Roles of Hydration and Magnetism on the Structure of Ferrihydrite from

(2,3,6,7) Its origins include biotic(8−11) and abiotic(12,13) aqueous Fe(II) oxidation ... hence, requiring careful control over temperature, pH, an...
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Roles of Hydration and Magnetism on the Structure of Ferrihydrite from First Principles Michel Sassi* and Kevin M. Rosso Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States

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S Supporting Information *

ABSTRACT: We report density functional theory calculations aimed at predicting thermodynamically stable structures for ferrihydrite across a range of possible compositions determined by the amount of structural water. Based on an assumed formula unit of Fe5O8H + nH2O, we performed ab initio calculations with evolutionary searching to find the lowest enthalpy structures as a function of the water content up to n = 2. This is the most exhaustive search for the ferrihydrite structure conducted so far; more than 5000 unique configurations were generated and evaluated over five states of hydration. Among them, the Michel akdaliate model was generated, along with several energetically comparable new structures at higher states of hydration. However, a direct comparison between calculated and experimental pair distribution function and X-ray diffraction patterns for the 50 lowest energy structures shows that none beyond the Michel model could be associated with ferrihydrite. Nevertheless, this energetically comparable structure set provides a novel basis for analyzing and understanding the effects of hydration and magnetism on the topology of ferrihydrite, from which we conclude that any tetrahedral Fe should be viewed as a metastable structural defect, created either as a result of the rapid kinetics of crystal growth or to accommodate a local magnetic stress between neighboring Fe atoms. KEYWORDS: ferrihydrite, hydration, density functional theory, structure, magnetism, tetrahedral iron, composition

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INTRODUCTION Named by Chukhrov et al.1 in 1973, ferrihydrite is one of the most important and enigmatic minerals of the iron oxide family. Ferrihydrite is a thermodynamically unstable2 poorly crystalline Fe(III)-oxyhydroxide and an important precursor to more stable goethite3−6 and hematite.2,3,6,7 Its origins include biotic8−11 and abiotic12,13 aqueous Fe(II) oxidation pathways, with a span of occurrence that likely includes extraterrestrial settings.14 Ferrihydrite exists exclusively as nanoparticles generally ranging from 2 to 10 nm in size and is thus categorized as a nanomineral.15 Despite a plethora of ongoing research since its first successful X-ray diffraction (XRD) analysis in 1966 by van der Giessen16 and then in 1967 by Towe and Bradley,17 a unequivocal description of the structure and composition of ferrihydrite remains elusive.18−20 Part of the challenge stems from the fact that ferrihydrite is variable in crystallinity and composition, being sensitive to the conditions of its formation and, hence, requiring careful control over temperature, pH, and the presence, type, and concentration of other ions in solution. The extent of structural ordering is generally categorized on the basis of the number of reflections present in the XRD pattern, yielding the convention of either two-line or six-line ferrihydrite. Over the past few decades, several detailed models for the structure of six- and © XXXX American Chemical Society

two-line ferrihydrite have been proposed, essentially based on XRD, neutron diffraction, and/or pair distribution function (PDF) analyses, but none so far have been unanimously accepted. Generally accepted notions about differences between two- and six-line ferrihydrite include that the former is more hydrated, with a OH/Fe ratio close to 1, is less ordered, and is the preferred phase for small particle sizes of about 3−4 nm.21 In the case of six-line ferrihydrite, which tends to be favored during precipitation at mildly elevated temperature, one aspect of the debate focuses on whether or not it contains tetrahedrally coordinated iron. Many studies have been devoted to resolve its controversial presence in the structure. For example, Mössbauer spectroscopy does not support the presence of tetrahedral Fe,22,23 whereas other experiments, mostly based on X-ray spectroscopy such as X-ray absorption near-edge structure (XANES) and X-ray magnetic circular dichroism (XMCD), provide evidence of the presence of tetrahedral Fe.24−26 From X-ray absorption fine structure Received: Revised: Accepted: Published: A

September 28, 2018 November 17, 2018 November 19, 2018 November 19, 2018 DOI: 10.1021/acsearthspacechem.8b00138 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry

The purpose of the present study is to exploit the ability of density functional theory (DFT) calculations to develop a fundamental understanding of the prospective relationship between various proposed ferrihydrite structures and water content. Critical attention is also given to magnetic structure effects, also readily accessible information from DFT. On the basis of prior work, one can already observe potential links between the structures and compositions of the most popular ferrihydrite models. In particular, it seems that a high OH/Fe ratio would tend to favor structures with octahedral Fe only, whereas a low OH/Fe ratio could lead to the presence of tetrahedral Fe in the structure. For example, the Drits and Manceau models, which contain only octahedral Fe, have stoichiometries of Fe5O12H9 and FeOOH formula units, giving an OH/Fe ratio of 1.8 and 1.0, respectively. However, the Michel model, which entails some structural tetrahedral Fe, has a stoichiometry of Fe5O8H, giving an OH/Fe ratio of 0.2. Furthermore, potentially useful structural clues may reside in the differences between the magnetic ordering in the Manceau and the Drits models, revisited by Jansen et al.,34 and that of the Michel model. Although the Manceau and Drits models are antiferromagnetic,47 the Michel model is ferrimagnetic. This suggests a possibly “universal” principle that magnetism in ferrihydrite generally arises primarily from tetrahedral Fe. Given the high surface-to-core Fe ratio, however, exceptions related to the properties of the surface such as defects, which are more difficult to isolate, cannot be excluded. For example, in cases where ferrihydrite is described by the Michel model, recent studies have shown that both the particle size48 and surface structure49 can affect its magnetic behavior. As has been done in the two prior DFT studies of the ferrihydrite structure, which focused on determining the thermodynamic, structural, and magnetic properties50 of the Michel model and on proton compensated iron vacancies,51 for simplicity, the current study also focuses on building an understanding of relationships within the computational framework of “virtual bulk lattices”. Surface structure effects will be explicitly treated in future follow-on work. However, different from prior DFT studies, which exclusively assume the Michel model topology and composition, here by performing DFT simulations coupled with an evolutionary searching algorithm we objectively explore a broad swath of conformation space for thermodynamically stable structure possibilities, doing this repeatedly for a variety of ferrihydrite formulas each bearing different water contents. Therefore, our calculations not only put the exclusivity of the Michel model to the test for the first time, they also enable predictions of possible energetically competitive “intermediate” structures that could have been overlooked. Five compositions of [Fe5O8H.nH2O] stoichiometry, where n = 0, 0.5, 1, 1.5, and 2, were explored. For each case, the evolutionary algorithm builds upon the calculated energies of generated structures to comprehensively explore the potential energy surface and find the lowest energy structure for a given composition. Out of this exercise, not only is the Michel model objectively “discovered”, but critical analysis of the three most energetically competitive hypothetical new structures on the basis of their theoretical XRD patterns and PDF shows that among the four only the Michel model is capable of describing ferrihydrite observables.

(XAFS) and XANES studies, it has been proposed that tetrahedral Fe arises from coordinatively unsaturated sites at the ferrihydrite surface,27,28 but that the “core” only contains octahedral Fe. An amount of 20−30% of coordinatively unsaturated tetrahedral Fe has been proposed, but arguments persist against it.29 It is interesting to note that experiments investigating the incorporation of Ge in ferrihydrite are, at the same time, both supportive30 and against31 the presence of tetrahedral Fe. For many years, the most popular model for six-line ferrihydrite, developed by Drits et al.,32 was a multiphase model having a hexagonal lattice (space group P31c) comprising 100% octahedral Fe. Initially, this model, obtained by comparing experimental and calculated XRD and XAFS spectra,33 was made of a mixture of three components, defectfree (f-phase) and defective (d-phase) ferrihydrite and ultradispersed hematite. Later it was shown that ultradispersed hematite was not necessary to obtain a good fit to the neutron diffraction pattern for six-line ferrihydrite.34 More recently, Michel et al.21,35 used real-space PDF data to develop a singlephase hexagonal model isostructural with the akdalaite mineral (Al10O14(OH)2) (space group P63mc), containing 20% tetrahedral Fe and low defect content. This model, although successful in many respects, also has been criticized beyond the controversial topic of tetrahedral Fe, based on subtle inconsistencies with XRD patterns, and that the formula unit (Fe10O14(OH)2) is anomalously H-poor compared to certain measurements of ferrihydrite.36,37 Although the Drits and Michel models each show generally satisfying agreement with XRD and PDF, respectively, neither agree fully with both measurements simultaneously. However, the most recent ferrihydrite model to date, proposed by Manceau,38 has been obtained by comparing both calculated and experimental PDF and XRD patterns. This model is comprised only of octahedral Fe, occupying 50% of the available sites in a hexagonal lattice with the space group P63mc. An aspect of this structure debate that remains poorly developed is its possible relationship with composition, because the amounts of OH and H2O relative to Fe in ferrihydrite are known to be variable.17,39−42 In particular, because a precise separation of structural hydroxyl and water from physically sorbed water is difficult, several chemical formula for ferrihydrite have been proposed43 such as Fe(OH) 3 , 19,44 5Fe 2 O 3 ·9H 2 O, 45 Fe 2 O 3 ·3H 2 O, 18 Fe 2 O 3 · 2H2O,18 FeOOH,38 and Fe5O8H,21,35 with the initially suggested Fe5O8H.4H2O17,45 formula being the most widely accepted though deemed excessively hydrous.19 Additionally, it is interesting to note that PDF analysis of neutron scattering measurements from deuterated two-line ferrihydrite46 have reinforced a picture that the core of ferrihydrite has the Fe5O8H stoichiometry, similar to the model proposed by Michel et al.35 for six-line ferrihydrite, leading to the suggestion that any additional water is mostly concentrated at particle surfaces. Using Fe5O8H as the basic formula unit for ferrihydrite, the range in the various water contents proposed can be illustrated by rewriting the formulas cited above as Fe5O8H·7H2O, Fe5O8H·4.5H2O, Fe5O8H·4H2O, Fe5O8H· 2H2O, and Fe5O8H, indicating that the potential amount of structural OH and H2O can vary from 0 to 7 H2O equivalents. Considering that these values correspond to ferrihydrites synthesized in the laboratory under highly controlled conditions, this range of uncertainty is remarkable.

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COMPUTATIONAL DETAILS In this study, two series of computational simulations were performed. In both cases the generalized gradient approxB

DOI: 10.1021/acsearthspacechem.8b00138 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry

Table 1. Unit Cell Composition, Structural Details, Symmetry, Lattice Parameters, and Energy Difference at the GGA+U Level of Theory of the Lowest Energy Structures Generated by USPEX for Different Values of na n

unit cell composition and structural details

0 0

Fe10O16H2−Michel, 20% IVFe, 80% VIFe Fe10O16H2, 100% VIFe, face sharing

1 2

Fe10O18H6, 100% VIFe, face sharing Fe10O20H10 100% VIFe, face sharing

0

Fe10O16H2−Michel ferrimagnetic, 20% IVFe, 80% VIFe Fe10O16H2 antiferromagnetic, 100% VIFe, face sharing Fe10O18H6 antiferromagnetic, 100% VIFe, face sharing Fe10O20H10 ferrimagnetic, 20% IVFe, 80% VIFe

0 1 2

Bravais lattice (Symmetry)

a (Å)

b (Å)

Nonmagnetic structures hexagonal (P63mc #186) 5.680 5.680 orthorhombic 5.290 5.290 (Cmc21 #36) monoclinic (Cc #9) 5.030 6.345 triclinic (P1 #1) 6.829 6.842 Magnetic structures 5.866 hexagonal (P63mc #186) 5.866

c (Å)

α (deg)

β (deg)

γ (deg)

ΔEGGA+U (eV/cell)

8.821 9.570

90.00 90.00

90.00 90.00

120.00 113.97

0.00 −0.49

9.568 9.516

103.94 102.62

90.00 85.09

113.31 129.28

−0.29 −0.39

9.374

90.00

90.00

120.00

0.00

orthorhombic (Cmc21 #36) monoclinic (Cc #9)

5.683

5.683

9.939

90.00

90.00

116.59

+0.10

5.151

6.641

10.495

102.05

90.00

112.81

+0.07

triclinic (P1 #1)

7.031

7.041

10.103

102.18

85.34

128.35

−0.35

The structure of the reference used to calculate the energy difference, ΔEGGA+U, for the nonmagnetic and magnetic cases is the nonmagnetic and ferrimagnetic Michel model, respectively. For stoichiometry balance, the calculation of the energy difference also used the energy of water molecules in the gas phase. a

cell is not the same. Indeed, to find goethite or lepidocrocite, an integer multiple of four FeOOH formula units per unit cell is required, but in this work we have 10 FeOOH per unit cell. This is an example of how constraint (ii) listed above limits the structural search. In the USPEX approach, the first generation counted an initial population of 70 randomly initialized structures satisfying the lattice parameters given. All subsequent generations counted a population of 50 structures, which were produced from the 60% lowest energy structures of the previous generation by using four variation operators. The half of the generation (25 structures) was produced by heredity, 16% (8 structures) were produced randomly, 20% (10 structures) were produced by soft-mutation, and 14% (7 structures) were produced by permutation. Additionally, each new generation counted the five lowest energy structures kept from the previous generation. Convergence of the structural search was achieved when the same structure was the lowest energy structure for ten consecutive generations. To ensure that each structure generated by the USPEX code was structurally and energetically well converged, optimization of the lattice parameters and atomic coordinates was done in five stages with increasing computational accuracy. The convergence criterion of the three last stages of optimization used a cutoff energy of the projector augmented wave57 pseudopotential of 520 eV and a γ-centered k-points mesh of 6 × 6 × 4 for the sampling of the Brillouin zone. The total energy was converged to 10−5 eV/cell and the force components were relaxed to below 10−3 eV/Å. Because the number of possible structural combination is important, we have performed the structural searches for nonmagnetic crystals. This simplification avoided the need to evaluate the same structure with different magnetic ordering, which greatly reduces the number of calculations, and hence the computational cost, and also allowed to use the atomic arrangement as the only reference for energy comparison. Altogether, the structural search has generated and evaluated 5236 unique structures, which represents the largest theoretical structural investigation ever performed for ferrihydrite. Because of the significant computational expense of the structure searching part in the USPEX calculations we relied

imation (GGA) and the Perdew−Burke−Ernzerhof (PBE) parametrization52 exchange-correlation functional were used. The first series of calculations focuses on the structure search, which was performed using the evolutionary algorithm implemented in the USPEX code,53,54 combined with the DFT formalism of the VASP package.55,56 The exploration of the structural possibilities has been constrained by two assumptions: (i) The compounds are based on the Fe5O8H formula with chemical species having an oxidation state of Fe3+, O2−, and H+ such that the unit cell is charge neutral. Therefore, adding structural water molecules preserve the charge neutrality of the unit cell without affecting the oxidation state or the number of iron atoms present in the unit cell. (ii) Each unit cell is exactly made of two [Fe5O8H + nH2O] units. Although this considerably reduces the number of possibilities for structural prediction, such that a structure having a slightly different composition as would be obtained by defects or a variation of the unit cell density will not be found, the list of formula units discussed in the Introduction suggests that a structure for ferrihydrite made of two [Fe5O8H + nH2O] units is a good focus point. Five structure searches were conducted, each with a composition of two [Fe5O8H + nH2O] per unit cell, by varying the amount of water in the structure such that n = 0, 0.5, 1, 1.5, and 2. For n = 0, the initial lattice parameters of the unit cell used for the creation of each structure were a = b = 5.928 Å, c = 9.363 Å, α = β = 90°, and γ = 120°, and the chemical composition of the unit cell was Fe10O16H2 (28 atoms/cell), which is exactly the same stoichiometry as that in the Michel model. For n = 0.5, 1, 1.5, and 2, the initial lattice parameters of the unit cell used for the creation of each structure were slightly increased to a = b = 6.300 Å, c = 9.400 Å, α = β = 90°, and γ = 120°, in order to accommodate the addition of water molecules, and the chemical composition of the unit cells were Fe10O17H4 (31 atoms/cell), Fe10O18H6 (34 atoms/cell), Fe10O19H8 (37 atoms/cell), and Fe10O20H10 (40 atoms/cell), respectively. For n = 2, we could rewrite the composition of the unit cell as ten FeOOH formula units. This means that we have the same stoichiometry as goethite or lepidocrocite. However, the approach taken cannot find these two minerals because the number of formula units in the unit C

DOI: 10.1021/acsearthspacechem.8b00138 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry upon a nonmagnetic treatment. Subsequently, we performed a second series of simulations for the ten lowest energy nonmagnetic structures found, taking into account magnetic ordering possibilities. It was generally observed that taking into account the magnetism could change the relative energy ordering of the few lowest energy structures with similar nonmagnetic energies (i.e., ∼0.5 eV/cell) but never resulted in a major inversion of thermodynamically least-stable outliers. For all these structures, a very accurate lattice and atomic coordinate optimization was performed, and the magnetic ground state was identified. The position of each hydrogen atom was carefully investigated by creating several structures with different positions for H. For this series of calculations, the cutoff energy was fixed to 800 eV and a γ-centered k-points mesh of 6 × 6 × 4 was used for the sampling of the Brillouin zone. The total energy was converged to 10−6 eV/cell, and the force was relaxed to 10−5 eV/Å. Spin-polarization and the Vosko−Wilk−Nusair local density approximation scheme58 were used. The GGA+U method, as described by Dudarev,59 was used for the Fe atoms to correct the poor description of the Coulomb repulsion of the 3d electrons60 in standard GGA. The Hubbard parameter U, describing the Coulomb interaction, was fixed to 4 eV, whereas the screened exchange energy, J, was fixed to 1 eV. The choice of U = 4 eV and J = 1 eV (Ueff = U − J = 3 eV) for iron-oxide compounds is known to be the best set of parameters, giving very good agreement with experiments.61,62

structure, composition and magnetism in ferrihydrite, as a function of its hydration. The case for which n = 0 is especially valuable because it involves the generation of structures having the exact composition of the Michel model,21,35 hence allowing closer scrutiny of this structure versus water content. During the nonmagnetic structure search, the Michel model was theoretically discovered at the seventh generation, as shown in Figure 1a. However, a new nonmagnetic structure with a more energetically favorable atomic arrangement (−0.49 eV/ cell) was found at the 12th generation. As shown in Table 1, more accurate subsequent GGA+U calculations indicate that

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RESULTS AND DISCUSSION At the end of the five structure searches from water contents from n = 0 to 2, we performed additional calculations on the 10 lowest energy structures of each case, so that 50 structures in total were reinvestigated, to determine with accuracy their structure, magnetic ordering, and energy. Among them, the Michel model was objectively found. However, it was not the lowest energy structure discovered. The structural details and energy differences of the most energetically competitive structures with respect to the Michel model, in both their nonmagnetic and magnetic states, are summarized in Table 1, and their atomic coordinates are provided in Supporting Information. In order to determine if one of the 50 structures reinvestigated could be associated with ferrihydrite, we directly compared calculated PDF and XRD patterns for each against experimental data. The PDF analysis was performed with the pdfgui63 interface and used the experimental PDF data of twoline ferrihydrite from Michel et al.,35 showing close similarities with the one of six-line up to 10 Å. The calculations of XRD patterns were carried out with the GDIS program64 and were compared with the experimental XRD pattern from Manceau.38 The results indicate that no new structures other than those already known in the literature could be associated with ferrihydrite. As a general trend, the ordering at intermediate distances (i.e., ∼5−15 Å) in the calculated PDF could not match that of the experimental PDF for two-line ferrihydrite, and the calculated XRD pattern showed some reflections at the wrong angle for each of these hypothetical structures. Out of the 50 low energy structures found, therefore, only the Michel model showed sufficient correspondence with the experimental observables to “survive” elimination. Nevertheless, these energetically competitive model structures are informative, as they allow an elaboration on the overall interplay between

Figure 1. (a) Evolution of the lowest energy structure search for n = 0 (Fe10O16H2) as a function of the number of generations. The green dashed line represents the energy of reference of the Michel model. Representation of the (b) Michel structure, theoretically predicted, and (c) orthorhombic structure parallel (top) and perpendicular (bottom) to the c-axis. The blue and orange polyhedra symbolize the different spin sublattices for the magnetic ground state. In (c), the black dashed rectangles highlight face sharing octahedra in the structure, for which a truncated closer representation is shown. (d) Comparison between the calculated XRD of the orthorhombic structure and the experimental XRD of goethite (ICDD 29-0713). D

DOI: 10.1021/acsearthspacechem.8b00138 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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For n = 1, the unit cell has a composition of Fe10O18H6. As shown in Figure 2a, this search resulted in a nonmagnetic

this new structure is orthorhombic (Cmc21), although in Table 1 we express the lattice parameters in a hexagonal reference to facilitate comparison with the optimized parameters of the Michel model. Analysis of this hypothetical orthorhombic structure, which is comprised exclusively of octahedrally coordinated Fe, suggests that its lower total energy arises from its higher density of Fe−O covalent bonds per unit cell. This is reinforced by the fact that this structure presents of a column of three face shared Fe octahedra, a unique feature shown in Figure 1c. Although the XRD pattern of the orthorhombic structure does not match that of ferrihydrite, it is worthy to note that it does, however, possess some interesting similarities with the XRD pattern of goethite, especially for 2θ peaks located between 20 and 30° at a cobalt Kα wavelength (λ = 1.79 Å), as shown in Figure 1d. A structural comparison between the orthorhombic structure and goethite shows common polyhedral arrangements even if the stoichiometry is different. The presence of these similarities suggests that for a solid-state transformation from ferrihydrite to goethite, as reported in cases of oriented aggregation,65 this discovered orthorhombic structure could represent a possible local minimum along the transformation path between the two phases. The predicted magnetic ground states of the theoretically found Michel and orthorhombic structures are illustrated in Figure 1b,c. For the Michel model, the optimized lattice parameters and predicted ferrimagnetic ground state are in good agreement with previous DFT calculations.50 As shown in Table 1, the inclusion of magnetism involves a change in their relative energies, such that the orthorhombic structure, having an antiferromagnetic ground state, becomes 0.1 eV/cell less favorable than the Michel structure. Importantly, from this we have a first indication that even if the atomic arrangement of the orthorhombic structure is more favorable than that of the Michel structure, the local magnetic ordering plays an important role in thermodynamic stability, at least in the Fe5O8H stoichiometry within the energy range of a few tenths of an eV. This example is direct evidence that the magnetic exchange energy between neighboring iron atoms could be one of the key factors governing the structure of ferrihydrite, as observed by Michel et al.21 For the case of increasing structural water content, at n = 0.5, the nonmagnetic structural search generated structures with energies at least 3.6 eV/cell less favorable than the reference, which entails decomposition into the nonmagnetic Michel model releasing one free water molecules (per simulation cell) into the gas phase (i.e., dehydration). Reinvestigation of the 10 lowest energy structures of this search with high-level calculations to find total energies in their respective magnetic ground states showed that they are still less favorable than dehydration into the ferrimagnetic Michel model by at least 2.9 eV/cell. Such difference in energy is due to the fact that the structures generated for n = 0.5 are made of a mixture of iron atoms with three different coordination numbers and various polyhedral shapes. For example, the lowest energy structure of that search, which has the Fe10O17H4 composition, was made of three tetrahedral, three octahedral, and four penta-coordinated iron cations in square pyramids. Because the energies of the structures obtained for n = 0.5 are highly unfavorable with respect to the dehydration reaction, these slightly more hydrated structures with a unit cell composition of Fe10O17H4 are unlikely to compete with the Michel model.

Figure 2. (a) Evolution of the lowest energy structure search for n = 1 (Fe10O18H6) as a function of the number of generations. The green dashed line represents the energy of reference of the Michel model with added gas phase water molecules. (b) Representation of the monoclinic structure theoretically predicted with a view parallel (top) and perpendicular (bottom) to the c-axis. The blue and orange polyhedral, as well as the black dashed rectangles, have the same meaning as in Figure 1.

monoclinic (Cc) structure more favorable than dehydration into the Michel model and gas-phase water molecules. As shown in Table 1, more accurate calculations leaded to a nonmagnetic monoclinic structure −0.29 eV/cell more favorable than the nonmagnetic Michel model. Similar to the atomic arrangement in the orthorhombic structure obtained for n = 0, the monoclinic structure is comprised only of octahedral Fe, and features two-by-two face-sharing Fe polyhedra. The antiferromagnetic ground state and atomic arrangement of the monoclinic structure are shown in Figure 2b. It is worth noting that this predicted structure bears many similarities to a reasonable conceptual model of a proton-rich hematite (α-Fe2O3). The antiferromagnetic ordering of the monoclinic structure is obtained from an antiparallel spin pattern similar to that found in hematite, with face-sharing Fe octahedra following the same (− + + −) and (+ − − +) patterns along the c-axis. The composition of this structure, Fe10O18H6, is equivalent to hematite if two Fe atoms were exchanged by six H atoms (i.e., three H+ per Fe3+). This means that for the extent of hydration corresponding to n = 1, a structure akin to proto-hematite appears. This result could be taken as an indication that adding water molecules to the initial Fe5O8H formula unit of the Michel model is a means to enable topotactic transformation of ferrihydrite to hematite by hydration,2,66 with proto-hematite as a possible local minimum along the transition pathway. That such a pathway is worthy of E

DOI: 10.1021/acsearthspacechem.8b00138 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry

feature of two penta-coordinated oxygen atoms. These three structures are in fact the same structure in term of Fe and O positions, but with a different distribution of hydrogens. Since penta-coordinated oxygen atoms are chemically not reasonable, we have manually modified the local environment of O atoms such that they are four-fold-coordinated oxygen. Highlevel calculations were subsequently performed on the modified structures, and as shown in Table 1, the nonmagnetic lowest energy structure, only made of octahedral Fe, is now −0.39 eV/cell more favorable than the nonmagnetic Michel model. Due to the high number of structural hydrogen atoms, this structure has a triclinic symmetry. This resulting triclinic (P1) structure, shown in Figure 3b, is informative because it involves a structural modification between its nonmagnetic and magnetic states. In particular, its lowest energy atomic arrangement alternates between two face-sharing Fe octahedra present in the nonmagnetic state (gray polyhedron in Figure 3b), and two corner-sharing Fe tetrahedra in the ferrimagnetic ground state. It is also interesting to note that this structural modification is reversible, such that reoptimizing the ferrimagnetic structure, with two tetrahedral Fe, without the inclusion of magnetism restores the formation of two face-sharing octahedra. These results suggest that the two face-sharing octahedra are the most favorable configurations from an atomic arrangement perspective because they are maximizing the number of Fe−O bonds formed, but they are not the most favorable configuration when the Fe are antiferromagnetically coupled. Thus, the formation of two tetrahedral Fe, as shown in Figure 3b, is the result of a relaxed stress imposed by the antiferromagnetic coupling in the two face-sharing octahedral configurations. In is important to note that in contrast to face sharing octahedra, we also found that edge-sharing octahedra are not affected by the antiferromagnetic coupling, as indicated in Figure 3b. Furthermore, in its ferrimagnetic state, the triclinic structure is comprised of 20% tetrahedral Fe, each connected to an octahedron by corner-sharing, whereas all the other octahedra are connected each other by edge sharing. In contrast to the orthorhombic and monoclinic structures, respectively obtained for n = 0 and n = 1, the energy of the triclinic structure is much less affected by the inclusion of magnetism. Indeed, Table 1 shows that the ferrimagnetic triclinic structure is 0.35 eV/cell more favorable than the corresponding dehydration reaction into the ferrimagnetic Michel structure. The fact that the triclinic structure always remains more energetically favorable than the Michel model in both the nonmagnetic and magnetic states is essentially due to the fact that it benefits from a magnetism-induced structural relaxation converting two face-sharing octahedra into two tetrahedra. Compared to an antiferromagnetic octahedral facesharing environment, the formation of corner-sharing tetrahedral Fe allows an energy gain of 0.54 eV per tetrahedron. An overall structural analysis from the results of the five searches indicates that the most favorable nonmagnetic structures always involve 100% octahedral Fe, connected to each other by both edge and face sharing. This result shows that an octahedral environment is structurally and energetically more favorable than a tetrahedral environment, and it stands to reason based on crystal chemical arguments that because the number of Fe−O bonds formed per iron atom per unit cell is higher this stabilizes the crystal by increasing its cohesive energy. However, increasing the number of O and OH groups relative to Fe, tantamount to hydrating the structure, also tends

further consideration is evident from the prediction that the antiferromagnetic monoclinic structure is only 0.07 eV/cell less favorable than dehydration into the ferrimagnetic Michel model. In the case of n = 1.5 and a composition of Fe10O19H8, the search generated nonmagnetic structures having energies at least 2 eV/cell less favorable than the corresponding dehydration reaction into the Michel model. Reinvestigation of the 10 lowest energy structures by high-level calculations showed that in their ground state magnetic structures they are still less favorable than dehydration into the ferrimagnetic Michel model by at least 1.1 eV/cell. Interestingly, the structures generated with n = 1.5 composition generally showed layered structures with a tetrahedral irons on both sides of an octahedral iron layer. The lowest energy structure among them was found to be ferrimagnetic and resembling a 2:1 phyllosilicate clay mineral made of six tetrahedral and four octahedral irons with three water molecules in between the tetrahedral/octahedral iron sheets. Nevertheless, based on the energy difference with respect to dehydration into the Michel model, structures with a unit cell composition of Fe10O19H8 are unlikely to compete. Finally, for the most hydrated formula considered, n = 2, the unit cell composition was Fe10O20H10. As shown in Figure 3a, the lowest energy nonmagnetic structure was found at the eighth generation and is 0.40 eV/cell less favorable than the corresponding dehydration reaction into the Michel model. Inspection of the 10 lowest energy structures generated, showed that the three lowest energy ones shared a common

Figure 3. (a) Evolution of the lowest energy structure search for n = 2 (Fe10O20H10) as a function of the number of generations. The green dashed line represents the energy of reference of the Michel model with added gas phase water molecules. (b) Representation of the triclinic structure theoretically predicted with a view parallel (right) and perpendicular (left) to the c-axis. The blue and orange polyhedra and the black dashed rectangles have the same meaning as in prior figures. F

DOI: 10.1021/acsearthspacechem.8b00138 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry to form additional Fe−O bonds, but in this case it also tends to reduce the number of face-sharing octahedra present, effectively lowering the density of the material. Specifically, although the three nonmagnetic lowest energy structures obtained for n = 0, 1, and 2 involve face-sharing iron octahedra, we also observe that the general effect of adding water molecules to a crystal made of a fixed number of Fe5O8H formula units is to create more open structures with larger cavities. The benefit of having a more open structure and larger cavities (or vacancies) is that it appears to provide conformational degrees of freedom that facilitate structural modifications that can accommodate a magnetic stress without a major change in structural topology, as illustrated in the case of n = 2. For n = 0 and n = 1, the formation of magnetism-induced tetrahedra is more difficult because the structures are more dense, and face-sharing octahedra cannot easily relax into a more favorable configuration, which therefore results in magnetic structures being less stable than the ferrimagnetic Michel structure. In a broader view, our results suggest that the interplay between structure, composition and magnetism is the source of the tetrahedral Fe asserted in the Michel model. Even though tetrahedral Fe3+ can be expected to be less stable than octahedral Fe3+ on the basis of less frequent occurrence in oxide crystals generally, from the present study we can more specifically refine this notion in that they might tend arise as structural defects, either related to the kinetics of crystal growth and/or created to accommodate local magnetic stresses with iron atoms nearby on the condition that the local environment contains enough structural space to allow such a relaxation. This hypothesis also seems to be supported by XMCD experiments which found an antiferromagnetic coupling between tetrahedral and octahedral sublattices.25 Additionally, it is interesting to note that the Michel model, either in its ferrimagnetic or antiferromangetic states,50 always shows that an antiparallel spin alignment occurs between the tetrahedral site (commonly referred to as Fe3) and the octahedral site (commonly referred to as Fe1). This tendency appears to be consistent across all ferrihydrite investigations so far, including the present one.

Fe, and this does not exclude the possibility of finding additional stable structure types within a different compositional framework. Nonetheless, the most important new insights from this study are the crystal chemical principles obtained. Adding water molecules in a structure containing a fixed number of Fe should create more open topologies with less face-sharing octahedra. We also have shown that the presence of tetrahedral Fe can be considered a structural defect generated to relax a local magnetic stress between two neighboring Fe atoms and/or arising from the kinetics of crystal growth. Since ferrihydrite is well accepted generally to contain a number of defects, its structure offers the potential for such local relaxations to occur.

CONCLUSIONS This work presents the largest theoretical structural search ever performed for the ferrihydrite nanomineral, enabling insights into the interplay between bonding, hydration, and magnetism giving rise to stable topologies. On the basis of an assumed two Fe5O8H formula units per unit cell that is incrementally hydrated, three structures, other than the Michel model, were found which have a similar total energy. However, comparison between calculated and experimental PDF and XRD patterns indicates that none of these new structures can be successfully associated with ferrihydrite. In the specific case of n = 0, which is the “driest” of the compositions considered, this indicates that the Michel model proposed is the most energetically favorable. A caveat is that this computational analysis, although exhaustive in one sense, also has not yet gone so far as to consider structure types that are based on a different number of formula units per unit cell (e.g., four, as in the case of FeOOH polymorphs). In our case, the amount of iron in the unit cell has been fixed to 10 and the number of Fe5O8H formula unit per unit cell has been limited to two. A great deal of additional work would be required to explicitly and fully encompass the optimal amount of H, OH, or H2O relative to

(1) Chukhrov, F. V.; Zvyagin, B. B.; Gorshkov, A. I.; Yermilova, L. P.; Balashova, V. V. Ferrihydrite. Izvestiya. Akad. Nauk. SSSR, Ser. Geol. 1973, 4, 23−33. (2) Cornell, R. M.; Giovanoli, R.; Schneider, W. Review of the hydrolysis of iron(III) and the crystallization of amorphous iron(III) hydroxide hydrate. J. Chem. Technol. Biotechnol. 1989, 46, 115−134. (3) Schwertmann, U.; Murad, E. Effect of pH on the Formation of Goethite and Hematite from Ferrihydrite. Clays Clay Miner. 1983, 31, 277−284. (4) Cornell, R. M.; Schneider, W. Formation of goethite from ferrihydrite at physiological pH under the influence of cysteine. Polyhedron 1989, 8, 149−155. (5) Liu, H.; Li, P.; Zhu, M.; Wei, Y.; Sun, Y. Fe(II)-induced transformation from ferrihydrite to lepidocrocite and goethite. J. Solid State Chem. 2007, 180, 2121−2128. (6) Liu, H.; Ma, M. R.; Qin, M.; Yang, L. J.; Wei, Y. Studies on the controllable transformation of ferrihydrite. J. Solid State Chem. 2010, 183, 2045−2050. (7) Liu, H.; Wei, Y.; Sun, Y. The formation of hematite from ferrihydrite using Fe(II) as a catalyst. J. Mol. Catal. A: Chem. 2005, 226, 135−140. (8) Tipping, E.; Woof, C.; Cooke, D. Iron oxide from a seasonally anoxic lake. Geochim. Cosmochim. Acta 1981, 45, 1411−1419. (9) Bigham, J. M.; Schwertmann, U.; Carlson, L.; Murad, E. A poorly crystallized oxyhydroxysulfate of iron formed by bacterial oxidation of

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsearthspacechem.8b00138. Crystal structure, atomic coordinates, and spin orientation of the energetically most favorable structures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Michel Sassi: 0000-0003-2582-3735 Kevin M. Rosso: 0000-0002-8474-7720 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This materials is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division through its Geosciences program at Pacific Northwest National Laboratory (PNNL).

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DOI: 10.1021/acsearthspacechem.8b00138 ACS Earth Space Chem. XXXX, XXX, XXX−XXX