Abstract
We report on a new x-ray imaging method, which combines the high spatial resolution of coherent diffraction imaging with the ability of dark field microscopy to map grains within thick polycrystalline specimens. An x-ray objective serves to isolate a grain and avoid overlap of diffraction spots. Iterative oversampling routines are used to reconstruct the shape and strain field within the grain from the far field intensity pattern. The limitation on resolution caused by the finite numerical aperture of the objective is overcome by the Fourier synthesis of several diffraction patterns. We demonstrate the method by an experimental study of a ~500 nm Pt grain for the two cases of a real and a virtual image plane. In the latter case the spatial resolution is 13 nm rms. Our results confirm that no information on the pupil function of the lens is required and that lens aberrations are not critical.
Highlights
In polycrystalline materials, the three-dimensional (3D) distribution of strain, defects, and lattice distortions within the individual grains strongly affects the macroscopic mechanical and physical properties
Compared to full-field microscopy methods using an objective lens between the sample and the detector, coherent diffraction imaging (CDI) avoids limitations due to aberrations and finite aperture of the lens, and spatial resolutions in the 10-nm range can be obtained with strain sensitivity on the order of a few times 10−4 [17]
Reconstructions were in all cases performed by using a combination of the hybrid input-output algorithm (HIO) [22] with a feedback parameter of β = 0.9, the error reduction algorithm (ER) [23], and the shrinkwrap algorithm [24] to update the support
Summary
The three-dimensional (3D) distribution of strain, defects, and lattice distortions within the individual grains strongly affects the macroscopic mechanical and physical properties. Nondestructive 3D grain mapping of millimeter-sized samples can be carried out by x-ray diffraction tomography methods [3,4,5,6] with a resolution of 2 μm These may be complemented by dark-field x-ray microscopy [7,8,9] where an x-ray objective lens is placed in the Bragg diffracted beam of a selected grain. Compared to full-field microscopy methods using an objective lens between the sample and the detector, CDI avoids limitations due to aberrations and finite aperture of the lens, and spatial resolutions in the 10-nm range can be obtained with strain sensitivity on the order of a few times 10−4 [17]. We show that the spatial resolution limitation introduced by the finite numerical aperture of the objective can be overcome by the introduction of Fourier synthesis approaches [20], applied in the x-ray regime
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