- © 2010 American Mineralogist
Schwertmannite is a poorly crystalline mineral that forms ochre rusts and precipitates in acid mine environments. Despite its ubiquity and its role as scavenger of important contaminants such as arsenic or selenium, its structure has not been yet determined. Here, a structure for schwertmannite is presented based on pair distribution function (PDF) data, X-ray diffraction (XRD) analyses, and density functional theory (DFT) calculations. We propose a structure formed by a deformed frame of iron octahedra similar to that of akaganeite. Simulations of X-ray diffraction patterns unveil the presence of long-range order associated with the position of the sulfate molecules, providing a useful way to discern two types of sulfate complexes in the structure. The simulations suggest that two sulfate molecules per unit cell are present in the structure forming one outer sphere and one inner sphere complex inside the channels formed by iron octahedra. Knowledge of the positions of the sulfates in the structure will help to better understand exchange processes with oxyanions of trace contaminants, such as arsenate, chromate, or selenate, that strongly influence their biogeochemical cycling in mining ecosystems.
Schwertmannite is a poorly crystalline ferric oxyhydroxysulfate that forms ochreous coatings on sulfide-bearing rocks and soils. It also precipitates in streams and lakes receiving acid-mine drainage where the weathering of iron sulfide minerals produces SO4 and Fe2+ acid solutions. When exposed to the atmosphere, bacterially mediated oxidation of Fe2+ occurs and large quantities of nanoparticulate Fe3+ phases may form. Moreover, schwertmannite is a key solid in removing acidity in treatment systems where Fe2+ is rapidly oxidized by addition of alkalinity to acid mine drainage (Gagliano et al. 2004; Rotting et al. 2008). Further, in anoxic environments such as acid lakes, flooded soils, and wetlands, schwertmannite particles can serve as electron acceptor for Fe3+-reducing bacteria, releasing the Fe2+ necessary for sulfate reduction and neoformation of iron sulfides (Burton et al. 2007). Schwertmannite forms aggregates of nanoparticles of typical hedgehog morphology.
Due to its high specific surface and positive charge in acid waters, schwertmannite efficiently removes oxyanions such as AsO43−, SeO42−, and CrO42− from water (Carlson et al. 2002; Regenspurg and Peiffer 2005; Waychunas et al. 1995). However, despite its ubiquity and its important geochemical role, schwertmannite was only recently recognized as a mineral (Bigham et al. 1994). Reasons for this late recognition include its poor crystallinity, its frequent association with more crystalline phases such as goethite and jarosite, and its metastable structure, which transforms into goethite and jarosite within months (Acero et al. 2006; Bigham et al. 1996).
The chemical composition of schwertmannite is also the object of controversy. Bigham et al. (1994) first proposed the chemical formula as Fe8O8(OH)8–x(SO4)x, with x varying from 1 to 1.75. Yu et al. (1999) later estimated x to vary from 1.74 to 1.86. Uncertainty on the range of x values may be caused by the different location of the sulfate groups in the structure. The first approach to solve the structure of a “poorly crystalline sulfate oxyhydroxide” was reported by Bigham et al. (1990), who synthesized akaganeite-like materials with different concentrations of sulfate, that reproduced the 8-diffraction lines characteristic of schwertmannite, suggesting similarities between the octahedral framework of schwertmannite and akaganeite. Although some authors have proposed a ferrihydrite-like structure (Loan et al. 2004), there is more general agreement in the literature about this idea of the schwertmannite structure being akin to that of akaganeite, with a channel-like framework of FeO6 octahedra (Barham 1997; Bigham et al. 1990; Waychunas et al. 2001, 1995). However, no clear experimental evidence on the structure or the positions of the sulfates has been reported yet. Recent publications by Figueiredo and da Silva (2007) and Majzlan and Myneni (2005) have suggested that pre-edge features in the X-ray absorption near-edge structure (XANES) spectra at the S K-edge may be very useful in the study of sulfate speciation in schwertmannite. Majzlan and Myneni (2005) have linked the speciation of Fe3+ and SO42− in solution to the speciation in schwertmannite, stating that H-bonding may be the main adsorption mechanism of sulfate at the schwertmannite-water interface. However, this attribution relies on data from Waychunas et al. (2001), where no XANES nor FTIR data are shown. In a recent paper, Boily et al. (2010) suggest from their analysis of their FTIR data that sulfate may form complexes both through hydrogen-bonding and direct binding to the iron structure. Figueiredo and da Silva (2007) have recently reported a collection of XANES spectra of different iron sulfate minerals, correlating the presence of a pre-edge shoulder with the number of O atoms shared between sulfate molecules and Fe octahedra. Future work, including schwertmannite XANES spectra, could shed more light on the exact sulfate speciation making use of the results by these two publications. Since trace element oxyanions like AsO43−, SeO42−, or CrO42− replace SO42−, knowing the allocation of the sulfate groups in the structure is essential to understand the retention of the oxyanions in the solid phase.
X-ray diffraction studies have been limited by the very small size of schwertmannite crystallites, which give broad diffraction peaks making it difficult to perform a detailed crystallographic analysis of the structure. In recent years, the pair distribution function (PDF) technique, classically known as the Patterson function technique (Guinier 1994), has been used to study poorly crystalline precipitates of environmental relevance like mackinawite (Michel et al. 2005; Scheinost et al. 2008), magnetite (Scheinost et al. 2008), or ferrihydrite (Michel et al. 2007a, 2007b). This technique relies on a Fourier transform of the whole diffraction pattern, and it is thus particularly well suited to the study of poorly crystalline phases of reduced crystallite size, where diffuse scattering has a significant contribution to the diffraction pattern. In this study, we present a combined high-energy X-ray diffraction and theoretical study of the structure of schwertmannite.
Materials and methods
Two types of schwertmannite specimens were used in this study: natural and synthetic. Natural samples were taken as fresh precipitates from the acid drainage in Monte Romero mine (Iberian Pyrite Belt), Spain. Synthetic schwertmannite was precipitated by adding ferric chloride to sodium sulfate solutions. The produced suspension was held at 60 °C for 12 min and then cooled to room temperature and dialysed for a period of 30 days (Schwertmann and Cornell 1991). Samples of natural schwertmannite were dried following two different procedures: air-dried and freeze-dried. This allowed us to check for any possible effect of the drying mechanism on the observed structure. Once dried, the powder samples were loaded into 0.8 mm diameter polymide capillaries that were sealed with wax.
High-energy X-ray total scattering experiments were performed at beamline ID15B of the European Synchrotron Radiation Facility, Grenoble, France. Scattering data were collected with a Pixium 4700 detector (Daniels and Drakopoulos 2009) using the rapid-acquisition pair distribution function technique (Chupas et al. 2003). Measurements of the samples, empty capillary, and the background were made at ambient temperature in a q-range of 0–25 Å−1. The X-ray wavelength of 0.14252 Å was refined using a Ni standard. Corrections for sample-detector distance, tilt angle of the detector with respect to the direction of the incident radiation, and polarization were performed using Fit2D (Hammersley et al. 1995). Total scattering structure functions and pair distribution functions (PDF) were obtained using the PDFGetX2 software (Qiu et al. 2004). A crystalline standard (LaB6) was measured and used to calculate the instrumental resolution effect on the PDF (Toby and Egami 1992). Fits of the PDFs were performed using the PDFGui software (Farrow et al. 2007). In a PDF, the partial pair correlation functions between two atoms i and j, gij(r), are weighted by a function, wij(r) (Egami and Billinge 2003):
ci and cj being the concentrations of the elements i and j, and fi and fj their atomic form factors evaluated at q = 0. q is the scattering vector
The goodness of the refinements was checked using the weighted agreement factor Rw (Egami and Billinge 2003).
All the geometry optimizations were performed using the DFT code CASTEP (Clark et al. 2005). The calculations were performed using Vanderbilt ultrasoft pseudopotentials, with a plane-wave basis set energy cut-off of 760 eV and the Revised Perdew-Burke-Ernzerhof functional (Perdew et al. 1996) of the generalized gradient approximation (GGA). Brillouin zone integrations were done at special k-points determined according to the Monkhorst-Pack method, which gave six special k-points. Preliminary calculations were performed on akaganeite structure (Post et al. 2003) with the aim of tuning the convergence in k-points, pseudopotentials and energy cut-off. The obtained cell parameters show good agreement with the experimental values, within 1% (see Table 4⇓).
Diffraction patterns of the resulting models of schwertmannite were generated using the code FORCITE (Accelrys Inc.). In this code, the diffraction pattern is calculated using the Debye formula of diffraction
where rnm is the distance between two pair of atoms n and m. A cutoff of 40 Å was used, meaning that only pairs of atoms placed at a distance rnm < 40 Å were included in the calculation.
The structure of akaganeite is composed of double chains of iron (95% occupancy) or nickel (5% occupancy) oxide (or hydroxide) octahedra, which share corners to form square 2 × 2 tunnels (see Fig. 2⇓) (Post et al. 2003). Each unit cell has two identical tunnels, with centers at (0, 0, 0) and (0.5, 0.5, 0.5) of the akaganeite unit cell. A note has to be made here about the indexing of the akaganeite and schwertmannite structures. In the early studies of schwertmannite by Bigham et al. (1990), the authors used an indexation in which the the channel of akaganeite’s structure lies parallel to the c axis. However, we built our models from the akaganeite structure published by Post et al. (2003) in which the channel extends along the b axis of akaganeite’s unit cell. We will use the setting of Post et al. (2003) in the text, with the exception that we have interchanged the a and b axis and reversed the sign of c to keep a right-handed coordinate system with an obtuse β angle.
The research strategy followed in this work is as follows: the structure of akaganeite was modified replacing all the nickel atoms by iron atoms. A supercell 1 × 2 × 1 was created, and the chlorine atoms were substituted by two sulfate molecules forming bidentate inner-sphere complexes on the internal surface of akaganeite’s channel (we call this model “sulfate-doped akaganeite”). Charge imbalance originated by these substitutions can be equilibrated by the deprotonation of doubly protonated hydroxyl groups existing in the structure of akaganeite. The PDF of the sulfate-doped akaganeite structure was simulated to determine the sensitivity of the X-ray PDF technique with respect to the relative positions of the different atoms within the unit cell. As it can be seen it Figure 1⇓, the result of the simulation shows that the PDF technique is mostly sensitive to the relative positions of Fe and O atoms only. The contribution of the sulfate molecules to the total PDF is very low, as it could be expected from previous theoretical estimations done using Equations 1–3. The atomic form factor fi is proportional to the atomic number Z. Of all the elements present in the structure of schwertmannite, iron is the one with highest atomic number (ZFe = 26), which emphasizes the weighting factors of the atomic pair-correlations (Eq. 1) involving iron atoms. This structure was used as the initial model for the fitting of the PDF data, imposing only translational P1 symmetry. In a first fit, the x and z coordinates of the iron atoms, the lattice parameters a, b, c, and β, the isotropic thermal atomic displacement parameters U, the particle size d, and the peak broadening factor σq were refined. In a second run, once the fits were close to local minima, the x and z atomic coordinates of the oxygen atom were also refined. Care was taken that the results fulfilled basic crystal-chemistry rules, including minimum distances for Fe-O of 1.75 Å. The reason why only the x and z atomic coordinates were refined is because we expect the changes in the structure coming from changes in the a and c lattice parameters, or from changes in the value of the β angle. The reason for not refining the positions of the sulfur and O atoms from the sulfate molecules is that, as shown in Figure 1⇓ and stated above, the correlations between Fe-Fe and Fe-O atom pairs are the dominant contributions in the PDF of schwertmannite. A recent publication and the results presented in this article suggest the existence of inner-sphere sulfate complexes in the structure of schwertmannite (Boily et al. 2010). Simple bond valence considerations suggest that a high degree of distortions may be present in the geometry of the iron octahedra to allow surface O atoms shared with sulfate molecules to satisfy bond valence requirements. For this reason, Fe-O bond lengths as short as 1.75 Å have been allowed to occur.
In parallel, the sulfate-doped akaganeite was optimized using DFT to understand some trends observed in the structures obtained in the PDF refinements. Charge equilibration was ensured in the unit cells by adjusting the number of hydrogen atoms present in the structures as OH groups so the total charge is zero. In addition, powder diffraction patterns were simulated and compared to alternative structures to check the consistency between the short-range order revealed by PDF analyses and the long-range order underlying the diffraction patterns.
PDF-fitted structures of the octahedral framework of schwertmannite are provided in accompanying CIF files1.
Results and discussion
PDFs of the natural and synthetic schwertmannite samples and simulated PDFs of the akaganeite (Post et al. 2003) and sulfate-doped akaganeite before and after DFT-optimization are presented in Figure 3⇓. PDF-fitted structures of the octahedral framework of schwertmannite are given in Table 1⇓; atomic coordinates are given in Tables 2⇓ and 3⇓. No major differences can be found between the PDFs of air-dried and freeze-dried samples. This indicates that, in contrast to ferrihydrite (Greffie et al. 2001), the schwertmannite structure does not undergo any major structural modifications when freeze-dried. The main difference is a slight increase in the intensity of the first peak in the PDF of natural freeze-dried schwertmannite. However, we do not think this is a structural effect nor a consequence of the drying procedure, as (1) the intensity of this peak is affected by vibrational correlations (Egami and Billinge 2003), and (2) we do not observe the same effect in the freeze-dried synthetic schwertmannite. A comparison with the PDF of the crystalline standard LaB6 (not shown) allows estimating the size of the coherent domains of schwertmannite. The decay in the intensity of the PDF of LaB6 at high r values can be ascribed to the effect of instrumental resolution (Toby and Egami 1992). Instead, a more pronounced decay (within the instrumental resolution) is found in the PDF of the schwertmannite samples. Fits of this decay with a function reproducing particles of spherical shape (Gilbert 2008) yield an average particle diameter of 3–4 nm (see Table 1⇓). The small size of the coherent domains contrasts with that of schwertmannite aggregates, which are usually described as having hedgehog-like morphologies with needles in the range of the micrometer.
The PDFs of akaganeite and schwertmannite structures reveal very similar local structures. Common structural features can be identified in the region from 1 to 7 Å: the position of the first peak at ~1.98 Å is the same for both structures. It corresponds to the Fe-O distance of Fe3+ in octahedral coordination. The presence of sulfates in sulfate-doped akaganeite and in schwertmannite can be discerned from a small peak appearing at a distance of ~1.64 Å, which corresponds to the S-O distance. The peaks at ~3 and ~3.45 Å, better resolved in the modeled PDFs of akaganeite, correspond to Fe-Fe distances of different types of edge-sharing iron octahedra: the distance at ~3 Å corresponds to two iron octahedra lying on the same equatorial plane, while the distance at ~3.45 Å comes from edge-sharing iron octahedra with different equatorial planes. The next three peaks (4.75, 5.45, and 6.33 Å) correspond to Fe-Fe and Fe-O correlations. Although there are some small differences, their positions and intensities are very similar. The main differences between these two structures arise from correlations in the region 7 Å < r < 10 Å. A significant decrease in the intensity of the peak at r = 7.5 Å is observed in the PDF of the schwertmannite samples. This peak corresponds to correlations between iron atoms placed on opposite sides of the akaganeite’s channel (atoms Fe1 and Fe2 in Fig. 2⇓). However, its intensity is affected by the presence of sulfate molecules in the structure, as can be observed in the case of sulfate-doped akaganeite, where it has lower intensity.
Fitting of the PDF data were performed with the aim of explaining the differences observed between the theoretical PDFs of akaganeite and sulfate-doped akaganeite, and the experimental PDFs of schwertmannite. The structure of sulfate-doped akaganeite was used as initial model in the refinements. The results of the refinements are presented in Figure 4⇓. All the fits converged yielding a structure where the initial akaganeite unit cell was deformed, with values of the β angle around β ≈ 93° (Table 1⇑). This deformation was observed in all the fits performed. We found a monoclinic unit cell, with three different values for the parameters a, b, and c (see lattice parameters in Table 1⇑). The unit-cell parameters obtained differ from those proposed by Bigham et al. (1994), who proposed a tetragonal unit cell with lattice parameters a = c = 10.66 Å and b = 6.04 Å.
The different values found for the lattice parameters a and c provide a partial explanation for the decreasing of the intensity of the correlation at r = 7.5 Å. A splitting of this distance into several distances in the range between 7.4–7.8 Å is found in the refined structures. This splitting is reflected in the PDF of schwertmannite by a decrease in the peak intensity and a broadening of its width. As shown in Figure 3⇓, the presence of sulfates in the structure affects the intensity of this peak, too. Two different configurations for the iron atoms within the unit cell of schwertmannite resulted from the PDF refinements. In a first model (Model 1), the distortion of the β angle causes the distance between some adjacent iron atoms (Fe1 and Fe2 in Fig. 5⇓) to become too long to form two corner-sharing iron octahedra (d ~ 4.3 Å). This model was obtained after the fitting procedure of the PDF of the natural freeze-dried schwertmannite sample. In the second model (Model 2), the distance between adjacent Fe octahedra (Fe2 and Fe3 in Fig. 6⇓) is also too long (d ~ 4.33 Å) and the Fe1 octahedron is rotated by 90°, sharing an edge with an iron octahedron from the neighbor frame (Fig. 6⇓). This second structure resulted from the fitting of the natural air-dried and synthetic freeze-dried schwertmannite samples. The fact that the PDFs of the three samples are almost identical and that the agreement factors of the three fits lie in the same range (Table 1⇑) tells us about the non-uniqueness of the result. The two models thus cannot be distinguished within the experimental resolution of the data. As shown in Table 1⇑, the obtained lattice parameters have large errors (in the order of 10−2 to 10−3 Å) in comparison to the values obtained for the crystalline standard (~10−4 Å). There are two reasons for this: (1) the coherent domain size of schwertmannite is about ~3 nm. This implies that a coherent domain would be formed, on average, by a 3 × 5 × 3 supercell. It seems then plausible that such a small particle is affected by structural relaxations at the surface, causing that the lattice parameters of the unit cells close to the surface have large deviations from those of the unit cells in the “bulk” of the nanoparticle. (2) Our approach is limited because we have chosen to use a periodic system with a relatively small unit cell (in comparison with the size of the nanoparticle) to describe the structure of a disordered nanoparticle.
To better understand the origin of the deformation of the unit cell, we performed DFT-based geometry optimization of the structure of sulfate-doped akaganeite. This structure has two sulfate molecules forming bidentate inner-sphere complexes (C2υ symmetry). The optimized and non-optimized structures are shown in Figure 7⇓, and their cell parameters are given in Table 4⇓. The simulated PDF of the DFT-optimized model of sulfate-doped akaganeite (Fig. 3⇑) compares very well with the PDFs from schwertmannite, although most of the peaks are displaced towards lower distances. This may be caused by an underestimation of the Fe-O distance, with its peak position decreasing from r = 2.01 Å in the experimental PDFs to r = 1.88 Å in the DFT-optimized structure. As it can be seen in Figure 7⇓, the optimized structure has a rectangular channel causing a decrease in the intensity of the peak at r = 7.5 Å, and the appearance of two small peaks corresponding to iron atoms placed at adjacent sides of the channel are found at r < 7.5 Å. This small deformation of the channel can be caused by the lack of water molecules in the optimized structure and by the uncertainty in the positions of the hydroxyl surface groups. Water molecules and surface hydroxyls are expected to play an important role in the structure of schwertmannite, since they will form a network of hydrogen bonding interactions that may cause the structure to swell. However, the initial positions of water and hydroxyl groups in the DFT optimization procedure are a critical parameter in the optimization procedure, strongly influencing the geometry of the final optimized structure. Unfortunately, the inclusion of water molecules entails a high increase in the degrees of freedom of the system, and thus we have preferred not to consider this interaction in our simulated structures. In spite of this, a structure deformed in a similar way as the experimentally observed one with β ≈ 93° was obtained. The volume of the optimized cell (V = 675 Å3) is slightly smaller than the experimental value for schwertmannite reported by Bigham et al. (1994) (V = 687 Å3), and it is in the same order of magnitude of the experimental values found by our PDF analysis (see Table 1⇑). The deformation of the unit cell can be monitored by looking at the values of the stress tensor calculated by CASTEP after the first optimization step. The presence of the sulfate molecules in the structure makes that the off-diagonal elements σxz and σzx have values higher than zero, indicating a shear stress that leads to the deformation of the angle β of the unit cell (see Table 5⇓). The non-zero values of the diagonal elements (σxx, σyy, and σzz) are responsible for changes in the lattice parameters and thus do not induce deformations of the unit-cell angles. The fact that this deformed structure fits the experimental PDF data well supports thus the hypothesis, suggested by FTIR data (Jonsson et al. 2005; Peak et al. 1999), that these inner-sphere complexes, with sulfates having C2υ symmetry, actually exist in the schwertmannite structure. It is worth noting the existence of a similar deformation in the unit cell of nanometric akaganeite (Deore et al. 2005). These authors have evoked surface energy as the driving parameter for the transition from a tetragonal to a monoclinic phase when the size of the akaganeite particles is decreased. Although a value for the coherent domain size has been estimated for schwertmannite from the PDF measurements, with a value between 3–4 nm, the concept of “particle surface” is not of straightforward application in this case. Our proposed structure for the schwertmannite octahedral framework is composed of a highly defective entangled network of structural motifs like those presented in Models 1 and 2. The existence of these defects can produce strains in the structure, reducing the coherent domain size to values smaller than the actual particle size. We consider that these effects (structural strains induced by the presence of defects) or the presence of inner-sphere bidentate sulfate complexes (as shown here by DFT calculations) may be the main driving force for the deformation of the structure, apart from surface energetics, as proposed by Deore et al. (2005) for akaganeite.
Position of the sulfate molecules
The non-overlapping first two peaks in the schwertmannite PDFs, corresponding to S-O and Fe-O atomic correlations, and Equation 1 provide an indirect way to estimate the concentration of sulfates in the samples. According to Equation 1, the weighting factors of each correlation can be expressed as
where cS and cFe are the concentrations of sulfur and iron atoms respectively, cO1 is the concentration of O atoms from sulfate molecules, which has been fixed to cO1 = 4cS, cO2 is the concentration of O atoms from iron octahedra, ZFe and ZS are respectively the atomic numbers of iron and sulfur. In the PDF, the ratio of intensities of both correlations is proportional to the ration between the weighting factors, yielding
where IS-O and IFe-O are the intensities of the peaks corresponding to the S-O and Fe-O correlations measured from the baseline of the PDF. Application of this formula to the PDFs of the three schwertmannite samples yields an average value of cS = 0.1 ± 0.03, which corresponds to a sulfate content in the schwertmannite unit cell used in this work (containing 16 Fe atoms) of 6.4 ± 2 sulfate molecules per unit cell. The high uncertainty in this value comes from the fact that the first peaks in the PDF, notably the peak corresponding to the S-O correlation, are affected by the Fourier oscillations originated by the Fourier transform of the intensity data. In addition, the baseline is poorly defined in this region of the PDF making a precise measurement of the peak intensity more difficult. The resulting sulfate concentration is higher than the reported concentrations calculated by analytical chemistry methods, which range from 2 to 3.72 sulfate molecules per unit cell (Bigham et al. 1990; Yu et al. 1999).
It is important to note that the PDF of schwertmannite is dominated by correlations involving iron and O atoms (see Fig. 1⇑). This implies that only the short-range order of the octahedral framework is refined in the PDF fitting procedure, rendering the determination of (1) the exact positions of the sulfates within the cell and (2) their orientations within the unit cell of schwertmannite from PDF data analysis impossible. In addition, PDF analysis gives information only about the local or short-range order of the schwertmannite structure. Information about the long-range order can be extracted by analyzing the powder diffraction pattern. This kind of analysis has been hindered by the broad diffraction peaks found in the schwertmannite diffraction patterns. For this reason, the use of X-ray diffraction for structural studies has been limited in the schwertmannite literature, serving mainly as a fingerprint for identification purposes. In contrast to these data collected by laboratory X-ray sources, synchrotron powder-diffraction data have a higher resolution and allow us to use it as a reference to compare our modeled powder diffraction patterns.
The fitting range used in our PDF analyses extended from 1 to 30 Å, which is longer than the three lattice parameters of the structural models used as input in the analyses. This implies that the long-range order arising from repetitions along the unit cell axes is already taken into account in the PDF analysis, and thus the resulting structure should reproduce both short-range and long-range order along the three dimensional directions. To check this consistency, we have calculated theoretical powder diffraction patterns of the refined structures, varying the number and positions of the sulfates molecules within the unit cell. The calculated diffraction patterns of schwertmannite Models 1 and 2 are presented in Figure 8⇓ and compared to the experimental patterns. It is important to note that, due to the different a and c lattice parameters, single peaks of akaganeite are split into two or more different peaks in schwertmannite diffraction patterns. However, due to the small coherent domain sizes of schwertmannite, these split reflections overlap, making it impossible to accurately determine their positions and intensities. This high degree of overlapping has prevented the application of analysis techniques such as Le Bail or Rietveld fits, which would be very useful to precisely determine the cell parameters. From now on, we will continue to use the original notation of akaganeite when referring to the diffraction lines, even though some of them are composed by several overlapping reflections due to the small size of the coherent domains. Note that in the accompanying CIF files1 the axis a and c have been interchanged and a has been changed to −a to keep a righ-handed coordinate system with β > 90°. There are only small differences between the two models, the most significant being a higher intensity for the (042) and (524) reflections of Model 2, which agrees better with the experimentally observed. The calculated patterns are in quite good agreement with the experimental ones, except for the intensities of some lines. The (040) reflection is lower in the Model 1 and 2 patterns than in the experiments and the (200) and (101) reflections have higher intensity in the models. This is especially true for the (101) reflection, which is absent in the experimental patterns. Bigham et al. (1990) observed how the intensity of this reflection decreased proportionally to the amount of sulfate added during the precipitation of akaganeite. They found that schwertmannite was the only precipitation product formed when the synthesis was made in the presence of 2000 ppm of sulfate. The precipitate showed the typical 8 diffraction lines characteristic of schwertmannite, while the akaganeite (101) reflection was missing. We have checked this correlation between the intensity of the (101) line and the unit-cell sulfate content by generating a series of diffraction patterns of the schwertmannite structure obtained from the PDF analysis loaded with different amounts of sulfate molecules. Only two different kind of sulfate molecules were considered: (1) a bidentate inner-sphere complex placed sharing two O atoms with the iron framework, as shown in Figure 9a⇓ (the shared O atoms were chosen to have the same x and z coordinates, but placed at a different y coordinate), and (2) an outer-sphere complex placed in the center of the channel, as shown in Figure 9a⇓. All the calculations were performed using the structure of Model 1 for the octahedral framework. The results are presented in Figure 9b⇓. Only the intensities of the reflections (101), (200), (301), (023), (042), and (524) are sensitive to the concentration of sulfate molecules in the structure and to their positions within the unit cell. The most important variations of intensity are found for the diffraction peaks (101), (200), and (301), as shown in Figures 9c–9e⇓. The intensity of the (101) peak decreases as long as more sulfates are introduced in the channel of the octahedral framework of schwertmannite, as reported by Bigham et al. (1990). The best agreement with the experimental intensity, with the (101) reflection practically absent, is found when four sulfates form outer-sphere complexes are present in the structure. The evolution of the (200) and (301) intensity shows opposite behaviors. The intensity of these two peaks are dependent on the positions of the sulfate within the structure. Their relative peak intensities have been calculated using the intensity of line (221) (the more intense in the experimental patterns) and are presented in Table 6⇓. A maximum intensity for the (200) reflection is found when four inner-sphere complexes are present in the structure. On the other hand, a maximum is found for the (301) peak for the structure with four outer-sphere complexes. The relative intensities of these two peaks can thus be used to estimate the sulfate content and the binding mechanisms to the structure, by comparison to the experimental values (see Table 6⇓). Simulations of structures where sulfates are present both as inner- and outer-sphere complexes were then performed to better reproduce the experimental data. The results are presented in Figure 10⇓, and compared with the experimental data. Relative intensities are reported in Table 6⇓. If only sulfates are considered to be present, none of the combinations matched the relative intensities found in the experimental patterns [see for example the intensity ratios of the structure with 4 outer-sphere SO4 complexes in Table 6⇓, which yield good I(101)/I(221) and I(200)/I(221) but very bad agreement for the I(301)/I(221)]. For this reason, we have considered the case where water is present in the structure. This hypothesis is supported by thermo-gravimetric data of Yu et al. (1999), who reported a range of 8.5 to 8.9 water molecules per unit cell, and it seems to be very reasonable in view of the exchange processes taking place between sulfates and other oxyanions, which are hydrated species. Preliminary calculations including eight molecules per cell do improve the agreement with the experimental XRD pattern (see Fig. 10⇓). The determination of the exact positions of the water molecules within the unit cell is challenging, especially using X-ray radiation as experimental probe. The use of DFT calculations is also limited by the fact that there are many degrees of freedom in the system, and it becomes thus difficult to explore all the possibilities of the positions of water molecules and outer-sphere sulfate molecules. For these reasons, the water molecules were placed in the structure with the only care that the minimum distance between atoms from different water molecules was 1.8 Å, as expected from hydrogen bonded water molecules. The best agreement with the experiment, as reported in Table 6⇓, is found for the structure containing two outer-sphere and two inner-sphere complexes with 8 water molecules per unit cell. This explains the range of stoichiometry reported for the mineral formula, with SO4 varying from 2 to 3.72 for each 16 Fe atoms (Bigham et al. 1994; Yu et al. 1999). The lower limit is coincident with the number of inner-sphere complexes in the structure, whereas the rest corresponds to outer-sphere complexes. This result suggests that the variability in the sulfate content may come from the different amounts of outer-sphere sulfate complexes, which may be energetically less stable than the inner-sphere ones. Attempts to introduce more sulfates in the structure to match the previously calculated value from PDF intensities of 6.4 ± 2 sulfates per unit cell failed, probably due to the existence of a large proportion of sulfate molecules on the external surfaces of the schwertmannite aggregates. No more than two sulfates per channel can be hosted in the structure, setting the limit for “structural” sulfates to 4 per unit cell.
This proposed structure allows interpreting an eventual transformation to goethite in structural terms. Goethite has an orthorhombic unit cell, with a rectangular pore extending along the c axis. The transformation of schwertmannite to goethite should include at least two steps: (1) the release of the sulfate molecules from the structure, and (2) the release of two iron octahedra, leading to the transformation of the squared schwertmannite channel to the rectangular one present in goethite. The weakening of the interactions between the iron octahedra observed experimentally in this work (Fig. 2⇑) makes that the step 2 would be facilitated.
The small size of the coherent domain found in the fits of the PDFs adds further complexity to the analyses and interpretations of the structure. It can be interpreted in two ways: as a result of structural disorder (vacancies, strains...) or as a real limit of a less defective nanoparticle. In the last case, the occurrence of adsorption sites at the external surface of the nanoparticle would influence the symmetry of the sulfate complexes. We have limited our analysis to the bulk phase, not considering schwertmannite crystallites’ external surfaces. Further spectroscopic studies would be required to complete the information presented in this work and to get more precise constraints for the symmetry of sulfate within the structure of schwertmannite. In addition, we believe that other different structural motifs for the octahedral iron framework could be reported using other techniques that explore the configurational space more effectively than the least-squares refinement method. An alternative approach in this direction would be the use of Reverse Monte-Carlo; work in this direction is on-going.
The authors thank Ian C. Bourg, Laurent Charlet, Andreas C. Scheinost, and two anonymous reviewers for fruitful discussions and comments during the preparation of the manuscript. A.F.-M. thanks the French Minister of National Education and Research for an “Allocation de Recherche,” and the Région Rhône-Alpes, France, for an “EXPLORA-DOC Fellowship.” The work has been funded by the Spanish R+D contract CTM2007-66724-C02-01/TECNO and a grant of the Catalonia Supercomputing Centre (CESCA). G.R.R. thanks the Spanish Minister of Science and Innovation and the Ramón y Cajal Program.
Manuscript handled by Richard Wilkin
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- Manuscript Received November 5, 2009.
- Manuscript Accepted April 27, 2010.