High-energy x-ray diffraction from surfaces and nanoparticles

U. Hejral, P. Müller, M. Shipilin, J. Gustafson, D. Franz, R. Shayduk, U. Rütt, C. Zhang, L. R. Merte, E. Lundgren, V. Vonk, and A. Stierle

Phys. Rev. B 96, 195433 – Published 27 November 2017

Abstract

High-energy surface-sensitive x-ray diffraction (HESXRD) is a powerful high-energy photon technique (E > 70 keV) that has in recent years proven to allow a fast data acquisition for the 3D structure determination of surfaces and nanoparticles under in situ and operando conditions. The use of a large-area detector facilitates the direct collection of nearly distortion-free diffraction patterns over a wide $q$ range, including crystal truncation rods perpendicular to the surface and large-area reciprocal space maps from epitaxial nanoparticles, which is not possible in the conventional low-photon energy approach ( $E = 10 - 20 keV$ ). Here, we present a comprehensive mathematical approach, explaining the working principle of HESXRD for both single-crystal surfaces and epitaxial nanostructures on single-crystal supports. The angular calculations used in conventional crystal truncation rod measurements at low-photon energies are adopted for the high-photon-energy regime, illustrating why and to which extent large reciprocal-space areas can be probed in stationary geometry with fixed sample rotation. We discuss how imperfections such as mosaicity and finite domain size aid in sampling a substantial part of reciprocal space without the need of rotating the sample. An exact account is given of the area probed in reciprocal space using such a stationary mode, which is essential for in situ or operando time-resolved experiments on surfaces and nanostructures.

Received 3 August 2017
Revised 27 October 2017

DOI:https://doi.org/10.1103/PhysRevB.96.195433

Physics Subject Headings (PhySH)

Surface scattering X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

U. Hejral^1,2,3,*, P. Müller^1,2, M. Shipilin³, J. Gustafson³, D. Franz^1,2, R. Shayduk^1,4, U. Rütt^1,5, C. Zhang³, L. R. Merte^3,6, E. Lundgren³, V. Vonk¹, and A. Stierle^1,2,†

¹Deutsches Elektronen-Synchrotron (DESY), D-22603 Hamburg, Germany
²Fachbereich Physik Universität Hamburg, Jungiusstrasse 9, D-20355 Hamburg, Germany
³Synchrotron Radiation Research, Lund University, Box 118, SE-221 00 Lund, Sweden
⁴European XFEL GmbH, Holzkoppel 4, D-22869 Schenefeld, Germany
⁵Argonne National Laboratory, Lemont, Illinois 60439, USA
⁶Max IV Laboratory, Fotongatan 8, SE-22594 Lund, Sweden

^*uta.hejral@sljus.lu.se
^†andreas.stierle@desy.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 19 — 15 November 2017

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Surface x-ray diffraction geometry at conventional photon energies in the 10–20-keV regime illustrating the scattering geometry and angles introduced in the text for a vertical (2+2) diffractometer with the detector rotations $δ$ and $γ$ independent of the sample rotations $θ$ and $α$ , similar to the geometry for a stationary 2D detector [22].
Reuse & Permissions
Figure 2
Surface x-ray diffraction geometry at (a) conventional ( $E = 12.4 keV$ ) and (b) high-photon energies ( $E = 88.6 keV$ ) drawn using the same scale.
Reuse & Permissions
Figure 3
Comparison of trajectories (black lines) of the diffracted beam along various CTRs as followed by the detector arm [(δ,γ) plane] at conventional (a) 12.4 keV and high-photon energies (b) 88.6 keV, when the sample is rotated around its surface normal. The plots in (a) and (b) cover the same in- and out-of-plane momentum transfer range $q_{| |}$ and $q_{⊥}$ of 70 and $60 n m^{- 1}$ , respectively.
Reuse & Permissions
Figure 4
(a) High-energy x-ray diffraction patterns from a Pd(100) surface at selected θ values taken during a rocking scan over a range of approximately 7°; last image: superposition of all 75 detector images performed during the scan plotting for each pixel the highest intensity in all of the detector frames. The boxes mark the intersection region of the reciprocal lattice with the Ewald sphere. (b) Experimental γ values of the respective intersection points between the CTR and the Ewald sphere (circles) as a function of the sample rotation θ; the red solid line represents the calculated dependency according to Eq. (1a); the blue bars correspond to the range Δγ along the CTR within which still 25% of the maximum intensity of the intersection point was monitored. The blue bars are missing for the cases in which this intensity range was blocked by beamstops securing the 2D detector from the high-intensity Pd Bragg peaks.
Reuse & Permissions
Figure 5
High-energy diffraction measurement scheme for epitaxial nanoparticles: (a) perspective view of the diffraction geometry for nanoparticles with an in-plane angular distribution $Δ Θ$ and finite diameter D; (b) diffraction pattern from epitaxial Rh nanoparticles on $MgA l_{2} O_{4}$ (100) recorded by a 2D detector in stationary geometry with fixed sample rotation $θ_{S}$ ; (c) (left) schematic view of a (100)-oriented, truncated octahedral nanoparticle with (001) top and (111) side facets, (right) corresponding reciprocal lattice with facet rod signals indicated.
Reuse & Permissions
Figure 6
(a) Accessible area in reciprocal space at high-photon energies for a nanoparticle mosaic distribution of $Δ Θ = 3.5^{\circ}$ around the surface normal (green). (b) Accessible area of reciprocal space at 12.4 keV is indicated (green). The half circles in the (δ, γ) plane fulfilling the scattering condition and going through the (111) Bragg peak are plotted as solid lines.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics