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Crystal structure determination of karibibite, an Fe3+ arsenite, using electron diffraction tomography

Abstract The crystal structure of karibibite, Fe3 3+(As3+O2)4(As2 3+O5)(OH), from the Urucum mine (Minas Gerais, Brazil), was solved and refined from electron diffraction tomography data [R 1 = 18.8% for F > 4σ(F)] and further confirmed by synchrotron X-ray diffraction and density functional theory (DFT) calculations. The mineral is orthorhombic, space group Pnma and unit-cell parameters (synchrotron X-ray diffraction) are a = 7.2558(3), b = 27.992(1), c = 6.5243 (3) Å, V = 1325.10(8) Å3, Z = 4. The crystal structure of karibibbite consists of bands of Fe3+O6 octahedra running along a framed by two chains of AsO3 trigonal pyramids at each side, and along c by As2O5 dimers above and below. Each band is composed of ribbons of three edge-sharing Fe3+O6 octahedra, apex-connected with other ribbons in order to form a kinked band running along a. The atoms As(2) and As(3), each showing trigonal pyramidal coordination by O, share the O(4) atom to form a dimer. In turn, dimers are connected by the O(3) atoms, defining a zig-zag chain of overall (As3+O2) n -n stoichiometry. Each ribbon of (Fe3+O6) octahedra is flanked on both edges by the (As3+O2) n -n chains. The simultaneous presence of arsenite chains and dimers is previously unknown in compounds with As3+. The lone-electron pairs (4s2) of the As(2) and As(3) atoms project into the interlayer located at y = 0 and y = ½, yielding probable weak interactions with the O atoms of the facing (AsO2) chain. The DFT calculations show that the Fe atoms have maximum spin polarization, consistent with the Fe3+ state.


Introduction
KARIBIBITE was discovered in a pegmatite in Namibia by von Knorring et al. (1973), where it occurs as an alteration product of löllingite (FeAs 2 ), forming yellow crusts and sub-micrometre-thick fibres. While not abundant, it has been reported in several other places (Voloshin et al., 1989;Favreau and Dietrich, 2006;Kampf et al., 2013;Larsen, 2013;Ohnishi et al., 2013;Calvo, 2015) but never in crystals suitable for single-crystal X-ray studies. Its formula was given by von Knorring et al. as Fe 3þ 2 As 4 O 9 . In addition to the interest in a full structural characterization of As-bearing minerals, as part of efforts aimed at a better understanding and management of this environmentally critical element (see reviews by Vaughan, 2006, Craw and Bowell, 2014, Mitchell, 2014, karibibite is also interesting as it is part of a small group of species containing the arsenite ion (i.e. Asφ 3 groups, where φ = O, OH).
Because of the size issue mentioned above, we applied electron diffraction tomography (EDT) to solve and refine the crystal structure of this mineral. Using EDT we could provide 3D quasi-kinematic data from sub-micrometre grains and, therefore, highly complete structural information from single nano-crystalline (minor) components of polyphasic mixtures (Kolb et al., 2007;Mugnaioli et al., 2009;Mugnaioli, 2015a). This has been purposefully applied to cases of mixtures at a very fine scale (such as the case of charoite, Rozhdestvenskaya et al., 2010, (S 2 ) 1+x [Bi 9-x Te x (OH) 6 O 8 (SO 4 ) 2 ] 2 , Capitani et al., 2014, and Fe 2 (As 2 O 4 )(HAsO 4 ) (OH)(H 2 O) 3 , Majzlan et al., 2016). While EDT is a very powerful technique, it is not devoid of experimental complications. Dynamic effects are still present, even if strongly reduced, and some phases may undergo structural changes when exposed to a high energy electron beam or high vacuum. Another potential pitfall is the possibility that diffraction data are collected from a volume which is not representative of the whole sample, or may not apply to the mineral of interest. Therefore, to confirm that the obtained crystal structure is that of karibibite, we measured a powder X-ray diffraction (XRD) pattern using synchrotron radiation. The same starting model used in the electron diffraction refinement was employed for the refinement from powder data. Agreement between the two refinements indicates that the structural model presented herein does indeed describe the atom arrangement of karibibite. Finally, the model was further checked with DFT calculations.

Sample description
The sample comes from the Urucum mine (Galiléia, Doce valley, Minas Gerais, Brazil), which exploits an LCT-type pegmatite famous for its gem-quality purple spodumene (kunzite) crystals. In the specimen studied karibibite occurs as compact fracture fillings in brecciated löllingite associated with anhedral colourless quartz. Vughs are coated with felted aggregates and radial tufts of brownish yellow acicular crystals of karibibite showing a silky lustre. X-ray diffraction shows that, in addition to the mentioned minerals, minor scorodite and goethite are also present.
Under the scanning electron microscope (SEM) and transmission electron microscope (TEM) many karibibite crystals appear bent. The thickness of individual crystals is less than 1 μm (Figs 1 and 2).

Chemical analysis
Karibibite was analysed at LAMARX (Universidad Nacional de Córdoba) by wavelength-dispersive spectroscopy (WDS) using a JEOL-8230 JXA electron microprobe operating at 15 kV and 10 nA. No zoning was evident in back-scattered electron images of the carbon-coated polished mount. The only elements detected by EDS were As, Fe and O but other probable elements were included in the analytical routine. Standards and crystals include lammerite (As, TAP), orthoclase (Al, TAP), rhodonite (Si, TAP and Mn, LIFH), kaersutite (Ca, PETJ) and fayalite (Fe, LIFH). Also sought but not detected were P (<320 ppm), Zn (<620 ppm) and Cu (<420 ppm). Kα lines were used, except for As (Lα). Count times were 10 s on peak and 5 s at each background position. Raw data were processed with the ZAF routine as implemented by the JEOL suite of programs. The average of seven analyses is (wt.

Electron diffraction
Data from TEM imaging and EDT were collected by a JEOL JEM 2010 microscope operating at 200 kV with a LaB 6 electron source. Data were recorded by an Olympus Tengra CDD camera (clipped at 2k × 2k). Karibibite powder was dispersed in ethanol, ultrasonicated and pipetted on a half copper mesh coated by a graphite film. A single tilt holder with a JEOL EM-21340HTR High Tilt Specimen Retainer, with a tilt range up to ±60°, was used for EDT experiments. The EDT data were acquired in beam precession mode (Vincent and Midgley, 1994) by a NanoMEGAS SpinningStar device, as described by Mugnaioli et al. (2009). The precession angle was kept at 1°.
Three crystals were examined for data quality. The direction of growth of all sampled rods is always a (parallel to the direction of elongation of Fe-O octahedral chains, as described below); b and  c are oriented randomly. Diffuse scattering along b is quite strong, and there are also hints of some rotational disorder around b. Data were measured with a camera length of 60 cm, giving a resolution of ∼1.1 Å. The electron diffraction dataset was collected from a relatively large rod, with a thickness of ∼130 nm. The rod as a whole was not a single crystal, and along its length bends several times. However, in the small area (∼100 nm diameter, Fig. 2) used for acquiring electron diffraction data, the crystalline domain was coherent. The material is stable under the conditions used for data acquisition (TEM mode with gun spot size = 5 and electron beam almost fully spread). Two ab initio solutions were calculated in the centrosymmetric space group Pnma on the basis of the electron diffraction dataset using Sir2014 (Burla et al., 2015) and delta recycling (Rius, 2012). They were topologically very similar. Further refinement from electron diffraction data was performed with SHELX-97 (Sheldrick, 2008) using the scattering factors of Doyle and Turner (1968). Other data collection and structure refinement details for karibibite appear in Tables 1 and 2.
Synchrotron X-ray diffraction: data collection and structure refinement A sample of powdered karibibite was loaded in a glass capillary 0.3 mm in diameter. The XRD pattern was collected at the MSPD line of the ALBA synchrotron (Barcelona, Spain). Structure refinement was performed with FullProf (Rodríguez-Carvajal, 2001). The crystal structures of quartz (Norby, 1997), scorodite (Hawthorne, 1976), goethite (Kaur et al., 2009) and löllingite (Lutz et al., 1987) were included in the refinement as well, but only their scale factors were allowed to vary (except for quartz, in which the atom coordinates could also be refined). Atom displacement parameters (ADP) were refined isotropically, forcing all the atoms of the same element to have the same ADP values. Data collection and other structure refinement details are listed in Table 3.

First-principles calculations
The experimentally proposed structure was used as input for a coordinate relaxation using the densityfunctional code SIESTA (Soler et al., 2002), which uses atomic orbital basis sets and norm conserving pseudopotentials. The proposed Pnma symmetry was imposed during the relaxation, which consisted of a minimization of the residual forces acting on the atoms. The final maximum force was 0.04 eV Å -1 . The cell parameters were maintained at the experimental values, with residual stresses of the order of 10 GPa, which are low enough and thus consistent. Best results for relaxation, including the lowest energy and much improved convergence properties, were obtained by freeing the spin degrees of freedom. Iron atoms show the maximum spin polarization (five unpaired electrons) consistent with Fe 3+ . No attempt has been made in this work to study the magnetic structure in detail. The visualization of the As lone pairs was achieved by computing the deformation charge density (the difference between the final total charge density and the superposition of the spherical free atom charge densities).

Results
In the unit-cell setting proposed by von Knorring et al. (1973) [a ≈ 28.4, b ≈ 6.5, c ≈ 7.5 Å] they observed the extinction rule h0l for l = 2n. Besides this extinction rule, the present study also confirms the additional one, hk0 for h + k = 2n (Fig. 3). Therefore, possible space groups are P2 1 cn or Pmcn (equivalent to Pna2 1 and Pnma in conventional setting).

Structure refinement
The internal consistency of the EDT dataset can be estimated roughly from the corresponding R (int) value. In the present case it is 24% which is normal for this technique (Mugnaioli, 2015b). With this limitation in mind, we used these data to carry out the least-squares refinement of the structural model obtained by delta recycling. Due to the limited accuracy, a preliminary analysis of the crystal structure is convenient to assist the refinement. It can be seen that in this structure, O atoms exhibit a limited number of coordination types. These are as follows:  (4)] are bonded to the same As(2) atom, to keep the balance at both O atoms, the bond strengths of As(2)-O(8) and As(2)-O(4) must be 1.5 and 0.5 vu, respectively. An initial unrestrained refinement showed that the distances roughly followed the lengths predicted by the bond strength, i.e. they were ∼1.77 Å for As 3+ -O and 2.00 Å for Fe 3+ -O.
To check if the observed discrepancies were meaningful a restrained refinement was subsequently performed by refining the average O distance to As (1) and As(3) and the average O distance to Fe(1) and Fe (2) [but allowing a small discrepancy for each bond]. Only for As(2) were fixed restraints introduced, calculated according to the expected bond strengths, i.e. 2.05(2) Å for As(2)-O(4), 1.601(15) Å for As(2)-O8 and 1.77(2) Å for As(2)-O(3) [Allmann, (1975)]. The resulting R value showed no significant increase, confirming the validity of the restraints. Atomic displacement parameters (ADP) of As and Fe were refined anisotropically, while those of the O atoms were refined isotropically. The final R 1 value is 18.8% for I > 2σ(I) and 22.0% for all data. Final fractional atom coordinates and ADPs are given in Tables 4  and 5. Selected interatomic distances are listed in Table 6. Final refined average distances are <As-O> = 1.762(20) Å for As(1) and As(3) and <Fe-O> = 1.989(20) Å for Fe(1) and Fe (2). Fine details such as ADPs of the structural models obtained using EDT data are not as reliable as those  (12) All atoms are located on general positions (8d ), except for Fe (1), OH(6) and O(7) which are on the special position 4c. obtained using single-crystal XRD data (Mugnaioli, 2015b). In spite of this, a rough analysis of the refined ADP values will be attempted. Preliminary refinements showed that most O atoms had similar refined ADPs. The exceptions were O6 and O8, which had slightly greater values. Accordingly, in the final refinement, ADPs of O6 and O8 were refined separately from  (2) the rest, which were grouped into a single one (the refined values are 0.12(1) and 0.10(1) Å 2 , respectively). Curiously, of all the O atoms having two non-H neighbour atoms, O6 and O8 are the only ones having at least one Fe replacing As. Regarding the ADPs of Fe atoms, as they are located within the ribbons, it seems logical that they show lower ADP values, 0.09(1) Å 2 ; in contrast, the As atoms, lying more externally, display slightly higher ADP values, 0.10 to 0.13(1) Å 2 . In order to check how well the model refined by DFT reproduces the observed electron diffraction intensities, these were calculated with fixed atom coordinates but free ADPs (Tables 7 and 8, deposited as Supplementary Material, have been deposited with the Principal Editor of Mineralogical Magazine and are available from http://www.minersoc.org/ pages/e_journals/dep_mat_mm.html). The resulting R 1 value, 27% for F > 4σ(F), confirms the general topology. To be sure that karibibite had not suffered structural changes during data acquisition, the same starting model was also refined with the Rietveld method. As can be seen in Fig. 4, the agreement between the experimental and calculated intensities is very good, proving that the structure described here does indeed correspond to karibibite. The corresponding refined fractional atom coordinates, ADPs and interatomic distances are given in Tables 9 and 10 (deposited as Supplementary Material and available from http://www.minersoc.org/pages/e_ journals/dep_mat_mm.html). We note that the powder XRD pattern was measured using a polyphasic sample where karibibite constitutes only ∼67% by weight. In addition, the large b unit-cell parameter (≅ 28 Å) leads to peak overlap even at relatively low 2θ angles, and this is increased by broad peaks caused by the very small crystallite size coupled with rotational disorder. Results obtained using EDT and the powder XRD data are not substantially different, but bond-valence calculations give values closer to ideal sums for the EDT dataset compared with powder XRD. Therefore, we think that the model refined with EDT data gives a more accurate description of the karibibite structure.

Crystal structure description
Unit-cell parameters obtained by electron diffraction tomography were a = 7.46(7), b = 28.6(3), c = 6.51(6) Å. As the accuracy of cell parameters is higher using synchrotron XRD, those values (listed in Table 3) were used in the structure refinement and related calculations.
The crystal structure of karibibite consists of: (1) bands of Fe 3+ O 6 octahedra running along [100], decorated with As 2 O 5 dimers; and (2) chains of AsO 2 trigonal pyramids. This means that As is coordinated in 2 symmetrically different arsenite groups, but in the same oxidation state (3+).

The bands
Each band is composed of ribbons of three edgesharing Fe 3+ O 6 octahedra, apex-connected with other ribbons in order to form a kinked band running along a. Individual octahedra are distorted, especially regarding O-Fe-O angles (Fig. 5); distances show a much smaller departure from ideal octahedral symmetry. There are two bands per cell. Bands are separated along c by As 2 O 5 dimers formed by two symmetry-related As(1) atoms and their respective O atoms (Fig. 6).

Arsenite chains
As(2) and As(3) each have trigonal pyramidal coordination and share one O atom, O(4), to form a dimer. In turn, dimers are connected by O(3) atoms, defining a zig-zag chain of overall (As 3 + O 2 ) Àn n stoichiometry. Each ribbon of (Fe 3+ O 6 ) octahedra described above is flanked on both edges by the (As 3+ O 2 ) Àn n chains (Fig. 5). Regarding bond lengths, arsenite groups are not symmetrical, with marked differences among As-O distances. The lone electron pairs of the As atoms projects into the interlayers at y = 0 and FIG. 6. View of the karibibite crystal structure. Strips formed by Fe-centred octahedra ( purple) are connected by As 2 O 5 dimers along c (As1 atom, green) and flanked at each side by AsO 2 chains (As2 and As3 atoms, yellow). The lone electron pairs of As 3+ project into the void space at y = 0 and y = ½. The unit cell is outlined. Oxygen atoms appear in red, except for O6 (cyan, bound to a proton). . The position of the H atom can only be speculated upon, but no refinement of atom coordinates is possible using either the electron diffraction or XRD datasets; however, based on charge balance constraints, there should be one H atom per unit formula, and it should be bound to O(6). Therefore, the H position should lie on the symmetry plane located at (0 ½ 0) or its equivalent at (0 ¾ 0). Although the O(6)-H bond points towards the opposite slab, the distance separating two adjacent slabs is too large to have appreciable contribution of Hbonding between slabs. The coordinates of the H position obtained by DFT calculations appear in Table 7. Based on the structure, the most correct way of expressing the karibibite formula is Fe 3þ 3 (As 3+ O 2 ) 4 (As 3þ 2 O 5 )(OH).

Balance of bond valences
Bond-valences v i were calculated from the individual (As,Fe)-O distances d i (in Å), with the expression v i = K·d i ·exp(-pd i ), where p As = 2.92 and p Fe = 3.11 Å -1 are taken from Rius and Plana (1982) and Allmann (1975). The normalizing constants K As and K Fe are fitted to satisfy the individual charges of As and Fe, respectively (Table 11). BVS for oxygen atoms are within ±4% of the expected value of 2.00 vu, except for O(8), which is within 7.5%. The good agreement between anion charge and sum of valence contributions from cations (Σ c v) supports the correctness of the model. Other relevant aspects of the bond valence balance have already been discussed in the structure refinement section.

Comparison with other arsenites
To the best of our knowledge, no other mineral displays a combination of As 2 O 5 dimers and (As 3+ O 2 ) Àn n chains. Minerals showing infinite (As 3+ O 2 ) Àn n chains are only leiteite (Ghose et al., 1987) and trippkeite (Pertlik, 1975). The first has the closest structural similarities with karibibite, in that it is composed of slabs of ZnO 4 tetrahedra flanked by (As 3+ O 2 ) Àn n chains on either side and cross-linked through weak As-O bonds. In addition, there are another five known minerals that only have the As 2 O 5 dimer. They are schneiderhöhnite (Hawthorne, 1985), gebhardite (Klaska and Gebert, 1982), fetiasite (Graeser et al., 1994), paulmooreite (Araki et al., 1980) and vajdakite (Ondruš et al., 2002). Both As and Fe are very common constituents of oxidation zones, yet karibibite is rather scarce. Its rarity probably stems from the unusual Eh and pH conditions necessary for its stabilization, where the As 3+ (stable under more reducing conditions than As 5+ ) and Fe 3+ (more oxidized than Fe 2+ ) stability fields overlap (O'Day, 2006). 3.00 3.00 3.00 3.00 3.00 and P. Leverett for their constructive reviews, and to A. Kampf for editorial handling.