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IUCrJ
Volume 13| Part 3| May 2026| Pages 282-290
ISSN: 2052-2525
https://doi.org/10.1107/S2052252526002782

3D atomic structure determination with ultrashort-pulse MeV electron diffraction

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Vincent Hennicke,a‡ Max Hachmann,b‡ Paul Benjamin Klar,c‡ Patrick Y. A. Reinke,a Tim Pakendorf,a Jan Meyer,a Hossein Delsim-Hashemi,b Miriam Barthelmess,a Sreevidya Thekku Veedu,a Pontus Fischer,a Ana C. Rodrigues,a Arlinda Qelaj,b Alexandra Tolstikova,b Oleksandr Yefanov,a Juna Wernsmann,b Francois Lemery,b Robin Schubert,d Iñaki de Diego,d Stuart Hayes,d Sebastian Günther,a Sven Falke,a Erik Fröjd,e Aldo Mozzanica,e Lukas Palatinus,f Kai Rossnagel,g,h Bernd Schmitt,e Henry N. Chapman,a,i,j Wim Leemans,b Klaus Flöttmannb* and Alke Meentsa*

aCenter for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany, bDeutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany, cFaculty of Geosciences and MAPEX Center for Materials and Processes, University of Bremen, Klagenfurter Str. 2, 28359 Bremen, Germany, dEuropean X-Ray Free-Electron Laser Facility GmbH, Holzkoppel 4, 22869 Schenefeld, Germany, ePaul-Scherrer Institut, Forschungsstrasse 111, 5323 Villigen, Switzerland, fInstitute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 21 Prague 8, Czechia, gInstitut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, Olshausenstr. 40, 24098 Kiel, Germany, hRuprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany, iThe Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany, and jDepartment of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
*Correspondence e-mail: [email protected], [email protected]

Edited by M. Gemmi, Istituto Italiano di Tecnologia, Italy (Received 16 December 2025; accepted 16 March 2026; online 17 April 2026)

Understanding structure at the atomic scale is fundamental for understanding the functioning and the development of materials with improved properties. Compared with other probes providing atomic resolution, electrons offer the strongest interaction in combination with minimal radiation damage, which makes them an ideal tool for investigating very small and radiation-sensitive samples [Henderson (1995View full citation), Q. Rev. Biophys. 28, 171–193]. However, these benefits are often offset by the laborious preparation of nanometre-sized samples that are not visible using a light microscope, and the fact that experiments are largely restricted to ultra-high vacuum [Duyvesteyn et al. (2018View full citation), Proc. Natl Acad. Sci. USA 115, 9569–9573; Gruene et al. (2021View full citation), Nat. Rev. Chem. 5, 660–668]. Here, we report the successful implementation of MeV electron diffraction for ab initio 3D structure determination of the quasi-2D material muscovite and the quantum material 1T-TaS2 at atomic resolution. By employing ultrashort electron pulses from the REGAE (Relativistic electron gun for atomic exploration) accelerator, we obtained high-quality diffraction datasets suitable for structural refinements based on dynamical scattering theory, enabling precise localization of even hydrogen atoms. The increased penetration depth of MeV electrons significantly expands the applicable thickness range of samples, overcoming previous restrictions associated with traditional electron diffraction. These findings establish MeV electron diffraction as a viable approach for investigating a broad range of materials, including nano­structures and radiation-sensitive compounds, and open up new opportunities for in situ and time-resolved experiments [Chao et al. (2023View full citation), Chem. Rev. 123, 8347–8394; Filippetto et al. (2022View full citation), Rev. Mod. Phys. 94, 045004].

B-IncStrDB reference: IAyACLYazaI

CCDC references: 2538230; 2545330

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1. Introduction

Understanding the three-dimensional structure of a material is crucial for unravelling its physical properties. Diffraction experiments using X-rays, neutrons or electrons are particularly well suited for determining structures with (sub)-atomic resolution.

Among these methods, electrons stand out as a superior probe owing to their significantly stronger elastic cross section and their ability to cause considerably less radiation damage to samples compared with X-rays (Henderson, 1995View full citation). Unlike X-rays, which primarily interact with electrons of the sample, electrons interact with the electrostatic potential. This interaction enhances the visibility of light elements, particularly hydrogen atoms (Palatinus et al., 2017View full citation). Furthermore, highly brilliant electron beams are relatively easy to produce and can be precisely focused into submicron spot sizes using electromagnetic lenses. These features make electrons a uniquely economical and effective tool for structural investigations of submicron-sized samples, especially radiation-sensitive low-Z materials. As a result, electron diffraction has emerged as a rapidly growing research field (Gruene et al., 2021View full citation). Today, three-dimensional electron diffraction (3D ED), also known as microcrystal electron diffraction (MicroED), is routinely used for structure determinations from nanocrystals. This technique is now being further advanced with the use of specialized devices designed specifically for electron crystallography (Nannenga et al., 2014View full citation; Gemmi et al., 2019View full citation; Ito et al., 2021View full citation; Simoncic et al., 2023View full citation).

The strong elastic interaction between electrons and matter, however, also leads to challenges in structure determination (Klar et al., 2023View full citation). In particular, multiple scattering of electrons in the sample leads to non-kinematical diffracted intensities Ihkl so that the simple relationship with the squared structure-factor amplitudes, Ihkl ∝ |Fhkl|2, does not hold. According to the well established dynamical theory of diffraction there is a non-linear dependence of Ihkl on experimental parameters such as the electron wavelength, crystal orientation, crystal shape and crystal thickness. Independent of that, electrons lose energy in the sample due to inelastic scattering events, which restricts the sample size for electron diffraction experiments. Depending on the density and chemical composition of the sample, the maximum tolerable thickness is typically limited to a few tens of nanometres in the case of inorganic (high-Z) samples and a few hundred nanometres for organic (low-Z) samples. These dimensions fall far below the resolution limit of optical microscopes, meaning that sample selection and preparation must be performed blindly, without the possibility of a straightforward light microscopic inspection before the experiment. This poses a significant limitation to the broader applicability of electron diffraction (ED) for structure determination (Duyvesteyn et al., 2018View full citation; Bücker et al., 2020View full citation).

Utilizing higher-energy electrons overcomes this limitation. Compared with 200 keV electrons, 3.48 MeV electrons have less than one-third of the elastic cross section, allowing for a more than threefold increase in permissible sample thickness (Henderson, 1995View full citation) while significantly reducing the impact of multiple scattering. As a result, organic and biological samples – previously limited to a maximum thickness of around 500 nm in conventional TEM devices – can now reach thicknesses of approximately 1.75 µm or even more in diffraction experiments using MeV electrons (Bozzola, 1992View full citation). This increase in tolerable sample thickness significantly broadens the applicability of ED to a much wider range of samples. Sample preparation steps, such as crystal growth, sample grinding and mounting samples on support structures, can now be performed under an optical microscope, similar to X-ray experiments.

Furthermore, the longer focal lengths in high-energy diffraction devices provide a larger working space around the sample, enabling the use of a wide range of advanced and diverse sample environments (Fig. 1[link]). This setup allows for in situ experiments over a broad temperature range – from milli-Kelvin to several thousand Kelvin – as well as the use of different gas atmospheres, which is particularly advantageous for catalysis research. The sample holder and space for sample environments of a typical TEM, in contrast, are limited to dimensions in the millimetre range and can reach a few centimetres for dedicated electron diffraction devices operating at energies of up to 160 keV.

[Figure 1]
Figure 1
Concept of accelerator-based high-energy electron diffraction with MeV electrons. Electrons are emitted by illumination of the photocathode with short UV pulses, and are then immediately accelerated to energies of 2–5 MeV in a 1.5 cell RF cavity with field gradients of up to 110 MV m−1. The electron pulses (red dots) then interact with the sample, which is mounted on a single-axis goniometer for crystallographic data collection. While the sample is rotated in the electron beam, diffraction patterns are recorded on a Jungfrau 1M integrating pixel detector.

Moreover, high-energy MeV electrons are far less affected by electric and magnetic fields, enabling experiments that are difficult or impractical with lower-energy electrons; thereby further broadening their potential applications.

However, achieving electron energies of several MeV with the beam stability and coherence length necessary for high-quality structure determination in electron crystallography has been experimentally challenging. For instance, in a transmission electron microscope, accelerating electrons to 1 MeV in static DC fields requires a complex 36-stage accelerator tube (Kawasaki et al., 2000View full citation).

A more promising approach is the use of well established radio frequency (RF)-based accelerator technology. Unlike conventional acceleration in a static field, RF-based accelerators deliver temporally short electron pulses with lengths varying between a few hundred picoseconds down to a few femtoseconds (Weathersby et al., 2015View full citation; Zeitler et al., 2015View full citation). Such ultrashort probe pulses in combination with a short wavelength enable femtosecond time-resolved experiments with atomic resolution, which so far are predominantly conducted at much larger X-ray free-electron laser (XFEL) facilities.

Ultrashort, high-energy electron pulses have already proven highly effective in time-resolved ultrafast electron diffraction (UED) experiments. Beyond their application to solids and crystalline samples, UED techniques have also been successfully employed to study liquid and gaseous samples (Kogar et al., 2020View full citation; Nunes et al., 2020View full citation; Lin et al., 2021View full citation). However, the application of UED for 3D structure determination at atomic resolution has been postulated to be unfeasible owing to limitations in adequate sampling of reciprocal space (Ishikawa et al., 2015View full citation). In fact, no diffraction experiments with ultrashort electron pulses that provided ab initio 3D structural information have yet been reported.

Here we report the first successful ab initio 3D structure determination at atomic resolution of the quasi-2D layered materials muscovite and the 1T phase of tantalum di­sulfide using the `Relativistic electron gun for atomic exploration – (REGAE)' facility at DESY. Muscovite is a layer silicate and has long been used as a very thin electrical insulator (Liang et al., 1998View full citation; Gatta et al., 2011View full citation). 1T-TaS2 belongs to the class of transition metal dichalcogenides (TMDCs) – a technologically highly relevant class of 2D quantum materials, which exhibit structurally very exciting properties such as charge-density waves (CDWs) and undergo several phase transitions (Spijkerman et al., 1997View full citation; Haupt et al., 2016View full citation; Manzeli et al., 2017View full citation).

2. Experimental

Additional detailed information on instrumentation, materials and methods is provided in the supporting information.

2.1. REGAE accelerator facility

Diffraction experiments were performed at the `Relativistic gun for atomic exploration – REGAE' facility at DESY in Hamburg, Germany (Manz et al., 2015View full citation). REGAE is a linear accelerator facility explicitly designed and built for time-resolved diffraction experiments with MeV electrons (Fig. 1[link], Fig. S1). At REGAE, electrons are generated by photoemission inside an S-band (3 GHz) RF gun and rapidly accelerated to an energy of 3 to 5 MeV using field gradients of up to 110 MV m−1 on the photocathode.

A cathode exchange system at REGAE allows selection between different photocathodes without breaking the UHV. For the current work, a CsTe cathode providing high quantum efficiency was used without any specific reasons. REGAE is capable of generating electron pulses at a repetition rate of 50 Hz and with typical bunch charges of up to 100 fC with a transverse emittance as low as 10 nm, which yields a lateral coherence length of about 2–10 nm at typical transverse r.m.s. beam sizes of 50–250 µm on the sample (Hachmann & Flöttmann, 2016View full citation).

2.2. UHV compatible diffraction setup

For diffraction experiments REGAE is equipped with a dedicated UHV-compatible diffraction setup consisting of an in-line sample viewing microscope and a high-precision goniometer for crystallographic data collection (Figs. 1[link], S2, S3, S4, S5). The design was inspired by existing in-air X-ray diffraction setups commonly used at synchrotron sources (Burkhardt et al., 2016View full citation).

For sample visualization and beamline alignment an in-line sample viewing microscope can be inserted into the electron beam path, allowing the user to permanently visualize the sample with optical light during the diffraction experiment. The in-line microscope allows the sample to be viewed with visible light collinear to the electron beam. For this, the electron beam passes through a 1.0 mm drill hole along the optical axis of the microscope objective.

The e−-Roadrunner goniometer is a compact and UHV-compatible single-axis crystallographic goniometer with a high-precision vertical rotation axis. The goniometer axis itself consists of a directly-servomotor-driven and UHV-compatible rotation axis based on ceramic bearings providing 360° rotation capability with an angular resolution of 0.001° in combination with a sphere of confusion smaller than 1 µm. A motorized centring stage mounted on top of the rotation axis provides travel ranges of ±6 mm in the x, y and z directions, and allows precise positioning of the sample in the centre of the rotation axis.

2.3. Jungfrau 1M detector for direct electron detection

Diffraction data are recorded with an in-vacuum version of a Jungfrau 1M detector (Fig. S7). The detector was originally developed for experiments with high-intensity X-ray pulses at XFELs (Mozzanica et al., 2018View full citation; Leonarski et al., 2018View full citation). In contrast to indirect, scintillator-based detectors, the Jungfrau detector directly records the electrical signal generated by the inelastic interactions of the electrons within the silicon sensor material, a signal that is proportional to the energy deposited in the sensor and which, given the high peak current, allows a higher signal-to-noise ratio. In addition, a gating function records data only during a very short period centred around the arrival time of the electron pulse. All other signals, for example dark current from the accelerator, arriving before and after the gating period are not recorded and hence do not contribute to the background signal in the data.

The Jungfrau detector is composed of two 500 kpixel modules and can be operated at frame rates of up to 2 kHz. By using an automatic in-pixel gain selection with three different feedback capacitors, it provides a sufficient dynamic range for detecting strong Bragg reflections of up to 1200 electrons at 3.48 MeV per pixel per pulse.

2.4. Muscovite and TaS2 samples

Muscovite, with chemical composition KAl3Si3O10(OH)2, crystallizes in space group C2/c with unit-cell parameters a = 5.21, b = 9.04, c = 20.03 Å and β = 95.8° (Gatta et al., 2011View full citation). Sheets of corner-sharing tetrahedra and edge-sharing octahedra are oriented perpendicular to the crystallographic b axis, resulting in extremely good cleavability between the layers. Muscovite samples were prepared by using the technique of exfoliation (Fig. S8).

The 1T-phase of TaS2 used for our experiments is described in the space group Mathematical equation with unit-cell parameters a = 3.365 Å and c = 5.883 Å (Spijkerman et al., 1997View full citation). A charge-density wave is formed by periodic, static displacements of Ta and S, giving rise to additional Bragg satellite reflections in the diffraction patterns. The incommensurately modulated structure was previously described with the superspace group X3(α, β, 0)0(−α − β, α, 0)0 (Spijkerman et al., 1997View full citation). 1T-TaS2 samples were prepared by microtome cutting perpendicular to the naturally occurring layers oriented parallel to the crystallographic ab plane (Fig. S9) (Haupt et al., 2016View full citation).

2.5. MeV electron diffraction data collection

Electron diffraction data for muscovite and 1T-TaS2 were recorded at REGAE at an energy of 3.48 MeV and a pulse duration of 600 fs at room temperature (293 K). No active beam stabilization based on beam diagnostics was used for measurements. To still achieve a high beam stability, only environmental parameters such as humidity and temperature were well controlled and the RF system was actively stabilized.

For data collection, the samples were rotated from −60° to +60° in discrete steps of 0.01° for muscovite and from −65° to +65° in discrete steps of 0.005° for 1T-TaS2, resulting in a pseudo-continuous rotation (Table S1). For each angular position, diffraction still images from 12 electron pulses were recorded. In total 153 600 diffraction images were recorded from muscovite and 312 000 diffraction images from TaS2, corresponding to total data collection times of about 3.5 h and 7.5 h, respectively. The diffraction images clearly show sharp Bragg reflections and very low noise levels between the reflections, highlighting the excellent achievable signal-to-noise ratio (Fig. 2[link]). For 1T-TaS2, weaker reflections around the Bragg peaks originating from the CDW can be clearly observed. The well resolved spatial separation of the reflections is a clear indication of the high transverse and longitudinal coherence lengths of the electron bunches from REGAE.

[Figure 2]
Figure 2
MeV electron diffraction patterns. Sum of 12 single-shot diffraction still images recorded with 3.48 MeV high-energy electron pulses at the REGAE facility from muscovite (a) and 1T-TaS2 (b) at a pulse rate of 12.5 Hz. The corresponding intensity profiles along the dashed lines indicated in the diffraction patterns highlight the achievable signal-to noise-ratio resulting from the high coherence of the electron beam and the low background scattering signal [(c) and (d)].

With a bunch charge of 60 fC and a beam diameter of 500 µm, an integrated fluence of 2.8 × 10−3 e− Å−2 was delivered to the central part of the muscovite sample. The integrated fluence for the 1T-TaS2 sample using pulse charges of less than 15 fC and a beam diameter of 50 µm was less than 0.14 e− Å−2. During data collection, we could not detect any decay in the diffraction signals and quality, indicating an absence of radiation-damage effects for the radiation doses applied here [Fig. 3[link](b)].

[Figure 3]
Figure 3
Results from dynamical structure refinement of the muscovite high-energy electron diffraction data. (a) Dependence of the Rall value from dynamical structure refinements as function of the adopted sample thickness. (b) Decay of the mean I/σ(I) ratio in the diffraction data as function of the increasing effective sample thickness caused by sample rotation and the corresponding goniometer angle. (c) View of the muscovite layer structure along the crystallographic a axis. (d) Detailed view of the muscovite structure with anisotropic thermal displacement parameters indicated as ellipsoids (potassium = violet, aluminium = blue, oxygen = red, hydrogen = pink). (e) Overlay of the OH group with anisotropic thermal displacement parameters shown as ellipsoids obtained with electron diffraction (ED, this work) and a reference model obtained with neutron diffraction (ND) (Gatta et al., 2011View full citation).

2.6. Data reduction and structure solution

Data reduction was performed with the software PETS2 (Palatinus et al., 2019View full citation). From PETS2 data processing a beam stability of about ±1 detector pixel (0.075 mm) in the x direction (horizontal) and ±2 pixels in the y direction (vertical) at the position of the Jungfrau detector was derived over the entire measurement time for each dataset. The quality of the diffraction datasets allowed a straightforward structure solution of the muscovite structure and the average 1T-TaS2 structure using well established software (Palatinus & Chapuis, 2007View full citation; Sheldrick, 2008View full citation; Burla et al., 2015View full citation). The (3+2)d superspace structure of 1T-TaS2 could be solved with SUPERFLIP (Palatinus & Chapuis, 2007View full citation). Initial kinematical refinements, neglecting multiple scattering events, were performed with Jana2020 (Petříček et al., 2023View full citation). They yielded Rall values of 17.3% for muscovite and 25.5% for the modulated room-temperature structure of 1T-TaS2. To obtain a better agreement between the measured and calculated structure amplitudes and hence a better model of the structures, Jana2020 was also used to carry out dynamical structure refinements (Klar et al., 2023View full citation; Palatinus, Petříček & Corrêa, 2015View full citation; Palatinus, Corrêa et al., 2015View full citation).

3. Results

3.1. Muscovite

Dynamical refinement against the muscovite dataset resulted in an improved merged Rall value of 9.4% (Table S3). The refinement appeared highly sensitive to the assumed crystal thickness and crystal mosaicity. The Rall values from the refinements show a distinct minimum for a thickness around 650 nm. When freely refined, a crystal thickness of 634 nm is obtained [Fig. 3[link](a)], which agrees well with the measured thickness of 670 nm. During data collection, the effective sample thickness, i.e. the length of the electron path through the crystal, increases up to 1.4 µm at a rotation angle of 60°. But even at this large thickness, excellent data quality with a reasonable I/σ(I) ≃ 10 could be obtained [Fig. 3[link](b)].

In the resulting structural model, all details are well resolved and meaningful anisotropic thermal displacement parameters are obtained [Figs. 3[link](c), 3[link](d); data in CIF format are available in the supporting information]. A comparison of atom-site coordinates with a reference structure of slightly different chemical composition (Gatta et al., 2011View full citation) using the tool COMPSTRU yielded an average deviation of 0.032 Å with a maximum deviation of 0.083 Å for the non-hydrogen sites (de la Flor et al., 2016View full citation). The high quality of the diffraction data in combination with the high resolution in reciprocal space accessible with our method even allows the identification and free refinement of the hydrogen-atom position with meaningful anisotropic thermal displacement parameters. The parameters obtained for the hydrogen atom and the resulting O—H bond length of 0.95 (4) Å and the ADPs agree very well with neutron reference data, stating a length of 0.939 (5) Å [Fig. 3[link](e), Table S4] (Gatta et al., 2011View full citation). A comparative X-ray structure determination conducted from exactly the same sample as used for our MeV ED experiments yielded an O—H bond length of 0.81 (6) Å and did not allow a free refinement of the ADPs within the independent-atom model.

3.2. 1T-TaS2

Dynamical refinement of the 1T-TaS2 dataset resulted in an improved merged Rall value of 4.3% for the main reflections and 12.0% for all reflections including the satellite reflections of 1T-TaS2 (Table S5). Similar to muscovite, all structural details are well resolved, and meaningful thermal displacement parameters are obtained [Fig. 4[link](a, b); data in CIF format are available in the supporting information]. The weak satellite reflections originating from the charge-density wave were about 1–2 orders of magnitude lower in counts than the main structural reflections. Including these in the dynamical structure refinement enabled us to refine the incommensurate structure of 1T-TaS2 [Fig. 4[link](c)]. In agreement with a previous study conducted with X-rays from a 300× thicker single crystal, an arrangement of star-like tantalum clusters within the layers is observed, each consisting of 13 tantalum atoms [Figs. 4[link](d), 4[link](e)] (Spijkerman et al., 1997View full citation).

[Figure 4]
Figure 4
TaS2 structure as determined by MeV electron diffraction at REGAE. (a) TaS2 layer structure viewed along the crystallographic a axis. (b) Octahedral coordination of the Ta atom by six sulfur atoms with thermal displacement parameters represented as ellipsoids. (c) Refined modulation displacement amplitudes of the Ta atom as a function of xs4 and xs5 analogous to the analysis by Spijkerman et al. (1997View full citation). (d) Real-space representation of the modulated structure of ∼75 × 75 crystallographic unit cells showing the arrangement of star-shaped Ta clusters, each consisting of 13 tantalum atoms. Ta atoms separated by less than 3.4 Å are connected by lines. Sulfur atoms are omitted. (e) View of a single star-shaped 13-atom tantalum cluster together with the coordinating sulfur atoms viewed along c (top) and rotated by 90° about a (bottom).

4. Conclusions and outlook

We have successfully applied accelerator-based high-energy electron diffraction to the field of 3D crystallographic structure determination, which has traditionally been dominated by X-rays. By integrating cutting-edge accelerator science with novel diffraction instrumentation, a direct electron-detection-capable detector, optimization of dark current and reduction of background scattering – paired with the latest software advances for dynamical diffraction data analysis – we were able to solve and refine the structure of the quasi-2D layered materials muscovite and 1T-TaS2 ab initio with dynamical refinements at very high quality, as clearly indicated by very low merged Rall values of 9.4% for muscovite and 4.3% for the unmodulated structure of TaS2.

Electron energies exceeding 1 MeV – specifically 3.48 MeV in our case – strike an optimal balance between penetration depth and scattering contrast, making them ideal for structural studies of micro- and nanocrystals. For muscovite, the reduced elastic cross sections of high-energy electrons enabled us to acquire high-quality diffraction data from a 670 nm thick sample, an achievement unattainable with current lab-based electron diffraction devices or electron microscopes. For proteins, which have a density approximately 2.5 times lower than muscovite, theoretical predictions and microscopy experiments on biological specimens (Cosslett, 1969View full citation) suggest that it should be possible to analyse crystals up to 2 µm in size. These would be easily visible under an optical microscope, significantly simplifying and streamlining sample preparation processes.

At the same time, the elastic cross section at 3.48 MeV remains sufficiently high to enable high-quality structure determination from samples as thin as 30 nm. This capability allowed us to precisely resolve the incommensurate structure of 1T-TaS2 using satellite reflections that are, on average, 1–2 orders of magnitude weaker than the main reflections. Given that the TaS2 measurements utilized only a small fraction of the available bunch charge, it should be entirely feasible to perform diffraction experiments on just a few or even single layers of quantum materials at REGAE.

A current limitation of the method is the transversely large electron beam size caused by space charge effects, necessitating the use of laterally large yet relatively thin pancake-like samples. To address this, we are implementing a bunch-train mode at REGAE (Mahnke et al., 2024View full citation), in which the bunch charge of up to 100 fC is evenly distributed across 4500 microbunches with a total duration of 1.5 µs. This approach enables the electron beam to be focused down to a few micrometres, allowing the investigation of isometric microcrystals of comparable size while preserving its excellent coherence properties.

For radiation-sensitive samples such as proteins, the larger penetration depth of MeV electrons, combined with their large scattering cross section and expected reduced radiation-damage effects, should allow routine collection of a complete dataset suitable for structure determination from a single micro- or nanocrystal, which is in most cases not possible with X-rays (Holton, 2009View full citation). This should make high-energy electrons the ideal probe for structure determination of such small crystals, for example in pharmaceutical compound screening experiments in the framework of structure-based drug discovery (Günther et al., 2021View full citation).

In addition, the more realistic hydrogen-atom positions obtained in electron diffraction experiments, as shown here for muscovite, should lead to a better understanding of enzyme and other catalytic reactions, where hydrogen bonding and transfer reactions play a very important role (Herschlag & Pinney, 2018View full citation).

One parameter not utilized in the present work is the high temporal resolution, down to the single-digit femtosecond range, achievable at linear accelerators such as REGAE. Currently, experiments that combine sub-atomic spatial resolution with femtosecond temporal resolution are predominantly conducted at XFEL sources. However, with significantly reduced radiation-damage effects, such UED experiments at accelerator facilities could enable similar investigations without requiring continuous sample replenishment. This approach would, for instance, allow the study of coherent phonons and ultrafast phase transitions in single layers of 2D quantum materials like 1T-TaS2 and other transition-metal dichalcogenides with exceptional sensitivity (Filippetto et al., 2022View full citation).

With significantly lower investment and operating costs – particularly in terms of electricity consumption – accelerator-based electron diffraction experiments using MeV electrons present an economically and ecologically promising approach for structural and dynamical investigations of micro- and nanometre-sized materials. These methods serve as a valuable complement to existing microfocus synchrotron beamlines and XFELs.

5. Related literature

The following references are cited in the supporting information: Bourhis et al., 2015View full citation; Brázda et al., 2022View full citation; Catti et al., 1994View full citation; Fröjdh et al., 2022View full citation; Kabsch, 2010View full citation; Khouchen et al., 2023View full citation; Novoselov et al., 2012View full citation; Redford et al., 2018View full citation; Sheldrick, 2015View full citation; Stokes et al., 2011View full citation; van Smaalen et al., 2013View full citation.

Supporting information

B-IncStrDB reference: IAyACLYazaI

CCDC references: 2538230; 2545330

Crystal structure: contains datablocks muscoviteElectron, muscoviteXray, TaS2. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup1.cif

Structure factors: contains datablocks global, muscoviteElectron. DOI: https://doi.org/10.1107/S2052252526002782/of5008muscoviteElectronsup2.hkl

Structure factors: contains datablock muscoviteXray. DOI: https://doi.org/10.1107/S2052252526002782/of5008muscoviteXraysup3.hkl

Structure factors: contains datablocks global, TaS2. DOI: https://doi.org/10.1107/S2052252526002782/of5008TaS2sup4.hkl

Supporting tables and figures, and full movie captions. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup5.pdf

Movie S1. Animated de Wolff section (xs1-xs4) of the Ta site. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup6.mp4

Movie S2. Animated de Wolff section (xs2-xs4) of the Ta site. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup7.mp4

Movie S3. Animated de Wolff section (xs3-xs4) of the Ta site. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup8.mp4

Movie S4. Animated de Wolff section (xs1-xs4) of the S site. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup9.mp4

Movie S4. Animated de Wolff section (xs2-xs4) of the S site. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup10.mp4

Movie S6. Animated de Wolff section (xs3-xs4) of the S site. DOI: https://doi.org/10.1107/S2052252526002782/of5008sup11.mp4


Computing details top

(muscoviteElectron) top
Crystal data top
KAl3Si3O12H2F(000) = 275.956
Mr = 398.3Dx = 2.808 Mg m−3
Monoclinic, C2/cElectron radiation, λ = 0.0031 Å
Hall symbol: -C 2ycCell parameters from 96357 reflections
a = 5.2037 (10) Åθ = 0.02–0.2°
b = 9.0305 (18) ŵ = 0 mm−1
c = 20.156 (4) ÅT = 293 K
β = 95.78 (3)°Exfoliated synthetic sample
V = 942.3 (3) Å33.00 × 0.75 × 0.001 mm
Z = 4
Data collection top
REGAE
diffractometer		4120 reflections with I > 3σ(I)
Radiation source: RF photocathode (Mo) gunθmax = 0.2°, θmin = 0.02°
continuous–rotation 3D electron diffraction scansh = −9→8
19751 measured reflectionsk = −13→15
4426 independent reflectionsl = −28→28
Refinement top
Refinement on F19 constraints
R[F2 > 2σ(F2)] = 0.098All H-atom parameters refined
wR(F2) = 0.108Weighting scheme based on measured s.u.'s w = 1/[σ2(Fo) + (0.009P)2]
where P = Fo
S = 4.38(Δ/σ)max = 0.044
4426 reflectionsΔρmax = 0.15 e Å−3
164 parametersΔρmin = −0.11 e Å−3
0 restraints
Special details top

Refinement. Calculated intensities based on dynamical theory of electron diffraction. Number of individual data blocks in refinement: 1 Block Thickness Nobs Nall Robs Rall wRall 1 6340.48 4120 4426 0.0975 0.0993 0.1076 Thickness given in Angstrom. A mosaic crystal with constant thickness is assumed. The effective crystal thickness was adapted based on the goniometer angle.

Refinement statistics relevant for the non-linear least-squares minimisation of wR(all): Number of reflections in refinement (obs/all): 4120 / 4426 Number of reflections present more than once: 383 Number of reflections unique in point group 1: 4043 Robs: 0.0975 Rall: 0.0993 wRall: 0.1076

Post-refinement analysis of symmetrically-equivalent reflections: Number of unique reflections (obs/all): 1756 / 1874 MRobs: 0.0923 MRall: 0.0940 MwRall: 0.0998

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
K10.50.5988 (2)0.250.0264 (13)
Si10.0493 (3)0.75904 (14)0.36421 (15)0.0080 (7)0.75
Al10.0493 (3)0.75904 (14)0.36421 (15)0.0080 (7)0.25
Si20.0350 (3)0.42975 (13)0.36450 (15)0.0073 (7)0.75
Al20.0350 (3)0.42975 (13)0.36450 (15)0.0073 (7)0.25
Al00.2502 (3)0.58363 (16)0.50015 (16)0.0073 (8)
O10.1177 (4)0.7515 (2)0.4465 (2)0.0098 (11)
O20.0381 (4)0.4442 (2)0.4465 (2)0.0095 (11)
O30.0864 (5)0.5925 (2)0.3319 (2)0.0158 (13)
O40.2492 (5)0.8718 (2)0.3317 (2)0.0139 (12)
O50.2479 (5)0.3093 (3)0.3432 (3)0.0182 (14)
O60.5431 (4)0.5625 (2)0.4497 (2)0.0131 (12)
H10.629 (6)0.651 (3)0.439 (3)0.09 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
K10.0206 (10)0.0307 (10)0.028 (4)00.0003 (13)0
Si10.0028 (5)0.0117 (6)0.010 (2)0.0000 (3)−0.0002 (7)−0.0017 (6)
Al10.0028 (5)0.0117 (6)0.010 (2)0.0000 (3)−0.0002 (7)−0.0017 (6)
Si20.0029 (5)0.0074 (6)0.011 (2)0.0006 (3)−0.0024 (7)−0.0022 (6)
Al20.0029 (5)0.0074 (6)0.011 (2)0.0006 (3)−0.0024 (7)−0.0022 (6)
Al00.0045 (6)0.0125 (6)0.005 (2)0.0007 (3)−0.0017 (8)−0.0019 (6)
O10.0060 (9)0.0137 (9)0.009 (3)0.0010 (5)−0.0024 (12)−0.0018 (9)
O20.0040 (9)0.0196 (10)0.005 (3)−0.0035 (6)−0.0009 (11)−0.0013 (10)
O30.0188 (12)0.0120 (9)0.016 (3)−0.0001 (6)0.0013 (15)−0.0011 (10)
O40.0074 (10)0.0200 (11)0.014 (3)−0.0021 (6)0.0004 (13)0.0010 (11)
O50.0099 (10)0.0203 (11)0.024 (4)0.0026 (7)−0.0007 (14)−0.0052 (12)
O60.0059 (9)0.0138 (10)0.020 (3)0.0003 (6)0.0032 (12)0.0011 (10)
H10.07 (2)0.032 (12)0.17 (7)−0.009 (10)0.02 (3)0.052 (19)
Geometric parameters (Å, º) top
K1—O32.843 (4)Al1—O41.638 (4)
K1—O3i2.843 (4)Al1—O5vi1.647 (3)
K1—O4ii2.857 (3)Si2—O21.657 (5)
K1—O4iii2.857 (3)Si2—O31.642 (3)
K1—O5iv2.884 (4)Si2—O4vii1.651 (3)
K1—O5v2.884 (4)Si2—O51.640 (3)
Si1—O11.662 (5)Al2—O21.657 (5)
Si1—O31.658 (3)Al2—O31.642 (3)
Si1—O41.638 (4)Al2—O4vii1.651 (3)
Si1—O5vi1.647 (3)Al2—O51.640 (3)
Al1—O11.662 (5)H1—O60.95 (3)
Al1—O31.658 (3)
O3—K1—O3i177.71 (10)O4—Si1—O5vi110.63 (19)
O3—K1—O4ii88.68 (10)O1—Al1—O3109.4 (2)
O3—K1—O4iii89.68 (10)O1—Al1—O4110.10 (19)
O3—K1—O5iv87.14 (11)O1—Al1—O5vi111.8 (2)
O3—K1—O5v94.38 (11)O3—Al1—O4107.7 (2)
O3i—K1—O4ii89.68 (10)O3—Al1—O5vi107.11 (18)
O3i—K1—O4iii88.68 (10)O4—Al1—O5vi110.63 (19)
O3i—K1—O5iv94.38 (11)O2—Si2—O3110.0 (2)
O3i—K1—O5v87.14 (11)O2—Si2—O4vii110.0 (2)
O4ii—K1—O4iii88.32 (10)O2—Si2—O5112.0 (2)
O4ii—K1—O5iv87.16 (9)O3—Si2—O4vii107.46 (19)
O4ii—K1—O5v174.53 (12)O3—Si2—O5110.3 (2)
O4iii—K1—O5iv174.53 (12)O4vii—Si2—O5106.83 (18)
O4iii—K1—O5v87.16 (9)O2—Al2—O3110.0 (2)
O5iv—K1—O5v97.51 (11)O2—Al2—O4vii110.0 (2)
O1—Si1—O3109.4 (2)O2—Al2—O5112.0 (2)
O1—Si1—O4110.10 (19)O3—Al2—O4vii107.46 (19)
O1—Si1—O5vi111.8 (2)O3—Al2—O5110.3 (2)
O3—Si1—O4107.7 (2)O4vii—Al2—O5106.83 (18)
O3—Si1—O5vi107.11 (18)
Symmetry codes: (i) −x+1, y, −z+1/2; (ii) x+1/2, y−1/2, z; (iii) −x+1/2, y−1/2, −z+1/2; (iv) x+1/2, y+1/2, z; (v) −x+1/2, y+1/2, −z+1/2; (vi) x−1/2, y+1/2, z; (vii) x−1/2, y−1/2, z.
(muscoviteXray) top
Crystal data top
Al5.975H4K2O24Si6V = 939.4 (3) Å3
Mr = 797.02Z = 2
Monoclinic, C2/cF(000) = 794.337
a = 5.203 (1) ÅDx = 2.818 Mg m−3
b = 9.0270 (18) ÅSynchrotron radiation, λ = 0.61991 Å
c = 20.103 (4) ŵ = 0.88 mm−1
β = 95.76 (3)°T = 293 K
Data collection top
Bruker APEX-II CCD
diffractometer		Rint = 0.018
ω scansθmax = 24.7°, θmin = 3.9°
2362 measured reflectionsh = −7→7
1039 independent reflectionsk = −12→11
1013 reflections with I ≥ 2u(I)l = −17→25
Refinement top
Refinement on F20 restraints
Least-squares matrix: full4 constraints
R[F2 > 2σ(F2)] = 0.050All H-atom parameters refined
wR(F2) = 0.179 w = 1/[σ2(Fo2) + (0.1485P)2 + 2.6644P]
where P = (Fo2 + 2Fc2)/3
S = 1.06(Δ/σ)max = −0.0005
1039 reflectionsΔρmax = 1.52 e Å−3
92 parametersΔρmin = −1.66 e Å−3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
K0010.50.59871 (12)0.250.0264 (4)
Al000.25034 (13)0.58344 (8)0.50002 (4)0.0075 (4)
O0010.1156 (4)0.75142 (19)0.44633 (12)0.0103 (5)
O0020.0380 (4)0.4440 (2)0.44635 (11)0.0111 (5)
O0030.0841 (4)0.5932 (2)0.33177 (12)0.0153 (5)
O0040.2503 (4)0.8708 (2)0.33103 (12)0.0154 (5)
O0050.2492 (4)0.3106 (2)0.34225 (12)0.0175 (5)
O0060.5422 (4)0.5616 (2)0.44976 (11)0.0113 (5)
Si020.04853 (14)0.75838 (9)0.36446 (4)0.0084 (4)0.750000
Si030.03494 (13)0.42988 (9)0.36455 (4)0.0084 (4)0.750000
H0060.612 (10)0.637 (6)0.440 (3)0.029 (13)*
Al020.04853 (14)0.75838 (9)0.36446 (4)0.0084 (4)0.250000
Al030.03494 (13)0.42988 (9)0.36455 (4)0.0084 (4)0.244 (7)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
K0010.0259 (6)0.0255 (7)0.0282 (7)−0.0000000.0042 (5)0.000000
Al000.0044 (5)0.0052 (6)0.0131 (6)0.0003 (2)0.0021 (4)−0.0002 (2)
O0010.0089 (10)0.0071 (10)0.0150 (11)−0.0002 (6)0.0019 (8)−0.0015 (6)
O0020.0081 (9)0.0091 (9)0.0163 (11)−0.0006 (7)0.0028 (7)0.0006 (7)
O0030.0185 (11)0.0106 (10)0.0170 (12)−0.0013 (7)0.0024 (8)−0.0004 (7)
O0040.0124 (9)0.0152 (10)0.0183 (12)−0.0035 (8)0.0003 (8)0.0005 (8)
O0050.0123 (9)0.0163 (11)0.0236 (12)0.0035 (7)0.0000 (8)−0.0036 (8)
O0060.0088 (9)0.0100 (9)0.0154 (11)0.0001 (7)0.0024 (7)0.0025 (7)
Si020.0051 (5)0.0054 (5)0.0150 (6)−0.0003 (2)0.0018 (3)−0.0003 (2)
Si030.0056 (5)0.0050 (5)0.0150 (6)0.0000 (2)0.0022 (3)−0.0001 (2)
Al020.0051 (5)0.0054 (5)0.0150 (6)−0.0003 (2)0.0018 (3)−0.0003 (2)
Al030.0056 (5)0.0050 (5)0.0150 (6)0.0000 (2)0.0022 (3)−0.0001 (2)
Geometric parameters (Å, º) top
K001—O003i2.846 (2)O001—Si021.649 (2)
K001—O003ii3.307 (2)O001—Al021.649 (2)
K001—O0032.846 (2)O002—Si031.648 (2)
K001—O003iii3.307 (2)O002—Al031.648 (2)
K001—O004i3.286 (2)O003—Si021.647 (2)
K001—O004iv2.856 (2)O003—Si031.645 (2)
K001—O004v2.856 (2)O003—Al021.647 (2)
K001—O0043.286 (2)O003—Al031.645 (2)
K001—O005vi2.880 (2)O004—Si021.651 (2)
K001—O005vii2.880 (2)O004—Si03vii1.653 (2)
K001—Si02i3.7382 (12)O004—Al021.651 (2)
K001—Si023.7382 (12)O004—Al03vii1.653 (2)
K001—Al02i3.7382 (12)O005—Si02iv1.645 (2)
K001—Al023.7382 (12)O005—Si031.644 (2)
Al00—O001viii1.929 (2)O005—Al02iv1.645 (2)
Al00—O0011.950 (2)O005—Al031.644 (2)
Al00—O0021.931 (2)O006—H0060.80 (6)
Al00—O002ix1.949 (2)Al02—Al032.9662 (12)
Al00—O006x1.918 (2)Al02—Al03vii2.9666 (10)
Al00—O0061.917 (2)
O003—K001—O003i178.00 (9)Si02—O001—Al00viii123.84 (11)
O003iii—K001—O003i115.25 (8)Al02—O001—Al00viii123.84 (11)
O003—K001—O003ii115.25 (8)Al02—O001—Al00127.60 (11)
O003iii—K001—O003ii178.28 (8)Al02—O001—Si020.0
O004—K001—O003i131.35 (6)Si03—O002—Al00123.75 (11)
O004i—K001—O003i50.61 (5)Si03—O002—Al00ix127.69 (12)
O004i—K001—O003ii82.44 (5)Al03—O002—Al00ix127.69 (12)
O004v—K001—O003ii128.05 (6)Al03—O002—Al00123.75 (11)
O004—K001—O003iii82.44 (5)Al03—O002—Si030.0
O004iv—K001—O003i89.27 (6)Si02—O003—K001iii92.88 (9)
O004v—K001—O003iii50.36 (5)Si02—O003—K001i109.69 (10)
O004iv—K001—O00389.29 (6)Si03—O003—K001i113.87 (10)
O004i—K001—O003131.35 (6)Si03—O003—K001iii92.32 (9)
O004iv—K001—O003ii50.36 (5)Si03—O003—Si02128.55 (16)
O004i—K001—O003iii98.86 (5)Al02—O003—K001i109.69 (10)
O004iv—K001—O003iii128.05 (6)Al02—O003—K001iii92.88 (9)
O004—K001—O003ii98.86 (5)Al02—O003—Si020.0
O004v—K001—O003i89.29 (6)Al02—O003—Si03128.55 (16)
O004v—K001—O00389.27 (6)Al03—O003—K001iii92.32 (9)
O004—K001—O00350.61 (5)Al03—O003—K001i113.87 (10)
O004v—K001—O004i115.85 (8)Al03—O003—Si02128.55 (16)
O004—K001—O004iv115.85 (7)Al03—O003—Si030.0
O004v—K001—O004iv87.82 (9)Al03—O003—Al02128.55 (16)
O004—K001—O004i83.27 (8)Si02—O004—K001vi113.75 (10)
O005vi—K001—O003i87.64 (6)Si02—O004—K001i92.39 (9)
O005vii—K001—O003ii50.06 (5)Si03vii—O004—K001vi109.79 (10)
O005vii—K001—O003iii131.44 (6)Si03vii—O004—K001i93.48 (9)
O005vi—K001—O003iii50.06 (5)Si03vii—O004—Si02127.81 (15)
O005vi—K001—O003ii131.44 (6)Al02—O004—K001vi113.75 (10)
O005vii—K001—O003i93.68 (6)Al02—O004—K001i92.39 (9)
O005vii—K001—O00387.64 (6)Al02—O004—Si020.0
O005vi—K001—O00393.68 (6)Al02—O004—Si03vii127.81 (15)
O005vi—K001—O004i50.16 (5)Al03vii—O004—K001vi109.79 (10)
O005vi—K001—O004v87.77 (6)Al03vii—O004—K001i93.48 (9)
O005vi—K001—O004iv174.65 (7)Al03vii—O004—Si02127.81 (15)
O005vi—K001—O00469.40 (6)Al03vii—O004—Si03vii0.0
O005vii—K001—O004iv87.77 (6)Al03vii—O004—Al02127.81 (15)
O005vii—K001—O00450.16 (5)Si02iv—O005—K001xi109.72 (10)
O005vii—K001—O004i69.40 (6)Si03—O005—K001xi109.69 (10)
O005vii—K001—O004v174.65 (7)Si03—O005—Si02iv139.69 (15)
O005vi—K001—O005vii96.79 (10)Al02iv—O005—K001xi109.72 (10)
Si02i—K001—O003iii107.62 (4)Al02iv—O005—Si02iv0.0
Si02—K001—O00324.51 (4)Al02iv—O005—Si03139.69 (15)
Si02i—K001—O003i24.51 (4)Al03—O005—K001xi109.69 (10)
Si02—K001—O003i157.42 (5)Al03—O005—Si02iv139.69 (15)
Si02i—K001—O003157.42 (5)Al03—O005—Si030.0
Si02—K001—O003ii107.62 (4)Al03—O005—Al02iv139.69 (15)
Si02i—K001—O003ii73.08 (4)H006—O006—Al00x117 (4)
Si02—K001—O003iii73.08 (4)H006—O006—Al00116 (4)
Si02i—K001—O004iv110.49 (4)O001—Si02—K001i121.11 (7)
Si02—K001—O004iv101.85 (5)O003—Si02—K001i45.80 (8)
Si02—K001—O004i108.73 (5)O003—Si02—O001110.04 (11)
Si02i—K001—O004v101.85 (5)O004—Si02—K001i61.43 (8)
Si02—K001—O004v110.49 (4)O004—Si02—O001110.50 (11)
Si02i—K001—O004i26.18 (4)O004—Si02—O003107.01 (12)
Si02—K001—O00426.18 (4)O005xii—Si02—K001i125.41 (9)
Si02i—K001—O004108.73 (5)O005xii—Si02—O001112.42 (12)
Si02—K001—O005vi82.55 (5)O005xii—Si02—O003106.98 (12)
Si02—K001—O005vii67.52 (4)O005xii—Si02—O004109.70 (12)
Si02i—K001—O005vi67.52 (4)O003—Si03—O002110.12 (12)
Si02i—K001—O005vii82.55 (5)O004xi—Si03—O002110.50 (11)
Si02—K001—Si02i134.64 (4)O004xi—Si03—O003107.15 (12)
Al02i—K001—O003iii107.62 (4)O005—Si03—O002112.57 (11)
Al02—K001—O003ii107.62 (4)O005—Si03—O003109.94 (12)
Al02i—K001—O003i24.51 (4)O005—Si03—O004xi106.35 (11)
Al02—K001—O003i157.42 (5)O001—Al02—K001i121.11 (7)
Al02i—K001—O003157.42 (5)O003—Al02—K001i45.80 (8)
Al02—K001—O003iii73.08 (4)O003—Al02—O001110.04 (11)
Al02i—K001—O003ii73.08 (4)O004—Al02—K001i61.43 (8)
Al02—K001—O00324.51 (4)O004—Al02—O001110.50 (11)
Al02i—K001—O004iv110.49 (4)O004—Al02—O003107.01 (12)
Al02—K001—O004iv101.85 (5)O005xii—Al02—K001i125.41 (9)
Al02—K001—O00426.18 (4)O005xii—Al02—O001112.42 (12)
Al02—K001—O004v110.49 (4)O005xii—Al02—O003106.98 (12)
Al02i—K001—O004108.73 (5)O005xii—Al02—O004109.70 (12)
Al02i—K001—O004v101.85 (5)Al03—Al02—K001i68.37 (2)
Al02i—K001—O004i26.18 (4)Al03vii—Al02—K001i67.22 (2)
Al02—K001—O004i108.73 (5)Al03—Al02—O00187.93 (7)
Al02i—K001—O005vii82.55 (5)Al03vii—Al02—O00185.66 (7)
Al02—K001—O005vi82.55 (5)Al03—Al02—O00325.71 (8)
Al02i—K001—O005vi67.52 (4)Al03vii—Al02—O003110.04 (9)
Al02—K001—O005vii67.52 (4)Al03—Al02—O004129.12 (9)
Al02i—K001—Si02i0.0Al03vii—Al02—O00426.11 (8)
Al02i—K001—Si02134.64 (4)Al03—Al02—O005xii105.33 (8)
Al02—K001—Si020.0Al03vii—Al02—O005xii129.42 (9)
Al02—K001—Si02i134.64 (4)O003—Al03—O002110.12 (12)
Al02—K001—Al02i134.64 (4)O004xi—Al03—O002110.50 (11)
O002ix—Al00—O001viii92.53 (10)O004xi—Al03—O003107.15 (12)
O002—Al00—O001viii166.06 (10)O005—Al03—O002112.57 (11)
O002ix—Al00—O00198.68 (9)O005—Al03—O003109.94 (12)
O002—Al00—O00192.51 (9)O005—Al03—O004xi106.35 (11)
O006—Al00—O001viii96.47 (10)Al02—Al03—O00285.73 (8)
O006x—Al00—O001166.90 (10)Al02xi—Al03—O00287.92 (7)
O006—Al00—O00192.75 (10)Al02xi—Al03—O003129.36 (9)
O006x—Al00—O001viii94.62 (10)Al02—Al03—O00325.74 (8)
O006—Al00—O00294.46 (9)Al02xi—Al03—O004xi26.08 (8)
O006x—Al00—O002ix92.62 (9)Al02—Al03—O004xi110.06 (8)
O006—Al00—O002ix166.68 (11)Al02xi—Al03—O005105.04 (8)
O006x—Al00—O00296.27 (10)Al02—Al03—O005129.63 (9)
Si02—O001—Al00127.60 (11)
K001iii—O003—Si02—K001i−118.14 (12)K001—O005vii—Si03vii—O0045.85 (13)
K001xiii—O003—Si02—K001i−118.14 (12)K001v—O005—Si03—O004xi5.85 (13)
K001iii—O003—Si02—O001127.50 (8)K001—O005vii—Al02ii—K001xiv41.14 (13)
K001—O003—Si02—O001−114.35 (11)K001—O005vi—Al02iii—K001xiii41.14 (13)
K001i—O003—Si02—O001−114.35 (11)K001xiii—O005xii—Al02—O001−127.12 (10)
K001xiii—O003—Si02—O001127.50 (8)K001iii—O005xii—Al02—O001−127.12 (10)
K001i—O003—Si02—O0045.74 (13)K001xiii—O005xii—Al02—O003−6.22 (14)
K001iii—O003—Si02—O004−112.40 (9)K001iii—O005xii—Al02—O003−6.22 (14)
K001—O003—Si02—O0045.74 (13)K001xiii—O005xii—Al02—O004109.50 (12)
K001xiii—O003—Si02—O004−112.40 (9)K001iii—O005xii—Al02—O004109.50 (12)
K001i—O003—Si02—O005xii123.25 (11)K001—O005vi—Al02iii—Al03xv129.40 (6)
K001—O003—Si02—O005xii123.25 (11)K001—O005vii—Al02ii—Al03xvi129.40 (6)
K001iii—O003—Si02—O005xii5.10 (12)K001iii—O005xii—Al02—Al03−32.96 (10)
K001xiii—O003—Si02—O005xii5.10 (12)K001xiii—O005xii—Al02—Al03−32.96 (10)
K001—O003—Si03—O002125.95 (11)K001xi—O005—Al03—O002127.00 (10)
K001iii—O003—Si03—O002−115.05 (8)K001v—O005—Al03—O002127.00 (10)
K001i—O003—Si03—O002125.95 (11)K001xi—O005—Al03—O003−109.83 (11)
K001xiii—O003—Si03—O002−115.05 (8)K001v—O005—Al03—O003−109.83 (11)
K001xiii—O003—Si03—O004xi5.18 (11)K001—O005vii—Al03vii—O0045.85 (13)
K001iii—O003—Si03—O004xi5.18 (11)K001v—O005—Al03—O004xi5.85 (13)
K001—O003—Si03—O004xi−113.82 (12)K001v—O005—Al03—Al02−129.14 (6)
K001i—O003—Si03—O004xi−113.82 (12)K001xi—O005—Al03—Al02−129.14 (6)
K001i—O003—Si03—O0051.35 (14)K001—O005vii—Al03vii—Al0232.93 (10)
K001iii—O003—Si03—O005120.36 (9)K001v—O005—Al03—Al02xi32.93 (10)
K001xiii—O003—Si03—O005120.36 (9)K001—Si02—O001—Al00viii101.35 (7)
K001—O003—Si03—O0051.35 (14)K001—Si02—O001—Al00−44.03 (6)
K001xiii—O003—Al02—K001i−118.14 (12)K001i—Si02—O001—Al00−44.03 (6)
K001iii—O003—Al02—K001i−118.14 (12)K001i—Si02—O001—Al00viii101.35 (7)
K001xiii—O003—Al02—O001127.50 (8)K001i—Si02—O003—K001iii−118.14 (7)
K001i—O003—Al02—O001−114.35 (11)K001—Si02—O003—K001iii−118.14 (7)
K001iii—O003—Al02—O001127.50 (8)K001i—Si02—O003—Si03146.58 (6)
K001—O003—Al02—O001−114.35 (11)K001—Si02—O003—Si03146.58 (6)
K001—O003—Al02—O0045.74 (13)K001—Si02—O003—Al03146.58 (6)
K001i—O003—Al02—O0045.74 (13)K001i—Si02—O003—Al03146.58 (6)
K001xiii—O003—Al02—O004−112.40 (9)K001i—Si02—O004—K001vi119.68 (4)
K001iii—O003—Al02—O004−112.40 (9)K001—Si02—O004—K001vi119.68 (4)
K001—O003—Al02—O005xii123.25 (11)K001i—Si02—O004—Si03vii−96.28 (7)
K001iii—O003—Al02—O005xii5.10 (12)K001—Si02—O004—Si03vii−96.28 (7)
K001i—O003—Al02—O005xii123.25 (11)K001—Si02—O004—Al03vii−96.28 (7)
K001xiii—O003—Al02—O005xii5.10 (12)K001i—Si02—O004—Al03vii−96.28 (7)
K001—O003—Al02—Al03vii−21.65 (11)K001—Si02—O005xii—K001xiii41.14 (6)
K001—O003—Al02—Al03−146.6 (3)K001—Si02i—O005xvii—K001xiv41.14 (6)
K001xiii—O003—Al02—Al0395.3 (2)K001—Si02—O005xii—Si03xii−151.54 (10)
K001i—O003—Al02—Al03vii−21.65 (11)K001xviii—Si02iv—O005—Si03−151.54 (10)
K001iii—O003—Al02—Al0395.3 (2)K001—Si02—O005xii—Al03xii−151.54 (10)
K001i—O003—Al02—Al03−146.6 (3)K001xviii—Si02iv—O005—Al03−151.54 (10)
K001iii—O003—Al02—Al03vii−139.79 (3)K001i—Al02—O001—Al00−44.03 (6)
K001xiii—O003—Al02—Al03vii−139.79 (3)K001—Al02—O001—Al00viii101.35 (7)
K001i—O003—Al03—O002125.95 (11)K001—Al02—O001—Al00−44.03 (6)
K001iii—O003—Al03—O002−115.05 (8)K001i—Al02—O001—Al00viii101.35 (7)
K001—O003—Al03—O002125.95 (11)K001i—Al02—O003—K001iii−118.14 (7)
K001xiii—O003—Al03—O002−115.05 (8)K001—Al02—O003—K001iii−118.14 (7)
K001xiii—O003—Al03—O004xi5.18 (11)K001i—Al02—O003—Si03146.58 (6)
K001iii—O003—Al03—O004xi5.18 (11)K001—Al02—O003—Si03146.58 (6)
K001—O003—Al03—O004xi−113.82 (12)K001i—Al02—O003—Al03146.58 (6)
K001i—O003—Al03—O004xi−113.82 (12)K001—Al02—O003—Al03146.58 (6)
K001i—O003—Al03—O0051.35 (14)K001i—Al02—O004—K001vi119.68 (4)
K001iii—O003—Al03—O005120.36 (9)K001—Al02—O004—K001vi119.68 (4)
K001xiii—O003—Al03—O005120.36 (9)K001i—Al02—O004—Si03vii−96.28 (7)
K001—O003—Al03—O0051.35 (14)K001—Al02—O004—Si03vii−96.28 (7)
K001xiii—O003—Al03—Al02−95.55 (19)K001i—Al02—O004—Al03vii−96.28 (7)
K001iii—O003—Al03—Al02−95.55 (19)K001—Al02—O004—Al03vii−96.28 (7)
K001i—O003—Al03—Al02xi−129.54 (7)K001—Al02i—O005xvii—K001xiv41.14 (6)
K001—O003—Al03—Al02xi−129.54 (7)K001—Al02—O005xii—K001xiii41.14 (6)
K001iii—O003—Al03—Al02xi−10.54 (11)K001xviii—Al02iv—O005—Si03−151.54 (10)
K001i—O003—Al03—Al02145.5 (3)K001—Al02—O005xii—Si03xii−151.54 (10)
K001—O003—Al03—Al02145.5 (3)K001—Al02—O005xii—Al03xii−151.54 (10)
K001xiii—O003—Al03—Al02xi−10.54 (11)K001xviii—Al02iv—O005—Al03−151.54 (10)
K001vi—O004—Si02—K001i119.68 (12)Al00—O001—Si02—O0035.68 (18)
K001xii—O004—Si02—K001i119.68 (12)Al00viii—O001—Si02—O003151.06 (14)
K001vi—O004—Si02—O001−125.21 (11)Al00viii—O001—Si02—O00433.11 (16)
K001—O004—Si02—O001115.11 (8)Al00—O001—Si02—O004−112.28 (15)
K001xii—O004—Si02—O001−125.21 (11)Al00—O001—Si02—O005xii124.80 (14)
K001i—O004—Si02—O001115.11 (8)Al00viii—O001—Si02—O005xii−89.82 (16)
K001xii—O004—Si02—O003114.99 (12)Al00viii—O001—Al02—O003151.06 (14)
K001i—O004—Si02—O003−4.68 (11)Al00—O001—Al02—O0035.68 (18)
K001vi—O004—Si02—O003114.99 (12)Al00viii—O001—Al02—O00433.11 (16)
K001—O004—Si02—O003−4.68 (11)Al00—O001—Al02—O004−112.28 (15)
K001—O004—Si02—O005xii−120.39 (9)Al00viii—O001—Al02—O005xii−89.82 (16)
K001vi—O004—Si02—O005xii−0.72 (14)Al00—O001—Al02—O005xii124.80 (14)
K001—O004iv—Si02iv—O005−0.72 (14)Al00viii—O001—Al02—Al03164.44 (13)
K001i—O004—Si02—O005xii−120.39 (9)Al00viii—O001—Al02—Al03vii41.30 (12)
K001v—O004xi—Si03—O002−127.30 (8)Al00—O001—Al02—Al0319.06 (13)
K001iii—O004xi—Si03—O002113.62 (11)Al00—O001—Al02—Al03vii−104.08 (14)
K001—O004—Si03vii—O002vii−127.30 (8)Al00—O002—Si03—O003−33.02 (17)
K001xiii—O004xi—Si03—O002113.62 (11)Al00ix—O002—Si03—O003112.48 (15)
K001xiii—O004xi—Si03—O003−6.37 (13)Al00ix—O002—Si03—O004xi−5.70 (17)
K001v—O004xi—Si03—O003112.71 (9)Al00—O002—Si03—O004xi−151.21 (13)
K001—O004—Si03vii—O003vii112.71 (9)Al00—O002—Si03—O00590.05 (15)
K001iii—O004xi—Si03—O003−6.37 (13)Al00ix—O002—Si03—O005−124.45 (14)
K001xiii—O004xi—Si03—O005−123.92 (12)Al00—O002—Al03—O003−33.02 (17)
K001—O004—Si03vii—O005vii−4.83 (11)Al00ix—O002—Al03—O003112.48 (15)
K001v—O004xi—Si03—O005−4.83 (11)Al00—O002—Al03—O004xi−151.21 (13)
K001iii—O004xi—Si03—O005−123.92 (12)Al00ix—O002—Al03—O004xi−5.70 (17)
K001xii—O004—Al02—K001i119.68 (12)Al00—O002—Al03—O00590.05 (15)
K001vi—O004—Al02—K001i119.68 (12)Al00ix—O002—Al03—O005−124.45 (14)
K001xii—O004—Al02—O001−125.21 (11)Al00—O002—Al03—Al02xi−164.52 (13)
K001—O004—Al02—O001115.11 (8)Al00—O002—Al03—Al02−41.38 (12)
K001vi—O004—Al02—O001−125.21 (11)Al00ix—O002—Al03—Al02104.12 (13)
K001i—O004—Al02—O001115.11 (8)Al00ix—O002—Al03—Al02xi−19.01 (13)
K001—O004—Al02—O003−4.68 (11)O001—Si02—O003—Si0332.22 (9)
K001xii—O004—Al02—O003114.99 (12)O001—Si02—O003—Al0332.22 (9)
K001i—O004—Al02—O003−4.68 (11)O001—Si02—O004—Si03vii18.84 (10)
K001vi—O004—Al02—O003114.99 (12)O001—Si02—O004—Al03vii18.84 (10)
K001i—O004—Al02—O005xii−120.39 (9)O001—Si02—O005xii—Si03xii40.20 (10)
K001—O004—Al02—O005xii−120.39 (9)O001—Si02—O005xii—Al03xii40.20 (10)
K001vi—O004—Al02—O005xii−0.72 (14)O001—Al02—O003—Si0332.22 (9)
K001—O004iv—Al02iv—O005−0.72 (14)O001—Al02—O003—Al0332.22 (9)
K001vi—O004—Al02—Al03130.05 (7)O001—Al02—O004—Si03vii18.84 (10)
K001xii—O004—Al02—Al03130.05 (7)O001—Al02—O004—Al03vii18.84 (10)
K001—O004—Al02—Al0310.37 (10)O001—Al02—O005xii—Si03xii40.20 (10)
K001vi—O004—Al02—Al03vii−144.0 (3)O001—Al02—O005xii—Al03xii40.20 (10)
K001—O004—Al02—Al03vii96.28 (19)O002—Si03—O003—Si02−19.50 (9)
K001i—O004—Al02—Al03vii96.28 (19)O002—Si03—O003—Al02−19.50 (9)
K001i—O004—Al02—Al0310.37 (10)O002—Si03—O004xi—Si02xi−31.56 (10)
K001xii—O004—Al02—Al03vii−144.0 (3)O002—Si03—O004xi—Al02xi−31.56 (10)
K001xiii—O004xi—Al03—O002113.62 (11)O002—Si03—O005—Si02iv−40.33 (10)
K001—O004—Al03vii—O002vii−127.30 (8)O002—Si03—O005—Al02iv−40.33 (10)
K001v—O004xi—Al03—O002−127.30 (8)O002—Al03—O003—Si02−19.50 (9)
K001iii—O004xi—Al03—O002113.62 (11)O002—Al03—O003—Al02−19.50 (9)
K001v—O004xi—Al03—O003112.71 (9)O002—Al03—O004xi—Si02xi−31.56 (10)
K001iii—O004xi—Al03—O003−6.37 (13)O002—Al03—O004xi—Al02xi−31.56 (10)
K001xiii—O004xi—Al03—O003−6.37 (13)O002—Al03—O005—Si02iv−40.33 (10)
K001—O004—Al03vii—O003vii112.71 (9)O002—Al03—O005—Al02iv−40.33 (10)
K001—O004—Al03vii—O005vii−4.83 (11)O003—Si02—O004—Si03vii−100.96 (11)
K001xiii—O004xi—Al03—O005−123.92 (12)O003—Si02—O004—Al03vii−100.96 (11)
K001v—O004xi—Al03—O005−4.83 (11)O003—Si02—O005xii—Si03xii161.10 (11)
K001iii—O004xi—Al03—O005−123.92 (12)O003—Si02—O005xii—Al03xii161.10 (11)
K001vi—O004—Al03vii—Al02145.2 (2)O003—Si03—O004xi—Si02xi−151.54 (11)
K001—O004—Al03vii—Al02vii139.73 (3)O003—Si03—O004xi—Al02xi−151.54 (11)
K001i—O004—Al03vii—Al02−95.74 (19)O003—Si03—O005—Si02iv82.84 (11)
K001v—O004xi—Al03—Al02139.73 (3)O003—Si03—O005—Al02iv82.84 (11)
K001—O004—Al03vii—Al02−95.74 (19)O003—Al02—O004—Si03vii−100.96 (11)
K001xiii—O004xi—Al03—Al0220.64 (11)O003—Al02—O004—Al03vii−100.96 (11)
K001xii—O004—Al03vii—Al02145.2 (2)O003—Al02—O005xii—Si03xii161.10 (11)
K001iii—O004xi—Al03—Al0220.64 (11)O003—Al02—O005xii—Al03xii161.10 (11)
K001—O005vii—Si02ii—K001xiv41.14 (13)O003—Al03—O004xi—Si02xi−151.54 (11)
K001—O005vi—Si02iii—K001xiii41.14 (13)O003—Al03—O004xi—Al02xi−151.54 (11)
K001xiii—O005xii—Si02—O001−127.12 (10)O003—Al03—O005—Si02iv82.84 (11)
K001iii—O005xii—Si02—O001−127.12 (10)O003—Al03—O005—Al02iv82.84 (11)
K001iii—O005xii—Si02—O003−6.22 (14)O004—Si02—O005xii—Si03xii−83.17 (11)
K001xiii—O005xii—Si02—O003−6.22 (14)O004—Si02—O005xii—Al03xii−83.17 (11)
K001xiii—O005xii—Si02—O004109.50 (12)O004xi—Si03—O005—Si02iv−161.48 (11)
K001iii—O005xii—Si02—O004109.50 (12)O004xi—Si03—O005—Al02iv−161.48 (11)
K001xi—O005—Si03—O002127.00 (10)O004—Al02—O005xii—Si03xii−83.17 (11)
K001v—O005—Si03—O002127.00 (10)O004—Al02—O005xii—Al03xii−83.17 (11)
K001xi—O005—Si03—O003−109.83 (11)O004xi—Al03—O005—Si02iv−161.48 (11)
K001v—O005—Si03—O003−109.83 (11)O004xi—Al03—O005—Al02iv−161.48 (11)
Symmetry codes: (i) −x+1, y, −z+1/2; (ii) x+1, y, z; (iii) −x, y, −z+1/2; (iv) x+1/2, y−1/2, z; (v) −x+1/2, y−1/2, −z+1/2; (vi) −x+1/2, y+1/2, −z+1/2; (vii) x+1/2, y+1/2, z; (viii) −x+1/2, −y+3/2, −z+1; (ix) −x, −y+1, −z+1; (x) −x+1, −y+1, −z+1; (xi) x−1/2, y−1/2, z; (xii) x−1/2, y+1/2, z; (xiii) x−1, y, z; (xiv) −x+2, y, −z+1/2; (xv) −x−1/2, y+1/2, −z+1/2; (xvi) x+3/2, y+1/2, z; (xvii) −x+3/2, y+1/2, −z+1/2; (xviii) −x+3/2, y−1/2, −z+1/2.
(TaS2) top
Crystal data top
TaS2Data reduction was performed with a non-centered unit cell, i.e. c = 5.87815 Angstrom. Modulation wave vectors used are q1 = (0.2450, 0.06809, 0.33429) and q2 = (-0.0681, 0.31312, 0.667321) Input files were adapted to the centered setting in which this CIF file is described before structure determination using self-written Python scripts.
Mr = 245.1Dx = 7.096 Mg m−3
Trigonal, X3†Electron radiation, λ = 0.0031 Å
q1 = 0.245300a* + 0.067900b*; q2 = -0.067900a* + 0.313200b*Cell parameters from 24142 reflections
a = 3.3553 (4) Åθ = 0.02–0.2°
c = 17.647 (2) ŵ = 0 mm−1
V = 172.06 (4) Å3T = 293 K
Z = 3Microtome-cut synthetic sample
F(000) = 69.5150.9 × 0.4 × 0.00003 mm
† Symmetry operations: (1) x1, x2, x3, x4, x5; (2) −x2, x1−x2, x3, −x5, x4−x5; (3) −x1+x2, −x1, x3, −x4+x5, −x4; (4) −x1, −x2, −x3, −x4, −x5; (5) x2, −x1+x2, −x3, x5, −x4+x5; (6) x1−x2, x1, −x3, x4−x5, x4; (7) x1, x2, x3+1/3, x4+2/3, x5+1/3; (8) −x2, x1−x2, x3+1/3, −x5+2/3, x4−x5+1/3; (9) −x1+x2, −x1, x3+1/3, −x4+x5+2/3, −x4+1/3; (10) −x1, −x2, −x3+1/3, −x4+2/3, −x5+1/3; (11) x2, −x1+x2, −x3+1/3, x5+2/3, −x4+x5+1/3; (12) x1−x2, x1, −x3+1/3, x4−x5+2/3, x4+1/3; (13) x1, x2, x3+2/3, x4+1/3, x5+2/3; (14) −x2, x1−x2, x3+2/3, −x5+1/3, x4−x5+2/3; (15) −x1+x2, −x1, x3+2/3, −x4+x5+1/3, −x4+2/3; (16) −x1, −x2, −x3+2/3, −x4+1/3, −x5+2/3; (17) x2, −x1+x2, −x3+2/3, x5+1/3, −x4+x5+2/3; (18) x1−x2, x1, −x3+2/3, x4−x5+1/3, x4+2/3.

Data collection top
REGAE
diffractometer		11910 reflections with I > 3σ(I)
Radiation source: RF photocathode (Mo) gun, REGAE, DESY, Hamburg, Germanyθmax = 0.2°, θmin = 0.02°
continuous–rotation 3D electron diffraction scansh = −8→8
112233 measured reflectionsk = −7→8
20621 independent reflectionsl = −31→29
Refinement top
Refinement on F135 parameters
R[F2 > 2σ(F2)] = 0.1000 restraints
wR(F2) = 0.0530 constraints
S = 7.37Weighting scheme based on measured s.u.'s w = 1/σ2(F)
20621 reflections(Δ/σ)max = 0.015
Special details top

Refinement. Calculated intensities based on dynamical theory of electron diffraction. Number of individual data blocks in refinement: 1 Block Thickness Nobs Nall Robs Rall wRall 1 562 (3) 11910 20621 0.1003 0.1518 0.0532 Thickness given in Angstrom. A crystal with a thickness distribution of a lens was used. The refined thickness corresponds to the maximum thickness of the lens. The effective crystal thickness was adapted based on the goniometer angle with a mixing factor of 0.8164.

Refinement statistics relevant for the non-linear least-squares minimisation of wR(all): Number of reflections in refinement (obs/all): 11910 / 20621 Number of reflections present more than once: 1550 Number of reflections unique in point group 1: 19071 Robs: 0.1003 Rall: 0.1518 wRall: 0.0532

Post-refinement analysis of symmetrically-equivalent reflections: Number of unique reflections (obs/all): 3435 / 4951 MRobs: 0.0886 MRall: 0.1237 MwRall: 0.0553

Refinement R factors and merged R factors (MR) for individual reflection groups (m,n):

- Group (0,0) Number of duplicates: 32 All reflections without duplicates: 533 'P1': 565 / 565 observed/all reflections. Merge: 136 / 136 observed/all reflections. MRobs 0.0280 Robs 0.0455 MRall 0.0280 Rall 0.0455 MwRall 0.0417 wRall 0.0388

- Group (1,0) Number of duplicates: 250 All reflections without duplicates: 3084 'P1': 3245 / 3334 observed/all reflections. Merge: 796 / 804 observed/all reflections. MRobs 0.0609 Robs 0.0848 MRall 0.0610 Rall 0.0856 MwRall 0.0532 wRall 0.0803

- Group (1,1) Number of duplicates: 257 All reflections without duplicates: 3102 'P1': 2743 / 3359 observed/all reflections. Merge: 726 / 800 observed/all reflections. MRobs 0.0724 Robs 0.0961 MRall 0.0774 Rall 0.1069 MwRall 0.0587 wRall 0.0878

- Group (2,0) Number of duplicates: 245 All reflections without duplicates: 3069 'P1': 2151 / 3314 observed/all reflections. Merge: 639 / 798 observed/all reflections. MRobs 0.0946 Robs 0.1180 MRall 0.1092 Rall 0.1484 MwRall 0.0847 wRall 0.1192

- Group (1,2) Number of duplicates: 268 All reflections without duplicates: 3105 'P1': 1579 / 3373 observed/all reflections. Merge: 519 / 806 observed/all reflections. MRobs 0.1390 Robs 0.1539 MRall 0.1924 Rall 0.2302 MwRall 0.1276 wRall 0.1673

- Group (2,1) Number of duplicates: 243 All reflections without duplicates: 3025 'P1': 907 / 3268 observed/all reflections. Merge: 349 / 792 observed/all reflections. MRobs 0.3212 Robs 0.3071 MRall 0.3874 Rall 0.4286 MwRall 0.3374 wRall 0.3506

- Group (3,0) Number of duplicates: 255 All reflections without duplicates: 3153 'P1': 720 / 3408 observed/all reflections. Merge: 270 / 815 observed/all reflections. MRobs 0.4692 Robs 0.3653 MRall 0.8177 Rall 0.8146 MwRall 0.3834 wRall 0.3876

Note: _refine_diff_potential_max/_min given in e/Angstrom

Number of refinement parameters: Sacle factors: 63 Thickness-related parameters: 3 Structure parameters: 69 Total: 135

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ta10000.01343 (9)
S10.6666670.3333330.08644 (4)0.01405 (16)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ta10.01065 (6)0.01065 (6)0.0190 (2)0.00532 (3)00
S10.01288 (11)0.01288 (11)0.0164 (4)0.00644 (5)00
Geometric parameters (Å, º) top
AverageMinimumMaximum
Ta1—S12.47 (3)2.32 (3)2.61 (3)
Ta1—Ta1i3.35 (3)3.11 (3)3.86 (3)
S1—Ta1—S1ii94.3 (7)82.2 (7)103.3 (7)
S1—Ta1—S1iii173.2 (7)167.3 (7)180
S1i—Ta1—S185.4 (6)81.7 (6)94.2 (7)
Ta1—S1—Ta1iv85.5 (8)77.4 (7)97.8 (8)
Ta1i—Ta1—Ta1iv120.00 (17)103.13 (16)129.17 (17)
Symmetry codes: (i) x1−1, x2−1, x3, x4, x5; (ii) −x1+1, −x2, −x3, −x4, −x5; (iii) −x1, −x2, −x3, −x4, −x5; (iv) x1+1, x2, x3, x4, x5.
 

Footnotes

‡These authors contributed equally to this work.

Acknowledgements

We thank Wolfgang Brehm and Marina Galchenkova for support with data handling. This research was supported in part through the Maxwell computational resources operated at DESY. We acknowledge Deutsches Elektronen-Synchrotron (DESY; Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III at beamline P11. Author contributions: VH – conceptualization, investigation, resources; MH – conceptualization, investigation; PBK – conceptualization, formal analysis, methodology, writing (original draft), writing (review and editing); PYAR – formal analysis, investigation; TP – resources; JM – resources, software; HDH – investigation, methodology; MB – resources; STV – investigation; PF – resources, software; ACR – investigation, software; AQ – resources; AT – software; OY – software; JW – investigation; FL – writing (review and editing); RS – resources; ID – resources; SH – resources; SG – project administration, writing (original draft) writing (review and editing); SF – project administration, writing (original draft), writing (review and editing); EF – investigation, resources; A. Mozzanica – investigation, resources; LP – formal analysis, writing (review and editing); KR – conceptualization, resources, writing (review and editing); BS – conceptualization, methodology, resources; HNC – funding acquisition, writing (review and editing); WL – funding acquisition, writing (review and editing); KF – conceptualization, methodology, project administration, writing (original draft), writing (review and editing); A. Meents – conceptualization, funding acquisition, methodology, project administration, writing (original draft), writing (review and editing).

Funding information

L. Palatinus acknowledges the Czech Science Foundation for funding (grant 21-05926X). H. N. Chapman acknowledges the German Research Foundation for funding via the Cluster of Excellence `CUI: Advanced Imaging of Matter' (EXC 2056 – project ID 390715994). A. Meents and H. N. Chapman received funds from the German Federal Ministry of Education and Research (project `MHz-SFX', ID 13 K20CHA). A. Meents acknowledges funding by the Helmholtz Association Impulse and Networking funds InternLabs-0011 `HIR3X' and project `FISVIR'.

References

Return to citationBourhis, L. J., Dolomanov, O. V., Gildea, R. J., Howard, J. A. K. & Puschmann, H. (2015). Acta Cryst. A71, 59–75.  Web of Science CrossRef IUCr Journals Google Scholar
 Return to citationBozzola, J. J. (1992). Electron Microscopy: Principles and Techniques for Biologists. Boston: Jones and Bartlett Publishers.  Google Scholar
 Return to citationBrázda, P., Klementová, M., Krysiak, Y. & Palatinus, L. (2022). IUCrJ 9, 735–755.  Web of Science CrossRef PubMed IUCr Journals Google Scholar
 Return to citationBücker, R., Hogan-Lamarre, P., Mehrabi, P., Schulz, E. C., Bultema, L. A., Gevorkov, Y., Brehm, W., Yefanov, O., Oberthür, D., Kassier, G. H. & Dwayne Miller, R. J. (2020). Nat. Commun. 11, 996.  Web of Science PubMed Google Scholar
 Return to citationBurkhardt, A., Pakendorf, T., Reime, B., Meyer, J., Fischer, P., Stübe, N., Panneerselvam, S., Lorbeer, O., Stachnik, K., Warmer, M., Rödig, P., Göries, D. & Meents, A. (2016). Eur. Phys. J. Plus 131, 56.  CrossRef Google Scholar
 Return to citationBurla, M. C., Caliandro, R., Carrozzini, B., Cascarano, G. L., Cuocci, C., Giacovazzo, C., Mallamo, M., Mazzone, A. & Polidori, G. (2015). J. Appl. Cryst. 48, 306–309.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationCatti, M., Ferraris, G., Hull, S. & Pavese, A. (1994). Eur. J. Mineral. 6, 171–178.  CrossRef ICSD CAS Google Scholar
 Return to citationChao, H.-Y., Venkatraman, K., Moniri, S., Jiang, Y., Tang, X., Dai, S., Gao, W., Miao, J. & Chi, M. (2023). Chem. Rev. 123, 8347–8394.  CrossRef CAS PubMed Google Scholar
 Return to citationCosslett, V. E. (1969). Q. Rev. Biophys. 2, 95–133.  CrossRef Google Scholar
 Return to citationde la Flor, G., Orobengoa, D., Tasci, E., Perez-Mato, J. M. & Aroyo, M. I. (2016). J. Appl. Cryst. 49, 653–664.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationDuyvesteyn, H. M. E., Kotecha, A., Ginn, H. M., Hecksel, C. W., Beale, E. V., de Haas, F., Evans, G., Zhang, P., Chiu, W. & Stuart, D. I. (2018). Proc. Natl Acad. Sci. USA 115, 9569–9573.  CrossRef CAS PubMed Google Scholar
 Return to citationFilippetto, D., Musumeci, P., Li, R. K., Siwick, B. J., Otto, M. R., Centurion, M. & Nunes, J. P. F. (2022). Rev. Mod. Phys. 94, 045004.  CrossRef Google Scholar
 Return to citationFröjdh, E., Baruffaldi, F., Bergamaschi, A., Carulla, M., Dinapoli, R., Greiffenberg, D., Heymes, J., Hinger, V., Ischebeck, R., Mathisen, S., McKenzie, J., Mezza, D., Moustakas, K., Mozzanica, A., Schmitt, B. & Zhang, J. (2022). J. Instrum. 17, C12004.  Google Scholar
 Return to citationGatta, G. D., McIntyre, G. J., Sassi, R., Rotiroti, N. & Pavese, A. (2011). Am. Mineral. 96, 34–41.  CrossRef ICSD CAS Google Scholar
 Return to citationGemmi, M., Mugnaioli, E., Gorelik, T. E., Kolb, U., Palatinus, L., Boullay, P., Hovmöller, S. & Abrahams, J. P. (2019). ACS Cent. Sci. 5, 1315–1329.  Web of Science CrossRef CAS PubMed Google Scholar
 Return to citationGruene, T., Holstein, J. J., Clever, G. H. & Keppler, B. (2021). Nat. Rev. Chem. 5, 660–668.  Web of Science CrossRef CAS PubMed Google Scholar
 Return to citationGünther, S., Reinke, P. Y. A., Fernández-García, Y., Lieske, J., Lane, T. J., Ginn, H. M., Koua, F. H. M., Ehrt, C., Ewert, W., Oberthuer, D., Yefanov, O., Meier, S., Lorenzen, K., Krichel, B., Kopicki, J.-D., Gelisio, L., Brehm, W., Dunkel, I., Seychell, B., Gieseler, H., Norton-Baker, B., Escudero-Pérez, B., Domaracky, M., Saouane, S., Tolstikova, A., White, T. A., Hänle, A., Groessler, M., Fleckenstein, H., Trost, F., Galchenkova, M., Gevorkov, Y., Li, C., Awel, S., Peck, A., Barthelmess, M., Schlünzen, F., Lourdu Xavier, P., Werner, N., Andaleeb, H., Ullah, N., Falke, S., Srinivasan, V., França, B. A., Schwinzer, M., Brognaro, H., Rogers, C., Melo, D., Zaitseva-Kinneberg, J. I., Knoska, J., Peña-Murillo, G. E., Mashhour, A. R., Hennicke, V., Fischer, P., Hakanpää, J., Meyer, J., Gribbon, P., Ellinger, B., Kuzikov, M., Wolf, M., Beccari, A. R., Bourenkov, G., von Stetten, D., Pompidor, G., Bento, I., Panneerselvam, S., Karpics, I., Schneider, T. R., Garcia-Alai, M. M., Niebling, S., Günther, C., Schmidt, C., Schubert, R., Han, H., Boger, J., Monteiro, D. C. F., Zhang, L., Sun, X., Pletzer-Zelgert, J., Wollenhaupt, J., Feiler, C. G., Weiss, M. S., Schulz, E.-C., Mehrabi, P., Karničar, K., Usenik, A., Loboda, J., Tidow, H., Chari, A., Hilgenfeld, R., Uetrecht, C., Cox, R., Zaliani, A., Beck, T., Rarey, M., Günther, S., Turk, D., Hinrichs, W., Chapman, H. N., Pearson, A. R., Betzel, C. & Meents, A. (2021). Science 372, 642–646.  PubMed Google Scholar
 Return to citationHachmann, M. & Flöttmann, K. (2016). Nucl. Instrum. Methods Phys. Res. A 829, 318–320.  CrossRef CAS Google Scholar
 Return to citationHaupt, K., Eichberger, M., Erasmus, N., Rohwer, A., Demsar, J., Rossnagel, K. & Schwoerer, H. (2016). Phys. Rev. Lett. 116, 016402.  CrossRef PubMed Google Scholar
 Return to citationHenderson, R. (1995). Q. Rev. Biophys. 28, 171–193.  CrossRef CAS PubMed Web of Science Google Scholar
 Return to citationHerschlag, D. & Pinney, M. M. (2018). Biochemistry 57, 3338–3352.  CrossRef CAS PubMed Google Scholar
 Return to citationHolton, J. M. (2009). J. Synchrotron Rad. 16, 133–142.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationIshikawa, T., Hayes, S. A., Keskin, S., Corthey, G., Hada, M., Pichugin, K., Marx, A., Hirscht, J., Shionuma, K., Onda, K., Okimoto, Y., Koshihara, S., Yamamoto, T., Cui, H., Nomura, M., Oshima, Y., Abdel-Jawad, M., Kato, R. & Miller, R. J. D. (2015). Science 350, 1501–1505.  CrossRef CAS PubMed Google Scholar
 Return to citationIto, S., White, F. J., Okunishi, E., Aoyama, Y., Yamano, A., Sato, H., Ferrara, J. D., Jasnowski, M. & Meyer, M. (2021). CrystEngComm 23, 8622–8630.  Web of Science CSD CrossRef CAS Google Scholar
 Return to citationKabsch, W. (2010). Acta Cryst. D66, 125–132.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationKawasaki, T., Matsui, I., Yoshida, T., Katsuta, T., Hayashi, S., Onai, T., Furutsu, T., Myochin, K., Numata, M., Mogaki, H., Gorai, M., Akashi, T., Kamimura, O., Matsuda, T., Osakabe, N., Tonomura, A. & Kitazawa, K. (2000). J. Electron Microsc. 49, 711–718.   CrossRef CAS Google Scholar
 Return to citationKhouchen, M., Klar, P. B., Chintakindi, H., Suresh, A. & Palatinus, L. (2023). Acta Cryst. A79, 427–439.  Web of Science CSD CrossRef ICSD IUCr Journals Google Scholar
 Return to citationKlar, P. B., Krysiak, Y., Xu, H., Steciuk, G., Cho, J., Zou, X. & Palatinus, L. (2023). Nat. Chem. 15, 848–855.  Web of Science CSD CrossRef CAS PubMed Google Scholar
 Return to citationKogar, A., Zong, A., Dolgirev, P. E., Shen, X., Straquadine, J., Bie, Y.-Q., Wang, X., Rohwer, T., Tung, I.-C., Yang, Y., Li, R., Yang, J., Weathersby, S., Park, S., Kozina, M. E., Sie, E. J., Wen, H., Jarillo-Herrero, P., Fisher, I. R., Wang, X. & Gedik, N. (2020). Nat. Phys. 16, 159–163.  CrossRef CAS Google Scholar
 Return to citationLeonarski, F., Redford, S., Mozzanica, A., Lopez-Cuenca, C., Panepucci, E., Nass, K., Ozerov, D., Vera, L., Olieric, V., Buntschu, D., Schneider, R., Tinti, G., Froejdh, E., Diederichs, K., Bunk, O., Schmitt, B. & Wang, M. (2018). Nat. Methods 15, 799–804.  Web of Science CrossRef CAS PubMed Google Scholar
 Return to citationLiang, J.-I., Hawthorne, F. & Swainson, I. (1998). Can. Mineral. 36, 1017–1027.  CAS Google Scholar
 Return to citationLin, M.-F., Singh, N., Liang, S., Mo, M., Nunes, J. P. F., Ledbetter, K., Yang, J., Kozina, M., Weathersby, S., Shen, X., Cordones, A. A., Wolf, T. J. A., Pemmaraju, C. D., Ihme, M. & Wang, X. J. (2021). Science 374, 92–95.  CrossRef CAS PubMed Google Scholar
 Return to citationMahnke, C., Grosse-Wortmann, U., Hachmann, M., Hennicke, V., Li, C., Meyer, J., Pakendorf, T., Flöttmann, K., Meents, A. & Hartl, I. (2024). EPJ Web Conf. 307, 02030.  Google Scholar
 Return to citationManz, S., Casandruc, A., Zhang, D., Zhong, Y., Loch, R. A., Marx, A., Hasegawa, T., Liu, L. C., Bayesteh, S., Delsim-Hashemi, H., Hoffmann, M., Felber, M., Hachmann, M., Mayet, F., Hirscht, J., Keskin, S., Hada, M., Epp, S. W., Flöttmann, K. & Miller, R. J. D. (2015). Faraday Discuss. 177, 467–491.  Web of Science CrossRef CAS PubMed Google Scholar
 Return to citationManzeli, S., Ovchinnikov, D., Pasquier, D., Yazyev, O. V. & Kis, A. (2017). Nat. Rev. Mater. 2, 17033.  Web of Science CrossRef Google Scholar
 Return to citationMozzanica, A., Andrä, M., Barten, R., Bergamaschi, A., Chiriotti, S., Brückner, M., Dinapoli, R., Fröjdh, E., Greiffenberg, D., Leonarski, F., Lopez-Cuenca, C., Mezza, D., Redford, S., Ruder, C., Schmitt, B., Shi, X., Thattil, D., Tinti, G., Vetter, S. & Zhang, J. (2018). Synchrotron Radiat. News 31, 16–20.  CrossRef Google Scholar
 Return to citationNannenga, B. L., Shi, D., Leslie, A. G. W. & Gonen, T. (2014). Nat. Methods 11, 927–930.  Web of Science CrossRef CAS PubMed Google Scholar
 Return to citationNovoselov, K. S. & Castro Neto, A. H. (2012). Phys. Scr. T146, 014006.  CrossRef Google Scholar
 Return to citationNunes, J. P. F., Ledbetter, K., Lin, M., Kozina, M., DePonte, D. P., Biasin, E., Centurion, M., Crissman, C. J., Dunning, M., Guillet, S., Jobe, K., Liu, Y., Mo, M., Shen, X., Sublett, R., Weathersby, S., Yoneda, C., Wolf, T. J. A., Yang, J., Cordones, A. A. & Wang, X. J. (2020). Struct. Dyn. 7, 024301.  Web of Science CrossRef PubMed Google Scholar
 Return to citationPalatinus, L., Brázda, P., Boullay, P., Perez, O., Klementová, M., Petit, S., Eigner, V., Zaarour, M. & Mintova, S. (2017). Science 355, 166–169.  Web of Science CSD CrossRef ICSD CAS PubMed Google Scholar
 Return to citationPalatinus, L., Brázda, P., Jelínek, M., Hrdá, J., Steciuk, G. & Klementová, M. (2019). Acta Cryst. B75, 512–522.  Web of Science CrossRef IUCr Journals Google Scholar
 Return to citationPalatinus, L. & Chapuis, G. (2007). J. Appl. Cryst. 40, 786–790.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationPalatinus, L., Corrêa, C. A., Steciuk, G., Jacob, D., Roussel, P., Boullay, P., Klementová, M., Gemmi, M., Kopeček, J., Domeneghetti, M. C., Cámara, F. & Petříček, V. (2015). Acta Cryst. B71, 740–751.  Web of Science CrossRef IUCr Journals Google Scholar
 Return to citationPalatinus, L., Petříček, V. & Corrêa, C. A. (2015). Acta Cryst. A71, 235–244.  Web of Science CrossRef IUCr Journals Google Scholar
 Return to citationPetříček, V., Palatinus, L., Plášil, J. & Dušek, M. (2023). Z. Kristallogr. Cryst. Mater. 238, 271–282.  Google Scholar
 Return to citationRedford, S., Andrä, M., Barten, R., Bergamaschi, A., Brückner, M., Dinapoli, R., Fröjdh, E., Greiffenberg, D., Lopez-Cuenca, C., Mezza, D., Mozzanica, A., Ramilli, M., Ruat, M., Ruder, C., Schmitt, B., Shi, X., Thattil, D., Tinti, G., Vetter, S. & Zhang, J. (2018). J. Instrum. 13, C01027.  Web of Science CrossRef Google Scholar
 Return to citationSheldrick, G. M. (2008). Acta Cryst. A64, 112–122.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationSheldrick, G. M. (2015). Acta Cryst. C71, 3–8.  Web of Science CrossRef IUCr Journals Google Scholar
 Return to citationSimoncic, P., Romeijn, E., Hovestreydt, E., Steinfeld, G., Santiso-Quiñones, G. & Merkelbach, J. (2023). Acta Cryst. E79, 410–422.  Web of Science CrossRef IUCr Journals Google Scholar
 Return to citationSpijkerman, A., de Boer, J. L., Meetsma, A., Wiegers, G. A. & van Smaalen, S. (1997). Phys. Rev. B 56, 13757–13767.  CrossRef ICSD CAS Google Scholar
 Return to citationStokes, H. T., Campbell, B. J. & van Smaalen, S. (2011). Acta Cryst. A67, 45–55.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationvan Smaalen, S., Campbell, B. J. & Stokes, H. T. (2013). Acta Cryst. A69, 75–90.  Web of Science CrossRef CAS IUCr Journals Google Scholar
 Return to citationWeathersby, S. P., Brown, G., Centurion, M., Chase, T. F., Coffee, R., Corbett, J., Eichner, J. P., Frisch, J. C., Fry, A. R., Gühr, M., Hartmann, N., Hast, C., Hettel, R., Jobe, R. K., Jongewaard, E. N., Lewandowski, J. R., Li, R. K., Lindenberg, A. M., Makasyuk, I., May, J. E., McCormick, D., Nguyen, M. N., Reid, A. H., Shen, X., Sokolowski-Tinten, K., Vecchione, T., Vetter, S. L., Wu, J., Yang, J., Dürr, H. A. & Wang, X. J. (2015). Rev. Sci. Instrum. 86, 073702.  Web of Science CrossRef PubMed Google Scholar
 Return to citationZeitler, B., Floettmann, K. & Grüner, F. (2015). Phys. Rev. ST Accel. Beams 18, 120102.   Google Scholar

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IUCrJ
Volume 13| Part 3| May 2026| Pages 282-290
ISSN: 2052-2525
https://doi.org/10.1107/S2052252526002782