation kinetics in the α‐Fe–Nb–C system

The fine-scale precipitation of NbC in ferrite has been quantitatively characterized in the temperature range 873-1073 K for two alloy compositions, containing respectively 800 p.p.m. Nb and 400 p.p.m. Nb (by weight). Transmission electron microscopy (TEM) has revealed that the precipitates are located on dislocations, and have a plate-like morphology with an average aspect ratio between 2 and 3. Small-angle neutron scattering (SANS) has been systematically used to determine the precipitation kinetics. The validity of the quantitative SANS measurements of size and volume fraction has been assessed by TEM image analysis and chemical dissolution experiments. The precipitation kinetics is observed to depend strongly on temperature but to be similar for the two alloy compositions. From the measurements, it is inferred that precipitate nucleation is extremely rapid, in relation to the nature of the nucleation sites. A time-temperature transformation diagram is built from the kinetic data, showing a maximum reaction rate between 973 and 1073 K.

DLS and SAXS investigations of organic gels and aerogels

Abstract Recent investigations have shown that the structure of organic aerogels can be significantly modified by changing the precursors, the solvent and the nature of the catalyst involved in the sol–gel reaction. It is therefore highly desirable to investigate the sol–gel mechanism. For this purpose, dynamic light scattering (DLS) measurements have been performed at different stages of the reaction for base- or acid-catalyzed gelation of resorcinol–formaldehyde (RF) using water or acetone as solvents. The structure of aged gels was investigated by small-angle X-ray scattering (SAXS) and compared to that of the aerogels obtained after exchange of solvent by supercritical CO2 and drying of the aged gels. It is shown that acid-catalyzed gelation of RF in acetone can be described by percolation, which explains that this series of aerogels consists of mass fractal aggregates (Dm=2.5). The partial collapse of this polymeric gel yielding colloidal particles in the aerogel can be attributed to deswelling in supercritical CO2. DLS indicates that gelation of RF with a base catalyst yields a colloidal gel whose structure remains practically unchanged in the aerogel, as shown by SAXS.

In-situ small-angle X-ray scattering study of dynamic precipitation in an Al-Zn-Mg-Cu alloy

Dynamic precipitation during room-temperature deformation of an Al-Zn-Mg-Cu alloy in solid solution has been investigated using in-situ small-angle X-ray scattering measurements during tensile tests, performed at the European Synchrotron Radiation Facility. Guinier-Preston (GP) zones are observed to form continuously during the deformation process, and the quantitative measurement of their size and volume fraction shows that their precipitation kinetics are much faster than those of static precipitation. A strong negative strain-rate sensitivity of dynamic precipitation has been observed. A model for the hardening effect of the GP zones is deduced from the evolution of yield stress during static ageing at room temperature. This model is applied to the dynamic precipitation kinetics in order to describe the anomalously high strain-hardening rate observed in these deformation conditions. The kinetics of dynamic precipitation are discussed in terms of semiphenomenological models based on the dynamic strain-ageing theory.

A new method for evaluating the size of plate-like precipitates by small-angle scattering

A methodology is presented for extracting the thickness and length of plate-like precipitates from streaking that appears in the small-angle scattering pattern of moderately textured polycrystalline samples. This methodology builds upon existing work on single crystals but is extended to polycrystals through a modeling of the streaking misalignment distribution. It is also shown that it is essential to take into account the Ewald sphere curvature. The protocol is applied to an in situ small-angle X-ray scattering study of the transition between θ′ and T1 in an Al–Li–Cu system, where the contributions of both phases are well separated, and the size, volume fraction and number density are monitored.

Study of precipitation kinetics: towards non-isothermal and coupled phenomena

A quantitative experimental study of precipitation kinetics in complex situations is presented, using a variety of experimental tools: small-angle X-ray scattering, transmission electron microscopy and differential scanning calorimetry. In addition, a modelling approach is developed to describe the evolution of precipitate population during these complex situations. The response of AA7108 aluminium alloy in the T4 and T7 conditions to welding and more simple non-isothermal treatments is evaluated. It is shown that the variety of phenomena encountered, which encompass precipitate dissolution and coarsening, can be appropriately described by a simple model based on the discretization of the precipitate size distribution and on simple evolution laws. Second, a consistent model for both isothermal and non-isothermal precipitation is developed on an Fe–Cu alloy, and a method is devised for the independent calibration of all physical parameters involved by the model. Last, a quantitative study of the microstructure of AA2024 aluminium friction stir welds is presented, and is shown to explain the occurrence of strain localisation when these welds are mechanically loaded.

X-ray intensity fluctuation spectroscopy by heterodyne detection.

A straightforward way of measuring X-ray intensity fluctuation spectroscopy in a small-angle X-ray scattering configuration is demonstrated using heterodyne techniques. Two examples are presented: the Brownian motion of latex spheres in glycerol, and a Doppler velocity experiment demonstrating the motion and the relaxation of carbon-black-filled elastomers after uniaxial stretching. In the latter case the effects of mechanical relaxation can be separated from those of aggregate diffusion. The results suggest that the dynamics of these filled elastomers are similar to the universal features observed in disordered jammed systems.

X-ray diffraction from rectangular slits

It is shown that for micrometre-sized beams the X-ray diffraction from slits is a source of strong parasitic background, even for slits of high quality. In order to illustrate this effect, the coherent diffraction from rectangular slits has been studied in detail. A large number of interference fringes with strong visibility have been observed using a single set of slits made of polished cylinders. For very small apertures, asymmetrical slits generate asymmetrical patterns. This pattern is calculated from the theory of electromagnetic field propagation and compared with experiment in the far-field regime. The use of guard slits to remove Fraunhofer diffraction from the beam-defining slits is treated theoretically. Numerical simulations yield the optimum aperture of the guard slits with respect to the distance to the primary slits. Diffraction theory is shown to be essential to understand how to reduce the background-to-signal ratio in high-resolution experiments.

Dynamics of long-wavelength phason fluctuations in the i-Al-Pd-Mn quasicrystal.

We report on the dynamics of phason modes in the i-Al–Pd–Mn icosahedral quasicrystal, measured between room temperature and 650°C, using the X-ray intensity fluctuation spectroscopy (XIFS) technique. Up to 500°C, the autocorrelation function, ℑ(q, t), displays almost no time evolution as expected for frozen-in phason fluctuations at low temperature. At higher temperatures, ℑ(q, t) follows a single exponential time decay from which the characteristic time τ c(q) is extracted. These results are compared to the expected shape of ℑ(q, t) as derived from the expressions of the eigenvalues and eigenvectors of the C ⊥ ⊥(q) phason dynamical matrix. In agreement with the hydrodynamic theory of quasicrystals, which predicts phasons with diffusive character, we find that τ c(q) varies linearly with q −2 at 650°C. The corresponding diffusion coefficient is 2.2(±0.5) × 10−18 m2 s−1 and the activation energy is estimated around 2.3(±1) eV.