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Real-space texture and pole-figure analysis using the 3D pair distribution function on a platinum thin film - PubMed

  • ️Sat Jan 01 2022

Real-space texture and pole-figure analysis using the 3D pair distribution function on a platinum thin film

Sani Y Harouna-Mayer et al. IUCrJ. 2022.

Abstract

An approach is described for studying texture in nanostructured materials. The approach implements the real-space texture pair distribution function (PDF), txPDF, laid out by Gong & Billinge {(2018 ▸). arXiv:1805.10342 [cond-mat]}. It is demonstrated on a fiber-textured polycrystalline Pt thin film. The approach uses 3D PDF methods to reconstruct the orientation distribution function of the powder crystallites from a set of diffraction patterns, taken at different tilt angles of the substrate with respect to the incident beam, directly from the 3D PDF of the sample. A real-space equivalent of the reciprocal-space pole figure is defined in terms of interatomic vectors in the PDF and computed for various interatomic vectors in the Pt film. Furthermore, it is shown how a valid isotropic PDF may be obtained from a weighted average over the tilt series, including the measurement conditions for the best approximant to the isotropic PDF from a single exposure, which for the case of the fiber-textured film was in a nearly grazing incidence orientation of ∼10°. Finally, an open-source Python software package, FouriGUI, is described that may be used to help in studies of texture from 3D reciprocal-space data, and indeed for Fourier transforming and visualizing 3D PDF data in general.

Keywords: 3D pair distribution functions; FouriGUI; materials modeling; nanostructure; real-space fiber plots; real-space pole figures; texture.

© Sani Y. Harouna-Mayer et al. 2022.

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Figures

Figure 1
Figure 1

Sections of detector images of the textured Pt sample at different tilt angles ϕ, and a simulated perfect powder Pt detector image. The colorscale is in arbitrary units.

Figure 2
Figure 2

Comparison of measured and best-fit calculated PDFs for diffraction images taken at different sample orientations. The blue circles are the experimental PDFs for sample tilt angles ϕ = 1, 11, 45 and 89°, and from the average of the diffraction images from 1 to 89°. The red curves are the best-fit calculated PDFs from an untextured face-centred cubic model. The green curves are the difference between the calculated and measured PDFs. The PDF refinement from the angle-averaged pattern yields a good result with R w = 13.5%. Among the single-angle PDFs, ϕ = 11° shows the best refinement result (R w = 18.1%) and ϕ = 89° shows the worst result (R w = 63.6%) (

Fig. S5

).

Figure 3
Figure 3

An SEM image of the Pt thin-film surface showing a polydisperse size distribution and different shapes of the Pt grains in the lateral direction.

Figure 4
Figure 4

The experimental and data-processing procedure. (a) Reconstruction of a tilt series of 2D scattering images to a 3D scattering volume I(Q). (b) Processing to the total scattering structure function S(Q), with application of symmetry averaging, interpolation, and cutoff beyond Q min and Q max. (c) Fourier transformation to the txPDF G(r).

Figure 5
Figure 5

Slices through (a)–(c) the raw reconstructed scattering volume, (d)–(f) the processed total scattering structure function and (g)–(i) the txPDF, with arbitrary units on a logarithmic scale. The slices in the first column are perpendicular to x s, in the second column are perpendicular to y s and in the third column are perpendicular to z s, where x s, y s and z s are the sample coordinates, see the main text for details. All slices are through the origin of the diffraction space. The edge length is from −23.9 to 23.9 Å−1 in (a)–(f) and from −26.3 to 26.3 Å in (g)–(i), respectively. The void features in (a)–(c) result from the relatively high tilt step size of the measurement. The straight void lines in (a) result from masked high-absorption features from the substrate. The void lines in (b) and (e) are due to the masking of the beamstop.

Figure 6
Figure 6

Reciprocal-space pole figures derived from the scattering volume S(Q). Peaks: (a) {111}, (b) {002}, (c) {022}, (d) {133} and (e) {222}.

Figure 7
Figure 7

Real-space pole figures derived from the txPDF G(r). Peaks: (a)

formula image

, (b) 0, 0, 1, (c)

formula image

, (d) 0, 1, 1 and (e) 1, 1, 1.

Figure 8
Figure 8

(a) Reciprocal-space fiber plots of the first five X-ray diffraction reflections. (b) Real-space fiber plots of the first five PDF peaks. Gaussian fits of the peaks in the fiber plots are shown as solid traces. The fit of the reciprocal 111 reflection at θ = 0° is omitted because of low data quality at that region and poor resolution at low Q after the conversion to polar coordinates. The fit of the real 111 peak at θ = 70.53° is omitted because of a poor fit result due to the low intensity. The intensities of the reciprocal- and real-space fiber plots were retrieved by summing over all intensity values at the H hkl value of the respective peak ± 0.1 Å−1 from the scattering volume S(Q) and over the r ij values of the respective interatomic distance ± 0.1 Å from the txPDF G(r), respectively. Increasing the integration width for the fiber-plot construction does not reduce the high noise in the reciprocal-space fiber plot. All intensities beyond the vertical line at θ = 20° in (a) are multiplied by 5 since intensity values at high θ are hardly visible if put on the same scale as the high intensities at low θ values.

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Grants and funding

Work on the theory and texture pair distribution function developments and analysis in the Billinge group was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences (DOE-BES) under contract No. DE-SC0012704. SYHM and DK acknowledge support from the Cluster of Excellence ‘CUI: Advanced Imaging of Matter’ of the Deutsche Forschungsgemeinschaft (DFG) – EXC 2056 – project ID 390715994 and from the Bundesministerium für Bildung und Forschung (BMBF) via project LUCENT under grant No. 05K19WMA.