Redetermination and new description of the crystal structure of vanthoffite, Na6Mg(SO4)4

The crystal structure of vanthoffite, Na6Mg(SO4)4, was redetermined and refined with anisotropic displacement parameters for all atoms. Here, for the first time, we give its detailed description.


Chemical context
Vanthoffite is an evaporitic mineral that occurs worldwide in various salt, potash and sulfate marine deposits. It is also reported from the fumaroles of Kamchatka (Pekov et al., 2015) and Iceland (Balić-Ž unić et al., 2016). Fischer & Hellner (1964) solved its crystal structure giving the crystal lattice parameters, space group and atomic coordinates with isotropic atomic displacement parameters. To the best of our knowledge the only other crystal structure determination and refinement of an isostructural compound is for Na 6 Mn(SO 4 ) 4 (Sharma et al., 2017).
Here we report a redetermination and refinement of the crystal structure of vanthoffite, complete with anisotropic displacement parameters and provide a more detailed description. The precision of the present results is significantly better compared to the previous data of Fischer & Hellner (1964) because of the capabilities of modern X-ray diffraction equipment based on a hybrid photon-counting detector. The obtained R factor for the observed reflection data is 3.2% compared to 6.4% for the previous refinement, and the standard deviations of the atomic coordinates and displacement parameters are three to five times smaller. Consequently, the standard deviations of bond lengths and angles are generally ten or more times smaller than previously reported. Comparing our results with those of Fischer & Hellner (1964), we conclude that no differences of substantial character can be observed, and this pays a special credit to the latter work done ISSN 2056-9890 with significantly more effort than needed for the present one. The improvement in precision that we obtained, however, allows us to evaluate important structural details that were until now lacking for vanthoffite.

Structural commentary
In this work, we use three distortion parameters for the description of deviations of atomic coordinations from an ideal geometrical arrangement, viz. asphericity, eccentricity and volume distortion, as defined by Balić-Ž unić & Makovicky (1996), and Makovicky & Balić-Ž unić (1998). Numerical values of these parameters are collated in Table 1. They are useful because they clearly define the type and reason for distortion (in the case of a Jahn-Teller effect or the presence of lone electron pairs), and at the same time define the closest type of the coordination polyhedron.

Coordination polyhedra of Mg and S atoms
The unique Mg atom is located on a symmetry centre and is octahedrally coordinated by O atoms, whereas the two independent S atoms form tetrahedral sulfate groups with oxygen atoms (Fig. 1). The coordinations of Mg and S show very small distortions from the ideal octahedral and tetrahedral arrangements, respectively. As can be seen from Table 1, both S coordination polyhedra have very similar parameters. They are slightly eccentric; the longest bonds are to the O atoms that they share with Mg. This is plausible, because Mg has a larger electronegativity and a higher charge than Na. The Mg coordination polyhedron is even less distorted than those of S. The eccentricity is zero, in accordance with the site being on a symmetry centre and the other two distortion parameters are very low. The anisotropy of the displacement parameters of oxygen atoms bonded to S and Mg, with the overall oblate character of their ellipsoids and the longest diameters approximately perpendicular to the bonding directions, suggests, together with a low anisotropy of S and Mg displacement parameters, a rotational displacement of the coordination polyhedra around their centres (Fig. 1). Each of the vertices of an [MgO 6 ] octahedron is shared with one sulfate tetrahedron, in an arrangement known as a pinwheel structure (Moore, 1973).

Coordination polyhedra of Na atoms
The coordination environment for Na atoms is distorted octahedral in the case of Na1 and split-octahedral with a  Table 1 The parameters of the coordination polyhedra calculated with the program IVTON (Balić-Ž unić & Vicković, 1996). Notes: CN = coordination number; <d> = average bond length; bvs = bond valence sum, calculated using the exponential function of Brown & Altermatt (1985) with the parameters of Brese & O'Keeffe (1991); Vp = polyhedral volume; vd = volume distortion; asp = asphericity; ecc = eccentricity.

Figure 2
Atomic coordination of the Na2 atom. Displacement ellipsoids are as in Fig. 1. [Symmetry codes:

Figure 1
The atomic grouping around the [MgO 6 ] coordination polyhedron. Anisotropic displacement ellipsoids are drawn at the 50% probability level.

Figure 3
Atomic coordination of the Na3 atom. Displacement ellipsoids are as in Fig. 1. [Symmetry codes: coordination number (CN) of 7 for the other two independent Na sites (Figs. 2 and 3). We consider only the O atoms closer than 3 Å to be bonded to Na. There are further O atoms in the neighbourhood of Na, listed by Fischer & Hellner (1964), but we note that the distance gap to these additional O atoms is significant and their bonding contribution negligible according to bond-valence calculations. The volume distortions of the coordination polyhedra around Na2 and Na3 lie between those of an ideal pentagonal bipyramid (0) and an ideal 'split octahedron' (0.1333). The latter type of coordination was described in detail by Edenharter (1976) and Makovicky & Balić-Ž unić (1998). The coordination polyhedron of Na2 ( Fig. 2) can either be described as a pentagonal bipyramid with O4 and O6 as polar vertices, or as a split octahedron with O5 and O8 as a split vertex. Likewise, the coordination polyhedron of Na3 (Fig. 3)  ] are shared with a S1 and a S2 coordination tetrahedron, respectively.

Description of the crystal structure as an arrangement of coordination polyhedra of cations
The crystal structure of vanthoffite can be described as an interchange of two types of layers parallel to {100}, here labelled A and B (Figs. 4 and 5). Layer A is centred on the (0, y, z) plane and built of coordination polyhedra of Mg, S1 and Na3 (Fig. 6). [MgO 6 ] octahedra share four vertices with four [S1O 4 ] tetrahedra. They form intersecting chains running along the <011> directions. Sharma et al. (2017) described the crystal structure of the vanthoffite type as having an infinite two-dimensional framework of Mg coordination polyhedra and sulphate groups in the bc plane (which we confirm), but describe this framework as being composed of interconnected chains parallel to [010], which is an obvious mistake, as can be seen from Fig. 6. In layer A, [Na3O 7 ] coordination polyhedra are arranged in pairs that share a common edge (O2-O2 0 ). If we consider the coordination polyhedra of Mg and Na3 alone, they form chains parallel to [001] in which the Mg and Na coordination polyhedra also share edges (O1-O3). The chains interconnect through common O7 vertices, belonging to both the Mg and Na3 coordination polyhedra. The [Na3O 7 ] polyhedron also shares its O2-O3 edge with an [S1O 4 ] tetrahedron as mentioned above, plus an O1 vertex with another [S1O 4 ] tetrahedron.
Fischer & Hellner (1964) described the crystal structure of vanthoffite as a distorted hexagonal close packing of sulfate groups, with Mg in 1 4 of the octahedral holes. The authors did not specify the orientation of the close-packed sulfate layers. There are indeed approximately eutactic layers of sulfate groups parallel to the (001) plane. Their composition and stacking, however, deviate considerably from an ideal eutaxy. Moreover, considering the full framework of coordination polyhedra and chemical bonds, the structure is best described as layered parallel to (100) as in this work and in Hawthorne et al. (2000). Most of the previous authors essentially ignored the function of the [NaO x ] coordination polyhedra in building the crystal structure, and just mentioned the placement of Na in the holes of the framework of the Mg and S coordination polyhedra. Only Fischer (1973) discussed the three Na coordination types in this structure in a conference abstract. Since Na is the dominating cation in vanthoffite, the structurebuilding role of the [NaO x ] coordination polyhedra also needs to be considered, as we have tried to do in this article.
Vanthoffite is characterized by having six times as many Na atoms as Mg ones. The availability of Na coordination polyhedra in close contact, defining a three-dimensional framework, makes it a potential Na + ionic conductor. Sharma et al. (2017) found a high Na + conductivity only in the material obtained after the transition of vanthoffite-type Na 6 Mn(SO 4 ) 4 to a high-temperature phase. We hope that the present detailed description can help in understanding why Na + conductivity is observed in the high-temperature form only (once its structure is known), but not in the vanthoffite structure itself.

Synthesis and crystallization
The crystal used for the crystal structure analysis originates from a sample from Surtsey, collected in 1971 by Dr Svein Peter Jakobsson from the Icelandic Institute of Natural History, four years after the end of eruption that formed this volcanic island. The sample number in the mineral collection of the Institute is IN7484.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 2. Atomic sites were labelled to correspond to the original description of the crystal structure (Fischer & Hellner, 1964). A chemical analysis of the analysed crystal was not performed because of its very small size. As is typical for minerals from volcanic fumaroles, the mineral is fine grained and intimately mixed with several other phases, which makes an accurate chemical analysis extremely difficult, Layer A formed by the coordination polyhedra of Mg, S1 and Na3, projected on (100), with the c axis vertical. Attachment of S2 and Na1, both visualized as spheres, is shown.

Figure 7
Layer B formed by the coordination polyhedra of Na1, Na2 and S2, projected on (100), with the c axis vertical. To enhance clarity, the coordination polyhedra of Na1 are not filled; attachment of S1 visualized as a sphere is shown. even on a larger sample. The correspondence of the current crystal-structure parameters to those of the synthetic compound and the results of structural refinement indicate that the chemical composition is indeed very close to ideal without apparent influence from chemical impurities.  , 2007); program(s) used to refine structure: Jana2006 (Petříček et al., 2014); molecular graphics: ATOMS (Dowty, 2005).