Single-crystal X-ray diffraction study of synthetic sodium–hydronium jarosite

Na–H3O jarosite was synthesized hydrothermally at 413 K for 8 days and investigated using single-crystal X-ray diffraction (XRD) and electron microprobe analysis (EMPA). The chemical composition of the studied crystal is [Na0.57(3) (H3O)0.36 (H2O)0.07]A Fe2.93(3) (SO4)2 (OH)5.70 (H2O)0.30, and Fe deficiency was confirmed by both EMPA and XRD analysis. The single-crystal XRD data were collected at 298 and 102 K, and crystal structures were refined in space group R3¯m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ R\overline{3}m$$\end{document}. The room-temperature data match structural trends of the jarosite group, which vary linearly with the c axis. The low-temperature structure at 102 K shows an anisotropic decrease in the unit cell parameters, with c and a decreasing by 0.45 and 0.03 %, respectively. Structural changes are mainly confined to the A site environment. Only minor changes occur in FeO6 and SO4 polyhedra. The structure responds upon cooling by increasing bond length distortion and by decreasing quadratic elongation of the large AO12 polyhedra. The structural parameters at low temperature follow very similar patterns to structural changes that correspond to compositional variation in the jarosite group, which is characterised by the flexibility of AO12 polyhedra and rigidity of Fe(OH)4O2–SO4 layers. The most flexible areas in the jarosite structure are localized at AO12 edges that are not shared with neighbouring FeO6 octahedra. Importantly, for the application of XRD in planetary settings, the temperature-related changes in jarosite can mimic compositional change.

to K-Na-H 3 O jarosite solid solutions with possible substitution of Al 3+ for Fe 3+ (Morris et al. 2006). Reflectance VIS-NIR spectra from the Mars Reconnaissance Orbiter of deposits south of Ius/Melas Chasma were assigned to nonstoichiometric H 3 O-bearing, Fe-deficient jarosite (Milliken et al. 2013).
Surface temperatures on Mars can range between 120 and 298 K, and crystal structure data at low temperatures can be relevant for in situ mineral identification. Only a limited number of single-crystal studies have investigated the jarosite group at low temperatures (H 3 O jarosite- Spratt et al. 2014;K jarosite-Mills et al. 2013;NH 4 jarosite- Basciano and Peterson 2007). Mills et al. (2013) is the only study covering a wide low-temperature range and demonstrated that K jarosite undergoes a strongly anisotropic thermal expansion, with the c axis changing much stronger than the a axis. The anisotropic change observed for K jarosite is mainly related to a strong distortion of the AO 12 polyhedron. Similar low-temperature effects could be inferred for H 3 O jarosite by comparing studies undertaken at room temperature (e.g. Majzlan et al. 2004;Plášil et al. 2014) and 173 K (Spratt et al. 2014). However, results from low-temperature data are still too limited to allow an extrapolation of structural mechanisms to other compositions within the jarosite group. For instance, the incorporation of smaller cations such as Na + or Ag + at the large A site could induce even larger structural distortions and related unit cell anisotropies. Our study focusses on Na-H 3 O jarosite, the crystal structure of which was investigated at room temperature and 102 K. Our observations are used to improve our knowledge of structural trends in the jarosite group and to further specify compositional and temperature induced changes of the jarosite topology.

Synthesis of Na-H 3 O jarosite
Na-H 3 O jarosite was synthesised using a similar method as described by Basciano and Peterson (2008). A 75-ml Parr pressure vessel was used as the reaction chamber. Starting materials were 18 g of ferric sulphate hydrate, 0.3825 g of sodium sulphate and 45 ml of deionised water. The sealed reaction vessel was placed inside a furnace and heated at 413 K for 8 days. The synthesis time was four times longer than described in Basciano and Peterson (2008) to promote the growth of large crystals.

Electron microprobe analysis (EMPA)
A jarosite crystal was embedded in epoxy resin and polished for EMPA. The polished cross section of the crystal was 50 × 30 µm. The composition of the crystal was determined using a Cameca SX-100 electron microprobe. Column conditions used were 15 keV and 10 nA with an electron beam spot size of 10 µm. Counting times were set to 10 s for Na, 20 s for S, and 30 s for Fe. Jadeite (Na), barite (S), and hematite (Fe) were used as standards. The PAP program was used for the matrix correction.
The chemical composition was calculated on the basis of two sulphur per formula unit (p.f.u.) and the general formula for Na-H 3 O jarosite was [Na x (H 3 O) 1−x−y (H 2 O) y ] A Fe 3−y (SO 4 ) 2 (OH) 6−4y (H 2 O) 4y . The calculation of the jarosite formula followed the approach of an NMR study of Nielsen et al. (2008) suggesting that potential non-stoichiometry at the B site is linked to hydronium deprotonation at the A site and protonation of four hydroxyl groups per vacant Fe site.

Single-crystal X-ray diffraction
A suitable subhedral crystal with dimensions of 100 × 80 × 50 μm was selected for single-crystal diffraction. The single-crystal measurements were carried out using an Agilent Xcalibur single-crystal diffractometer equipped with an EOS CCD area detector. Graphite-monochromated Mo Kα radiation was used and tube operation conditions were 50 kV and 40 mA. The crystal-to-detector distance was 70 mm. Data collection was performed at 298 and 102 K. A Cryojet system from Oxford instruments delivered a nitrogen stream in the cooling experiment at 102 K.
For both experiments (298 and 102 K), the frame width of the ω scans was 1º and counting time per frame was 21 s. A sphere of intensity data were collected to 60º 2θ with 100 % completeness. The intensity data were corrected for Lorentz polarization and an empirical absorption correction was applied using CrysalisRED software (Agilent Technologies). The crystal structure was solved and refined using the SHELX program (Sheldrick 2008) within the WinGX environment (Farrugia 1999). The details of data collection are given in Table 1.

Results and discussion
Chemical composition EMPA data of seven analyses from the single crystal are listed in Table 2 (Nielsen et al. 2008). Compositional variations between the single analyses are 5 % for Na 2 O, 1 % for Fe 2 O 3 and 1 % for SO 3 . The totals including calculated water contents of the single analysis are 100.4-101.3 wt% ( Table 2). It indicates that the employed EMPA method using low voltage and current, a large beam spot size, and short counting times could successfully minimize potential beam damage due to Na and H 2 O contents of the crystal.

Crystal structure refinement
Details of data collection and structure refinement are summarized in Table 1. The room-temperature structure was solved in space group R3m using direct methods. The space group choice R3m (R int = 0.034) is in agreement with previous single-crystal studies of Na jarosite and H 3 O jarosite (Grohol et al. 2003;Nestola et al. 2013;Majzlan et al. 2004;Plášil et al. 2014;Spratt et al. 2014).
An identical refinement strategy was carried out with the XRD data from the low-temperature experiment at 102 K. No phase transition was observed, and the structure was refined in R3m. The final refinement resulted in R 1 = 0.0184, wR 2 = 0.0367 and GooF = 1.124 and data are shown in Tables 3 and 4. An additional refinement of the low-temperature analysis using A and B site occupancies as free variables converged to Na = 0.51(3) Fe = 0.97(1) with a rather similar R 1 = 0.0184, wR 2 = 0.0361 and GooF = 1.121. The Fe occupancies refined by the room-and low-temperature XRD data conform closely with the EMPA data. The refined Na occupancies by XRD are slightly lower than the EMPA data. It is assumed that non-refinable small contributions from the hydronium/water hydrogen could affect the refinement of the A site occupancy.
The hydronium oxygen atom O4 was located at the 3m site (3a Wyckoff site, coordinates 0, 0, 0) which is in agreement with H 3 O jarosite studies (Plášil et al. 2014;Majzlan et al. 2004). However, a potential displacement of O4 along the c axis was discussed in previously published work (Wills and Harrison 1996; Majzlan et al. 2004;Spratt et al. 2014) because the hydronium ion has usually 3m symmetry, which is inconsistent with 3m symmetry of hydronium in H 3 O jarosite. An attempt was made to refine O4 at a 3m site (coordinates 0, 0, z). The refinement converged to (0, 0, 0) which confirmed that the most probable position of the hydronium oxygen O4 is the 3m site. Furthermore, anisotropic displacement factors with elongation along the a-b plane do not support a displacement of the hydronium oxygen along the c axis direction (  Okada et al. 1987). Compared to H 3 O jarosite (e.g. Majzlan et al. 2004), incorporation of the smaller Na + cation causes a decrease in the unit cell parameters, in which c decreases to a greater extent (−1.7 %) than a (−0.4 %), confirming the well-known observation that substitution of univalent cations at the A site in jarosite results in strong variation of the c parameter while the a parameter experiences only minor changes (e.g. Menchetti and Sabelli 1976). Our unit cell data fall close to the linear a-c trend refined from powder data of Na-H 3 O jarosite solid solutions (Fig. 3 in Basciano and Peterson 2008).
The decrease in unit cell parameters is controlled by changes of the A site environment (Fig. 2). The A site is coordinated to 12 oxygens (O2 and O3) forming an icosahedron. O2 corners (×6) are shared by FeO 6 and SO 4 polyhedra, whereas O3 corners (×6) are shared by two FeO 6 polyhedra and hydrogen. All A-O bond lengths decrease compared to H 3 O jarosite (ΔA-O3 = −0.062 Å, ΔA-O2 = −0.036 Å). In contrast, SO 4 and FeO 6 polyhedra show only minor changes and their bond lengths remain constant (this study: <S-O> = 1.476 Å, <Fe-O> = 2.008 Å; H 3 O jarosite: <S-O> = 1.476 Å, <Fe-O> = 2.009 Å, Majzlan et al. 2004). As a result, the AO 12 polyhedron for Na-H 3 O jarosite becomes more regular and its edge lengths become more similar (Fig. 3a, b). Here, the longer polyhedron edges of AO 12 , that are not shared with FeO 6 octahedra, change most with Na incorporation.  Baur (1974). Quadratic elongation was used as a measure of polyhedral distortion (Robinson et al. 1971). Here, calculations of the ideal coordination polyhedron were based on icosahedra for AO 12 , octahedra for FeO 6 and tetrahedra for SO 4 . Figures 4, 5, and 6 reveal that most trends are a linear function of the c parameter reflecting the simple response of the jarosite structure for A site substitutions. The A-O bond lengths decrease with smaller cation size, whereas Fe-O and S-O bonds remain relatively unchanged (Fig. 4). Our data match the linear trend very well. The linear change for A-O bond lengths is anisotropic, with A-O3 decreasing more strongly than A-O2 with smaller cation size, resulting in increasing bond length distortion around the A site (Fig. 5). On the other hand, polyhedron distortion (quadratic elongation) of the AO 12 icosahedron decreases with smaller cation size (Fig. 6). The AO 12 polyhedron becomes more regular with decreasing cation size as length differences between polyhedron edges get smaller. As shown above for H 3 O jarosite and Na-H 3 O jarosite (Fig. 3a, b), increased regularity is mainly a result of shortening of the less constrained polyhedron edges that are not shared with FeO 6 octahedra. In contrast, the bond length distortion and polyhedral distortion of FeO 6 and SO 4 polyhedra remain unchanged throughout the jarosite group and are independent of substitution effects on the A site (Figs. 5, 6). A possibility to modify the relative rigidity of the Fe(OH) 4 O 2 -SO 4 network would be ordering of vacancies at the B site which can be observed in monoclinic jarosite. Although not naturally occurring,     (Basciano and Peterson 2007) monoclinic Na-H 3 O and K-H 3 O jarosite with C2/m symmetry could be synthesised (Scarlett et al. 2010;Grey et al. 2011Grey et al. , 2013. Vacancy ordering occurs at the Fe1 site, which is one of the two non-equivalent Fe sites. A major effect of the ordered disruption of the structure is an increase of the average bond length around the vacancy-bearing site <Fe1-O>, whereas the bond length of <Fe2-O> remains close to rhombohedral values of <Fe-O> (e.g. <Fe1-O> = 2.04 Å, <Fe2-O> = 2.01 Å, sample Najar-D1, Grey et al. 2011; <Fe-O> = 2.008 Å, this study). A large thermal displacement U eq of 0.052 A 2 was observed in this study for the A site (Na/O4). Similar high values were reported by Nestola et al. (2013) for Na jarosite (U Na eq = 0.053 Å 2 ). Excepting Ag jarosite (U Ag eq = 0.031 Å 2 Groat et al. 2003), there is a general trend of increasing U eq for smaller A cations (Fig. 7), reflecting greater thermal motion of smaller cations within the large A site. Anisotropic displacement factors for the A site are more pronounced in the a-b plane (Table 3, U 11 = U 22 > U 33 ), which can also be observed in Ag, H 3 O and K jarosites (Groat et al. 2003;Plášil et al. 2014;Mills et al. 2013). Smaller A cations induce a major shortening in the c direction via the A-O3 bond and a minor shortening along the a-b directions (via A-O2), possibly indicating that insufficient shortening of the A-O2 bond triggers increasingly stronger thermal motion in the a-b plane for smaller cations.

Crystal structure at 102 K
The low-temperature structure of Na-H 3 O jarosite at 102 K showed a volume decrease of 0.5 % (ΔV = 3.9 Å 3 ) compared to the structure at room temperature. The volume reduction is mainly controlled by a change of the unit cell along the c axis which decreases by 0.45 %, whereas the a axis decreases only by 0.03 %. The strong axial anisotropy upon cooling mainly correlates with bond length changes in the AO 12 polyhedron (Table 4). Upon cooling, the average bond length <A-O> decreases −0.010 Å whereas <Fe-O> and <S-O> show only minor changes (<0.001 and 0.003 Å, respectively). The main shortening occurs for A-O3 bonds which are major connectors of the A site in c direction. To compensate for lower temperatures, bond length distortion in the AO 12 polyhedron increases slightly from 0.038 at 298 K to 0.039 at 102 K (Fig. 5). Polyhedral distortion of the AO 12 icosahedron is decreasing from 1.0085 to 1.0080 (Fig. 6). It indicates that the AO 12 polyhedron becomes more regular at lower temperature, in similar fashion as with incorporation of smaller A cations. By comparing Fig. 3b, c it becomes clear that the cell edges of the icosahedron are less different upon cooling. In contrast, FeO 6 octahedra and SO 4 tetrahedra do not change significantly at lower temperatures.
Comparable temperature effects were observed for K jarosite (297-133 K, Mills et al. 2013;298-575 K, Xu et al. 2010a) and can also be inferred for H 3 O jarosite by comparing studies undertaken at room temperature (Majzlan et al. 2004;Plášil et al. 2014) and 173 K (Spratt et al. 2014). Arrows in Figs. 4, 5, and 6 confirm the presence of comparable trends for K, H 3 O and Na-H 3 O jarosites, e.g. with lower temperatures: (1) bond length shortening within the AO 12 polyhedron, (2) increasing bond length distortion of A-O bonds, (3) decreasing quadratic elongation (polyhedron distortion) for AO 12 towards a more regular icosahedron, and (4) negligible changes in FeO 6 and SO 4 polyhedra. The controlling factor of the A site deformation on the jarosite structure can also be observed with increasing pressure. A high-pressure study of Na jarosite (up to 8.8  Fig. 6 Quadratic elongation versus c axis for jarosite group minerals. Room-temperature data are shown except assigned otherwise. Variation in composition and temperature affects mainly distortion of the AO 12 polyhedron. Literature data: Ag jarosite Groat et al. (2003); Na jarosite Nestola et al. (2013) Groat et al. (2003); Na jarosite Nestola et al. (2013); H 3 O jarosite Plášil et al. (2014), Majzlan et al. (2004); K jarosite Mills et al. (2013) GPa, Nestola et al. 2013) showed that the main deformation mechanism is governed by shortening of Na-O bonds with only minor or no shortening of Fe-O and S-O bonds. The large contraction of the NaO 12 polyhedron with pressure is mainly responsible for strong shortening along the c axis and minor shortening along the a axis. A large axial cell anisotropy with increasing pressure was also reported for K jarosite (up to 8.1 GPa, Xu et al. 2010b).

Implications for identification of jarosite minerals
The jarosite crystal structure is clearly affected by nonambient conditions. Structural data are required for in situ XRD identification of jarosite in potentially lowtemperature environment, such as on the Mars surface. Understanding how the jarosite structure varies upon cooling is relevant because XRD patterns of jarosite group minerals at low temperature could mimic roomtemperature structures with smaller cations on the A site; e.g. an initially assigned Na jarosite could actually be a Na-H 3 O jarosite analysed at low temperature. Splitting of jarosite peaks in XRD patterns (e.g. indices 033 and 027, Scarlett et al. 2010) could indicate formation of monoclinic jarosite.
The structure data for room temperatures and low temperature are still limited given the wide range of solid solutions in the jarosite group. However, the available data for K, H 3 O and Na-H 3 O jarosite comprise important compositions commonly observed in nature. Structural changes within this compositional range are predictable given the linearity of the structural trends (Figs. 4,5,6). Therefore, interpolation of structural models for K-H 3 O-Na jarosite solid solutions at room temperature and low temperature should be a reasonable approach if there is lack of data for specific compositions.

Conclusion
It can be concluded that temperature-and compositionaldependent changes of bond lengths and distortion parameters follow similar patterns for all minerals in the jarosite group (Figs. 4,5,6). Structural changes upon cooling resemble effects caused by the incorporation of smaller cations at the A site. Co-linear trends with composition and temperature suggest that the jarosite lattice activates a simple mechanism which is controlled by the flexibility of the large AO 12 polyhedra and the rigidity of Fe(OH) 4 O 2 -SO 4 layers. Similar structural effects can also be observed with increasing pressure ). The major flexibility of the AO 12 polyhedron can be found around edges that are not shared with FeO 6 octahedra. The environment around these non-sharing edges of the AO 12 polyhedron is mainly responsible for structural changes with composition and temperature.