Three-Dimensional Imaging of Phase Ordering in an Fe-Al Alloy by Bragg Ptychography

Chan Kim, Virginie Chamard, Jörg Hallmann, Thomas Roth, Wei Lu, Ulrike Boesenberg, Alexey Zozulya, Steven Leake, and Anders Madsen

Phys. Rev. Lett. 121, 256101 – Published 19 December 2018

Abstract

We show three-dimensional images of phase ordering in a ${Fe}_{55} {Al}_{45}$ alloy obtained by coherent x-ray diffraction Bragg ptychography. Fe-Al alloys display ordered phases where the atoms organize on sublattices resulting in the emergence of otherwise forbidden superlattice reflections. The degeneracy of the ordering results in antiphase domain boundaries that, in addition to the general lattice strain, provide phase shifts of the diffracted beam depending on the reflection. The reconstructed phase images can be separated into components originating from $B 2$ phase domains and lattice strain by performing Bragg ptychography on both the (002) fundamental and the (001) superlattice reflections.

Received 1 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.256101

Physics Subject Headings (PhySH)

Phase transitions

Coherent X-ray scattering X-ray imaging

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chan Kim^1,*, Virginie Chamard^2,†, Jörg Hallmann¹, Thomas Roth^1,‡, Wei Lu¹, Ulrike Boesenberg¹, Alexey Zozulya¹, Steven Leake³, and Anders Madsen^1,§

¹European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
²Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
³ESRF–The European Synchrotron, 71 Avenue des Martyrs, 38000 Grenoble, France

^*chan.kim@xfel.eu
^†virginie.chamard@fresnel.fr
^‡Present address: ESRF–The European Synchrotron, 71 Avenue des Martyrs, 38000 Grenoble, France.
^§anders.madsen@xfel.eu

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Issue

Vol. 121, Iss. 25 — 21 December 2018

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Images

Figure 1
Sketch of the Bragg ptychography experiment. A partially coherent x-ray beam is defined by slits and focused onto the sample by a Fresnel zone plate (FZP) with an order sorting aperture (OSA). The intensity scattered by the sample in Bragg condition is measured by a pixel detector over a range of $θ$ rotation of the sample (rocking scan). This translates the detector plane through the crystal grain recording a 2D slice of the 3D intensity distribution for every $θ$ angle. In addition, for every angular position overlapping exposures (ptychography) are taken by moving the sample ( $x − y$ surface coordinates) relative to the beam. If the sample is removed, the defocused x-ray beam can be measured by a CCD detector placed far downstream and the intensity in the focal point retrieved (Quiney method, bottom right).
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Figure 2
Top left: schematic of bcc structure with antiphase domain boundaries (ADBs). Bottom left: general bcc structure. The blue arrow shows $⟨ \frac{1}{2} \frac{1}{2} \frac{1}{2} ⟩$ which is the nearest neighbor direction where same-element atoms may become neighbors and create an ADB. Right: (110) plane with possible ADB intersections (dotted blue lines).
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Figure 3
2D detector images (a),(c) and integrated intensity maps (b),(d) at 17.412° (001) and 37.178° (002) (vicinity of Bragg peaks). An area of reciprocal space, marked by white dotted rectangles in (a),(c), was selected for intensity integration to generate the maps shown in (b),(d). The white arrows in (b),(d) indicate the pixel corresponding to the detector images (a) and (c). Map (b) appears elongated in the $y$ direction compared with map (d) due to the difference in incidence angles. The “islands” of scattering in (b) and (d) originates from the same crystallite and this marker allows us to overlay data from (001) and (002) measurements.
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Figure 4
(a),(b) Sectioned central slices of the reconstructed (001) phase (a) and (002) phase (b). (c),(e) Line profiles of (001) phase (blue lines) and (002) phase (red lines), which correspond to the yellow dotted lines in (a) and (b). (d),(f) Results of $ϕ_{sub}$ , calculated from the line profiles in (c) and (e). A strong $π$ phase shift from an ADB is visible in (d) while the profile in (f) has a constant phase. (g) 3D APD image in the selected region, yellow rectangles in (a) and (b). The empty area corresponds to one phase ordered domain and the gray colored area corresponds to another. The length of the coordinate system arrows is 250 nm. (h),(i) 2D cuts showing a domain in the binary representation (h) and the corresponding (002) strain (i).
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