# The lattice contraction of UO2 from Cr doping as determined via high resolution synchrotron X-ray powder diffraction

Gabriel L. Murphy, Volodymyr Svitlyk, Maximilian Henkes, Daniil Shirokiy, Christoph Hennig, Philip Kegler, Dirk Bosbach, Andrey Bukaemskiy

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## To cite this version:

Gabriel L. Murphy, Volodymyr Svitlyk, Maximilian Henkes, Daniil Shirokiy, Christoph Hennig, et al.. The lattice contraction of UO2 from Cr doping as determined via high resolution synchrotron X-ray powder diffraction. Journal of Nuclear Materials, 2024, 595, pp.155046. 10.1016/j.jnucmat.2024.155046. hal-05099507

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Submitted on 5 Jun 2025

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Short communication

# The lattice contraction of UO₂ from Cr doping as determined via high resolution synchrotron X-ray powder diffraction

Gabriel L. Murphy<sup>a, *</sup>, Volodymyr Svitlyk<sup>b, c</sup>, Maximilian Henkes<sup>a</sup>, Daniil Shirokiy<sup>a</sup>, Christoph Hennig<sup>b, c</sup>, Philip Kegler<sup>a</sup>, Dirk Bosbach<sup>a</sup>, Andrey Bukaemskiy<sup>a</sup>

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## ARTICLE INFO

Keywords:

Diffraction

Rietveld

Synchrotron

Cr-doped UO₂

X-ray

Nuclear fuel

## ABSTRACT

High resolution synchrotron powder X-ray diffraction analysis of Cr-doped UO₂ samples with additions of Cr₂O₃ as 0, 500, 1000, 1500, 2500 to 3500 ppm prepared under sintering conditions of -420 kJ/mol and 1700 °C is reported. The lattice dependence from Cr doping is established through the Rietveld refinement method where the rate of linear lattice parameter contraction from Cr doping, Δa<sub>cr</sub>, was found to be considerably smaller and more subtle than previously described. This investigation highlights the need for high resolution and precise specimen preparation when measuring and interpreting subtle changes to nuclear material crystal structures due to trace doping.

## 1. Introduction

Cr-doped UO₂ is used commonly as a part of modern nuclear fuel blends due its ameliorated properties over classical non-doped UO₂, where it has been deployed in both North American and European power reactor units [1]. The addition of chromia (Cr₂O₃) during fuel fabrication results in enhanced grain growth that enables improved fission gas retention and fuel density leading to improved thermal conductivity allowing the fuel to be used at higher burn ups [2]. Chemically, the addition of Cr into UO₂ is a complex process where the combination of the small size Cr⁺³ cation compared to U⁺⁴ coupled with the variable behaviour at sintering temperatures results in only ppm level solubility of Cr in the UO₂ matrix. This is further exacerbated by the formation of a variety of secondary phases [3–7], including eutectic compositions, whilst precise Cr addition control often suffers from volatilisation effects during sintering [8]. The formation of eutectic compositions in addition to the lattice matrix incorporation of Cr is understood to be the leading cause of improved grain growth in the material [6,9]. The solubility of Cr in UO₂ is further highly dependent on the specific conditions used during sintering, specifically the oxygen partial pressure (µO₂) and temperature applied. Under an µO₂ and temperature of -420 kJ/mol and 1700 °C respectively the solubility of Cr in

UO₂ is understood to be 750 ppm as Cr [3,6]. Higher solubilities can be obtained towards 1000 ppm Cr via higher temperatures and increased µO₂ [10]. Consequently, this results in only a subtle contraction of the UO₂ fluorite structure as Cr is incorporated into it progressively [10,11]. The incorporation of Cr into UO₂ was recently determined via high resolution spectroscopic methods of single crystal grains and bulk material to follow the mechanism (Crₓ⁺³U₁⁻⁴)O₂·0.5x that had been subject to strong debate prior, with the additional formation of oxide and metallic phases including Cr⁰, Cr⁺² and Cr₂⁻³O₃ [3]. The relevant abundance and distribution of these phases was found to be consistent and corroborate previous thermodynamic estimates of Cr-doped UO₂ [6].

Although good progress has been made in the determination of the Cr-doped UO₂ redox chemistry, disagreement remains regarding the lattice parameter as Cr is progressively incorporated into the UO₂ fluorite structure and the associated rate of contraction. The contraction has been frequently used to indirectly monitor the content of Cr in UO₂ in addition to inferring chemistry of Cr in UO₂ [11,12]. However, when literature values are considered, a wide variation of lattice parameters are reported [10,11,13], which appears to have contributed to disagreement over redox determination of Cr in the UO₂ lattice [6,11, 12]. Critically, inspection of these values shows that these previous studies have all been conducted using standard laboratory X-ray powder

<footnote><sup>a</sup> Institute of Energy and Climate Research (IEK-6), Forschungszentrum Jülich GmbH, Jülich 52428, Germany</footnote>

<footnote><sup>b</sup> Institute of Resource Ecology, Helmholtz Zentrum Dresden-Rossendorf, Dresden 01328, Germany</footnote>

<footnote><sup>c</sup> The Rossendorf Beamline at ESRF, The European Synchrotron, CS40220, Grenoble CEDEX 9 38043, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: g.murphy@fz-juelich.de (G.L. Murphy).</footnote>
diffraction often on pellet samples rather than fine powders. Although such devices provide well for rudimentary sample characterisation, the described subtle shift in lattice parameter from Cr incorporation into $UO_2$ can be difficult to precisely track due effects arising from instrument related peak width broadening, asymmetry and $K\alpha_2$ components (when a Cu X-ray source is used) in addition to sample related effects such as displacement, transparency or surface roughness in the case of pellets. These effects complicate accurate determination of Bragg positions and require careful corrections to ensure accurate and precise measurement, particularly on pellet samples [14,15], in order to ascertain correct and meaningful chemical and structural interpretations.

To precisely resolve accurate and precise changes to lattice parameters, high resolution methods are necessary in which synchrotron X-ray powder diffraction is often considered the gold standard owing to superior brilliance of the beam source often combined with state-of-the-art detection equipment, which often exceeds that of standard laboratory X-ray tube-based methods. Interestingly, there does not appear to be any reported studies on Cr-doped $UO_2$ utilising high resolution diffraction, despite many successful applications of it to many other actinide oxides [16–19]. Accordingly, in order to precisely determine the lattice contraction of $UO_2$ as Cr is incorporated progressively into it, the present investigation has used high resolution synchrotron X-ray diffraction measurements to examine fine powders of Cr-doped $UO_2$ samples with additions of Cr at 0, 500, 1000, 1500, 2500 to 3500 ppm additions of Cr (as $Cr_2O_3$) where each sample was prepared using consistent sintering conditions of -420 kJ/mol and 1700 °C. Collected diffractograms were analyzed using the Rietveld refinement method where the precise structural dependence of the $UO_2$ contraction from Cr doping was established. These results are discussed in detail together with other related investigations of the lattice parameter contraction Cr doping in $UO_2$, with particular regard to type of measurement performed and resolution.

Cr-doped $UO_2$ ceramics with 0, 500, 1000, 1500, 2500 and 3500 ppm additions of Cr (as $Cr_2O_3$) were generated using a co-precipitation method beginning with doped ammonium diuranate (ADU) based on a previously established method [7]. The doped ADU was prepared using stoichiometrically controlled amounts of uranyl nitrate ($UO_2(NO_3)_2$) and chromium nitrate ($Cr(NO_3)_3$) that were mixed in solution, followed by precipitation using ammonia ($NH_3$) involving a 300 % excess. Samples with targeted 0, 500, 1000, 1500, 2500 and 3500 ppm additions of Cr (as $Cr_2O_3$) (0, 342, 684, 1026, 1711 and 2395 ppm respectively as Cr elemental) were generated via this method. The ADU mixtures were firstly calcined under air to oxide form using a box furnace at 800 °C for 5 h prior to reduction to $UO_2$ at 600 °C under 4 % $H_2$–96 % Ar atmosphere for additional 5 h. In both steps the samples were in powder form. Finally, the pre-treated powders were compacted into pellets and heated to 1700 °C using a tube furnace for 10 h with a $\mu_{O_2}$ of -420 kJ/mol that was monitored and produced via a 4 % $H_2$–96 % Ar and 1 % $O_2$–99 % Ar gas mixture. The furnace was cooled to room temperature using a ramp rate of 6 °C/min whilst the gas mixture was maintained.

Ambient temperature synchrotron X-ray powder diffraction (S-XRD) experiments were performed at the BM20 Rossendorf beamline [20] (ROBL) at the European Synchrotron Radiation Facility (ESRF), Grenoble, France. Diffraction data were collected on high-resolution XRD1 machine equipped with a Dectris Eiger CdTe 500k photon counting detector at 23 °C. Synthesised samples were finely ground and packed in glass capillaries of 0.3 mm diameter enclosed in 1 mm Kapton tubes that serve as confinement barriers. The monochromator energy was calibrated against the K-edge X-ray absorption spectrum of a yttrium metal foil using the first inflection point at 17 038 eV which provides an uncertainty of ± 0.3 eV (± 0.000013 Å). The energy was then shifted and set to 16 000 eV and detector geometry of the experimental setup was calibrated using silver behenate and a LaB₆ NIST standard reference. The wavelength was subsequently determined to be 0.7749 Å. Experiments were performed in transmission mode at 23 °C and corresponding 2D

data were reduced using the PyFAI library adapted for diffractometers mounted on a goniometer arm [21]. Structural analysis was performed using the Rietveld method as implemented in the program GSAS-II [22]. The peak shapes were modelled using a pseudo-Voigt function and the background was estimated using a 6–12 term shifted Chebyshev function. The scale factor, absorption detector zero-point and lattice parameters were refined together with the peak profile parameters.

## 2. Results

Precise determination of the lattice parameters for studied compositions was made using the Rietveld refinement method in which fluorite structures in space group *Fm$\bar{3}$m* were refined against each of collected S-XRD data sets. Inspection of the diffraction patterns indicated contraction of the fluorite structure as evident by shifting of Bragg reflections to higher 2θ but only subtly. The Rietveld profiles for each collected sample are provided in Fig. 1 and determined lattice parameters are given in Table 1. The lattice parameter for the as measured $UO_2$ sample was determined to be 5.46894(2) Å which is slightly smaller than that reported by Leinders et al. [23] at 5.47127(8) Å, nevertheless, the value is considered acceptable and consistent with other previous studies. Attempts were made to perform the Rietveld refinements with Cr in the structural model corresponding to the expected amount in the lattice based on the amount of Cr addition and considering the Cr phase distribution given by recent spectroscopic phase analysis [24] thermodynamic modelling [6] and volatility studies of Cr-doped $UO_2$ [8]. From this, the maximum occupancy of Cr on the U position is 0.01. However it was found that no significantly meaningful improvement of the refinement could be obtained.

The determined lattice parameters from S-XRD measurements provided in Table 1 are plotted as a function of Cr content in Fig. 2a with previous literature values from Leenaers et al. [10], Kegler et al. [7], Cardinaels et al. [11] and Milena-Pérez et al. [13] who all studied Cr-doped $UO_2$ but used laboratory XRD methods all using pellet measurements [7,10,11,13]. The normalized lattice parameter ($a/a_0$) is additionally plotted in Fig. 2b with described reference values.

Apparent from Fig. 2a is the relatively large spread of lattice parameter values reported from different studies for Cr-doped $UO_2$ as a function of Cr doping. Notably all other investigations used laboratory XRD and particularly measured pellet samples rather than fine powders. Specific conditions used during synthesis would affect uptake of Cr into the $UO_2$ lattice matrix, which in turn affect the amount of lattice contraction, in addition to the amount and distribution of Cr secondary states in the bulk including $Cr_2O_3$ or metallic Cr [3,6]. Pertinent to the investigation, when the rate of lattice parameter contraction ($\Delta a_{cr}$) is considered, the present study provides the smallest values with $-1.845 \times 10^{-7}$ and $-0.390 \times 10^{-7}$ for absolute and normalised data respectively determined from line-of-best-fit fitting. The calculated $\Delta a_{cr}$ for the present and described studies can be found in Table 2, which provides the line of best fit, $a = (\Delta a_{cr})x + a_0$, for the absolute and normalized data in this study and references. This stark difference in contraction can be readily observed in Fig. 2b with the shallowest line of best fit for the present investigation for both absolute and normalized lattice parameter data. The normalised $\Delta a_{cr}$ for the present investigation is over 2-fold smaller than that of the nearest study of Leenaers et al. [10], who used conditions that only slightly better favour structure incorporation and enhanced lattice parameter contraction, a two-fold difference would not account for this [6]. It is previously understood that measurement of pellet samples can carry significant error and drift in acquired data [14], particularly if the heights of the samples are not properly calibrated relative to the source X-ray beam [15]. Further error is then found due common roughness of ceramic materials compared to thin-films or metallic samples [25]. Such effects may not significantly impact rudimentary sample measurement and data analysis, for example classical solid solutions, but when changes to the lattice parameter are
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Rietveld profiles made against S-XRD data collected on Cr-doped UO₂ powder samples with 0, 500, 1000, 1500, 2500 and 3500 ppm additions as Cr₂O₃ all recorded at 23 °C for λ = 0.7749 Å. All structures were refined using a fluorite model in space group *Fm*3m. Aberrations in the background are due to merging of the datasets during image processing whereas differences in intensities are a result of different packing densities of capillaries.</figcaption></figure>

<caption>**Table 1**</caption>

Refined structural parameters for Cr-doped UO₂ with 0, 500, 1000, 1500, 2500 and 3500 ppm as Cr₂O₃ addition from S-XRD data recorded at 23 °C with λ = 0.7749 Å. The structures were refined in cubic fluorite structures with space group *Fm*3m.

<table><thead><tr><td>Cr addition ppm (Cr<sub>2</sub>O<sub>3</sub>/Cr)</td><td>Lattice parameter (Å)</td></tr></thead><tbody><tr><td>0/0</td><td>5.46894(2)</td></tr><tr><td>500/342</td><td>5.46872(2)</td></tr><tr><td>1000/684</td><td>5.46868(3)</td></tr><tr><td>1500/1026</td><td>5.46856(3)</td></tr><tr><td>2500/1711</td><td>5.46842(4)</td></tr><tr><td>3500/2395</td><td>5.46824(4)</td></tr></tbody></table>

on the order 0.1-0.01 % in the case of trace Cr doping in UO₂ they do become significant. A solution to the roughness issue can be achieved using a finely polished surface, however it is known that the polishing of ceramic surfaces may introduce material strain that can impact acquired data [26]. The use of a finely ground powder sample mounted in a capillary assists in negating these described challenges of pellet measurement, dramatically increasing measurement quality, and importantly, reliability. Notwithstanding, some errors can be encountered from capillaries relating to packing density which affects acquired diffraction intensity in addition to the use of fine powders which can be susceptible to enhanced oxidation, depending on the atmosphere used during preparation.

It is important to highlight that although conditions were used in the present investigation that should result in a maximum solubility of 750 ppm Cr [6], lattice parameter contraction is observed above this value in
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** (a) Absolute lattice parameter of Cr-doped UO₂ as a function of Cr doping (as Cr₂O₃ addition during synthesis) and (b) Normalized lattice parameter (a/a₀) for values determined from the present investigation via S-XRD measurements using fine powders and reference values from Leenaers et al. [10], Kegler et al. [7], Cardinaels et al. [11] and Milena-Pérez et al. [13]. The linear line-of-best-fits, *a* = (Δ*a*<sub>cr</sub>)*x* + *a*₀, are provided, where *x* is the amount of Cr added as Cr₂O₃, Δ*a*<sub>cr</sub> is the rate of contraction, *a*₀ is the initial lattice parameter and *a* is the determined lattice parameter. Determined values for the linear line-of-best-fit are provided in Table 2.</figcaption></figure>

terms of amount of Cr added in synthesis. This is due to the distribution
of Cr among the Cr bearing phases in bulk UO₂ including matrix
incorporated (Crₓ³⁺U₁⁻ₓ)O₂₀.₅x, and secondary metallic and oxide phases
that occur across grain boundaries and as precipitates [3,4,6,27].
Additionally, the synthesis is consistently susceptible to volatilisation of
Cr [8], further affecting the amount of actual Cr that enters the UO₂
lattice matrix. We previously showed [3] using high energy resolution
fluorescence detection X-ray absorption near edge spectroscopy
(HERFD-XANES) and quantifying using iterative transformation factor
analysis (ITFA) for Cr-doped UO₂ with 3500 ppm addition Cr as Cr₂O₃
(2395 ppm as Cr) the Cr redox states in the bulk material can be
accounted for as 65 % Cr⁺³, 26 % Cr⁺², and 9 % Cr metallic. In which
chemically these are attributed to lattice matrix (Crₓ³⁺U₁⁻ₓ)O₂₀.₅x (44

‰), precipitate Cr<sub>x</sub><sup>+3</sup>O<sub>3</sub> (21 ‰), grain boundary/sub-stoichiometric chromia Cr<sup>+2</sup>, and metallic Cr<sup>0</sup>. This phase assemblage distribution was found to match the thermodynamic model described for Cr-doped UO<sub>2</sub> by Riglet-Martial et al. [6]. When accounting for the volatility of Cr which reaches approximately 30 % [8], this results in 1677 ppm Cr (as Cr) to be distributed among these phases. Noting the solubility limit of Cr under synthesis conditions used, this results in a distribution of approximately 750 ppm for (Cr<sub>x</sub><sup>+3</sup>U<sub>1-x</sub><sup>+4</sup>)O<sub>2-0.5x</sub>, 340 ppm for Cr<sub>2</sub><sup>+3</sup>O<sub>3</sub>, 436 ppm for Cr<sup>+2</sup> and 151 ppm for metallic Cr<sup>0</sup>. If we then consider lower addition of Cr, for instance 2500 ppm Cr<sub>2</sub>O<sub>3</sub> (1711 ppm as Cr), after 30 % volatilization this results in 1198 ppm of Cr (as Cr) for distribution among the phases. The thermodynamic model for consistent conditions implies a similar distribution of Cr phases resulting in 535 ppm Cr for (Cr<sub>x</sub><sup>+3</sup>U<sub>1-x</sub><sup>+4</sup>)O<sub>2-0.5x</sub>, 243 ppm Cr for Cr<sub>2</sub><sup>+3</sup>O<sub>3</sub>, 311 ppm for Cr<sup>+2</sup> and 107 ppm for metallic Cr<sup>0</sup>, hence the lattice structure is undersaturated with Cr and is less contracted relative to the sample prepared at 3500 ppm addition as Cr<sub>2</sub>O<sub>3</sub>. This described analysis pertinently carries errors particularly from the ITFA analysis with a known 5 % [28], but nevertheless guides the distribution of states and allows understanding of continual linear contraction of the UO<sub>2</sub> lattice at what could be considered high doping amounts of Cr. Accordingly, it is pertinent to highlight in this study and others that the addition of Cr does not correspond to the amount of Cr that enters the UO<sub>2</sub> lattice matrix and affects the lattice parameter, but depends on the conditions used during synthesis and associated distribution of Cr states [6]. Notably, direct determination of the Cr content in the UO<sub>2</sub> lattice matrix can be achieved using electron microprobe analysis (EPMA). However, EPMA has not been commonly used in Cr-doped UO<sub>2</sub> investigations in part due to its impressive cost of acquisition. Nevertheless, as shown in the present investigation and others, diffraction is a relatively inexpensive means of tracking the incorporation of Cr into UO<sub>2</sub>.

The use of a synchrotron X-ray source for precise lattice determina-
tion is a pertinent component of this investigation. Synchrotron sources
provide far superior measurement resolution which subsequently results
in more precise and accurate structural data, in this instance the lattice
parameter of UO₂ as Cr is incorporated into it. Consequently, we argue
that the results of this investigation provide the highest precision and
best describe the structural dependence of Cr incorporation into UO₂.
Pertinently, we emphasis caution in the interpretation of data acquired
from measurements intended for more rudimentary analysis, particu-
larly on non-ideally prepared sample states. This is not to say such re-
sults are invalid, as they can readily guide and assist in the fabrication of
Cr-doped UO₂ fuel bodies for material property research and applica-
tion. However, in interpreting subtle atomic effects such as the degree to
which the fluorite structure contracts based on the specific redox states
that occur due to trace dopants, caution and insurance is needed via high
resolution measurement and careful specimen preparation.

The lattice dependence of the UO₂ fluorite structure as a function of
Cr doping with 0, 500, 1000, 1500, 2500 and 3500 ppm addition as
Cr₂O₃ when prepared under conditions of 1700 °C and -420 kJ/mol has
been established via Rietveld refinements against high resolution syn-
chrotron X-ray powder diffraction data. The results obtained, which
appear to be the first using a high-resolution X-ray measurement, indi-
cate that the lattice parameter contraction is considerably lessened and
much more subtle than previous investigations have shown. The
enhanced lattice parameter values obtained in this investigation
compared to previous are attributed to the accuracy and resolution of
synchrotron measurements performed on fine powders mounted in
capillaries compared to standard laboratory X-ray measurements often
performed on pellets which can carry significantly higher uncertainty
and potential error from incorrect preparation. Methods are available to
correct against specific errors arising from certain sample types, how-
ever, care and consideration is required to ensure correct mitigation
particularly when considering the desired property of a material to be
measured and determined. Moreover, the investigation has provided
critical guidance to previous varying descriptions of the Cr-doped UO₂
<caption>**Table 2**</caption>

Linear equations for line-of-best-fit for UO₂ fluorite lattice as a function of Cr₂O₃ addition, a = (Δa<sub>cr</sub>)x + a<sub>o</sub> for absolute and normalized lattice parameter data where x is the amount of Cr added as Cr₂O₃, Δa<sub>cr</sub> is the rate of contraction, a<sub>o</sub> is the initial lattice parameter and a the determined lattice parameter. Δa<sub>cr</sub> is bolded for clarity.

<table><thead><tr><th>Study and measurement type</th><th>Absolute linear line-of-best-fit</th><th>R<sup>2</sup></th><th>Normalised line-of-best-fit</th><th>R<sup>2</sup></th><th>Conditions (T/ µO<sub>2</sub>)</th></tr></thead><tbody><tr><td>Present Investigation<br>S-XRD | Powder</td><td>a = (-1.845×10<sup>-7</sup>)x + 5.4689</td><td>0.967</td><td>a = (-0.390×10<sup>-7</sup>)x + 1</td><td>0.928</td><td>1700 °C/-420 kJ/mol</td></tr><tr><td>Leenaers et al. [10].<br>XRD | Polished Pellet</td><td>a = (-4.547×10<sup>-7</sup>)x + 5.4707</td><td>0.989</td><td>a = (-0.824×10<sup>-7</sup>)x + 1</td><td>0.989</td><td>1760 °C/-390 kJ/mol</td></tr><tr><td>Kegler et al. [7].<br>XRD | Pellet</td><td>a = (-41.055×10<sup>-7</sup>)x + 5.4686</td><td>0.956</td><td>a = (-7.732×10<sup>-7</sup>)x + 1</td><td>0.955</td><td>1700 °C/-420 kJ/mol</td></tr><tr><td>Kegler et al. [7].<br>XRD | Pellet</td><td>a = (-14.106×10<sup>-7</sup>)x + 5.4692</td><td>0.983</td><td>a = (-2.425×10<sup>-7</sup>)x + 1</td><td>0.977</td><td>1700 °C/-520 kJ/mol</td></tr><tr><td>Cardinaels et al. [11].<br>XRD | Polished Pellet</td><td>a = (-8.014×10<sup>-7</sup>)x + 5.4711</td><td>0.998</td><td>a = (-1.511×10<sup>-7</sup>)x + 1</td><td>0.977</td><td>1760 °C/-390 kJ/mol</td></tr><tr><td>Milena-Pérez et al. [13].<br>XRD | Polished Pellet</td><td>a = (-19.237×10<sup>-7</sup>)x + 5.4724</td><td>0.972</td><td>a = (-3.890×10<sup>-7</sup>)x + 1</td><td>0.952</td><td>1675 °C/NA</td></tr></tbody></table>

lattice parameter dependence, in which it highlights the importance of using high resolution diffraction methods to determine subtle changes precisely to crystal structures of ceramics when doped with trace elements and supports the scientific understanding of Cr-doped UO₂ nuclear fuels.

### CRediT authorship contribution statement

**Gabriel L. Murphy:** Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Volodymyr Svitlyk:** Writing – review & editing, Methodology, Formal analysis, Investigation. **Maximilian Henkes:** Writing – review & editing, Methodology, Investigation. **Daniil Shirokiy:** Writing – review & editing, Methodology, Formal analysis, Investigation. **Christoph Henning:** Formal analysis, Investigation. **Philip Kegler:** Writing – review & editing, Methodology, Investigation. **Dirk Bosbach:** Writing – review & editing, Formal analysis, Methodology, Investigation. **Andrey Bukaemskiy:** Writing – review & editing, Methodology, Investigation, Formal analysis, Conceptualization.

### Declaration of competing interest

The authors all declare they have no competing financial interests or potential relationships that could have appeared to influence the world to reported in this paper.

### Data availability

Data will be made available on request.

### Acknowledgments

The authors are grateful to funding and support from the German Federal Ministry of Education and Research (BMBF), Project No. 02NUK060 that enabled this research.

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