Geometrical-optics formalism to model contrast in dark-field X-ray microscopy

Simulations of dislocation contrast in dark-field X-ray microscopy

Dark-field X-ray microscopy (DFXM) is a full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM, an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. This work explores contrast methods and optimizes the DFXM setup specifically for the case of mapping dislocations. Forward projections of detector images are generated using two complementary simulation tools based on geometrical optics and wavefront propagation, respectively. Weak and strong beam contrast and the mapping of strain components are studied. The feasibility of observing dislocations in a wall is elucidated as a function of the distance between neighbouring dislocations and the spatial resolution. Dislocation studies should be feasible with energy band widths of 10-2, of relevance for fourth-generation synchrotron and X-ray free-electron laser sources.

Real-time imaging of acoustic waves in bulk materials with X-ray microscopy

The dynamics of lattice vibrations govern many material processes, such as acoustic wave propagation, displacive phase transitions, and ballistic thermal transport. The maximum velocity of these processes and their effects is determined by the speed of sound, which therefore defines the temporal resolution (picoseconds) needed to resolve these phenomena on their characteristic length scales (nanometers). Here, we present an X-ray microscope capable of imaging acoustic waves with subpicosecond resolution within mm-sized crystals. We directly visualize the generation, propagation, branching, and energy dissipation of longitudinal and transverse acoustic waves in diamond, demonstrating how mechanical energy thermalizes from picosecond to microsecond timescales. Bulk characterization techniques capable of resolving this level of structural detail have previously been available on millisecond time scales-orders of magnitude too slow to capture these fundamental phenomena in solid-state physics and geoscience. As such, the reported results provide broad insights into the interaction of acoustic waves with the structure of materials, and the availability of ultrafast time-resolved dark-field X-ray microscopy opens a vista of new opportunities for 3D imaging of materials dynamics on their intrinsic submicrosecond time scales.

Extensive 3D mapping of dislocation structures in bulk aluminum

Thermomechanical processing such as annealing is one of the main methods to tailor the mechanical properties of materials, however, much is unknown about the reorganization of dislocation structures deep inside macroscopic crystals that give rise to those changes. Here, we demonstrate the self-organization of dislocation structures upon high-temperature annealing in a mm-sized single crystal of aluminum. We map a large embedded 3D volume ([Formula: see text] [Formula: see text]m[Formula: see text]) of dislocation structures using dark field X-ray microscopy (DFXM), a diffraction-based imaging technique. Over the wide field of view, DFXM's high angular resolution allows us to identify subgrains, separated by dislocation boundaries, which we identify and characterize down to the single-dislocation level using computer-vision methods. We demonstrate how even after long annealing times at high temperatures, the remaining low density of dislocations still pack into well-defined, straight dislocation boundaries (DBs) that lie on specific crystallographic planes. In contrast to conventional grain growth models, our results show that the dihedral angles at the triple junctions are not the predicted 120[Formula: see text], suggesting additional complexities in the boundary stabilization mechanisms. Mapping the local misorientation and lattice strain around these boundaries shows that the observed strain is shear, imparting an average misorientation around the DB of [Formula: see text] 0.003 to 0.006[Formula: see text].

Simulating dark-field X-ray microscopy images with wavefront propagation techniques

The simulation of a dark-field X-ray microscopy experiment using wavefront propagation techniques and numerical integration of the Takagi–Taupin equations is shown. The approach is validated by comparing with measurements of a near-perfect diamond crystal containing a single stacking-fault defect.

Dark-field X-ray microscopy is a diffraction-based synchrotron imaging technique capable of imaging defects in the bulk of extended crystalline samples. Numerical simulations are presented of image formation in such a microscope using numerical integration of the dynamical Takagi–Taupin equations and wavefront propagation. The approach is validated by comparing simulated images with experimental data from a near-perfect single crystal of diamond containing a single stacking-fault defect in the illuminated volume.

X-ray free-electron laser based dark-field X-ray microscopy: a simulation-based study

Dark-field X-ray microscopy (DFXM) is a nondestructive full-field imaging technique providing three-dimensional mapping of microstructure and local strain fields in deeply embedded crystalline elements. This is achieved by placing an objective lens in the diffracted beam, giving a magnified projection image. So far, the method has been applied with a time resolution of milliseconds to hours. In this work, the feasibility of DFXM at the picosecond time scale using an X-ray free-electron laser source and a pump–probe scheme is considered. Thermomechanical strain-wave simulations are combined with geometrical optics and wavefront propagation optics to simulate DFXM images of phonon dynamics in a diamond single crystal. Using the specifications of the XCS instrument at the Linac Coherent Light Source as an example results in simulated DFXM images clearly showing the propagation of a strain wave.

Fourier ptychographic dark field x-ray microscopy

Dark-field x-ray microscopy (DFXM) is an x-ray imaging technique for mapping three-dimensional (3D) lattice strain and rotation in bulk crystalline materials. At present, these maps of local structural distortions are derived from the raw intensity images using an incoherent analysis framework. In this work, we describe a coherent, Fourier ptychographic approach that requires little change in terms of instrumentation and acquisition strategy, and may be implemented on existing DFXM instruments. We demonstrate the method experimentally and are able to achieve quantitative phase reconstructions of thin film samples and maps of the aberrations in the objective lens. The method holds particular promise for the characterization of crystalline materials containing weak structural contrast.

In situ visualization of long-range defect interactions at the edge of melting

Connecting a bulk material's microscopic defects to its macroscopic properties is an age-old problem in materials science. Long-range interactions between dislocations (line defects) are known to play a key role in how materials deform or melt, but we lack the tools to connect these dynamics to the macroscopic properties. We introduce time-resolved dark-field x-ray microscopy to directly visualize how dislocations move and interact over hundreds of micrometers deep inside bulk aluminum. With real-time movies, we reveal the thermally activated motion and interactions of dislocations that comprise a boundary and show how weakened binding forces destabilize the structure at 99% of the melting temperature. Connecting dynamics of the microstructure to its stability, we provide important opportunities to guide and validate multiscale models that are yet untested.