We report the results of resonant x-ray scattering experiments performed at the Np M(4,5) edges in NpO2. Below T(0)=25 K, the development of long-range order of Np electric quadrupoles is revealed by the growth of superlattice Bragg peaks. The polarization and azimuthal dependence of the intensity of the resonant peaks are well reproduced assuming anisotropic tensor susceptibility scattering from a triple-q(-->) longitudinal antiferroquadrupolar structure. Electric-quadrupole order in NpO2 could be driven by the ordering at T0 of magnetic octupoles of Gamma(5) symmetry, splitting the Np ground state quartet and leading to a singlet ground state with zero dipole-magnetic moment.

Many physical and mechanical properties of crystalline materials depend strongly on their internal structure, which is typically organized into grains and domains on several length scales. Here we present dark-field X-ray microscopy; a non-destructive microscopy technique for the three-dimensional mapping of orientations and stresses on lengths scales from 100 nm to 1 mm within embedded sampling volumes. The technique, which allows ‘zooming’ in and out in both direct and angular space, is demonstrated by an annealing study of plastically deformed aluminium. Facilitating the direct study of the interactions between crystalline elements is a key step towards the formulation and validation of multiscale models that account for the entire heterogeneity of a material. Furthermore, dark-field X-ray microscopy is well suited to applied topics, where the structural evolution of internal nanoscale elements (for example, positioned at interfaces) is crucial to the performance and lifetime of macro-scale devices and components thereof.

Dislocations are mobile at low temperatures in surprisingly many ceramics but sintering minimizes their densities. Enabling local plasticity by engineering a high dislocation density is a way to combat short cracks and toughen ceramics.

A formalism is presented for dark-field X-ray microscopy using refractive optics. The new technique can produce three-dimensional maps of lattice orientation and axial strain within millimetre-sized sampling volumes and is particularly suited to in situ studies of materials at hard X-ray energies. An objective lens in the diffracted beam magnifies the image and acts as a very efficient filter in reciprocal space, enabling the imaging of individual domains of interest with a resolution of 100 nm. Analytical expressions for optical parameters such as numerical aperture, vignetting, and the resolution in both direct and reciprocal spaces are provided. It is shown that the resolution function in reciprocal space can be highly anisotropic and varies as a function of position in the field of view. Inserting a square aperture in front of the objective lens facilitates disjunct and space-filling sampling, which is key for three-dimensional reconstruction and analysis procedures based on the conservation of integrated intensity. A procedure for strain scanning is presented. Finally the formalism is validated experimentally at an X-ray energy of 17 keV.

We report direct experimental evidence for long-range antiferro ordering of the electricquadrupole moments on the U ions. Resonant x-ray scattering experiments at the uranium M 4 absorption edge show a characteristic dependence in the integrated intensity upon rotation of the crystal around the scattering vector. Although quadrupolar order in uranium dioxide was advocated already in the 1960s no experimental evidence for this phenomenon was provided until now.We conclude with a possible model to explain the phase diagram of the solid solutions of UO 2 and NpO 2 . We suggest that in the region 0.30 < x < 0.75 neither the transverse nor the longitudinal quadrupole ordering can dominate, leading to frustration and only short-range ordering.