# Incorporation Mechanism of Tc(IV) in Magnetite Revealed by EXAFS Measurements and Ab Initio Simulations

Anita S. Katheras, Matthias Krack, Thomas Zimmermann, Andreas C. Scheinost, Sergey V. Churakov

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Anita S. Katheras, Matthias Krack, Thomas Zimmermann, Andreas C. Scheinost, Sergey V. Churakov. Incorporation Mechanism of Tc(IV) in Magnetite Revealed by EXAFS Measurements and Ab Initio Simulations. Journal of Physical Chemistry C, 2025, 129 (12), pp.5921-5930. 10.1021/acs.jpcc.5c00357. hal-05149615

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# Incorporation Mechanism of Tc(IV) in Magnetite Revealed by EXAFS Measurements and Ab Initio Simulations

Anita S. Katheras, Matthias Krack, Thomas Zimmermann, Andreas C. Scheinost, and Sergey V. Churakov*

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Cite This: J. Phys. Chem. C 2025, 129, 5921–5930

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## ACCESS

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Supporting Information

**ABSTRACT:** The reductive immobilization of Tc, a long-lived fission product present in nuclear waste, is an important geochemical mechanism regarding Tc transport in the repository near-field. Based on the ionic radius and similarity in charge, Tc(IV) is expected to substitute for Fe(II,III) in octahedral positions in magnetite, a common iron oxide. Several mechanisms have been proposed in the past for how the necessary charge compensation for the aliovalent cation substitution is obtained. In this study, we developed a reliable computational approach based on density functional theory to investigate the Tc-magnetite interaction. By comparing our simulation results to spectroscopic data, we can confirm a preference for the incorporation mechanisms, including the formation of a vacancy. For both the magnetite

bulk structure as well as its commonly observed (111) surface, these findings are based on structural information and thermodynamic considerations. Our results are in line with the experimentally observed topotactic transition of the magnetite crystal structure toward the more oxidized iron mineral maghemite and reflect a component in long-term geochemical mineral transformations.

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## INTRODUCTION

Technetium is the lightest element in the periodic table without stable isotopes. Among its nuclides, the short-lived gamma-emitting isotope ⁹⁹mTc is routinely used for medical imaging of tissues and organs in the human body.¹ Trace quantities of Tc form from natural processes such as the spontaneous fission of U and neutron capture by Mo. The major inventory of Tc is contained in spent nuclear fuel as a U and Th fission product in the nuclide ⁹⁹Tc, which has a long half-life of 200 ka. The mobility of Tc in the environment is strongly controlled by its oxidation state. Tc(VII) is very soluble and mobile as the pertechnetate anion (TcO₄), whereas Tc(IV)O₂ was found to remain immobilized over a wide pH range.²

In many countries, the disposal of radioactive waste is planned in deep geological repositories, aiming for long-term separation of hazardous elements from the living environment. To ensure this separation, repository safety relies on a system of natural and engineered barriers.³ The retention mechanisms and mobility are influenced by the surrounding chemical conditions, including salinity⁴,⁵ and the presence of ligands. In contact with oxygen-containing porewater, technetium from spent nuclear fuel can be oxidized and mobilized into the form of Tc(VII). Considering the long-term reducing conditions expected in the near field of geological repositories,⁶ it can be reduced to Tc(IV) in the presence of Fe(II), e.g., in clay minerals such as nontronite,⁷ preferably by Fe(II) associated

with the solid phase of clay minerals,⁸,⁹ or on Fe precipitates by a surface-mediated mechanism.¹⁰ Furthermore, the reduction has been shown to occur at Fe(II)-bearing minerals such as mackinawite, siderite, chukanovite, and magnetite.⁴,¹¹,¹² The latter mineral might also contain Ti (titanomagnetite), in which the presence of Ti stabilizes Fe(II), leading to increased Tc reduction capabilities.¹³ The reduction may lead to the formation of insoluble colloids.¹⁴

Moreover, Tc(IV) can be immobilized by sorption or structural incorporation, e.g., on humic substances¹⁴ or in other environmentally relevant Fe compounds such as hematite,¹⁵ goethite,¹⁶ pyrite,¹⁷ zerovalent iron,¹⁸ or chukano-vite.¹² It has been observed that the interaction of Tc with Fe-containing minerals often leads to the formation of magnetite.¹⁷,¹⁸ Significant quantities of iron oxide minerals, and magnetite in particular, are expected to form as the main corrosion product of the disposal casks containing high-level nuclear waste.¹⁹⁻²⁴ Thus, magnetite is likely among the first mineral phases that mobile Tc(VII) might come into contact

Received: January 16, 2025

Revised: March 5, 2025

Accepted: March 7, 2025

Published: March 18, 2025

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with after the breaching of the disposal casks and the ingress of formation water.

The interaction of Tc with magnetite and other corrosion products<sup>25</sup> has been studied both experimentally, e.g., using X-ray absorption spectroscopy (XAS),<sup>4,11,26</sup> as well as by computational methods.<sup>27-29</sup> It was found that at high Tc concentrations, stabilization of a TcO<sub>2</sub> precipitate in solution occurs first,<sup>4,26</sup> resembling β-TcO<sub>2</sub>,<sup>30</sup> before it may become sorbed onto the magnetite surface.<sup>11,29</sup> On the other hand, at low concentrations of Tc and under low alkaline pH,<sup>11</sup> the structural incorporation of Tc(IV) occurs at octahedral sites of the magnetite structure.<sup>26,27,31-34</sup> Moreover, the resulting Tc-magnetite structure was found to be quite stable under alkaline or acidic leaching conditions<sup>35</sup> and even under oxidation,<sup>36</sup> although this leads to a partial transformation to maghemite/goethite.<sup>37</sup>

The incorporation of Tc into the octahedral Fe position in magnetite can be explained by the concordance of the ionic radii of Fe(III) and Tc(IV).<sup>38</sup> However, the details of the charge substitution mechanism and the potential formation of structural vacancies remain a subject of debate.<sup>29,32</sup> This study reveals the molecular mechanism of Tc uptake by magnetite by combining spectroscopic investigations and theoretical modeling at the level of density functional theory (DFT). For this purpose, we rely on previous characterizations of the magnetite surface regarding stability and speciation as a function of environmental E<sub>h</sub> and pH conditions.<sup>39</sup> This study discusses the thermochemical conditions for redox processes coupled to Tc incorporation and reveals the important role of vacancy formation leading to the maghemitization of the magnetite surface.

## THEORETICAL AND EXPERIMENTAL METHODS

**Modeling Setup.** *Ab Initio* Simulations. Atomistic simulations were performed following the methodology developed and validated in our previous studies.<sup>39,40</sup> In brief, density functional theory (DFT)-based spin-polarized structural optimizations were performed using the PBE functional (PBEsol parametrization). The Gaussian plane waves (GPW) method implemented in the Quickstep module<sup>41</sup> of CP2K (version 2023.1)<sup>42</sup> was used, applying 3D periodic boundary conditions. GTH<sup>43-45</sup>-like norm-conserving scalar-relativistic pseudopotentials were applied to avoid explicit consideration of the core electrons. MOLOPT basis sets (DZVP)<sup>46</sup> were used to describe the wave functions of the valence electrons. To expand the electronic density, an auxiliary basis set of plane waves with an electronic density cutoff of 600 Ry was employed. The target accuracy (EPS SCF) of the self-consistent field (SCF) cycles, 3.0 × 10<sup>-7</sup> Ha, was achieved using the orbital transformation method<sup>47</sup> for wave function optimization. To improve the description of the 3d electronic states of iron, the DFT+U method<sup>48,49</sup> was employed with an effective Hubbard U parameter of 1.9 eV, as validated in a previous study.<sup>39</sup> In all simulations, unless stated otherwise, the valence electron count in the system fulfilled the electroneutrality condition.

Furthermore, spin polarization was applied to the initialization of wave functions in the magnetite systems. For ferrous iron, it measured (2S + 1)<sub>Fe<sup>2+</sup></sub> = 5 and (2S + 1)<sub>Fe<sup>3+</sup></sub> = 6 for ferric iron, respectively. Ferric and ferrous irons are assumed to alternate in the octahedral positions of the magnetite structure, resulting in (2S + 1)<sub>Fe<sub>oct</sub></sub> = 5.5 with all spins aligned up. The

ferric tetrahedral sites in magnetite were considered as spin down. Tc(IV) was initialized as 5s<sup>04</sup>d<sup>3</sup> with an initial up-spin multiplicity of (2S + 1)<sub>Tc<sup>4+</sup></sub> = 4.

**Benchmarking of the Hubbard U Parameter for Tc.** In line with our previous studies<sup>39,40</sup> on the magnetite structure, surface stability, and nanoparticle speciation, the DFT+U approach<sup>48,49</sup> was applied to improve the description of the Tc 4d orbitals.<sup>50-52</sup> The necessary preparatory step in this study was, hence, the determination of the U parameter for tetravalent Tc octahedrally coordinated by oxygen. Based on the commonly used chemical analog Re<sup>53,54</sup> as presented in the comparative study by Oliveira et al.,<sup>30</sup> the three polymorphs of Tc(IV) oxide exhibiting octahedrally coordinated Tc were simulated. The crystal structure of α-TcO<sub>2</sub> is monoclinic (space group: P2<sub>1</sub>/c)<sup>55</sup> and it is the only experimentally proven polymorph. In analogy to Re, β- and γ-TcO<sub>2</sub> are assumed to be orthorhombic (space group: Pbcn) and tetragonal (space group: P4<sub>2</sub>/mnm), respectively.<sup>30</sup>

For the 4d electronic states of Tc, several values ranging from 0 to 4 eV were tested as the Hubbard U parameter in different Tc(IV) oxides. For comparison of the obtained benchmarking results and further method validation, spin-polarized PBE+U simulations on α-, β-, and γ-TcO<sub>2</sub> were performed in VASP<sup>56-59</sup> (version 5.4.4) with an electronic cutoff of 600 eV and 8 × 8 × 8 k-points for α- and β-TcO<sub>2</sub> and 8 × 8 × 16 k-points for γ-TcO<sub>2</sub>, respectively.

To identify an optimal value of the Hubbard U parameter for Tc, the lattice constants and angles of simulated structures were compared with literature data. As they are predicted to be the most stable phases,<sup>30</sup> the α- and β-structures were tested as 3 × 3 × 3 superstructures in CP2K, the main simulation program for this study. Complementarily, VASP simulations using 1 × 1 × 1 supercells of each of the three polymorphs were tested. The best structural agreement was obtained with U<sub>eff</sub>, Tc(IV) = 0 eV, which was then applied in the simulations investigating the interactions with magnetite. Moreover, β-TcO<sub>2</sub> chains were identified as the expected sorbed Tc species by Oliveira et al.<sup>30</sup> and for additional validation of the intended modeling setup, these zigzag chains of six TcO<sub>6</sub> octahedra were simulated. Further details can be found in the *Supporting Information*.

**Potential Mechanisms of Tc Incorporation and System Setup.** Magnetite has a cubic inverse spinel structure (space group: Fd<sub>3</sub>m) with octahedrally (Fe<sub>oct</sub>) and tetrahedrally (Fe<sub>tet</sub>) coordinated Fe. The tetrahedral positions are occupied by ferric iron (Fe<sup>3+</sup>), while the octahedral positions are occupied by equal amounts of ferric and ferrous iron (Fe<sup>2+</sup>). As Tc(IV) and Fe(III) in octahedral coordination by oxygen have the same ionic radius of 78.5 pm,<sup>38</sup> incorporation based on substituting Fe with Tc is possible.<sup>32</sup> Two distinct mechanisms can be envisaged to maintain local charge balance for the Tc-Fe aliovalent substitution: first, an isostructural substitution of Tc for Fe<sub>oct</sub> (mechanism “Iso”); second, the substitution of two Fe in edge-shared octahedra for one Tc(IV) and one vacancy, as proposed by Smith et al.<sup>32</sup> (mechanism “Vac”). Compared to the previous study,<sup>32</sup> the possible mechanism of substituting four Fe(III) by three Tc(IV) and a vacancy was not considered, as it represents a striking alteration of the magnetite crystal structure and was found to require stabilization by external factors.<sup>32</sup> Hence, for the current study, in both investigated cases (Iso and Vac), the total system charge is assigned to zero, implying a redox reaction between Tc and Fe present in the system.
<figure><img src="image_10.png" /><figcaption>**Figure 1.** (a) Side view of half of the symmetric magnetite (111) surface slab, adapted with permission from Katheras et al.,³⁹ Copyright 2024 American Chemical Society. Tetrahedrally coordinated Fe are shown in orange, octahedrally coordinated Fe (Fe<sub>oct</sub>) in blue, O in red, and H in pale pink. (b) Substitution of octahedrally coordinated Fe by Tc (pink) representing the isostructural substitution (Iso mechanism) and (c) with an additional vacancy (white) in place of an edge-connected octahedrally coordinated Fe (Vac mechanism). Atomic sizes are adapted for visualization.</figcaption></figure>

The molecular geometry and substitution energy for both mechanisms were investigated in the bulk crystal structure of magnetite with a lattice parameter of 8.375 Å⁶⁰ using a 2 × 2 × 2 supercell. Moreover, systems resembling the saturated magnetite (111) surface³⁹ were tested as an incorporation matrix. These systems followed the slab geometry with slab dimensions of 23.69 Å × 20.52 Å × 14.04 Å, as tested in our previous study.³⁹ Under repository conditions,⁶ the prevailing surface termination has been identified as protonated FeO₆ octahedra (Figure 1a). The protonation state of the surfaces for the present study was chosen according to the setup with an idealized Fe<sub>oct</sub> charge of 2.5+³⁹ for comparison with bulk magnetite. In the bulk magnetite structure, the octahedrally coordinated Fe occupy equivalent crystallographic sites; hence, for the Iso mechanism, one Fe<sub>oct</sub> was replaced with one Tc (Figure 1b).

The alternative Vac mechanism with a vacancy was realized by additionally removing Fe<sub>oct</sub> from an edge-sharing FeO₆ octahedron (Figure 1c). In this way, Tc makes up around 0.6 wt %, similar to the Tc incorporation in hematite.¹⁵ For the magnetite surface slab, several options were possible due to the layered structure of the magnetite (111) surface slab. The symmetric slab has three distinctive Fe<sub>oct</sub> layers: one in the center, one intermediate Fe<sub>oct</sub> layer between two Fe<sub>tet</sub> layers, and another Fe<sub>oct</sub> layer close to the surface (Figure 1a). Each of these Fe<sub>oct</sub> layers was tested for the Iso mechanism, and they will be referred to based on the respective position of the substituted Fe<sub>oct</sub> with an abbreviated subscript: Iso<sub>cent</sub>, Iso<sub>oct2</sub>, and Iso<sub>surf</sub>.

Similarly, for the Vac mechanism, all six possible options for positioning Tc and the vacancy were tested. The options can be differentiated by the position of the initial Fe<sub>oct</sub> that is replaced by a Tc ion and a vacancy (Figure S3). The naming convention is similar to the Iso mechanisms but uses two subscripts separated by a hyphen to depict the position of Tc-Vac: both octahedral positions in the same layer of center Fe<sub>oct1</sub> (Vac<sub>cent-cent</sub>) or surface Fe<sub>oct1</sub> (Vac<sub>surf-surf</sub>), Tc in the center with the vacancy in Fe<sub>oct2</sub> (Vac<sub>cent-oct2</sub>) or vice versa (Vac<sub>oct2-cent</sub>), or Tc in the Fe<sub>oct2</sub> position and the vacancy in the surface-Fe<sub>oct1</sub> position (Vac<sub>oct2-surf</sub>) or vice versa (Vac<sub>surf-oct2</sub>). A substitution only within the Fe<sub>oct2</sub> layer is not possible due to the magnetite crystal structure.

**EXAFS Spectra.** In this study, experimental and theoretical EXAFS spectra were compared to investigate the Tc

incorporation mechanism. **Caution:** ⁹⁹Tc is a β-emitter. All experimental operations were carried out in a laboratory equipped to handle this isotope.

Experimentally, a Tc magnetite coprecipitation sample with 600 ppm Tc was prepared in a glovebox under anoxic conditions (c(O₂) < 1 ppm). First, 110 mg of Fe(II)Cl₂·4H₂O and 280 mg of Fe(III)Cl₃·4H₂O (resulting in 200 mg of magnetite) were dissolved in 20 mL of 0.01 M HCl. Subsequently, an aliquot of a 10 mM KTcO₄ stock solution was added to the Fe(II) and Fe(III) solution, followed by the addition of 2.5 mL of 6 M NH₄OH under vigorous shaking. The resulting black solid was washed three times with Milli-Q water and then stored in the final washing solution for 7 days.

After centrifugation, the wet paste was mounted with Kapton tape in a doubly sealed HDPE plastic sample holder inside the glovebox. To prevent alteration of the sample during further storage and transport to the synchrotron facility, the sample was flash-frozen with liquid nitrogen immediately after removal from the glovebox and stored in a liquid nitrogen container for transportation. Experimental spectra were acquired at the Rossendorf Beamline (BM20 at ESRF)⁶¹ in fluorescence mode at the Tc K-edge (21 044 eV). The energy of the Si(111) double-crystal monochromator was calibrated using a Mo foil (edge energy: 20 000 eV). Two Rh-coated mirrors at a 2.5 mrad grazing angle were used to suppress higher harmonics and to collimate the beam onto the monochromator crystal. Fluorescence spectra were collected with an 18-element, high-purity, solid-state Ge detector (Ultra-LEGe, GUL0055, Mirion Technologies) with a digital spectrometer (XIA Falcon-X). During the measurement, the samples were kept at 15 K within a closed-cycle He cryostat to avoid photon-induced changes of the oxidation state and to reduce thermal disorder.

Theoretical EXAFS spectra were obtained with the FEFF code⁶²⁻⁶⁴ (version 8.4) for each structural configuration considered in the ab initio calculations. A cluster with a radius of 9.0 Å around each Tc cation was used as input. The synthetic spectra were used for linear combination fitting of experimental data in the range of 2 Å⁻¹ ≤ *k* ≤ 10 Å⁻¹. Different approaches and parameter combinations were tested. The best agreement with the experimental data could be obtained with the synthetic data set generated using a non-SCF muffin-tin potential model, a Debye–Waller factor (σ²) of 0.005, and an amplitude reduction factor (S₀²) of 0.99.
<table><caption>Table 1. Structural Parameters of Different TcO₂-Polymorphs Were Obtained by DFT Calculations with the Hubbard U-Correction Set to 0 eV</caption><thead><tr><th></th><th>method</th><th>init. spin</th><th>a [Å]</th><th>b [Å]</th><th>c [Å]</th><th>β [°]</th></tr></thead><tbody><tr><td rowspan="5">α-TcO<sub>2</sub></td><td>Rodriguez et al.<sup>55</sup></td><td>(experiment, RT)</td><td>5.689</td><td>4.755</td><td>5.520</td><td>121.5</td></tr><tr><td>Oliveira et al.<sup>30</sup></td><td><sup>a</sup></td><td>5.733</td><td>4.825</td><td>5.588</td><td>121.5</td></tr><tr><td>CP2K</td><td>AFM</td><td>5.631</td><td>4.771</td><td>5.512</td><td>121.4</td></tr><tr><td></td><td>FM</td><td>6.241</td><td>4.680</td><td>5.571</td><td>124.1</td></tr><tr><td>VASP</td><td>AFM</td><td>5.663</td><td>4.792</td><td>5.558</td><td>121.3</td></tr><tr><td rowspan="5">β-TcO<sub>2</sub></td><td>Oliveira et al.<sup>30</sup></td><td><sup>a</sup></td><td>5.663</td><td>4.792</td><td>5.558</td><td>121.3</td></tr><tr><td>CP2K</td><td>AFM</td><td>4.760</td><td>5.708</td><td>4.706</td><td>90.0</td></tr><tr><td></td><td>FM</td><td>4.717</td><td>5.600</td><td>4.625</td><td>90.0</td></tr><tr><td>VASP</td><td>AFM</td><td>4.536</td><td>5.653</td><td>5.166</td><td>90.0</td></tr><tr><td></td><td>FM</td><td>4.763</td><td>5.636</td><td>4.649</td><td>90.0</td></tr></tbody></table>

## ■ RESULTS AND DISCUSSION

Determination of the Hubbard U Parameter for Tc(IV). A possible Hubbard U correction for the transition metal element Tc was investigated for a wide range of U-values with two different computational codes. Table 1 lists the lattice parameters and angles of the two polymorphs with the lowest total energy, α- and β-TcO₂. A reasonable fit to available literature data, using the aforementioned basis sets and pseudopotentials in CP2K and VASP, could be obtained using U<sub>eff</sub> = 0 eV, in line with findings by Taylor.<sup>65</sup> The analysis of the density of states (DOS) resolves TcO₂ to be metallic, both from Oliveira et al.<sup>30</sup> and from the simulations conducted in the present study (Figure S1). In contrast, the use of a U parameter would in turn shift the unoccupied d-states to higher energies and open a band gap.

Our simulations energetically favor the β-TcO₂ polymorph (Table S3) and achieve good agreement with literature data, including for ReO₂ as the TcO₂ analog. Furthermore, focusing on β-TcO₂ as the polymorph with the lowest energy, both the initial anti- and ferromagnetic setups converge into the same antiferromagnetic state, in agreement with previous studies.<sup>52,65,66</sup> Thus, this setting was used for the following simulations if at least two neighboring TcO₆ octahedra are present in the system.

In this way, a system of a β-TcO₂ chain was tested, as suggested by Oliveira et al.,<sup>30</sup> as the dominant sorption product developing on the magnetite surface over a long time. Each of the Tc(IV) atoms is expected to be octahedrally coordinated by two OH₂ groups and four oxygen connecting to the next TcO₆ octahedra in the zigzag chain (Figure S2). However, as can be observed from Table S4, neither the use of dispersion correction nor larger basis sets for O and H leads to improvements in all structural parameters relative to the previous study.<sup>30</sup> Hence, for the main subject of this study, the simulations were continued with the DZVP basis sets.

### Substitution of Octahedrally Coordinated Fe Ions by Tc in the Magnetite Crystal Structure.
*Analysis of Structural and Electronic Properties.* The substitution of Tc for Fe in the magnetite structure is feasible due to the concordance of the ionic radii of Fe³⁺ and Tc⁴⁺ in octahedral coordination.<sup>38</sup> Structural parameters of the Fe<sub>oct</sub> and Tc<sub>oct</sub> coordination shells in bulk magnetite are compared in Table 2; analogous results for the substitution in the magnetite (111) surface slab can be found in Table S5. The Tc–O distance in the first coordination shell is slightly shortened compared to the original magnetite structure, whereas the Tc–Fe distances

<table><caption>Table 2. Coordination Numbers (CN) and Distances (r) of the Coordinating Shells around Tc Substituting an Octahedrally Coordinated Fe Ion in a 2 × 2 × 2 Supercell of Magnetite without (Iso) or with a Vacancy (Vac)<sup>a</sup></caption><thead><tr><th rowspan="2">shell</th><th colspan="2">Mag</th><th colspan="2">Iso</th><th colspan="2">Vac</th><th colspan="2">EXAFS<sup>11</sup></th></tr><tr><th>CN</th><th>r [Å]</th><th>CN</th><th>r [Å]</th><th>CN</th><th>r [Å]</th><th>CN</th><th>r [Å]</th></tr></thead><tbody><tr><td>O</td><td>6</td><td>2.038</td><td>6</td><td>2.027</td><td>6</td><td>2.025</td><td>6</td><td>2.01</td></tr><tr><td>Fe<sub>oct</sub></td><td>6</td><td>2.951</td><td>6</td><td>2.973</td><td>5</td><td>2.962</td><td>6</td><td>3.08</td></tr><tr><td>Fe<sub>tet</sub></td><td>6</td><td>3.450</td><td>6</td><td>3.476</td><td>6</td><td>3.482</td><td>6</td><td>3.49</td></tr></tbody></table>

in the second and third coordination shells to edge-sharing Fe<sub>oct</sub> and corner-sharing Fe<sub>tet</sub> are increased.

The predicted changes in the Tc-magnetite coordination environment for both substitution mechanisms agree well with the structural results obtained from the analysis of experimental EXAFS data.<sup>11</sup> The distances match experimental observations with a maximum deviation of radius below 3% in the O shell, below 7% deviation in the Fe<sub>oct</sub> shell, and below 0.4% deviation in the Fe<sub>tet</sub> shell. The coordination numbers agree within the known uncertainties as well. Hence, the local structural environment of Tc in magnetite can be confirmed by two independent methods.

Compared to the pristine magnetite system, both systems with Tc substitution reveal only a few changes in the total density of states (TDOS, Figure S4a). These merely small changes can be expected from the substitution of one to two (with vacancy) out of 128 Fe<sub>oct</sub> in the system. However, the Tc d-states (Figure S4b) contribute to the electronic density around the Fermi level, leading to a slight overall decrease in the electronic band gap (Table S6). This is especially true for the Vac mechanism, where the decrease of both the α and β band gaps may reflect an increased conductivity of the system. Moreover, as the valence states of Tc have slightly lower energy, a preferred occupation of these compared to the Fe valence states can be assumed. This behavior is reflected in the increased Mulliken occupation (Table S7).

### Interpretation of EXAFS Spectra.
In Figure 2, the experimental and simulated EXAFS spectra for the substitution mechanisms in bulk magnetite are depicted. As can be seen, the spectra of the individual mechanisms are very different from each other and in comparison to the experimental data.

<footnote><sup>a</sup>Oliveira et al.<sup>30</sup> did not specify how the spin polarization of the setup was initialized; antiferromagnetic (AFM) or ferromagnetic (FM).</footnote>

<footnote><sup>a</sup>For comparison, equivalent results for the pristine magnetite structure (Mag) around octahedrally coordinated Fe, as well as the fit results of experimental EXAFS assuming incorporated Tc, are given.</footnote>
<figure><img src="image_11.png" /><figcaption>**Figure 2.** Theoretical *k*³-weighted EXAFS spectra of systems based on the 2 × 2 × 2 magnetite supercell with substitution of one Tc (Iso, blue), one Tc, and one vacancy (Vac, orange) for experimentally obtained EXAFS data (red). The black line represents a fit as combination of both mechanisms with approximately 30.7% Iso and 69.3% Vac.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 3.** Theoretical *k*³-weighted EXAFS spectra of systems based on the magnetite (111) surface slab with substitution of one Tc (mechanisms Iso, blue), one Tc, and one vacancy (mechanisms Vac, orange, and gray) to experimentally obtained EXAFS data (red). The black line represents a fit as a combination of all surface mechanisms with approximately 60.3% Vac<sub>cent-cent</sub>, 16.7% Vac<sub>surf-surf</sub>, and 23.0% Vac<sub>oct2-surf</sub>.</figcaption></figure>

However, the best fit to qualitatively reproduce the experimental spectrum can be achieved by combining the two substitution mechanisms. With this fit, the mechanism including a vacancy appears to be dominant and can be assumed to prevail at approximately 69.3%.

For substitution in the magnetite (111) surface slab, a similar result is achieved. The corresponding plot is shown in Figure 3, displaying the best fit with approximately 60.3% Vac<sub>cent-cent</sub>, 16.7% Vac<sub>surf-surf</sub>, and 23.0% Vac<sub>oct2-surf</sub>. The other mechanisms, including all Iso mechanisms, each account for

below 1 × 10⁻⁶% in the superposition of the fit and can, hence, be considered of less importance.

Concluding, the prevalence of the substitution mechanism, including the formation of a vacancy, can be deduced. Moreover, with a preference for Tc in the central and almost central position (center Fe<sub>oct1</sub> and Fe<sub>oct2</sub>), Tc seems to be surrounded by octahedrally coordinated Fe, predominantly in a three-dimensional arrangement.

**Relative Stability of Tc Substitutions in Magnetite.** To reveal the favorable thermodynamic conditions for the different mechanisms of Tc incorporation in magnetite, the
<figure><img src="image_13.png" /><figcaption>**Figure 4.** Formation energy, *E*<sub>form</sub>, as a function of the chemical potential of oxygen, *μ*'<sub>O</sub>,<sup>29</sup> for the different Tc incorporation mechanisms for (a) magnetite bulk substitution, and (b) substitution in the magnetite surface slab.</figcaption></figure>

formation energy of the Fe<sup>2.5+</sup>-Tc<sup>4+</sup> exchange as a function of oxygen potential was calculated (Figure 4) following the same approach proposed by Bianchetti et al.<sup>29</sup> (for further details, see the Supporting Information). The predicted stability fields for different Tc incorporation mechanisms agree with the data reported in the literature for similar systems.<sup>29</sup> For mechanisms with a substitution in the bulk magnetite structure (Figure 4a), at lower oxygen potentials (*μ*'<sub>O</sub> = -1 eV), the Iso mechanism results in a lower formation energy. Hence, it can be assumed that the mechanism without the formation of a vacancy is favored at low oxygen pressures. In contrast, at high oxygen potentials (*μ*'<sub>O</sub> = 0 eV), the Vac mechanism is favored energetically. For incorporation in bulk magnetite, the generally positive formation energy signifies a less favorable setting, as the ideal magnetite structure is disturbed.

To better understand the dynamics of Tc incorporation during crystal growth and the role of surface structure in Tc entrapment, corresponding stability calculations were conducted and displayed in Figure 4b denoting the Tc-Vac distance to the surface. Over the whole range of relevant oxygen potentials, the Vac mechanisms with the vacancy located close to the surface (Vac<sub>oct2-surf</sub> and Vac<sub>surf-surf</sub>) yield the lowest energy. The Iso mechanisms are energetically less favorable.

It can be assumed that, in a dynamic process of dissolution and recrystallization at the dominant (111) surface of magnetite, layers containing only octahedrally coordinated Fe ions (oct1, here center Fe and surface Fe) are more likely to incorporate Tc. This might be due to their higher number of octahedrally coordinated Fe ions, which is three times greater than those in the oct2 layer with oxygen-coordinated Fe<sub>oct2</sub>. Moreover, the oct1 layers have been found to exhibit higher stability under geochemically relevant conditions<sup>39</sup> and may experience prolonged exposure allowing for extended fluid-surface interaction and, hence, serving as the substitution matrix. In the process of crystal growth of magnetite nanoparticles, these oct1 layers may become overgrown. A position of Tc not directly at the surface, in line with the EXAFS results, might also be more stabilized by the surrounding magnetite structure. The resulting structure of a (potential) nanoparticle with a magnetite core, a subsequent shell enriched in Tc, and an outer Tc-depleted shell has been observed experimentally for octahedrally shaped magnetite nanocrystals,<sup>67</sup> corroborating this assumed growth mechanism.

Compared to the previous study on Tc(IV) incorporation into the magnetite (001) surface,<sup>29</sup> we report higher formation

energies for incorporation into the idealized magnetite (111) surface. These differences can be attributed to the principally different facet types and their surface reconstruction. Moreover, the system studied by Bianchetti et al.<sup>29</sup> includes undercoordinated Fe at the surface, contrasting with the hydrogen-saturated surface oxygen present in our models, which reflect environmental conditions. However, the identified preferred incorporation mechanisms for both surface types include the formation of a vacancy. This may alter the magnetite crystal structure and, in the long term, with several incorporated Tc-Vac pairs, lead to a transition toward maghemite, as observed experimentally during the oxidation of magnetite.<sup>68</sup>

**Octahedrally Coordinated Tc Ions Surrounded by Oxygen—Interpretation of Tc(IV).** Tc is initialized in this study as Tc(IV), as expected from experiments.<sup>11</sup> Based on the idealized chemical conception of perfect ionic behavior of the species involved, this requires a change in the electron configuration from [Kr] 5s<sup>2</sup>4d<sup>5</sup> for Tc(0) to [Kr] 5s<sup>0</sup>4d<sup>3</sup> for Tc(IV). However, the idealized viewpoint does not necessarily hold perfectly in the simulations.

First, by analogy with Tc, the octahedrally coordinated Fe, as a mix of Fe(II) and Fe(III), can be investigated as was done previously.<sup>39,40</sup> From an idealized perspective, a shift from [Ar] 4s<sup>2</sup>3d<sup>6</sup> for Fe(0) to [Ar] 4s<sup>0</sup>3d<sup>6</sup> for Fe(II) and [Ar] 4s<sup>0</sup>3d<sup>5</sup> for Fe(III) would be expected. Due to the high-spin configuration in magnetite, for both oxidation states, the five d-orbitals would be half-filled with the same spin alignment (spin up, majority spin), whereas for Fe(II), the sixth 3d-electron would be paired with an antiparallel orientation (spin down, minority spin) in one of the d-orbitals.<sup>69</sup> The occupation can be analyzed by different methods; this study is based on the Mulliken population analysis.<sup>70</sup> As can be observed from the actual values of occupation (Figure S5 and Table S6) for the pristine magnetite system, the minority spin is approximately 0.5, signifying an intermediate oxidation state of all Fe<sub>oct</sub> equivalent to an assumed average charge of +2.5.

Second, by analogy to Fe, the occupation of Tc states in TcO<sub>2</sub> (Table S2) was analyzed. Surprisingly, the sum of both spin-up and spin-down lies between 3.7 and 4.7, contrasting the idealized chemical conception. Yet, these investigated Tc systems have only octahedrally coordinated Tc surrounded by O and, hence, can be assumed to yield a reasonable interpretation of Tc(IV) in the simulations. In comparison, if Tc-substituted magnetite is considered (Table S7), the occupation resembles that of the Tc dioxides, indicating a stable configuration, especially for the ferromagnetic (FM)
phases. This is in line with the design of the present study, where single Fe<sub>oct</sub> ions are substituted by Tc ions, representing a ferromagnetic setup, of course. Deriving the present oxidation state of Tc by comparing it with Tc oxide is also commonly done in XAS experiments, e.g., deducing Tc(IV) in the presence of magnetite by comparing XANES spectra to those of TcO<sub>2</sub>·xH<sub>2</sub>O (s).<sup>11</sup>

The exchange of cations by substituting Fe with Tc results in a repartitioning of electron density according to the electrochemical potential difference between these two redox-sensitive elements. It has to be considered, however, that magnetite is a conductive material and the Tc:Fe<sub>oct</sub> ratio is lower than 1:100. In such a system, a change of the electron density of Fe<sub>oct</sub> in the range of 0.8% would be sufficient to explain the observed electronic state of Tc and is indeed of the same order of magnitude of Fe<sub>oct</sub> occupation change perceived (Table S6). Moreover, a test simulation was performed on the isostructural substitution setup with the total system charge imposed to be +1, mimicking a substitution of Fe<sup>3+</sup> with Tc<sup>4+</sup>. It resulted in a nearly identical electronic occupation state of Tc (Table S7), whereas the charge compensation is almost entirely provided and reflected in a decreased minority spin of the Fe<sub>oct</sub> ions, signifying a slight overall tendency toward Fe(III). In contrast, in a system with a total charge of zero, the substitution of one Fe<sub>oct</sub> with one Tc leads to a slight increase of minority spin.

This indicates that Fe<sub>oct</sub> buffers the redox equilibrium in the system; i.e., a substitution of one Fe<sup>2.5+</sup> with Tc<sup>4+</sup> results in an excess of positive charge (+1.5), which is, in turn, compensated by a reduction of the other octahedrally coordinated Fe. Similarly, the substitution of two Fe<sup>2.5+</sup> by one Tc<sup>4+</sup> and a vacancy results in a deficit of positive charge (-1), which is compensated by oxidizing the other Fe<sub>oct</sub>, hence a decrease in Fe minority spin. These shifts are observed only among the group of octahedrally coordinated Fe, as these have, from the beginning, an intermediate oxidation state in the (semi)-conductive material magnetite.

**Interpretation in the Context of Nuclear Waste and Geochemical Implications.** The structural incorporation of Tc(IV) into iron minerals promises a stable separation of radiotoxic elements from the environment. With the Fe(II)-bearing minerals goethite and magnetite, a stable incorporation product can be achieved, and these minerals can be used in the treatment of waste streams<sup>31</sup> such as the vitrification of nuclear waste, e.g., emerging from the Hanford site.<sup>71</sup> During the subsequent long-term disposal of radioactive waste, magnetite, especially, can play a major role in retention. Under expected repository conditions, the incorporation of Tc(IV), replacing octahedrally coordinated Fe ions, has been experimentally proven.<sup>11</sup> In the present study, the dominant incorporation mechanism could be identified based on structural and spectroscopic analysis in comparison with these experiments. The incorporation favors the associated formation of a vacancy, while the octahedrally coordinated Fe cations can adapt to changing charge conditions.

The formation of a vacancy in magnetite leads to the
topotactic formation of a crystal structure resembling
maghemite. The associated trivalent state of all Fe cations
was observed in our previous computational studies on the
magnetite surface<sup>39</sup> and magnetite nanoparticles.<sup>40</sup> Moreover,
maghemite has been observed as an oxidation product at the
magnetite surface, commonly leading to particles with a
magnetite core and a maghemite shell.<sup>68,72</sup> These were also

observed in large-scale geological systems, such as marine
sediments.⁷³ In the oxidation process, the formation of
vacancies has been found to stabilize magnetite toward further
oxidation,⁶⁸,⁷⁴ leading to less strain in the crystal structure
compared to a mere oxidation of the Fe cations.⁷⁵
Furthermore, the presence of vacancies might facilitate the
uptake of ions that would otherwise not enter the magnetite
structure.⁷⁶ Moreover, maghemite has been shown to act as a
better sorption matrix compared to magnetite for other
environmentally toxic elements such as Se⁷⁷ and As.⁷⁸

The substitution of Fe(III) by a tetravalent cation provides the possibility for the formation of an adapted mineral phase. Octahedrally coordinated Ti(IV) has been observed in titanomagnetites⁷⁹ (TiₓFe₃₋ₓO₄) and titanomaghemites.⁸⁰ Especially, the mixed-valence Fe cations in magnetite allow for a system with a perfectly tunable Fe oxidation state depending on the amount of incorporated Ti.⁸¹ In this case, an elevated amount of Fe(II) supports the reduction of mobile Tc(VII), and the incorporation of Tc(IV) into titanomagnetite may subsequently occur.¹³ Hence, magnetite/maghemite and adapted systems have the ability to ensure long-term retention of Tc, reducing risks to the living environment.

<figure><img src="image_14.png" /></figure>

CONCLUSIONS

The incorporation of Tc(IV) into the magnetite structure was investigated following the mechanism previously discussed in the literature, in which Tc substitutes for octahedrally coordinated Fe. However, this aliovalent cation substitution hypothesis left the question of charge compensation. Based on the findings obtained in the present study, this question could be answered, revealing the dominant substitution mechanism to include the formation of a vacancy. Moreover, for the first time, the incorporation into the (111) magnetite surface was studied, and the favorable position of the vacancy close to the crystal surface was revealed. These findings agree well with the spectroscopic results obtained from X-ray absorption spectroscopy (XAS). Especially, the XAS-derived method of extended X-ray absorption fine structure (EXAFS) spectroscopy provided valuable information about the coordination environment.

<figure><img src="image_15.png" /></figure>

ASSOCIATED CONTENT

<figure><img src="image_16.png" /></figure>

**Supporting Information**

The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.jpcc.5c00357.

The determination of a suitable *U*-value for Tc(IV)
(structural and electronic properties) and the substitu-
tion of octahedral Fe in the magnetite structure by Tc
(with or without a vacancy) (PDF)

<figure><img src="image_17.png" /></figure>

AUTHOR INFORMATION

**Corresponding Author**

Sergey V. Churakov – PSI Center for Nuclear Engineering and Sciences, Villi gen PSI 5232, Switzerland; University of Bern, Institute of Geological Sciences, Bern 3012, Switzerland; ● orcid.org/0000-0001-8213-9206; Phone: +41 (0) 56 310 41 13; Email: sergey.churakov@psi.ch
## Authors

Anita S. Katheras – University of Bern, Institute of Geological Sciences, Bern 3012, Switzerland; ● orcid.org/0009-0001-4337-3451

Matthias Krack – PSI Center for Scientific Computing Theory and Data, Villigen PSI 5232, Switzerland; ● orcid.org/0000-0002-2082-7027

Thomas Zimmermann – Helmholtz-Zentrum Dresden-Rossendorf, Institute of Resource Ecology, Dresden 01328, Germany

Andreas C. Scheinost – The Rossendorf Beamline (BM20), European Synchrotron Radiation Lab, Grenoble 38043, France; Helmholtz-Zentrum Dresden-Rossendorf, Institute of Resource Ecology, Dresden 01328, Germany; ● orcid.org/0000-0002-6608-5428

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.jpcc.5c00357

## Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

The authors acknowledge funding from the German Federal Ministry of Education and Research (BMBF, KRIMI project-02NUK056C), access to the Swiss National Supercomputing Centre (CSCS, project number s1179), and access to UBELIX, the high-performance computing cluster at the University of Bern.

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