Dark-field X-ray microscopy is a new full-field imaging technique for nondestructively mapping the structure of deeply embedded crystalline elements in three dimensions. Placing an objective in the diffracted beam generates a magnified projection image of a local volume. By placing a detector in the back focal plane, high-resolution reciprocal space maps are generated for the local volume. Geometrical optics is used to provide analytical expressions for the resolution and range of the reciprocal space maps and the associated field of view in the sample plane. To understand the effects of coherence a comparison is made with wavefront simulations using the fractional Fourier transform. Reciprocal space mapping is demonstrated experimentally at an X-ray energy of 15.6 keV. The resolution function exhibits suppressed streaks and an FWHM resolution in all directions of ÁQ/Q = 4 Â 10 À5 or better. It is demonstrated by simulations that scanning a square aperture in the back focal plane enables strain mapping with no loss in resolution to be combined with a spatial resolution of 100 nm.
We present an instrument for dark-field x-ray microscopy installed on beamline ID06 of the ESRF — the first of its kind. Dark-field x-ray microscopy uses full field illumination of the sample and provides three-dimensional (3D) mapping of micro-structure and lattice strain in crystalline matter. It is analogous to dark-field electron microscopy in that an objective lens magnifies diffracting features of the sample. The use of high-energy synchrotron x-rays, however, means that these features can be large and deeply embedded. 3D movies can be acquired with a time resolution of seconds to minutes. The field of view and spatial resolution can be adapted by simple reconfiguration of the x-ray objective lens, reaching spatial and angular resolution of 30-100 nm and 0.001°, respectively. The instrument furthermore allows pre-characterization of samples at larger length scales using 3DXRD or DCT, such that a region of interest (e.g. a single grain) can be selected for high-resolution studies without the need to dismount the sample. As examples of applications we show work on mapping the subgrains in plastically deformed iron and aluminum alloys, mapping domains and strain fields in ferroelectric crystals, and studies of biominerals. This ability to directly characterize complex, multi-scale phenomena in-situ is a key step towards formulating and validating multi-scale models that account for the entire heterogeneity of materials. As an outlook, we discuss future prospects for such multi-scale characterization by combining DFXM with 3DXRD/DCT, and coherent x-ray methods for coarser and finer length-scales, respectively.
We report angle resolved characterization of nanostructured and conventionally
The electric-field-induced and temperature induced dynamics of domains, defects, and phases play an important role in determining the macroscopic functional response of ferroelectric and piezoelectric materials. However, distinguishing and quantifying these phenomena remains a persistent challenge that inhibits our understanding of the fundamental structure–property relationships. In situ dark field x-ray microscopy is a new experimental technique for the real space mapping of lattice strain and orientation in bulk materials. In this paper, we describe an apparatus and methodology for conducting in situ studies of thermally and electrically induced structural dynamics and demonstrate their use on ferroelectric BaTiO3 single crystals. The stable temperature and electric field apparatus enables simultaneous control of electric fields up to ≈2 kV/mm at temperatures up to 200 °C with a stability of ΔT = ±0.01 K and a ramp rate of up to 0.5 K/min. This capability facilitates studies of critical phenomena, such as phase transitions, which we observe via the microstructural change occurring during the electric-field-induced cubic to tetragonal phase transition in BaTiO3 at its Curie temperature. With such systematic control, we show how the growth of the polar phase front and its associated ferroelastic domains fall along unexpected directions and, after several cycles of electric field application, result in a non-reversible lattice strain at the electrode–crystal interface. These capabilities pave the way for new insights into the temperature and electric field dependent electromechanical transitions and the critical influence of subtle defects and interfaces.
Sm-Modified BiFeO3 multiferroic ceramics experience two simultaneous electric field induced phase transformations, both of which have strong grain orientation dependences and slow transformation kinetics in the order of several minutes.
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