Stoichiometric partially-protonated states in hydroxide perovskites: the jeanbandyite enigma revisited

Abstract The original description of the hydroxide perovskite jeanbandyite gives a formula (Fe1–x 3+,□x)(Sn1–y,□y) (OH)6 (□= vacancy), which implies the possibility of stoichiometric vacancies at B and B' sites. The validity of this formula has been questioned subsequently. Furthermore, jeanbandyite has metrically a cubic unit cell, but it is optically uniaxial. It is clear that a structure determination is needed to clarify the nature of this enigmatic mineral. Previous studies could find no crystals of sufficient quality for structure determination using X-ray diffractometers available at the time. Crystals of jeanbandyite from Hingston Down, Cornwall, UK and the type locality Llallagua, Bolivia, have been found that are of a quality that allows structure refinement by single-crystal X-ray diffraction. Structural data for crystals from each locality are presented that clarify the nature of jeanbandyite and raise some interesting questions concerning the significance of partially deprotonated states in perovskite-type structures. The structures of both jeanbandyite crystals are cubic with space group Pn3 and unit-cell parameters a = 7.658(2) Å (Llallagua) and 7.6427(2) Å (Hingston). The octahedral tilt system is a + a + a + and corresponds to that of the aristotype of BB'(OH)6 hydroxide double perovskites. Structure determination demonstrates that B is very Fe3+-rich and B' is filled by Sn, thereby requiring revision of the general jeanbandyite formula to Fe x 3+Fe(1–x) 2+Sn(OH)(6–x)Oxfor 1≥ × > 0.5, with an ideal end-member formula Fe3+Sn(OH)5O. As such, jeanbandyite corresponds to oxidized natanite with partially deprotonated oxygen sites. This stoichiometry cannot be represented in space group Pn3̄ for the observed unit cell as it implies more than one non-equivalent oxygen atom. Consequently, it is inferred that there is no long-range ordering of deprotonated oxygen sites. It is, however, conceivable that the uniaxial optical character of jeanbandyite is linked to the local short-range order of deprotonated domains.

The absence of an A-site cation and the presence of strong hydrogen-bonding between next-nearestneighbour octahedra leads to collapse of the framework and highly tilted octahedra compared with conventional perovskites. Recent structural and spectroscopic studies have revealed a richness of crystal chemistry relating to partially occupied H sites (Lafuentes et al., 2015;Welch, unpublished data) and transitional behaviour (Kleppe et al., 2012;Welch and Kleppe, 2016).
In the original study by Kampf (1982) of jeanbandyite from the type locality of Llallagua, Bolivia, unit-cell parameters were refined from powder X-ray diffraction data as a = c = 7.648(7) Å, recognizing that while the unit cell is metrically cubic the mineral is optically uniaxial and, therefore, likely to be tetragonal. Systematic absences were consistent with space groups Pn 3, Pn 3m and P4 2 /n, and so the latter was inferred to be the correct space group.
The identification of jeanbandyite as a hydroxide perovskite was based upon the similarity of its unitcell parameters, powder diffraction pattern and general stoichiometry to stottite-group minerals. Poor crystal quality (extremely high mosaicity) prevented structure determination using X-ray diffractometers available at the time. Although identifying jeanbandyite as a hydroxide perovskite, the formula proposed by Kampf (1982) is problematic in that it implies that stoichiometric proportions of vacant octahedra can occur. The empirical formula given by Kampf (1982) is not consistent with full occupancy of octahedra that is characteristic of all hydroxide perovskites studied so far.
In the light of recent progress in understanding the crystal chemistry of hydroxide perovskites, and the vast improvement since 1982 of diffractometer performance in handling challenging materials, the present study of the hydroxide perovskite jeanbandyite was undertaken to resolve ambiguities relating to its stoichiometry and structural state.
In view of the inconsistencies described above and the improbability of stoichiometrically significant proportions of B-site vacancies in hydroxide perovskites (severe underbonding of oxygens), we have undertaken a structural study of jeanbandyite from Hingston and Llallagua using single-crystal X-ray diffraction, and report the results here.

Samples
The two samples of jeanbandyite came from Hingston Down, Cornwall, UK (Natural History Museum catalogue number BM1985,772) and the type locality Llallagua, Bolivia (Kampf, 1982). The jeanbandyite crystal from Llallagua was obtained from a specimen in the collections of the Natural History Museum of Los Angeles County (catalogue number 19756). This specimen was donated to the museum in 1978 by Jean Bandy as part of the Mark and Jean Bandy Collection. The specimen was presumably collected by Mark Chance Bandy in the late 1930s or early 1940s and is labelled as coming from the Contacto-Dolores vein. This was one of 36 specimens in the collection that contain jeanbandyite and it was examined for the description of the species by Kampf (1982); however, it is not designated as a cotype. The reader is referred to these two papers for details relating to the geological setting and petrogenesis of the jeanbandyite-bearing rocks. A more general description of the mineralogy and geology of Llallagua is provided by Hyrsl and Petrov (2006).

Single-crystal X-ray diffraction
Structures were refined from single-crystal X-ray diffraction data collected for several jeanbandyite crystals from each locality. The structures of the best crystal from each locality are reported here. The dataset for the Hingston crystal (0.09 mm × 0.07 mm × 0.06 mm) was collected using an XcaliburE single-crystal X-ray diffractometer (Rigaku Oxford Diffraction) with graphitemonochromatized MoKα radiation operated at 45 kV, 40 mA and equipped with an EoS 1K CCD area detector. The data collection strategy was based upon a 25-min pre-experiment. Reflection intensities were corrected for Lorentz-polarization effects and absorption (empirical multi-scan) and converted to structure factors using the program CrysalisPro © (Rigaku Oxford Diffraction).
The dataset for the Llallagua crystal (0.04 mm × 0.04 mm × 0.03 mm) was obtained using an R-Axis Rapid II curved imaging plate microdiffractometer, with monochromatic MoKα radiation operated at 50 kV, 40 mA. The Rigaku CrystalClear software package was used for processing of structure data, including the application of an empirical multi-scan absorption correction using ABSCOR (Higashi, 2001).
Information relating to the data collections for the two crystals is given in Table 1.

Crystal structure refinement
The unit cells of both crystals are, within the small standard uncertainties, metrically cubic. Systematic absences for both crystals indicate space group Pn 3. Structure refinements were carried out in cubic space group Pn 3 and, given the uniaxial optics reported by Kampf (1982), also in tetragonal space group P4 2 /n in order to see how the latter structure compares with the cubic structure. Space group Pn 3m was discounted on the grounds that its mirror planes bisect all octahedra and lead to gross geometrical distortions, as exemplified by the published structure of natanite by Strunz and Contag (1960). Atom coordinates of wickmanite and tetrawickmanite (Lafuente et al., 2015) were used for refinement of cubic and tetragonal structures, respectively, substituting Fe for Mn. Neutral atomic scattering factors for Fe, Sn and O were taken from International Tables for Crystallography, Volume A (Wilson, 1992). The structures of both crystals were refined using SHELX (Sheldrick, 2008) within the WinGX program suite (Farrugia, 1999).
positions for H atoms were evident in the final difference-Fourier map. Refinement of Llallagua jeanbandyite in Pn 3 had very similar characteristics to those just described for the Hingston crystal. Again, no plausible H positions were evident. In contrast to the good results obtained for both cubic structures, refinements of both crystals in P4 2 /n were problematic. Data reduction for reflections and unit-cell parameters for both crystals was carried out for a tetragonal structure with P4 2 /n symmetry, for which Hingston has a = 7.6469(2) Å, c = 7.6329(4) Å, V = 446.34(3) Å 3 , and Llallagua has a = 7.671(1) Å, c = 7.6616(6) Å, V = 450.9(1) Å 3 . Initial isotropic refinement of the Hingston crystal resulted in several very similar electron-density residua (4−5 e/Å 3 ) that were associated with oxygens O(1) and O(2) three non-equivalent oxygen atoms; at this stage R 1 = 0.114, wR 2 = 0.477 and Gof = 3.125, with no reflection weighting possible. The positions of residual maxima suggested the possibility of merohedral twinning by (0 1 0/1 0 0/0 0 −1), as used for the cubic refinements. Isotropic refinement with merohedral twinning resulted in only minor improvement to R 1 = 0.098, wR 2 = 0.442 and Gof = 2.867, but it did allow refinement of reflection weights. Isotropic refinement with twinning and reflection weighting converged to R 1 = 0.097, wR 2 = 0.337 and Gof = 1.197, with a persistent residual maximum of ∼4 e/Å 3 and large U iso values for O(1) and O(2) atoms (0.059 Å 2 and 0.068 Å 2 , respectively), contrasting with the relatively small U iso value of 0.011 Å 2 for O(3). Finally full anisotropic weighted refinement of the Hingston crystal gave R 1 = 0.077, wR 2 = 0.287, Gof = 1.169 and the 4 e/Å 3 remained. The persistence of the significant residual electron density near O(1) and O(2) atoms can be rationalized as being due to the wrong space group, rather than merohedral twinning.
A very similar result was obtained for tetragonal refinement of the Llallagua crystal, except that it was not possible to refine atoms anisotropically, as nonpositive-definite U ij values for oxygen atoms were obtained and refinement was slow to converge, with persistent weighting problems. Isotropic refinement with reflection weighting and merohedral twinning gave final values of R 1 = 0.068, wR 2 = 0.237, Gof = 1.061, and a residual electron-density maximum of 3 e/Å 3 . Consequently, it is clear that the correct space group of jeanbandyite is Pn 3.
Information relating to the structure refinements is summarized in Table 1. Atom coordinates and displacement parameters are given in Table 2.
Crystallographic information fiiles and tables of structure factors for both jeanbandyite crystals 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. Bond distances, bond valences and site-scattering values for jeanbandyite are also given in Table 1. The structure of Hingston jeanbandyite for cubic and tetragonal refinements is shown in Fig. 1. The Fe(OH) 6 and Sn(OH) 6 octahedra of the tetragonal structure (Fig. 1c,d) have highly variable bond-lengths that reflect the incorrect space group.
The structures of the Hingston and Llallagua crystals are very similar. With the exception of the B site of Llallagua jeanbandyite, the observed sitescattering values for B and B′ sites of the two jeanbandyite crystals are in good agreement with those calculated from their average empirical formulas reported by Betterton et al. (1998) and Kampf (1982), when these formulas are correctly formulated as described above.
Bond-valence sums of the B sites of the two jeanbandyite crystals (Table 1) clearly demonstrate that Fe is predominantly ferric. The volume of the Fe(OH) 6 octahedron of Hingston jeanbandyite is 11.15 Å 3 . This value compares with 10.80 Å 3 for Fe 3+ (OH) 6 in bernalite Fe(OH) 3 (Birch et al. 1993), and 13.13 Å 3 for Fe 2+ (OH) 6 in stottite FeGe(OH) 6 (Kleppe et al., 2012). Assuming a linear variation in octahedral volume with composition, then the value observed for Hingston jeanbandyite implies 85% Fe 3+ , 15% Fe 2+ at this site. A similar calculation for Llallagua jeanbandyite, which has an Fe(OH) 6 octahedral volume of 11.31 Å 3 , implies a composition 78% Fe 3+ , 22% Fe 2+ . Thus, the high Fe 3+ content of jeanbandyite is confirmed. The higher volume of the Fe(OH) 6 octahedron of Llallagua jeanbandyite is consistent with the higher Mn content of this sample.
The volumes of the Sn(OH) 6 octahedron of both jeanbandyite crystals are similar (11.79 Å 3 , 11.86 Å 3 ), but they are significantly larger than those of burtite (11.54 Å 3 ), schönfliesite (11.44 Å 3 ) and wickmannite (11.48 Å 3 ) (Basciano et al., 1998). This difference can be rationalized in terms of the higher Fe 3+ content of the B site which shortens Fe-O bonds and expands the Sn-O bond length. The tilt angle Fe-O-Sn of jeanbandyite is 137.6°( Hingston) and 137.5°(Llallagua). These values compare closely with 136.8°for schönfliesite and 135.4°for wickmanite. Thus, the larger volume of the Sn(OH) 6 octahedron in jeanbandyite is probably a consequence of the contraction of the Fe site due to Fe 3+ , rather than being due to tilting of octahedra.

Discussion
Crystal structure determination shows unambiguously that jeanbandyite is cubic with space group Pn 3 and that Fe is predominantly in the ferric state. The implied ideal formula is Fe 3+ Sn(OH) 5 O. If we recalculate the empirical formula of Betterton et al. (1998) assuming that all Fe 3+ was originally Fe 2+ , we obtain a much more reasonable stoichiometry, which is very near to that of a binary natanite-wickmanite solid solution: calculated to six negative charges (six OH) the revised formula is (Fe  (Kampf, 1982 comments that it is questionable as to whether or not it is meaningful) and the formula recalculated to one Sn apfu, then a charge-balanced formula (Fe 3þ 0:78 Mn 2þ 0:15 Mg 0.04 ) Σ=0.97 Sn(OH) 5.28 O 0.72 is obtained that has, within the small analytical uncertainties, fully occupied cation sites.
We note that in their study of synthetic natanite FeSn(OH) 6 , Nakayama et al. (1977) found evidence for a phase corresponding to oxidized natanite for which they proposed a formula FeSn(OH) 5 O. Although no structural data were presented, the powder diffraction pattern could be indexed as a cubic unit cell with a = 7.64 Å for synthetic 'FeSn(OH) 5 O' compared with a = 7.83 Å for their synthetic natanite. The former value is close to those reported here for jeanbandyite.
Identification of Pn 3 as the correct space group of jeanbandyite, rather than P4 2 /n as originally proposed by Kampf (1982), is significant inasmuch as the oxygen positions and hydrogen-bonding topologies of the two structures are very different, reflecting their different tilt systems (Pn 3 is a + a + a + , P4 2 /n is a + a + c − ). The reverse tilt of the tetragonal structure (Fig. 1b) leads to chains of hydrogenbonded ···O-H···O-H···O-H··· linkages that are absent from the cubic structure, which has only isolated rings of four hydrogen-bonded OH groups.
A consistent picture has emerged: jeanbandyite is compositionally equivalent to oxidized natanite and is a bona fide hydroxide perovskite and mineral TABLE 2. Atom coordinates, anisotropic and equivalent-isotropic displacement parameters (Å 2 ) for Hingston (upper entries) and Llallagua (lower entries) jeanbandyites in space group Pn 3. Occupancies of B and B′ sites were refined using the neutral atomic scattering factors of Fe and Sn, respectively, and are expressed in terms of fractions of those atoms present. species in its own right. Despite its uniaxial optical character, jeanbandyite is cubic, space group Pn 3. How partial deprotonation is achieved at the local level remains to be explored. If there are shortrange-ordered domains containing deprotonated sites, then these may lead to the anomalous uniaxial optical behaviour that appears to be characteristic of jeanbandyite. The recognition of such stoichiometric partially-deprotonated states raises interesting questions concerning their stability relative to fullyprotonated hydroxide perovskites. It is conceivable that the M 3+ Sn(OH) 5 O stoichiometry could be  6 and Sn(OH) 6 octahedra of the tetragonal structure showing anisotropic displacement ellipsoids for all atoms drawn at the 68% level. As well as implausibly large displacements of O(1) and O(2) atoms, both octahedra of the tetragonal structure have highly variable bond-lengths not seen in hydroxide perovskites, and being due to the incorrect choice of space group P4 2 /n. accessed by other elements with variable oxidation states, such as Co and Mn. Furthermore, the extent of solid solution between divalent and trivalent cations could be increased, corresponding to a general stoichiometry M 3þ x M 2þ 1x ð Þ Sn(OH) (6−x) O x (1 ≥ x > 0.5).