American Mineralogist, Volume 96, pages 521–533, 2011

Critical evaluation of the revised akdalaite model for ferrihydrite A. MAnceAu* ISTerre-Maison des Géosciences, CNRS and Université J. Fourier, BP 53, 38041 Grenoble, France

AbstrAct The defect-free akdalaite model (fhyd6) for six-line ferrihydrite (6Fh) derived from a pair distribution function (PDF) analysis of high-energy X-ray scattering (HEXS) data was revised (model ferrifh) by Michel et al (2010) using data from a sample produced by heating two-line ferrihydrite (2Fh) at 175 °C for 8 h in the presence of citrate. We show here that the scattering pattern for this sample is similar if not the same as that for hydromaghemite, which in turn is a mixture of maghemite (γ-Fe2O3), hematite and 6Fh. As in the case of fhyd6, the PDF of ferrifh was regressed using the structure of the weakly hydrated phase akdalaite [Al10O14(OH)2] after substituting Fe for Al as a starting model. We show that the ferrifh model is implausible for the following reasons. (1) It is derived from a sample, ferrifh, that appears to be hydromaghemite, not pure 6Fh. (2) It has 20% tetrahedral Fe, a coordination that had been eliminated previously using XANES, Mössbauer, and EELS spectroscopies. (3) 75% of the Fe octahedra have shared edge lengths considerably longer than the shortest unshared edges in violation of Pauling’s distortion rule. (4) Three tetrahedral Fe-O bonds are longer than three octahedral Fe-O bonds, inducing significant polyhedral distortions. And (5) the calculated composition [Fe10O14(OH)2⋅1.2H2O] disagrees with literature data on weight loss from dehydration for 6Fh. We present an alternative interpretation of the histogram of Fe-Fe distances up to 3.7 Å obtained from the PDF of the fhyd6 ferrihydrite as a mixture of local structures of goethite/akaganeite (α/βFeOOH) and feroxyhite/hematite (δ-FeOOH/α-Fe2O3). Within this interpretation Fe only occupies octahedra that are bonded to each other by faces, edges, or double-corners. This polyhedral connectivity is confirmed experimentally by analysis of the EXAFS spectra of six-line ferrihydrites measured at room and liquid helium temperature. The Fe-Fe pairs from EXAFS data are described reasonably well by a mixture of approximately 70% feroxyhite (containing some nanohematite) and 30% akaganeite, without resorting to other phases. This set of evidence indicates that HEXS data are consistent with the Drits model for ferrihydrite (Drits et al. 1993a). Keywords: Ferrihydrite, diffraction, HEXS, PDF, EXAFS, structure, oxyhydroxide, nanoparticle

IntroductIon Ferrihydrite (Fh) is a widespread poorly crystallized hydrous ferric oxyhydroxide at the Earth’s surface (Jambor and Dutrizac 1998; Cornell and Schwertmann 2003) and a likely constituent in extraterrestrial materials (Fortin and Langley 2005; Farrand et al. 2009). In the laboratory, it is formed typically by the rapid neutralization of a ferric nitrate solution (Flynn 1984). Fresh precipitates contain only two broad X-ray diffraction (XRD) bands if the hydrolysis is performed at room temperature and a maximum of six strong lines if the ferric solution is heated to about 80 °C (Towe and Bradley 1967). The principal difference between these two diffraction end-members is the size of the constitutive crystallites (Combes et al. 1989, 1990; Drits et al. 1993a; Manceau and Drits 1993). Numerical simulations of homogenous precipitation with fast nucleation rates suggest that Fh is a mixture of nanoparticles with different metastable structures and can never be a single phase (Marchand and Rancourt 2009). The coexistence of different structures, predicted for nucleation in the highly supersaturated conditions at which Fh is synthesized, is consistent with the structural model established by X-ray diffraction (Drits et al. 1993a) that describes Fh as a mixture of two principal components, named f- and d-phases (Fig. 1), with * E-mail: [email protected] 0003-004X/11/0004–521$05.00/DOI: 10.2138/am.2011.3583

521

minor nanohematite (α-Fe2O3). This model is hereafter referred to as Drits model. The f-phase is a defect-free double-hexagonal ABAC stacking of close-packed oxygen and hydroxyls (space group P31c). The Fe atoms are randomly distributed over octahedral sites having an occupancy probability of 0.5, and displaced in the direction of the B and C anionic planes. This displacement suggests that: (1) the hexagonal ABA and ACA domains have no, or few, shared faces; (2) the B and C planes contain mainly O atoms (occ. = 0.85); and (3) the A planes contain mainly hydroxyls (occ. = 1) to satisfy electrostatic requirements. The d-phase is defective and modeled by random sequences of enantiomorphous ABA and ACA layers. The Fe octahedra share faces within each layer and the Fe-Fe pairs have a high degree of local ordering in and perpendicular to the anionic planes similar to feroxyhite (δ-FeOOH; Drits et al. 1993b). Individual crystallites and their coherently diffracting domains have a spherical or polyhedral habit (Supplementary Fig. 11; Cowley et al. 2000; Pan et al. 2009). Deposit item AM-11-015, Supplementary materials, tables, and figures. Deposit items are available two ways: For a paper copy contact the Business Office of the Mineralogical Society of America (see inside front cover of recent issue) for price information. For an electronic copy visit the MSA web site at http://www.minsocam. org, go to the American Mineralogist Contents, find the table of contents for the specific volume/issue wanted, and then click on the deposit link there. 1

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MANCEAU: FERRIHYDRITE STRUCTURE

2 .6 7Å

c

E-2.95Å

2.904Å

E-3.017Å

c

2.54Å

IVFe

IVFe

Å .912

E-2

3.39 Å

c a

c

b

b

a F-2.88Å

b

f-phase

2.96 Å

3.30 Å

2.88 Å

E-2.907Å

d-phase (feroxyhite-like)

Fhyd6 model b a

3.0 5Å

Ferrifh model

4.43 Å

H 2O F-2.88Å

E-3.39Å

3.50 Å

c

Å

O

F-2.88Å

Å E-3.01

DC

-3. 39

OH

O

c b

a

b

c b

Akaganeite

a

Å .43

-4

5

-3.

O

DC

0Å

.3 E-3

E-2.96Å

OH

DC

0Å

c a

Goethite

OH

E-3

.02

Å

b

9Å 2.5

4Å 2.9

Å

c

2.68 Å

a

5 3.4

b

b

DC

a

c

O

2.68 Å

E-3.3

0Å

O1

O2 (OH)

FIgure 1. Structural representation of the two akdalaite-like models (ferrifh and fhyd6), the f- and d-phases (defective feroxyhite) of the Drits model, goethite and akaganeite. The f-phase is represented in projection along the [1 10] axis and in perspective to show the goethite- and akaganeite-like polyhedral associations. The two polyhedral depictions of the d-phase are from Figures 6 (top) and 8 (bottom) of Drits et al. (1993b). Figure 1

The f- and d-phases were confirmed by neutron diffraction (Jansen et al. 2002), and all three components have been observed using high-resolution transmission electron microscopy (HRTEM), including single-crystal electron nanodiffraction (Janney et al. 2000, 2001; Cowley et al. 2000). The feroxyhite-type local structure of the d-phase was described in terms of a “doublechain structure” by Janney et al. (2000), but in reality the two structural components are the same (Manceau 2009). Maghemite (γ-Fe2O3), magnetite (Fe3O4), and even wüstite (FeO) grains also

were observed by TEM, but are essentially artifacts produced by the migration of Fe atoms from octahedral to tetrahedral sites and the reduction of Fe3+ to Fe2+ induced by exposure to the electron beam (Drits et al. 1995; Pan et al. 2006, 2009, 2010). An alternative model, named fhyd6, was derived from the pair distribution function (PDF) analysis of high-energy X-ray scattering (HEXS) data (Fig. 1; Michel et al. 2007). The new model is single-phase and isostructural with the mineral akdalaite [Al10O14(OH)2] and its synthetic isomorph tohdite, a crystalline

MANCEAU: FERRIHYDRITE STRUCTURE

and essentially anhydrous aluminum hydroxide compound consisting of a periodic assemblage of Baker-Figgis δ-Keggin isomers (i.e., Al13 entities; Yamaguchi et al. 1964; Yamaguchi and Okumiya 1969; Hwang et al. 2006). The anionic packing is also ABAC and the hydroxyls are also on the A planes, but three-fourth of the A positions are occupied by O atoms and 20% of the Fe atoms are tetrahedral. Akdalaite has a similar local coordination environment to maghemite (γ-Fe2O3), a ferrimagnetic spinel ferrite where each oxygen of an Fe tetrahedron is shared by three edge-sharing Fe octahedra, and which has no shared polyhedral faces. The fhyd6 model has been challenged by four groups using different and complementary arguments (Rancourt and Meunier 2008; Hiemstra and van Riemsdijk 2009; Manceau 2009; Pan et al. 2010). The main criticisms were the following. (1) The fhyd6 model is completely periodic (i.e., defect-free), does not describe X-ray diffraction and EXAFS spectroscopic data, and is inconsistent with electron microscopy, XANES, Mössbauer, and EELS results. (2) Bond-valence calculation shows that it has 20% tetravalent octahedral iron (VIFe4+), 20% divalent tetrahedral iron (IVFe2+), and some IVFe-O distances equal to or larger than the VIFe3+-O distances, thus violating Pauling’s 2nd rule. (3) It is anomalously H-poor for a hydrous oxyhydroxide formed at the surface of the earth. And (4) its molar mass is unrealistically close to that of hematite (M = 82 g/mol Fe vs. 81 g/mol Fe) and its mass density is significantly higher than experimental and calculated values (ρ = 4.8–4.9 g/cm3 vs. 3.96 and 4.15 ± 0.1 g/cm3). More recently, Michel et al. (2010) proposed a new akdalaitelike structural model, named ferrifh, as a replacement of the former fhyd6 model (Michel et al. 2007). Ferrifh was formed by heating a two-line ferrihydrite (named fh) at 175 °C for 8 h in the presence of citrate, a protocol followed usually to synthesize hydromaghemite (Barron et al. 2003; Liu et al. 2008). This synthesis procedure differs from the ferric salt hydrolysis route at ∼80 °C where no organic molecule is used. This latter hydrolysis route is generally used to synthesize 6Fh (Towe and Bradley 1967), and was followed previously to synthesize the sample from which the fhyd6 model was derived. The ferrifh and fhyd6 models share however the same basic polyhedral structure of akdalaite, have a low density of defects, and all O and Fe sites are fully occupied (occ. = 1). Therefore, ferrifh also has 20% tetrahedral Fe (IVFe) and no shared octahedral faces, in contrast to the Drits model (Drits et al. 1993a). The two akdalaite models mainly differ from each other in the positions of Fe and O atoms in the unit cell, where the coordinates of ferrifh better satisfy Pauling’s second rule. The ferrifh model was considered general by the authors because it described equally well the PDFs of the initial two-line ferrihydrite sample (fh) and the heated sample (ferrifh). The fh and ferrifh samples differ mainly in terms of particle size, structural relaxation (i.e., unit-cell parameters), and the presence in fh of defects in the form of cation vacancies filled with protons as hydroxyls to balance the total charge. Between 45 and 50% of the tetrahedral sites are empty in fh, whereas they are all occupied in ferrifh (occ. = 1), which implies that the amount of tetrahedral Fe in ferrihydrite increases from approximately 10 to 20% in going from two-line to six-line ferrihydrite. This article has two main objectives. The first is to discuss the new ferrifh model, which is problematic with respect to fundamental crystal-chemical rules similarly to the previous fhyd6 model.

523

The second objective is to examine and discuss the Fe-Fe distances obtained by PDF and EXAFS spectroscopy from the perspective of the Drits model (Drits et al. 1993a). Interatomic distances from the PDF of fhyd6 reveals good agreement with EXAFS data of 6Fh, and shows that this mineral can be described as a simple assemblage of akaganeite-type (β-FeOOH) and feroxyhite-type (δ-FeOOH) polyhedral structures at the local scale. This result is consistent with the Drits model, which excludes tetrahedral coordination and includes the sharing of faces (F), edges (E), and double corners (DC) among Fe octahedra. Ferrifh is hydromaghemite, not ferrihydrite The XRD pattern of ferrifh is the same as that of hydromaghemite and differs from the pattern of six-line ferrihydrite by the presence of a double peak at 1.60–1.64 Å (Fig. 2). The absence of this peak in 6Fh is not a particle shape effect because the diffracting nano-crystallites of 6Fh are rounded and their domain size is isometric (Supplementary Fig. 11). Hydromaghemite has been described previously and named in analogy to hydrohematite (Barron et al. 2003; Liu et al. 2008). However, this compound is not a pure phase because, according to XRD, it is a mixture of 6Fh, hematite, residual 2Fh, and low tetrahedral maghemite (γ-Fe2O3; de Boer and Dekkers 2001). Two-line ferrihydrite (2Fh) converts directly to hematite upon heating, but evolves partially toward an intermediate spinel phase (i.e., maghemite) in the presence of organic reductants, such as citrate (Campbell et al. 1997). In contrast to 2Fh, 6Fh always transforms directly to hematite (Mazzetti and Thistlethwaite 2002; Barron et al. 2003). The formation of spinel from 2Fh is considered to proceed by partial reduction of ferric iron followed by partial (magnetite, Fe3O4) or total (maghemite) reoxidation depending on oxygen availability. As the formation of spinel requires the reduction of ferric iron, and thus a reductant such as a carbon source, this intermediate IVFe-containing phase in the transformation of 2Fh into hematite cannot be used as evidence of the existence of tetrahedral Fe in 2Fh (Campbell et al. 1997). Maghemite contains approximately 20 to 37% IVFe (Greaves 1983; Shmakov et al. 1995; Corrias et al. 2000), and hydromaghemite less because it is a mixture of IVFe-free (i.e., hematite, Fh) and IVFe-depleted (i.e., low-tetrahedral maghemite) (oxyhydr)oxides (Liu et al. 2008). The hydromaghemite nature of the ferrifh sample is consistent with its pronounced ferrimagnetism as maghemite is ferrimagnetic and six-line ferrihydrite antiferromagnetic (Pankhurst and Pollard 1992; Guyodo et al. 2006). Thus, the revised akdalaite model was established on a material that is a phase mixture and contains IVFe in another constituent (maghemite) than 6Fh. Non-uniqueness of PDF models for defective minerals The HEXS data from Michel et al. (2010) were recorded on a series of two-line ferrihydrites heated at 175 °C for 0 to 14 h. The 2Fh component dominated in the first few hours (sample fh), hydromaghemite (ferrifh) at 8 h, and hematite after 12 h. Thus, the PDFs from the heated samples represented a mixture of at least three compounds: two-line ferrihydrite, hydromaghemite, and hematite. Michel et al. (2010) extracted PDFs for each of the three materials using multivariate curve resolution (MCR) analysis (de Juan and Tauler 2003), which is similar to principal

524

MANCEAU: FERRIHYDRITE STRUCTURE

component analysis (Malinowski 1991; Manceau et al. 2002) in that individual PDFs are mathematically independent (i.e., their eigenvectors are orthogonal). Consequently, the PDFs of fh and hydromaghemite cannot be reproduced theoretically with the same structural model (ferrifh). A single model that can explain data from at least two different materials (2Fh/6Fh and hydromaghemite), the last one being a mixture of three phases (2Fh/6Fh, maghemite, hematite; Barron et al. 2003; Liu et al. 2008), indicates that the data were overfit. The derivation of two akdalaite-like structures, both violating Pauling’s rules, suggests that PDF does not contain enough information to uniquely determine crystallographic models for defective minerals (Juhas et al. 2006), and that independent scientific and statistical constraints on parameters are required to obtain meaningful parameter values from HEXS measurements. In fact, the PDFfit2 (PDFgui) User Guide provides a warning against the non-uniqueness of solutions for nanocrystalline materials (Farrow et al. 2007; Manceau 2010). A similar cautionary note was made by Fernandez-Martinez et al. (2010) on their PDF study of schwertmannite, another defective Fe oxyhydroxide. These authors also concluded that information about the long-range order of defective minerals is more reliably extracted from the quantitative analysis of powder diffraction data than PDF.

1.60 Å

3.41 Å 2.95 Å , Mh

1.64 Å

2.512 Å

1.47 Å

Mh

Hydromaghemite Citrate/Fe = 3

Ht

Ht

Hydromaghemite CONC (magnetic fraction)

Ferrifh experimental Ht

Ht

1.47 Å

1.72 Å

2.24 Å

1.97 Å

100 - 101 2.55 - 2.50 Å

6Fh experimental

1.50 Å

Crystal-chemical irregularities of the revised akdalaite model

1

2

1.78 Å 1.71 Å 1.64 Å 1.60 Å 1.50 Å 1.47 Å

2.48 8Å 1.97 Å

2.95 Å

5.11 Å

4.6 Å

3.4 Å

Ferrifh model

2.24 Å

2.64 Å

f-phase model

4 5 3 °2θ (λ = 0.13702 Å)

6

F Igure 2. Experimental X-ray diffraction patterns for hydromaghemite (Barron et al. Figure 2003), ferrifh 2 (Michel et al. 2010), and six-line ferrihydrite (6Fh from Manceau 2009), and calculated patterns for the f-phase (Drits et al. 1993a) and ferrifh. CONC is the magnetic fraction of the citrate/Fe = 3 hydromaghemite (Barron et al. 2003). From the position and symmetry of the 2.50–2.55 Å line, the 6Fh sample has a higher proportion of the d-phase than the 6-Fh sample modeled by Drits et al. (1993a). See also Figure 7.

The unbalance of electrical charges, which was a major shortcoming of the fhyd6 model, has been addressed in the revised (i.e., ferrifh) model. However, a new problem has emerged, which is the violation of Pauling’s distortion rule (1929) combined with the presence of unusually short FeE-FeE distances of 2.907 Å. The cation-cation Coulombic repulsive force, which increases quadratically when two polyhedra are brought closer together by the sharing of an edge (E) or a face (F), is shielded in ionic structures by the shortening of shared (sh) edges and the compensatory lengthening of unshared (unsh) edges. In hematite, d(Osh-Osh) = 2.67 Å and d(Ounsh-Ounsh) = 2.89–3.03 Å for a face-sharing Fe separation of d(FeF-FeF) = 2.90 Å (Blake et al. 1966). In goethite (α-FeOOH), the edge lengths and FeFe separations are d(OHsh-OHsh) = 2.59 Å, d(FeE-FeE) = 3.30 Å; d(Osh-OHsh) = 2.68 Å, d(FeE-FeE) = 3.02 Å; and d(Ounsh-Ounsh) = 2.90–3.02 Å (Hazemann et al. 1991). In tohdite, the akdalaite model structure used to simulate HEXS data, d(Osh-OHsh) = 2.63 Å and d(Ounsh-Ounsh) = 2.72 Å (Yamaguchi and Okumiya 1969), all in agreement with Pauling’s distortion rule (Fig. 1). In contrast, the ferrifh model has shared edge lengths [d(OshOHsh) = 2.904 Å] considerably longer than the shortest unshared edges [d(Ounsh-Ounsh) = 2.67 Å], in violation of the distortion rule. It also produces unrealistically short FeE-FeE distances of 2.907 Å across the long shared edges (Fig. 1). The model FeE-FeE distance provides indirect evidence for face-sharing octahedra because the shortest FeE-FeE distance observed in ferric oxyhydroxides is that of 3.02 Å in goethite (Hazemann et al. 1991). In the Drits model, this short Fe-Fe distance is observed and attributed to the sharing of faces between Fe-Fe octahedral pairs from the d-phase (Fig. 1). In addition to the questionable structural assignment of these O-O and Fe-Fe pair correlations seen in the reported PDFs derived from the HEXS data, the improbability of the ferrifh model is further supported by the presence of longer tetrahedral

MANCEAU: FERRIHYDRITE STRUCTURE

Fe-O distances than the octahedral Fe-O (i.e., 1.932 vs. 1.882). This is in contrast to the Fe-O distances observed in maghemite: IV Fe-O = 1.85 ± 0.02 Å vs. VIFe-O = 2.05 ± 0.03 Å and 2.11 ± 0.01 Å (Shmakov et al. 1995). Pauling’s deformation rule can be violated, however, in severely distorted materials, such as the transition alumina κ-Al2O3 (Ollivier et al. 1997) and the low-chlorine akaganeite (Takagi et al. 2010). In low-Cl akaganeite, some Ounsh-Ounsh pairs are closer together (2.54 Å) than Osh-Osh pairs (3.21 Å). However, the FeE-FeE distances across the long edges are 3.29 Å, compared to 2.90 Å in the ferrifh model, and the shortest FeE-FeE distance in this akaganeite is 3.03 Å, similar to goethite. Therefore, what is really atypical in the ferrifh model is the combination of two crystal-chemical irregularities: the elongation of shared edges and the extreme shortening of the Fe-Fe distances across these shared edges. If, for whatever reason, one shared edge is elongated beyond normal, then for electrostatic reasons the two cations from the shared octahedra should move apart, not get closer to each other. In addition, EXAFS results presented below suggest that the Fe(O,OH)6 octahedra are less distorted in 6Fh than in low-Cl akaganeite. In summary, the revised akdalaite model of ferrihydrite is structurally and chemically implausible for the following reasons. (1) It is derived from a sample, ferrifh, which is hydromaghemite, not a six-line ferrihydrite. (2) It has 20% tetrahedral Fe. (3) 75% of the Fe octahedra have shared oxygen edges longer than unshared edges, and three tetrahedral Fe-O distances are longer (1.932 Å) than three octahedral distances (1.882 Å). (4) The short correlation at 2.907 Å attributed to two Fe atoms across the abnormally long Osh-OHsh shared edge of 2.904 Å is more typical of a shared face, not a shared edge. And (5) ferrifh has a calculated composition [Fe10O14(OH)2⋅1.2H2O] in disagreement with the measured weight loss from dehydration for six-line ferrihydrite equal to 5–12% at temperatures 100%).

5

References Ankudinov, A.L. and Rehr, J.J. (1997) Relativistic calculations of spin-dependent X-ray-absorption spectra. Physical Review, B56, 1712-1716 Brown, I.D. and Altermatt, D. (1985) Bond-valence parameters obtained from a systematic analysis of the Inorganic Crystal Structure Database. Acta Crystallographica, B41, 244-247. De Boer, C.B. and Dekkers, M.J. (2001) Unusual thermomagnetic behaviour of haematites: neoformation of a highly magnetic spinel phase on heating in air. Geophysical Journal International, 144, 481-494. Drits, V.A., Sakharov, B.A., Salyn, A.L., and Manceau, A. (1993) Structural model for ferrihydrite. Clay Minerals, 28, 185-208. Farrow, C.L., Juhas, P., Liu, J.W., Bryndin, D., Bozin, E.S., Bloch, J., Proffen, T., and Billinge S.J.L. (2007) PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals. Journal of Physics: Condensed Matter, 19, 335219. Janney, D.E., Cowley, J.M., and Buseck, P.R. (2000) Transmission electron microscopy of synthetic 2- and 6line ferrihydrite. Clays and Clay Minerals, 48, 111-119. Janney, D.E., Cowley, J.M., and Buseck P.R. (2001) Structure of synthetic 6-line ferrihydrite by electron nanodiffraction. American Mineralogist, 86, 327-335. Liu, Q., Barron, V., Torrent, J., Eeckhout, S.G., Deng, C. (2008) Magnetism of intermediate hydromaghemite in the transformation of 2-line ferrihydrite into hematite and its paleoenvironmental implications. Journal of Geophysical Research, 113, 1-12. Manceau, A (2009) Evaluation of the structural model for ferrihydrite derived from real-space modeling of highenergy X-ray diffraction data. Clay Minerals, 44, 19-34. Manceau, A. (2010) PDF analysis of ferrihydrite and the violation of Pauling’s Principia. Clay Minerals, 45, 225-228. Michel, F.M., Barrónc, V., Torrent, J., Morales, M.P., Serna, C.J., Boily, J.F., Liu, Q., Ambrosini, A., Cismasu, A.C., and Brown Jr. G.E. (2010) Ordered ferrimagnetic form of ferrihydrite reveals links among structure, composition, and magnetism. Proceedings of the National Academy of Science of the United States of America, 107, 2787-2792. Pan, Y., Brown, A., Brydson, R., Warley, A., Li, A., and Powell, J. (2006) Electron beam damage studies of synthetic 6-line ferrihydrite and ferritin molecule cores within a human liver biopsy. Micron, 37, 403-411. Ressler, T. (1998) WinXAS: a program for X-ray absorption spectroscopy data analysis under MS-Windows. Journal of Synchrotron Radiation, 5, 118-122. Ressler, T., Walter, A., Scholz, J., Tessonnier, J.P., and Su, D.S. (2010) Structure and properties of a Mo oxide catalyst supported on hollow carbon nanofibers in selective propene oxidation. Journal of Catalysis, 271, 305–314. Wells, D.M., Jin, G.B., Skanthakumar, S., Haire, R.G., Soderholm, L., Ibers, J.A. (2009) Quaternary neptunium compounds: Syntheses and characterization of KCuNpS3, RbCuNpS3, CsCuNpS3, KAgNpS3, and CsAgNpS3. Inorganic Chemistry, 48, 11513-11517. Zhu W., Hausner D.B., Harrington R., Lee P.L., Strongin D.R., Parise J.B. (2011) Structural water in ferrihydrite and constraints this provides on possible structure models. American Mineralogist, DOI: 10.2138/am.2011.3460

6

Table S1. Confidence limits of the fitting parameters calculated from a variation of the residual (Res) within 90% of its optimal value Fe-O1

Feroxyhite – 3rd model-fit

Fe-O2

Fe-Fe1

Fe-Fe2/Fe3

CN

R (Å)

 (Å)

CN

R (Å)

 (Å)

CN

R (Å)

 (Å)

CN

R (Å)

 (Å)

-

0.01

-

0.1

0.01

0.03

0.7(0.62)

0.01

-

1.0(0.80)

0.01

-

0.8(0.70)

0.02

0.01

- 1st strategy

-

0.01

0.03(0.46)

0.1

0.01

0.04(0.50)

1.0(0.70)

0.02

-

1.3(0.79)

0.01

0.02

- 2nd strategy

-

0.01

0.03(0.48)

0.1

0.01

0.04(0.43)

1.3(0.73)

0.02

0.07(0.53)

1.1(0.72)

0.01

0.05(0.61)

6-Fh 30K – 2nd model-fit

0.3

0.01

-

0.3(0.55)

0.05(0.68)

0.02

1.0(0.74)

0.01

0.05(0.58)

0.5(0.66)

0.008

0.04(0.63)

High-Cl akaganeite 77K

-

0.014

0.04(0.76)

0.2

0.023

0.06(0.54)

0.5(0.48)

0.01

-

0.6(0.57)

0. 04

-

0.9(0.67)

0.02

0.02

6Fh

In parenthesis are correlations from the F-test. Parameters with 0.5 < F < 0.8 are moderately correlated and those with 0.8 < F < 1.0 are highly. Correlated values have higher standard deviations.