In this presentation, I will highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, I will discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of supercooled water [1,2] and proteins [3]. Finally, I will provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.

[1] F. Perakis, K. Amann-Winkel, F. Lehmkühler, M. Sprung, D. Mariedahl, J. A. Sellberg, H. Pathak, A. Späh, F. Cavalca, D. Schlesinger, A. Ricci, A. Jain, B. Massani, F. Aubree, C. J. Benmore, T. Loerting, G. Grübel, L. G. M. Pettersson and A. Nilsson, Proc. Natl. Acad. Sci. U.S.A. 114, 8193-8198 (2017)
[2] F. Perakis, G. Camisasca, T. J. Lane, A. Späh, K. T.Wikfeldt, J. A. Sellberg, F. Lehmkühler, H. Pathak, K. H. Kim, K. Amann-Winkel, S. Schreck, S. Song, T. Sato, M. Sikorski, A. Eilert, T. McQueen, H. Ogasawara, D. Nordlund, W. Roseker, J. Koralek, S. Nelson, P. Hart, R. Alonso-Mori, Y. Feng, D. Zhu, A. Robert, G. Grübel, L. G. M. Pettersson, and A. Nilsson, Nature Comm. 9, 1917 (2018)
[3] F. Perakis and C. Gutt, Phys. Chem. Chem. Phys., 22, 19443-19453 (2020)

Additives provide a versatile strategy for controlling crystallization processes, enabling selection of properties including crystal sizes, morphologies, and structures. The additive species can also be incorporated within the crystal and even the crystal lattice itself, leading for example to enhanced mechanical properties. However, while many techniques are available for analysing particle shape and structure, it remains challenging to characterize the structural inhomogeneities and defects introduced into individual crystals by these additives, where these govern many important material properties. Here, we exploit coherent diffraction imaging methods to visualize the distribution of additives within as well as the effects additives have on the internal structure of individual calcite crystals. Highlighted are how factors including supersaturation, solution composition and additive-crystal interactions govern the distribution of additives in single crystals. Further, emphasized is the emergence of a range of complex strain and zonation patterns depending on the nature of the additive, diverging in part and locally from commonly suggested distribution models. This work contributes to our understanding of the factors that govern the structure-property relationships of crystalline materials, where a controlled utilization of additives will ultimately inform the design of next-generation materials.

Cateretê, the coherent X-ray scattering beamline at the new Brazilian synchrotron 5bent-achromat source, Sirius [1] is dedicated to coherent diffraction imaging (CDI) as well as X-ray photon correlation spectroscopy (XPCS) studies. Making the most of the coherence properties of the ultra-low emittance of the Sirius accelerator, will enable to perform 3D imaging of micrometer sized specimen down to few nanometers spatial resolution.

The Cateretê beamline is equipped with an undulator source, in a low-beta straight section, and two cryo-cooled focussing mirrors creating a 41 x 36 mm² (FWHM at 9 keV) coherent beam at 88 m from the source. The beamline operates in the 4 to 24 keV energy range using a horizontally deflecting 4-bounce crystal monochromator (4CM). Moving the 4CM laterally by a few mm, enables to operate the beamline in pink beam mode, maintaining the beam position unchanged. The experimental station is located 88 m from the source, followed by a 28 meters vacuum chamber hosting the Medipix (3k x 3k pixels²) in-vacuum detector.

The beamline, now under commissioning, will enable to perform imaging in reciprocal space, with a particular focus on in situ imaging as well as cryo-imaging experiments [2], [3]. To date, we measured and obtained the first three-dimensional reconstruction of a 6 microns cube zeolite crystal. XPCS studies of zeolite nucleation and growth have also been performed and will be presented.

An operando reaction cell, enabling to image catalysts under realistic catalytic conditions and a cryogenic sample environment are under development. The latter will allow 2D and tomographic data acquisition of specimens loaded in capillaries or flat substrates such as Si₃N₄membranes. The cryo-system is based on a low-flow cryo-cooled He gas preserving the sample stability and operates in a controlled humidity atmosphere preventing ice formation.

I will describe the Cateretê beamline and present the latest results obtained using plane-wave CDI as well as XPCS.

[1] L. Liu, N. Milas, A. H. C. Mukai, X. R. Resende, and F. H. De Sá, “The sirius project,” J. Synchrotron Radiat., vol. 21, no. 5, pp. 904–911, 2014.

[2] A. R. Passos et al., “Three-dimensional strain dynamics govern the hysteresis in heterogeneous catalysis,” Nat. Commun., vol. 11, no. 1, pp. 1–8, 2020.

[3] C. C. Polo et al., “Correlations between lignin content and structural robustness in plants revealed by X-ray ptychography,” Sci. Rep., vol. 10, no. 1, pp. 1–11, 2020.

Acknowledgements: MCTI, CNPq, Fapesp (2014/25964-5).

Topological defects are at the heart of many intriguing phenomena in fields as diverse as biology and materials science. Ability to manipulate the topological order at will has transformative implications for nanotechnology, particularly for next generation spintronic devices, solar cells, photonics, reconfigurable electronics, catalysts, and energy and information storage. To achieve such control, we must deepen our understanding of topological textures. It is therefore essential to comprehend their nature in 3D.
While electron microscopy methods achieve very high spatial resolution even in 3D, for this they rely on destructive slicing/milling techniques that (1) induce excessive strain on the samples, potentially significantly altering the energy landscape; and (2) render time-dependent studies impossible. On the other hand, X-rays have high penetration depth that allows them to access whole-volume information and are (mostly) non-destructive, preserving the structures under study. Moreover, X-rays do not interfere with electric and magnetic fields (as well as with visible light photons), allowing studies to be performed under external influences.
In this talk, we will show how Bragg coherent diffractive imaging, with help of Landau phase-field modelling, can be extended to the studies of ferroelectric domains, polar vortices [1] and 1D strings [2] in individual nanoparticles under external electric fields. Our results show that topological structures in ferroic materials can modulate the structural phase transition driven by electric field. When analyzing projections of toroidal moment, we also observed controllable chirality, which can be applied in next generation electronics. Tracking of the domain morphology and the vortex core lines suggests that some ferroic materials feature topological structures of the same universality class as hypothetical cosmic strings. This suggests that our methodology can be applied to the studies as exciting and fundamental as cosmology. We will further discuss how the same methodology can be adapted to the studies of large-scale topological textures in photonic networks imaged using ptychographic X-ray computed tomography [3]. We will emphasize the similarities between imaged topological entities and discuss implications of next generation synchrotron sources for the field.

[1] D. Karpov, Z. Liu, T. dos Santos Rolo, R. Harder, P. V. Balachandran, D. Xue, T. Lookman, and E. Fohtung, “Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field”, Nat. Comm. 8, 280 (2017)[2] D. Karpov, Z. Liu, A. Kumar, B. Kiefer, R. Harder, T. Lookman, and E. Fohtung, “Nanoscale topological defects and improper ferroelectric domains in multiferroic barium hexaferrite nanocrystals”, Phys. Rev. B 100, 054432 (2019)[3] High-resolution three-dimensional imaging of topological textures in gyroid networks (manuscript in preparation).

On one hand, coherent diffraction imaging (CDI) in Bragg geometry has emerged as a unique 3D microscopy of nanocrystals thanks to 3rd generation synchrotron sources. Away from absorption edges and at space-group allowed reflections, it provides not only the electronic density, but also, encoded in the phase, the atomic displacement field with respect to the mean lattice, which in turn reveals crystal strain, defects and domains [1–3]. On the other hand, some crystal structures have crystallographic reflections which are forbidden by the space-group symmetry but can nevertheless be observed at a suitable X-ray absorption edge, due to the anisotropy of the tensor of scattering (ATS) [4]. They are several orders of magnitude weaker than allowed reflections, but the absence of Thomson scattering allows the observation of various electronic phenomena related to electronic orders (magnetic, charge, orbital), static and dynamic atomic displacements.
The new generation of synchrotron sources, such as the ESRF “Extremely Bright Source”, opens opportunities to perform CDI on such weak reflections. Here we report on the measurement of the (115) forbidden reflection of a GaN nanopillar at the Ga K edge. Sufficient statistics could be obtained in a total accumulation time of ~30 minutes for an entire rocking curve to retrieve the phase of the scattering function. Such measurement at high temperature would provide an image of the inhomogeneity of thermal motion in the crystal [5], which would be particularly interesting close to surfaces, inversion domain boundaries [3] and crystal defects. This proof-of-principle experiment demonstrates that forbidden reflections are a new opportunity for CDI with the new synchrotron sources.

[1] Robinson, I. & Harder, R. (2009). Nature Materials 8, 291.
[2] Clarke, J., Ihli, J., Schenk, A. S., Kim, Y.-Y., Kulak, A. N., Campbell, J. M., Nisbet, G., Meldrum, F. C. & Robinson, I. K. (2015). Nature Materials 14, 780.
[3] Labat, S., Richard, M.-I., Dupraz, M., Gailhanou, M., Beutier, G., Verdier, M., Mastropietro, F., Cornelius, T. W., Schülli, T. U., Eymery, J. & Thomas, O. (2015). ACS Nano 9, 9210.
[4] Dmitrienko, V. E. (1983). Acta Cryst. A 39, 29.
[5] Beutier, G., Collins, S. P., Nisbet, G., Ovchinnikova, E. N. & Dmitrienko, V. E. (2012). Eur. Phys. J. Special Topics 208, 53.

The authors ackowledge the ESRF for beamtime allocation under project number MI-1377.

A solution to the crystallographic “phase problem” was proposed by David Sayre immediately after the announcement of Shannon’ Information Theorem, requiring the diffraction to be sampled more than twice as finely as the Bragg peak spacing [1]. The implicit need for X-ray coherence has been happily solved with the development of the latest synchrotron sources, where Bragg Coherent Diffraction Imaging (BCDI) experiments are routinely performed. The fringed diffraction patterns can be oversampled so as to overdetermine the phase problem. Iterative algorithms that converge on the solution. Despite meeting all the oversampling requirements of Sayre and Shannon, current iterative phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. We propose to overcome this limitation by employing Machine Learning in a Convolutional Neural Network model which combines supervised training with unsupervised refinement. Remarkably, our model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate “loss function” alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms [1,2].