Technetium Incorporation into Goethite (Î±-FeOOH): An Atomic-Scale

Article pubs.acs.org/est

Technetium Incorporation into Goethite (α-FeOOH): An Atomic-Scale Investigation Frances N. Smith,*,† Christopher D. Taylor,§,∥ Wooyong Um,† and Albert A. Kruger‡ †

Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, United States Fontana Corrosion Center, Materials Science and Engineering, The Ohio State University, Columbus, Ohio 43210, United States ∥ Strategic Research and Innovation, DNV GL, Dublin, Ohio 43017, United States ‡ United States Department of Energy, Office of River Protection, P.O. Box 450, Richland, Washington 99352, United States §

S Supporting Information *

ABSTRACT: During the processing of low-activity radioactive waste to generate solid waste forms (e.g., glass), technetium-99 (Tc) is of concern because of its volatility. A variety of materials are under consideration to capture Tc from waste streams, including the iron oxyhydroxide, goethite (αFeOOH), which was experimentally shown to sequester Tc(IV). This material could ultimately be incorporated into glass or alternative low-temperature waste form matrices. However, questions remain regarding the incorporation mechanism for Tc(IV) in goethite, which has implications for predicting the long-term stability of Tc in waste forms under changing conditions. Here, quantum-mechanical calculations were used to evaluate the energy of five different chargecompensated Tc(IV) incorporation scenarios in goethite. The two most stable incorporation mechanisms involve direct substitution of Tc(IV) onto Fe(III) lattice sites and charge balancing either by removing one nearby H+ (i.e., within 5 Å) or by creating an Fe(III) vacancy when substituting 3 Tc(IV) for 4 Fe(III), with the former being preferred over the latter relative to gas-phase ions. When corrections for hydrated references phases are applied, the Fe(III)-vacancy mechanism becomes more energetically competitive. Calculated incorporation energies and optimized bond lengths are presented. Proton movement is observed to satisfy undercoordinated bonds surrounding Fe(III)-vacancies in the goethite structure.

■

oxides and oxyhydroxides13,14 are considered as potential crystalline hosts for Tc. While iron oxides and oxyhydroxides are important potential primary hosts for Tc that could ultimately be incorporated into glass waste forms to help stabilize Tc,8,13,14 they may also serve as secondary hosts for any Tc liberated by the corrosion of metal alloy waste forms8 or Tc released from used nuclear fuel that interacts with corrosion products of the steel waste packaging material surrounding fuel assemblies in a storage environment.15,16 Furthermore, iron oxides and oxyhydroxides are ubiquitous in nature17,18 and can act as sinks for redox-sensitive radionuclides in the “near-field” or “far-field” geologic disposal environment.19 Iron oxides and oxyhydroxides make up a dynamic chemical system where Eh, pH, and major cations or anions in the system affect which phase will be most stable under the given environmental or experimental conditions.17,18 Based on changing conditions, some iron oxide and oxyhydroxide phases can also transform into one another while still maintaining

INTRODUCTION In order for nuclear energy to remain a competitive part of the world’s carbon dioxide-free electrical energy portfolio into the future, it is essential to demonstrate effective management of current commercial as well as defense-related radioactive wastes.1 During the long-term storage of nuclear materials (e.g., used nuclear fuel or high-level and low-activity waste from reprocessing), technetium-99 (Tc) is a major concern tied to its long half-life (2.13 × 105 y), high thermal fission yield (∼6%),2 high mobility in the environment as the oxidized pertechnetate anion [Tc(VII)O4−], and radioactivity as a beta emitter.3,4 At the Hanford Site in Washington State, 177 underground tanks store up to 200,000 m3 (∼55 million gallons) of mixed solid and liquid waste from decades of plutonium generation.5 Ultimately, this waste will be separated into high-level and lowactivity waste streams for vitrification, with the majority of Tc following the low-activity waste streams.6 During this process, Tc presents a unique challenge because of its volatility during the high-temperature vitrification process, thus requiring additional methods to capture it for incorporation into borosilicate nuclear waste glass6,7 or as a separate nonglass waste form. To this end, a variety of compounds from metallic iron−technetium alloys,8,9 to technetium sulfides,10−12 to iron © 2015 American Chemical Society

Received: Revised: Accepted: Published: 13699

July 10, 2015 October 13, 2015 October 14, 2015 October 29, 2015 DOI: 10.1021/acs.est.5b03354 Environ. Sci. Technol. 2015, 49, 13699−13707

Article

Environmental Science & Technology

The unrestricted Hartree−Fock (UHF) level of theory was used because it allows for representation of ions with unpaired electronic spin and, subsequently, magnetic structure testing. This method was previously applied to modeling Tc in the hematite (α-Fe2O3) system where discrete Fe(II)/Fe(III) and Tc(IV)/Tc(VII) charge distinctions were maintained during energy minimization and structural optimization of this antiferromagnetic compound34 and for Fe(II)/Fe(III) distinctions in magnetite (Fe3O4) which has a net magnetic moment.35 Mulliken spin density analysis was used to determine the number of unpaired electrons, and subsequently oxidation state, for each atom following single point energy and geometry optimizations.36 While there is a trade-off in using UHF methods versus density-functional theory (DFT) methods, which account for electron exchange versus electron exchange and correlation contributions to the ground-state energy, respectively, UHF methods have been demonstrated to successfully capture the localized behavior of electrons in iron oxides which is important because of their categorization as small polaron materials.32,34,35,37 Recent simulations on the suite of polymorphic iron oxy-hydroxides, goethite (αFeOOH), akaganeite (β-FeOOH), and lepidocrocite (γFeOOH), demonstrate the charge localized (i.e., small polaron) behavior of electron transport in these phases.38 Parameter space testing was performed on single unit cells of goethite with a ferromagnetic (FM) spin structure. Specifically, k-point grids were generated using the Monkhorst−Pack method39 leading to the selection of 63 electronic sampling points in reciprocal space (see SI, Table S2 and accompanying text). While higher k-point sampling densities led to lower optimized energy values, the difference of 2.7 × 10−4 eV for 112 versus 63 k-points was small enough to warrant the selection of the smaller number of k-points to optimize computational efficiency. For the final energies reported in this study, structures were deemed converged when the change in energy between SCF optimization cycles and geometry optimization steps was less than 2.7 × 10−4 eV and thresholds for atom displacements and energy gradients were reached. For geometry optimization cycles, the root-mean-square (RMS) and maximum gradients were considered converged when energy changes were less than 8.2 × 10−3 and 1.2 × 10−2 eV, respectively, and when maximum and RMS displacements were less than 4.9 × 10−2 and 3.3 × 10−2 eV, respectively. Goethite is antiferromagnetic (AFM) below the Neél temperature of 130 °C,40 and the computational details of magnetic structure testing are provided in the SI (Table S3). In summary, four different magnetic orientations were tested (one FM and three AFM) with variations in spin orientation of the iron atoms changing along the b-axis of the single unit cell. The two lowest-energy configurations were AFM with Fe(III) spinup and spin-down alternating along the b-axis in a (+-+-) pattern, or a (+--+) pattern (see SI, Figure S1), with energies varying by only 5.4 × 10−3 eV. Based on comparison with experiment40 and other computational studies,26,38,41 the alternating (+-+-) AFM pattern was selected to describe the magnetic structure in goethite supercells, even though the (+--+) AFM ordering was lower in energy here. The variation in competition between lowest-energy magnetic structures is not unexpected based on the energetic similarities of those AFM orderings.42 Differences between results obtained here versus other computational studies may be reflective of UHF versus DFT computational approaches, respectively.

similar coordination environments for iron and oxygen atoms in the crystalline lattice.20 The most stable and most common iron oxyhydroxide in nature, goethite (α-FeOOH),21 was chosen for investigation because it is also a common steel corrosion product,22−24 and experiments demonstrate that goethite can incorporate Tc(IV) into its structure,13,14 as well as a variety of other cations with varying oxidation states, such as Al(III),25,26 Mn(III),27 Co(II),21 Sn(IV),28 and even U(VI).29 For the latter, simulations show strong agreement between theoretical and experimental bond lengths for U(V) or U(VI) incorporation for Fe(III) in the goethite structure, charge balanced by the creation of hydrogen vacancies (i.e., deprotonation).30 The purpose of this study is to explore different chargebalanced mechanisms for Tc(IV) incorporation into goethite on the atomic-scale to determine which one is most energetically favorable and, hence, most likely to occur in natural or engineered environments. In turn, the incorporation mechanism has implications for predicting Tc behavior in goethite under changing environmental or waste-processing conditions. While spectroscopic data points toward Tc(IV), rather than Tc(VII), incorporation in goethite in an octahedral coordination environment,13,14 the charge-balancing mechanism remains unresolved at present. Building off of experimental data,13,14 quantum-mechanical calculations were used to evaluate five different charge-balanced mechanisms for Tc(IV) incorporation in goethite. Theoretical incorporation energies are presented for the most stable cases, and optimized bond lengths are provided for comparison with experimental data. The role of hydrogen movement is explored in vacancydriven cases, as well as the importance of hydration energy corrections in general.

■

METHODS Computational Details. Charge-localized, quantum-mechanical calculations were used to explore possible Tc incorporation scenarios in bulk goethite. Specifically, the modeling software CRYSTAL1431 was used to calculate single-point energies and optimized geometries for crystalline compounds and gas-phase species at 0 K temperature. In CRYSTAL14, the electronic structure of each element is described by atomic orbitals, which are linear combinations of Gaussian-type functions.31 The overall electronic structure of the solid is, in turn, described by a linear combination of spacesymmetry adapted Bloch functions defined by the atomic orbitals.31 Basis sets were chosen for this study based on previous success in modeling Tc incorporation in iron oxide phases and include the Durand-21d41G effective core potential (ECP) for Fe3+ and Fe2+, the Durand-41G ECP basis sets for O2−,32 Pople’s 3-21 basis set for H+,33 and a 21d41 electron core pseudopotential for Tc(IV) optimized in a previous study using the Hay-Wadt large core pseudopotential.34 Fullgeometry optimization results from basis set testing are included in Table S1 of the Supporting Information (SI) and indicate that lattice parameters for representative iron oxides all fall within 2% of experimental data for Fe(II)O and αFe(III)2O3, whereas Tc(IV)O2 fall within 10% of experimental data. The large deviation of lattice parameters for TcO2 in the a parameter may indicate the need for taking correlation effects into consideration for unpaired electrons in this system; however, localized bonding environments in iron oxyhydroxide matrices are captured well, as will be demonstrated in the Results section. 13700

DOI: 10.1021/acs.est.5b03354 Environ. Sci. Technol. 2015, 49, 13699−13707

Article


Figure 1. Goethite supercells (2 × 2 × 2) representing (a) pure end-member, (b-e) H-vacancy cases: (b) nearest neighbor, (c) next-nearest neighbor, (d) to-the-left case, (e) next-nearest-neighbor inside, and (f) Fe(III)-vacancy case with three Tc(IV) in the bottom-left corner. Purple spheres are Fe(III) spin up, cyan spheres are Fe(III) spin down, yellow spheres are Tc(IV) with the same spin as the Fe(III) being replaced, red spheres are O2−, white spheres are H+, and black spheres represent H+ or Fe(III) vacancies.

Supercells. All single unit cells and supercells of goethite in this study were modeled after the lattice parameters and atomic positions described in Yang et al.,43 where a = 4.5979 Å, b = 9.9510 Å, and c = 3.0178 Å; α, β, and γ are all 90°. A single goethite unit cell is orthorhombic with Pbnm space-group symmetry and contains 16 atoms.42 In goethite, each iron atom is octahedrally coordinated by 3 oxygen atoms and 3 hydroxyl groups. Two Fe atoms in the center of the unit cell are edgesharing, and each of those Fe atoms shares a corner with an additional Fe atom at the top right and bottom left corners of the unit cell. When extended in three dimensions, all Fe atoms share edges with Fe atoms in neighboring unit cells, forming chains parallel to the c-axis (see Figure 1a). Another way to describe the unit cell is that half of the octahedral sites created by the oxygen sublattice are occupied by Fe atoms.44 A 2 × 2 × 2 supercell of goethite containing 8 formula unit cells and 128 atoms was generated so that variations of multiple Tc-incorporation schemes could be evaluated. In this system, there are 32 iron atoms, 32 hydrogen atoms, and 64 oxygen atoms. The substitution of one Tc atom for one Fe atom is approximately 3 atomic weight % impurity in the system, and for one case, up to 9 atomic weight % impurity was tested. While exact limits of Tc incorporation into goethite are not currently well established, this size supercell provides comparison with Tc incorporation levels observed in other iron oxide systems. For example, in prior studies of Tc

incorporation into hematite, 1−3 atomic weight % impurity loading was explored based on experimental data.34 Incorporation Energy Calculations. A variety of approaches exist for calculating the incorporation energy for trace elements in a solid-state structure, mainly differing in the reference phases used to perform the incorporation reaction (e.g., solids, aqueous species, and gas-phase ionic species).45 As in a previous study,34 Tc(IV) incorporation energies (Einc) are calculated relative to gas phase ions, as well as “pure” and “defect” solids in a “products” minus “reactants” approach. Eq 1 describes a charge-balanced substitution case where a Tc(IV)− Fe(II) pair replaces two lattice Fe(III) in goethite: Fe(II ) ‐ balanced goe‐pure goe ‐ defect Einc : Etot + nETc 4 + + nEFe2 + → Etot + 2nEFe3 + (1)

For convention, a positive Einc value suggests the defect state is not favorable relative to the pure state, while a negative value suggests that the substitution is energetically favorable and could take place. Here, Egoe‑pure and Egoe‑defect represent the tot tot optimized energies of 2 × 2 × 2 pure and defect goethite supercells, respectively, where atomic positions are allowed to relax but lattice parameters are held constant. For consistency in the calculations, lattice parameters for pure and defect goethite were held to experimentally determined values after Yang et al.43 Regarding the energies of the gas-phase ions (Tc4+, Fe2+, and Fe3+), a 0-dimensional (i.e., molecular), UHF approach was used in CRYSTAL14 that allows for energy 13701


Article


the goethite supercell. This calculation provides information about how strongly the ions are attracted to one another in the solid phase47 and is a calculated term arising from the challenge of measuring the energy of individual ions in the gas phase. Hydration Energy Corrections to Incorporation Energies. In order to translate gas-phase reference energies into species that would be more relevant under environmental or waste-processing conditions, the following corrections are applied once Einc have been calculated using the methodology described above. The first thermodynamic correction described below (reactions R1−R5) relates the free energy of Tc(VII)O4− (aq), the most prevalent environmental form of Tc in solution, to the Tc4+ ion reference state used in the determination of Einc. The difference in oxidation states means that the incorporation will be an electrochemical reaction. The correction is made through a series of hypothetical reactions, with known free energies based on reference data in the literature:

minimization of charged species. Energy values for these oxidized species are provided in Table S4 (SI) along with calculated ionization energies for comparison with experimental data based on the stepwise removal of electrons from a neutral atom to the desired oxidation state. Results indicate that for Fe3+ and Tc4+, ionization energies are within 3−4 eV of experimental values for the final ionization steps (e.g., Fe2+ to Fe3+ and Tc3+ to Tc4+) using the basis sets chosen for this study. For Fe, this equates to −11.5% versus experimental energies and for Tc, +6%. While the energy of lower ionization steps is not captured as accurately, this is to be expected as basis sets used here were optimized for structures bearing the highest oxidation states in most cases.32,34 For H+, the energy of the ion must be referenced to experimental data since there is no ground-state electron density to calculate; therefore, a value of 0.01 eV is used in this study.33 A total of five different incorporation scenarios for Tc(IV) in goethite were evaluated. As mentioned earlier, Tc(VII) incorporation was not considered in this study based on experimental evidence pointing to the incorporation of Tc(IV) in goethite.13,14 In addition to the Fe(II)-balanced case described in eq 1, four other cases represented by the equations below include a Tc(IV) lattice substitution for Fe(III) charge balanced by the removal of one hydrogen atom (“H-balanced”; eq 2), an interstitial Tc(IV) charged balanced by the removal of four nearest-neighbor hydrogen ions (“Interstitial”; eq 3), a Tc(IV) lattice substitution accompanied by the removal of two Fe(III)-hydroxyl groups (“2 FeOH”; eq 4), and a vacancy driven Tc(IV) case where three Tc(IV) replace four lattice Fe(III) (“Fe(III)-vacancy”; eq 5):

TcO4 −(aq) + 4H+(aq) + 3e− → TcO2 (s) + 2H 2O(l) (R1) +

(2) (3)

2FeOH goe ‐ pure goe ‐ defect Einc : Etot + nETc 4+ → Etot + 2nEFe3+ + 2nEO2−

+ 2nE H +

(4)

Fe(III ) ‐ vacancy goe ‐ pure goe ‐ defect Einc : Etot + 3nETc 4+ → Etot + 4nEFe3+

(5)

As for the original Tc(IV)/Fe(II) charge-balanced substitution for two lattice Fe(III), incorporation energies are calculated using a “products” minus “reactants” approach. The same gasphase ionization energies and total energy of the pure goethite phase are referenced in each calculation. The total energy of the “defect” substituted goethite is what varies in each case. While not considered explicitly in the calculations described here, the effect of hydration energies on the gas-phase ions and ultimately Einc is discussed in the Results section. Finally, lattice energies (Elat) were calculated for the pure and defect goethite phases. Lattice energy is equal to the energy of the solid phase (e.g., 2 × 2 × 2 goethite supercell) relative to the energy of the gas phase ions of the constituents at infinite separation.46 For pure goethite, the lattice energy calculation would be goe ‐ pure goe ‐ pure Elat = Etot − xEFe3+ − 2xEO2− − xE H +

TcO2 (s) + 4H (aq) + 4e → Tc(s) + 2H 2O(l)

(R2)

Tc(s) → Tc(g)

(R3)

Tc(g) → Tc 4 +(g)1atm,300K + 4e−

(R4)

Tc 4 +(g)1atm,300K → Tc 4 +(g)vac,0K

(R5)

The free energies for steps 1 and 2 can be determined from the Pourbaix atlas of electrochemical phase diagrams.48 The free energy for the third step is the decohesion energy of metallic Tc.8 The free energy for the fourth step is the ionization energy,49 and the electron can be referenced to the absolute hydrogen electrode potential using the value of 4.44 V.50 The final term can be determined using the SackurTetrode equation.51 Using standard conditions coinciding with a pH of 0, Eh = 0 V NHE and a pertechnetate concentration of 1 M, the total correction is +79.99 eV per Tc4+ ion. This correction by itself would make the incorporation energies strongly endothermic. As such, similar corrections need to be made for the Fe3+ and H+ product states of the incorporation reactions (e.g., eqs 1−5), which are described in the following section.

H ‐ balanced goe ‐ pure goe ‐ defect Einc : Etot + nETc 4 + → Etot + nEFe3 + + nE H +

Interstitial goe ‐ pure goe ‐ defect Einc : Etot + nETc 4+ → Etot + 4nE H +

−

■

RESULTS AND DISCUSSION Gas-Phase Incorporation Energies and Calculated Bond Lengths. Five different scenarios for Tc(IV) incorporation into the bulk goethite structure were evaluated. For each scenario, different distributions of Tc(IV) relative to the chargecompensation mechanism were tested resulting in a total of 35 unique cases. Specifically, 15 unique cases were tested for the Fe(II)-balanced case (eq 1); 8 unique cases for the H-balanced case (eq 2); 1 case for the interstitial mechanism (eq 3); 1 case for the removal of 2 Fe−OH groups (eq 4); and 10 unique cases for the vacancy-driven mechanism (eq 5). For incorporation schemes where more than one arrangement of Tc(IV) relative to the charge-compensating defect was tested, models differed by the atomic distances between Tc(IV) and the defect. An example of each incorporation model is shown in Figure S2 (SI), and results from the most stable incorporation schemes (H-vacancy and Fe(III)-vacancy driven), with respect to maintaining the correct spin density for Tc(IV), are illustrated in Figure 1. For all 35 cases, abbreviated geometry

(6)

where refers to the minimized energy of a 2 × 2 × 2 goethite supercell where experimental lattice parameters are held fixed while atomic positions are allowed to relax, and x refers to the stoichiometric number of Fe3+, O2−, and H+ ions in Egoe‑pure tot

13702


Article

Environmental Science & Technology Table 1. Total, Lattice, and Incorporation Energies for Tc(IV) Substitution into Goethitea case

wt % Tc

(a) pure goethite (b) H-vacancy (2.559 Å) nearest neighbor (c) H-vacancy (2.728 Å) next-nearest neighbor (d) H-vacancy (4.076 Å) to-the-left inside (e) H-vacancy (4.976 Å) next-nearest neighor inside (f) Fe(III)-vacancy corner case

0 3 3 3 3 9

Tc-defect dist (Å) 2.559 2.728 4.076 4.976 3.0183.438

Etot

Elat

Einc

Einc/# Tc

Einc/# Tc (eV)

−1713.35 −1702.93 −1702.92 −1702.91 −1702.92 −1662.28

−119.25 −120.14 −120.14 −120.13 −120.14 −121.60

−0.90 −0.89 −0.88 −0.89 −2.35

−0.90 −0.89 −0.88 −0.89 −0.78

−24.62 −24.30 −24.06 −24.21 −21.35

a

All energies are reported in Hartrees where 1 hartree (Ha) = 27.211 eV or 627.51 kcal/mol, unless otherwise noted. Cases (b−e) correlate to eq 2; case (f) correlates to eq 5.

geometry optimization. The two scenarios include 4 unique “Hvacancy” cases (i.e., eq 2) and 1 “Fe(III)-vacancy” case (i.e., eq 5). Incorporation energies reported in Table 1 are normalized to the number of Tc(IV) for Fe(III) substitutions made. Comparing incorporation energies, the “H-vacancy” scenario is the most energetically favorable followed by the “Fe(III)vacancy” scenario relative to gas-phase ionic species. The starting geometries for each of those incorporation scenarios are illustrated in Figure 1b−f, with a pure end-member goethite supercell shown in Figure 1a. For the H-vacancy scenario (eq 2; Figure 1b−e), Tc(IV)defect distances range from 2.559 Å−4.976 Å; however, incorporation energies do not vary significantly, nor systematically, depending on distance and are all very similar for this scenario (Table 1). This result suggests that a variety of protons within at least a 5 Å vicinity of Tc(IV) substituted for lattice Fe(III) may be used as favorable charge compensating mechanisms in goethite, even if they are not directly part of the immediate ⟨Tc−O,OH⟩ octahedral coordination environment. In Table 2a, Tc(IV) coordination environments are listed

optimization runs (e.g., 100 steps) were used to determine if the correct spin densities, and subsequently atomic charges, were maintained for Tc(IV), Fe(III), and, as applicable, Fe(II), based on Mulliken population analysis. Only the cases where the correct spin densities were maintained were evaluated further using longer (e.g., 999 steps) fixed-cell geometry optimizations. Since gas-phase ionic species with specific electronic configurations are used as reference phases, incorporation energies presented in Table 1 are for cases where Tc(IV) maintained a spin of 3 unpaired electrons and net spin was maintained between starting and optimized models. It should be noted that for the Fe(II) charge-balanced scenario (eq 1), one case appeared to maintain the correct spin density for Tc(IV) and Fe(II) for a short number of geometry optimization cycles (e.g., 100); however, upon being allowed to run for a larger number of optimization steps (e.g., 999), the energy became lower and the Tc became “reduced” to a Tc(III)-like state (i.e., having a spin of 4) and the Fe(II) became “oxidized” to a Fe(III)-like state (spin of 5). As such, energies were not included in Table 1; however, this case could warrant further investigation. Even though the gas-phase Einc is −0.46 eV/Tc(IV) and is not competitive versus energies reported in Table 1, the hydration energy corrected Einc is −2.33 eV/Tc(IV) and would be competitive if the spin distribution remained stable. In other instances, for the same Fe(II)-balanced case, Tc(IV) became oxidized to a Tc(V)-like state, and Fe(II) to an Fe(III)-like state, but it was unclear where the excess spin density was absorbed (i.e., net spin of metal cations was not maintained), and it likely was accommodated by O and H in the structure. While these results may point to some oxidation or reduction of substituted Tc(IV), it may also be the result of insufficient spacing between defect species, as was observed in previous studies investigating Tc(IV) and Fe(II) incorporation in hematite.34 Similar apparent oxidation and reduction results occurred for Tc(IV) interstitial cases (eq 3 and eq 4, respectively) with surrounding oxygen atoms likely taking-up or donating excess electron density. For clarity, comparisons in this study are kept to cases where spin density is comparable to Tc oxidation states observed experimentally (e.g., Tc(IV)).13,14 In Table 1, total energies, lattice energies, and incorporation energies are reported for the Tc(IV) incorporation cases where the correct spin density was maintained for ionic species in these systems. While four out of the five incorporation scenarios tested resulted in energetically favorable incorporation energies for Tc(IV) substitution into goethite, the exception being the case where Tc(IV) replaces two Fe(III)hydroxyl groups, only two out of the five scenarios led to cases where the assigned spin density was maintained upon fixed-cell

Table 2a. Optimized Tc(IV) Bond Lengths Tc-Substituted Goethite Supercellsb case

bonding pair

3 short (Å)

3 long (Å)

average (Å)

(b) H-vacancy nearest neighbor (c) H-vacancy nextnearest neighbor (d) H-vacancy to-theleft inside (e) H-vacancy nextnearest neighbor inside (f) Fe(III)-vacancy corner case (top 2 are from the same row)

⟨Tc(IV)−O,OH⟩

1.915

2.012

1.963

⟨Tc(IV)−O,OH⟩

1.918

2.025

1.971

⟨Tc(IV)−O,OH⟩

1.898

2.016

1.957

⟨Tc(IV)−O,OH⟩

1.928

2.044

1.986

⟨Tc(IV)−O,OH⟩

1.923 1.923 1.934 1.965

2.034 2.034 2.015 1.998

1.979 1.979 1.975 1.982

experiment (pure TcO2)a

(row w/ vacancy) ⟨Tc(IV)−O⟩

a

Rodriguez et al. (2007). bLetters before each case name correspond to images in Figure 1 (a−f). Cases (b−e) refer to eq 2; case (f) refers to eq 5.

for the “H-vacancy” cases; comparisons are made with existing data for pure TcO2 with the main difference being that Tc(IV) is in octahedral coordination with 6 oxygen atoms in TcO2 versus 3 oxygen and 3 hydroxyl groups in goethite. For the “Hvacancy” cases with the shortest Tc(IV)-defect distances (Figure 1b−d), the ⟨Tc−O,OH⟩ averaged bonding environment is contracted by approximately 1.3% relative to Tc(IV) in TcO2 (experimental). For the case with the longest Tc(IV)13703


Article

Environmental Science & Technology defect distance, the ⟨Tc−O,OH⟩ averaged bonding environment is 0.2% longer. In all cases, the difference between the longer ⟨Tc−OH⟩ and ⟨Tc−O⟩ bonds is approximately 0.1 Å opposed to the more uniform ⟨Tc−O⟩ bonding environment in TcO2 where all ⟨Tc−O⟩ shorter and longer bond lengths are within 0.03 Å of one another, suggesting that the goethite structure exerts similar control on the Tc(IV)-substituted Fe(III) site, regardless of the occupying cation (i.e., Fe(III) or Tc(IV)). For comparison with Tc-substituted goethite, averaged ⟨Tc−O,OH⟩ distances reported by Um et al.14 range from 2.014 to 2.020 Å, depending on the sample. This range of bond distances falls within the range of ⟨Fe−O,OH⟩ bond distances in pure goethite, both experimentally and from computer optimizations (Table 2b), supporting the likelihood

mechanism would be needed for direct comparison. The stability of the three Tc(IV) in the bottom left corner (Figure 1f) suggests that defects may cluster in the goethite structure since for cases where the three Tc(IV) ions were more spread out in the structure, the final spin densities were not maintained accurately. In terms of bonding environment, the ⟨Tc−O,OH⟩ averaged bond distances are all within 0.004 Å of one another and are within 0.25% of averaged ⟨Tc−O⟩ bond lengths in TcO2; however, differences between averaged short and long bond lengths for Tc(IV) substituted goethite are on the order of 0.1 Å versus 0.03 Å for TcO2 suggesting that even the clustered Tc(IV) ions maintain a goethite-like bonding environment rather than a TcO2-like bonding environment. When equivalent ⟨Fe(III)−O,OH⟩ bond distances were measured for a formula unit cell above and to the right of the substituted formula unit cell in the goethite supercell, ⟨Fe− O,OH⟩ bond distances were within 0.001−0.010 Å of experimental data and optimized pure goethite suggesting that the Fe(III) bonding environment in goethite is wellmaintained at least one unit cell away from the incorporated defects. The most striking observation for the Fe(III)-vacancy case is the movement of two protons from bridging hydroxyl groups one formula unit-cell above the Tc(IV)-substituted formula unit cell to bridging oxygen atoms between the Fe(III) vacancy and neighboring Tc(IV) ions (Figure 2). A second pair of

Table 2b. Optimized Fe(III) Bond Lengths for Pure and TcSubstituted Goethite Supercellsc case (a) Pure Goethite

(b) H-vacancy nearest neighbor (c) H-vacancy nextnearest neighbor (d) H-vacancy to-theleft inside (e) H-vacancy nextnearest neighbor inside (f) Fe(III)-vacancy corner case (top 2 are from the same row) experiment (pure α-FeOOH)a

bonding pair

3 short (Å)

3 long (Å)

average (Å)

⟨Fe(III)−O,OH⟩ (atom 2)b (atom 3) (atom 4) ⟨Fe(III)−O,OH⟩

1.962 1.961 1.962 1.962 1.951

2.097 2.097 2.096 2.097 2.102

2.029 2.029 2.029 2.029 2.027

⟨Fe(III)−O,OH⟩

1.968

2.082

2.025


1.954

2.099

2.026


1.954

2.105

2.030


1.970 1.970 1.952 1.948

2.080 2.080 2.117 2.104

2.025 2.025 2.035 2.026

(row w/ vacancy) ⟨Fe(III)−O,OH⟩

a

Yang et al., 2006. bAtom numbers refer to Fe(III) positions along the crystallographic b-axis (see Figure S1). cLetters before each case name correspond to images in Figure 1 (a−f). Cases (b−e) refer to eq 2; case (f) refers to eq 5. All Fe(III) measurements were made on atoms in equivalent positions in the unit cell above where the substitution occurred.

Figure 2. Optimized structure for Fe(III)-vacancy charge-balanced Tc(IV) incorporation model (corner). Note the movement of protons from the Fe(III)−Fe(III) bridging hydroxyl groups above the vacancy to the bridging oxygens closest to the Fe(III) vacancy (arrows). A second pair of bridging hydroxyls also moves from the hydroxyls in the top-left corner of the supercell to formerly bridging oxygens where at one Fe(III) bridges directly to the defect site or is in close proximity to the defect site. Also notice the distortion of H+ orientations surrounding the vacancy relative to other parts of the supercell. Yellow sticks are Tc(IV), purple sticks are Fe(III) spin up, cyan sticks are Fe(III) spin down, red sticks are O2−, and white sticks are H+.

of direct lattice substitution of Tc(IV) in goethite. For comparison, cases where Tc(IV) substitutes interstitially have starting ⟨Tc(IV)−O⟩ bond lengths of 1.630 to 2.706 Å. Bonding environments for Fe(III) were also measured in each optimized H-vacancy case for an Fe(III) site one formula unit cell directly above the Tc(IV) substituted location, and ⟨Fe− O,OH⟩ distances are within 0.005 Å of both experimental and simulated pure goethite. As such, distortion caused by the presence of Tc(IV) in the supercell appears to be localized. For the Fe(III)-vacancy driven case (eq 5, Figure 1f), incorporation energies are approximately 2.95 eV less favorable than for the H-vacancy case when normalized to the number of Tc being incorporated into the model. In a number of cases tested, one or two of the Tc ions, but not all, retained the correct spin density to represent Tc(IV); however, only the case where all three Tc remained as Tc(IV) is reported here. Compared with the H-vacancy case, the Fe(III) vacancy scenario could possibly come into play with increasing numbers of Tc(IV) ions substituting into the goethite structure; however, higher Tc-loading calculations for the H-balanced

protons from the top-left corner of the supercell is also observed to move to bridging oxygens associated with the Fe(III) defect through two lattice Fe(III) (Figure 2). Due to the creation of the vacancy, the nearest bridging oxygen atoms become undercoordinated with respect to electron density, as such, the movement of protons to those sites helps to alleviate some of that deficit. For the second pair, proton movement may be due to excess electron density on oxygens coordinated to Tc(IV) defects in the supercell above (see Figure S3 in the SI for discussion and comparison with fully relaxed cases). When comparing the left-hand side of the supercell in Figure 2 to the right-hand side, proton movement is localized to the left 13704


Article


the solution (TcO4− concentration and Fe3+ concentration) may shift this preference. A few elements missing from these rough free energy estimates include the entropy of the defects and vacancy states induced in the goethite lattice and the enthalpic and entropic terms for the solid phases based on lattice vibrations and additional degrees of configuration. Also, as mentioned above, changing the pH or electrochemical condition will vary the free energies and could lead to a difference in ordering among the preferred states. In summary, corrections for hydration energy of the reference ions suggest that under certain Eh-pH conditions, the Fe(III)-vacancy mechanism becomes lower in energy (and possibly more favorable) than the H-balanced state, making it also a competitive charge-balancing mechanism for Tc(IV) incorporation into the goethite structure depending on the environmental conditions. These corrections also highlight the importance of including reference-phase corrections in Einc calculations because of the profound effect they may have on interpreting the most energetically favorable incorporation mechanism. Implications for Tc Stability in Other Iron Oxides and in Waste Forms. One of the main conclusions from this study is that while two different Tc(IV) incorporation scenarios were found to be energetically favorable in goethite, the H-vacancy scenario appears to be favored over the Fe(III)-vacancy scenario at low-levels of impurity incorporation relative to gas-phase ions. When hydration energies of the gas-phase ions are included, the Fe(III)-vacancy scenario becomes more energetically competitive. These results have implications for Tc(IV) incorporation in other iron oxides because despite experimental and theoretical evidence pointing toward Tc(IV) occupying the octahedral Fe(III) lattice site in goethite,13,14 hematite,34 and magnetite,53 the preferred charge compensation mechanisms appear to be different depending on the host phase. For goethite, the favorability of the H-vacancy and Fe(III)-driven vacancy scenarios are supported by experimental evidence for Sn(IV) substitution in goethite where no increase in Fe(II) was measured using X-ray photoelectron spectroscopy (XPS), and empirical potential calculations favored a Fe(III)vacancy charge-compensation mechanism.54 In contrast, an increase in Fe(II) was measured in Ti(IV)-substituted thin films of hematite, also using XPS,55 suggesting that the Fe(II) charge-balancing mechanism is preferred in that phase. This mechanism is the same one that was tested using atomic-scale simulations for Tc(IV) versus Tc(VII)O4− incorporation in hematite, where Tc(IV)/Fe(II) substitution for two lattice Fe(III) was found to be energetically favorable, while the substitution of an interstitial pertechnetate anion for an Fe3O4+ vacancy charge balanced by the addition of two protons was not.34 More recently, experimental evidence for Tc(IV) incorporation into magnetite suggests that it prefers the octahedral Fe lattice site as in goethite and hematite.53 In contrast to goethite and hematite, studies on Tc(VII)O4− interaction with Ti(IV)-doped titanomagnetite suggest that the oxidation of octahedral Fe(II) to Fe(III) occurs to reduce Tc(VII)O4− to Tc(IV)O2, coupled with Fe(III) release and Tc(IV) incorporation into a ferrihydrite-like phase (i.e., an oxidative, vacancy-driven charge-compensation mechanism).56 Further investigation is needed to determine the exact factors guiding the preference of different charge-balancing mechanisms for the same substituent species in these materials. When dealing with high-level or low-activity nuclear waste generated by reprocessing of commercial or defense-related

half of the supercell bearing the Fe(III) vacancy and is not observed on the right where no Tc(IV) were substituted. Additionally, there is tilting of the protons surrounding the Fe(III) vacancy toward the defect site (e.g., in the nearest bridging hydroxyl groups). This distortion is not observed in other parts of the supercell, except for the formula unit cell above the one with the Fe(III) defect where bridging hydroxyls between Fe atom #2 and #3 (Figure 2) are slightly offset, likely tied to their proximity to the Fe(III) defect which would be in a formula unit cell immediately above them because of the 3-D periodic nature of the model. The movement of these protons suggests that there is an energy-lowering driver for using protons to offset over or underbonding that accompanies the formation of an Fe(III) vacancy used to neutralize Tc(IV) substitution in the goethite structure. This movement is plausible considering the transformation of goethite into hematite as a function of increasing temperature.44 For example, “protohematite” (i.e., α-Fe2−x/3(OH)xO3−x where x is the number of residual hydroxyls in the structure) is observed to retain extra protons in its structure to help charge balance the formation of Fe(III) vacancies, and protons were determined to be mobile in the structure.43 Effects of Hydration Energy on Incorporation Energies. Incorporation energy (Einc) values reported in Table 1 are referenced to the gas-phase ions Tc4+, Fe3+, Fe2+, and H+ in vacuum at 0 K. When converted to eV, it is apparent that the incorporation energies are all large and negative (∼−25 eV) with the implication that the incorporation of Tc will be spontaneous and liberate a significant amount of energy. However, in a geological scenario, the appropriate reference states would be closer to ambient temperatures and pressures and the hydrated states of the ions, with the caveat that Tc4+(aq) is not a stable phase. Rather, the more likely stable phase would be the pertechnetate anion TcO4−(aq). In order to assess whether this is the case for the incorporation of Tc4+ into goethite by the given mechanisms, thermodynamic arguments were used to approximate the free energy of incorporation with regards to these “environmental” reference states. A series of thermodynamic corrections are defined in the Methods section and then applied to the incorporation energies for the Hbalanced state and the Fe(III)-vacancy balanced state (Table 1). Changes to trends in incorporation energies as a result of hydration energy corrections are described below. For the case in which the displaced Fe3+ and a proton (H+) are used to provide the charge balance (eq 2), the compensating correction is provided by the hydration free energies of the Fe3+ ion and the proton. These amount to −10.88 eV for the proton and −44.20 eV for the Fe3+ ion.52 The Sackur-Tetrode entropic terms for the ions also need to be considered, −0.49 eV for Fe3+ and −0.34 eV for H+. Including all these terms together changes the incorporation energy to −0.54 eV per TcO4− ion. Thus, given the conditions assumed herein, it is expected that the goethite host will still favorably incorporate pertechnetate reduced to Tc(IV). The second case to consider is the replacement of 4Fe3+ ions with 3Tc4+ ions, leaving a Fe3+ vacancy in the lattice (eq 5). The incorporation energy is −21.35 eV using the gas phase ion reference states (see Table 1). Applying the corrections described above and normalizing to Tc yields an overall free energy of incorporation of −0.80 eV. Hence, there is a higher driving force to form this defect state under the assumed conditions, although changes in the pH and ionic chemistry of 13705



■

materials, Tc often becomes part of a liquid waste stream that must ultimately be solidified.6 Here, the importance of understanding the role of impurity retention in iron oxides and iron oxyhydroxides becomes critical when topotactic transformations are concerned, especially under extreme temperature conditions encountered during the vitrification process. For example, goethite is known to undergo a temperature-driven transition to hematite at between 200 and 270 °C.44 As such, if goethite were a primary host for Tc(IV), then incorporated into a glassy matrix at elevated temperatures, it is critical not only to understand how stable Tc is in the resulting iron oxide phase (e.g., hematite) but also to know how stable impurities are under changing conditions (e.g., the effect of temperature on impurity diffusion within the crystal lattice). Impurities in iron oxides and iron oxyhydroxides can also have effects on the transition temperatures between allotropes or between topotactic transformations between one compound and another (e.g., Co-substituted magnetite).57 By determining the most energetically preferred mechanisms for impurity incorporation in iron oxides and iron oxyhydroxides, a more fundamental understanding of impurity stability in these related phases begins to emerge that can better inform our predictions of material behavior under changing environmental and waste form processing conditions.

■

REFERENCES

(1) Ansolabehere, S.; Deutch, J.; Driscoll, M.; Gray, P. E.; Holdren, J. P.; Joskow, P. L.; Lester, R. K.; Moniz, E. J.; Todreas, N. E.; Jeckjord, E. S.; Hottle, N.; Jones, C.; Parent, E. The Future of Nuclear Power; Massachusetts Institute of Technology: Cambridge, MA, 2003. (2) Choppin, G.; Liljenzin, J.-O.; Rydberg, J. Radiochemistry and Nuclear Chemistry; Butterworth-Heinemann: Woburn, MA, 2002. (3) Lieser, K. H.; Bauscher, C. Technetium in the hydrosphere and in the geosphere I. Chemistry of technetium and iron in natural waters and influence of the redox potential on the sorption of technetium. Radiochim. Acta 1987, 42, 205−213. (4) Meyer, R. E.; Arnold, W. D.; Case, F. I.; O’Kelley, G. D. Solubilities of Tc(IV) oxides. Radiochim. Acta 1991, 55 (1), 11−18. (5) Gephart, R. E. A short history of waste management at the Hanford Site. Phys. Chem. Earth 2010, 35, 298−306. (6) McCloy, J. S.; Riley, B. J.; Goel, A.; Liezers, M.; Schweiger, M. J.; Rodriguez, C. P.; Hrma, P.; Kim, D.-S.; Lukens, W. W.; Kruger, A. A. Rhenium solubility in borosilicate nuclear waste glass: Implications for the processing and immobilization of technetium-99. Environ. Sci. Technol. 2012, 46, 12616−12622. (7) Darab, J. G.; Smith, P. A. Chemistry of technetium and rhenium species during low-level radioactive waste vitrification. Chem. Mater. 1996, 8, 1004−1021. (8) Taylor, C. D. Cohesive relations for surface atoms in the irontechnetium binary system. J. Metall. 2011, 2011, 954170. (9) Taylor, C. D. Surface segregation and adsorption effects of irontechnetium alloys from first-principles. J. Nucl. Mater. 2011, 408, 183− 187. (10) Livens, F. R.; Jones, M. J.; Hynes, A. J.; Charnock, J. M.; Mosselmans, J. F. W.; Hennig, C.; Steele, H.; Collison, D.; Vaughan, D. J.; Pattrick, R. A. D.; Reed, W. A.; Moyes, L. N. X-ray absorption spectroscopy studies of reactions of technetium, uranium and neptunium with mackinawite. J. Environ. Radioact. 2004, 74, 211−219. (11) Liu, Y.; Terry, J.; Jurisson, S. Pertechnetate immobilization with amorphous iron sulfide. Radiochim. Acta 2008, 96, 823−833. (12) Fan, D.; Anitori, R. P.; Tebo, B. M.; Tratnyek, P. G.; Pacheco, J. S. L.; Kukkadapu, R. K.; Kovarik, L.; Engelhard, M. H.; Bowden, M. E. Oxidative remobilization of technetium sequestered by sulfidetransformed nano-zerovalent iron. Environ. Sci. Technol. 2014, 48, 7409−7417. (13) Um, W.; Chang, H.-S.; Icenhower, J. P.; Lukens, W. W.; Serne, R. J.; Qafoku, N. P.; Kukkadapu, R. K.; Westik, J. H. J. Iron oxide waste form for stabilizing 99Tc. J. Nucl. Mater. 2012, 429, 201−209. (14) Um, W.; Chang, H.-S.; Icenhower, J. P.; Lukens, W. W.; Serne, R. J.; Qafoku, N. P.; Westik, J. H. J.; Buck, E. C.; Smith, S. C. Immobilization of 99-technetium (VII) by Fe(II)-goethite and limited reoxidation. Environ. Sci. Technol. 2011, 45, 4904−4913. (15) Ferriss, E. D. A.; Helean, K. B.; Bryan, C. R.; Brady, P. V.; Ewing, R. C. UO2 corrosion in an iron waste package. J. Nucl. Mater. 2009, 384, 130−139. (16) Carbol, P.; Fors, P.; Gouder, T.; Spahiu, K. Hydrogen suppresses UO2 corrosion. Geochim. Cosmochim. Acta 2009, 73, 4366−4375. (17) Cornell, R. M.; Schwertmann, U. The Iron Oxides: Structure, Properties, Reactions, Occurrences and Uses, 2nd ed.; Wiley-VCH Verlag GmbH & Co: KGaA: Weinheim, FRG, 2003. (18) Navrotsky, A.; Mazeina, L.; Majzlan, J. Size-driven structural and thermodynamic complexity in iron oxides. Science 2008, 319, 1635− 1638. (19) Freeze, G.; Gardner, W. P.; Vaughn, P.; Sevougian, S. D.; Mariner, P.; Mousseau, V.; Hammond, G. Enhancements to Generic Disposal System Modeling Capabilities; Sandia National Laboratories: Albuquerque, NM, 2013. (20) Cudennec, Y.; Lecerf, A. Topotactic transformations of goethite and lepidocrocite into hematite and maghemite. Solid State Sci. 2005, 7, 520−529. (21) Alvarez, M.; Sileo, E. E.; Rueda, E. H. Structure and reactivity of synthetic Co-substituted goethites. Am. Mineral. 2008, 93, 584−590.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.5b03354. Basis set testing, parameter space testing, magnetic structure testing, gas phase ionization energies, starting models for all five Tc(IV) incorporation scenarios in goethite, and details about hydrogen movement (PDF)

■

Article

AUTHOR INFORMATION

Corresponding Author

*Phone: 509-375-5645. Fax: 509-375-5684. E-mail: frances. [email protected]. Corresponding author address: Pacific Northwest National Laboratory, P.O. Box 999, MS-IN P7-25, Richland, WA 99352. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was performed under activities FT-13PN030416 Metal Corrosion Mechanisms and FT-14PN080404 Waste Form Degradation Modeling funded by the U.S. Department of Energy (DOE) Fuel Cycle Research and Development and Used Fuel Disposition Campaigns. The authors are grateful for additional support from the U.S. DOE Office of River Protection to complete this work. F.N.S. thanks D. J. Sassani, E. Kim, X. Liu, W. L. Ebert, J. D. Vienna, and E. C. Buck for insightful conversations and guidance regarding this work. This research was performed using PNNL Institutional Computing at Pacific Northwest National Laboratory. F.N.S. gratefully acknowledges T. S. Carlson and K. R. Glaesemann for computational support. The authors thank the Editor and four anonymous reviewers for their helpful comments to help strengthen this manuscript. 13706


Article

Environmental Science & Technology (22) Oh, S. J.; Cook, D. C.; Townsend, H. E. Atmospheric corrosion of different steels in marine, rural and industrial environments. Corros. Sci. 1999, 41, 1687−1702. (23) Dodge, C. J.; Francis, A. J.; Gillow, J. B.; Halada, G. P.; Eng, C.; Clayton, C. R. Association of uranium with iron oxides tpically formed on corroding steel surfaces. Environ. Sci. Technol. 2002, 36, 3504− 3511. (24) Betancur, J. D.; Barrero, C. A.; Greneche, J. M.; Goya, G. F. The effect of water content on the magnetic and structural properties of goethite. J. Alloys Compd. 2004, 369, 247−251. (25) Manceau, A.; Gates, W. P. Incorporation of Al in iron oxyhydroxides: implications for the structure of ferrihydrite. Clay Miner. 2013, 48, 481−489. (26) Fuente, S. A.; Belelli, P. G.; Castellani, N. J.; Avena, M. LDA + U and GGA + U studies of Al-rich and bulk goethite (α-FeOOH). Mater. Chem. Phys. 2013, 137, 1012−1020. (27) Alvarez, M.; Rueda, E. H.; Sileo, E. Simultaneous incorporation of Mn and Al in the goethite structure. Geochim. Cosmochim. Acta 2007, 71, 1009−1020. (28) Berry, F. J.; Helgason, Ö .; Bohórquez, A.; Marco, J. F.; McManus, J.; Moore, E. A.; Mørup, S.; Wynn, P. G. Preparation and characterization of tin-doped α-FeOOH (goethite). J. Mater. Chem. 2000, 10, 1643−1648. (29) Nico, P. S.; Stewart, B. D.; Fendorf, S. Incorporation of oxidized uranium into Fe (hydr)oxides during Fe(II) catalyzed remineralization. Environ. Sci. Technol. 2009, 43, 7391−7396. (30) Kerisit, S.; Felmy, A. R.; Ilton, E. S. Atomistic simulations of uranium incorporation into iron (hydr)oxides. Environ. Sci. Technol. 2011, 45, 2770−2776. (31) Dovesi, R.; Saunder, V. R.; Roettie, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, P.; Llunell, M.; Causà, M.; Noël, Y. CRYSTAL14 User’s Manual; Torino, 2014. (32) Iordanova, N.; Dupuis, M.; Rosso, K. M. Charge transport in metal oxides: A theoretical study of hematite α-Fe2O3. J. Chem. Phys. 2005, 122, 144305−1−10. (33) Hehre, W. J.; Radom, L.; Schleyer, P. V. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (34) Skomurski, F. N.; Rosso, K. M.; Krupka, K. M.; McGrail, B. P. Technetium incorporation into hematite (α-Fe2O3). Environ. Sci. Technol. 2010, 44, 5855−5861. (35) Skomurski, F. N.; Kerisit, S.; Rosso, K. M. Structure, charge distribution, and electron hopping dynamics in magnetite (Fe3O4) (100) surfaces from first principles. Geochim. Cosmochim. Acta 2010, 74, 4234−4248. (36) Mulliken, R. S. Electronic populations analysis on LCAO-MO molecular wave functions. I. J. Chem. Phys. 1955, 23 (10), 1833−1840. (37) Rosso, K. M.; Smith, D. M.; Dupuis, M. An ab initio model of electron transport in hematite (α-Fe2O3) basal planes. J. Chem. Phys. 2003, 118 (14), 6455−6466. (38) Alexandrov, V.; Rosso, K. M. Electron transport in pure and substituted iron oxyhydroxides by small-polaron migration. J. Chem. Phys. 2014, 140, 234701−1−8. (39) Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13 (12), 5188−5192. (40) Forsyth, J. B.; Hedley, I. G.; Johnson, C. E. The magnetic structure and hyperfine field of goethite (α-FeOOH). J. Phys. C: Solid State Phys. 1968, 1 (1), 179−188. (41) Guo, H.; Barnard, A. S. Modeling the iron oxides and oxyhydroxides for the prediction of environmentally sensitive phase transformations. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 1−18. (42) Pankhurst, Q. A.; Fernández Barquín, L.; Lord, J. S.; Amato, A.; Zimmermann, U. Intrinsic magnetic relaxation in goethite. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 1−11. (43) Yang, H.; Lu, R.; Downs, R. T.; Costin, G. Goethite, αFeO(OH), from single-crystal data. Acta Crystallogr., Sect. E: Struct. Rep. Online 2006, 62, i250−i252.

(44) Gualtieri, A. F.; Venturelli, P. In situ study of the goethitehematite phase transformation by real time synchrotron powder diffraction. Am. Mineral. 1999, 84, 895−904. (45) Shuller-Nickles, L. C.; Bender, W. M.; Walker, S. M.; Becker, U. Quantum-mechanical methods for quantifying incorporation of contaminants in proximal minerals. Minerals 2014, 4, 690−715. (46) Kittel, C. Introduction to Solid State Physics; John Wiley & Sons, Inc.: Hoboken, NJ, 2004. (47) Zumdahl, S. S. Chemistry, 4th ed.; Houghton Mifflin Company: Boston, MA, 1997. (48) Deltombe, E.; deZoubov, N.; Pourbaix, M. Atlas of Electrochemical Equilibria in Aqueous Solutions; National Association of Corrosion Engineers: Houston, TX, 1974. (49) NIST, Atomic Spectra Database Ionization Energies Form. http://physics.nist.gov/PhysRefData/ASD/ionEnergy.html (accessed Oct 1, 2015). (50) Reiss, A.; Heller, A. The absolute potential of the standard hydrogen electrode: a new estimate. J. Phys. Chem. 1985, 89 (20), 4207−4213. (51) Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, UK, 1998. (52) Marcus, Y. Thermodynamics of solvation of ions. Part 5. Gibbs Free Energy of Hydration at 298.15 K. J. Chem. Soc., Faraday Trans. 1991, 87 (18), 2995−2999. (53) Marshall, T. A.; Morris, K.; Law, G. T. W.; Mosselmans, J. F. W.; Bots, P.; Parry, S. A.; Shaw, S. Incorporation and retention of 99Tc(IV) in magnetite under high pH conditions. Environ. Sci. Technol. 2014, 48, 11853−11862. (54) Berry, F. J.; Helgason, Ö .; Bohórquez, A.; Marco, J. F.; McManus, J.; Moore, E. A.; Mørup, S.; Wynn, P. G. Preparation and characterisation of tin-doped α-FeOOH (goethite). J. Mater. Chem. 2000, 10, 1643−1648. (55) Droubay, T.; Rosso, K. M.; Heald, S. M.; McCready, D. E.; Wang, C. M.; Chambers, S. A. Structure, magnetism, and conductivity in epitaxial Ti-doped α-Fe2O3 hematite: Experiment and density functional theory calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 104412. (56) Liu, J.; Pearce, C. I.; Qafoku, O.; Arenholz, E.; Heald, S. M.; Rosso, K. M. Tc(VII) reduction kinetics by titanomagnetite (Fe3‑xTixO4) nanoparticles. Geochim. Cosmochim. Acta 2012, 92, 67− 81. (57) Pati, S. S.; Gopinath, S.; Panneerselvam, G.; Antony, M. P.; Philp, J. High temperature phase transformation studies in magnetite nanoparticles doped with Co2+ ion. J. Appl. Phys. 2012, 112, 054320.

13707


Technetium Incorporation into Goethite (Î±-FeOOH): An Atomic-Scale

Recommend Documents