“X-ray diffraction with high spatial resolution is commonly used to characterize (poly)crystalline samples with, for example, respect to local strain, residual stress, grain boundaries and texture. However, the investigation of highly absorbing samples or the simultaneous assessment of high-Z materials by X-ray fluorescence have been limited due to the utilization of low photon energies. Here, a goniometer-based setup implemented at the P06 beamline of PETRA III that allows for micrometre spatial resolution with a photon energy of 35 keV and above is reported. A highly focused beam was achieved by using compound refractive lenses, and high-precision sample manipulation was enabled by a goniometer that allows up to 5D scans (three rotations and two translations). As experimental examples, the determination of local strain variations in martensitic steel samples with micrometre spatial resolution, as well as the simultaneous elemental distribution for high-Z materials in a thin-film solar cell, are demonstrated. The proposed approach allows users from the materials-science community to determine micro-structural properties even in highly absorbing samples.”
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High-resolution micro X-ray diffraction (µ-HRXRD) utilizes focused X-ray beams to study local defects on the nanoscale.
Examples of µ-HRXRD include the study of local microstrain and tilt distribution in CuInSe2 functional thin films with average grain sizes below 1 µm, a photon energy of 8.9 keV, a spot size of 100 nm × 100 nm and a strain sensitivity of the order of 10−4 at the ID01 beamline of the European Synchrotron Radiation Facility (Schäfer et al., 2016 ▸). A similar characterization of CdTe crystallites with sub-100-nm grain sizes occurs in fully operational photovoltaic cells with similar experimental parameters at the hard X-ray nanoprobe (HXN) beamline 3-ID of the National Synchrotron Light Source II (Calvo-Almazan et al., 2019 ▸). Another example is the determination of local microstructure of martensite-retained austenite steel utilizing a photon energy of 12 keV and a spot size of 4 µm × 1 µm at the 2-ID-D undulator beamline of the Advanced Photon Source (Cai et al., 2001 ▸), where the grain size was found to be much smaller than the focal spot size. A final example is the renovated high-pressure XRD setup at the BL10XU beamline of SPring-8 (Hirao et al., 2020 ▸) utilizing a photon energy of 30 keV and a spot size of 1 µm × 1 µm, where the angular sensitivity – conservatively estimated as the ratio between pixel size and sample-to-detector distance – was ∼2.2 × 10−4 rad and the maximal sample thickness without compromising angular resolution was ∼150 µm.
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2. Experimental setup
All measurements presented here were obtained at the microhutch of beamline P06 of PETRA III at DESY, Hamburg (Falkenberg et al., 2020 ▸). The incident photon energy of 35 keV was selected by a double-crystal monochromator. Compound refractive lenses (CRLs) were used to focus the beam to a spot size of 2.0 µm × 1.2 µm, which was measured by knife-edge scans of crossed gold wires. The focal distance of the CRLs was 660 mm measured from the pinhole exit (0.4 mm diameter) of the N 2-rinsed CRL box, which leads to a longitudinal spot size of a few millimetres and a photon flux above 109 at the focal position (Falkenberg et al., 2020 ▸).
A six-axes goniometer (SmarAct) fixed on a kinematic mount was used for sample manipulation [see Fig. 1▸(b)]. Fig. 1▸(c) shows the goniometer that was used for our experiment at P06, PETRA III. It featured three rotation circles with nominal angular resolutions below 0.1 µrad. Additional x, y and z translation stages on top of the last rotation enabled horizontal alignment along the beam (x) and scanning of the sample (y and z) with fixed rotation angles and a nominal position accuracy of 1 nm. Actual angular and positional accuracies have not yet been determined and upper bounds will be estimated below. The goniometer provides up to 5D scans for characterization of reciprocal space as a function of sample position. The XRD signal was obtained with a GaAs Lambda 2M detector (XSpectrum) with 55 µm pixel size, a 24-bit range and 1 ms readout frequency ∼1 m downstream of the sample and 25° from the incident beam [Fig. 1▸(a)]. In order to minimize absorption in the sample and, thus, to maximize detectable intensity, the incident beam impinged the sample through one side and exited through an orthogonal side. Thus, only a part of the diffraction pattern was measured, in contrast to the experiments listed in the Introduction , which all utilized transmission geometry and measured the full Laue rings. The conservative estimate for the angular resolution of this setup is 5.5 × 10−5 rad, which implies a sensitivity to strain of 2.5 × 10−4 or better for the average 2θ of 25°. The maximum sample thickness without compromising angular resolution is ∼150 µm. The XRF signal was obtained using a Vortex silicon-drift detector (Hitachi High-Tech) located at 90° from the incident beam. The setup allowed photon energies of up to 42 keV.
(a) The setup geometry (top view). (b) A technical drawing of the goniometer. The positioners are stacked from outer to inner in the order Φ, Ψ, ω, y, x and z. (c) A photograph of the goniometer.
The cross point of the rotation axes defines the desired scan position on the sample. Alignment of the cross point into the beam focus was achieved by a two-step procedure: first, an optical microscope was used to move the tip of a tomographic pin into the cross point and, second, the XRF signal of the pin was used to move the entire goniometer and, therefore, the cross point, into the beam focus.
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In order to translate pixel positions on the detector into 2θ values, we calibrated the setup geometry using the calibration routine provided by PyFAI (Ashiotis et al., 2015 ▸; Kieffer & Karkoulis, 2013 ▸) and used lanthanium hexaboride (LaB6) as a diffraction standard. For automatic peak detection, all the diffraction patterns were summed up [Fig. 2▸(b)]. Single diffraction patterns [Fig. 2▸(a)] were transformed from Cartesian coordinates (u, v) to polar coordinates (2θ, χ) by so-called caking (or regrouping) (Kieffer & Karkoulis, 2013 ▸), and an example result is shown in Fig. 2▸(c). Subsequent vertical (i.e. azimuthal) integration provided the diffraction signal over 2θ. Fig. 2▸(d) shows that the first 12 martensitic diffraction peaks [i.e. from (200) to (510)] were detected. A slight texture can be seen in some of the Laue rings of the single scan points [Fig. 2▸(a)], but, in this proof-of-concept study these influences are neglected during azimuthal integration.
(a) A diffraction pattern of a single scan point of a martensitic steel sample. (b) A diffraction pattern of a martensitic steel sample summed over 2601 translation scan points. (c) Caking of the diffraction pattern in (b). (d) Final azimuthal integration of (c) yielding the 2θ positions of martensitic diffraction peaks. The yellow stripes in the upper right of (b) and the lower right of (c) are artefacts.
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