Contributions to the stereochemistry of zirconium oxysalts—part IV: syntheses and crystal structures of Zr2(OH)2(XO4)3·4H2O (X = S, Se), Zr(SO4)2·4H2O, and Zr(SeO3)2

Zr2(OH)2(XO4)3·4H2O (X = S, Se), Zr(SO4)2·4H2O, and Zr(SeO3)2 were synthesized at low-hydrothermal conditions from mixtures of Zr2O2(CO3)(OH)2, the respective acids, and minor amounts of water. While Zr2(OH)2(XO4)3·4H2O (X = S, Se) and Zr(SO4)2·4H2O form crystals up to several tenths of a mm, Zr(SeO3)2 was mainly obtained as microcrystalline powder, single crystals rarely exceeded 10 μm in size. Samples were investigated by single-crystal X-ray techniques and in the case of Zr(SeO3)2 also by X-ray powder diffraction. The compounds Zr2(OH)2(XO4)3·4H2O (X = S, Se) crystallize in the Ce2(OH)2(SO4)3·4H2O structure type (C2/c, Z = 4, a = 13.034(2) / 13.308(3), b = 6.500(1) / 6.683(2), c = 15.056(3) / 15.383(4) Å, β = 96.27(1) / 96.81(1)°, V = 1267.9(4) / 1358.5(6) Å3 for X = S / Se, respectively). Tetragonal aniprisms Zr[8]O8 are edge-connected to dimers that share corners with XO4 tetrahedra forming a three-dimensional network. Zr(SO4)2·4H2O (Fddd, Z = 8, a = 5.498(1), b = 11.618(3), c = 25.893(6) Å, V = 1653.9(6) Å3) is isotypic with the respective selenate compound. Occasionally, pseudomerohedral twinning is observed, simulating a larger monoclinic C-centered unit cell. Again, tetragonal antiprisms Zr[8]O8 are formed; however, they are corner-linked with SO4 tetrahedra to Zr(SO4)2 layers interconnected solely by hydrogen bonds. Zr(SeO3)2 crystallizes in P21/c, Z = 2; a = 4.9724(3), b = 8.5992(5), c = 6.9447(3) Å, β = 110.128(3)°, V = 278.81(3) Å3 (unit cell from powder data) and belongs to the β-Sn(SeO3)2 structure type established further for Ti(SeO3)2 and Pb(SeO3)2. Isolated ZrO6 octahedra share corners with the selenite groups forming a three-dimensional network.

The crystal structure of Zr 2 (OH) 2 (SO 4 ) 3 ·4H 2 O was originally described by [4] but the experimental localisation of the hydrogen atoms was not possible at that time. The isotypic analogue Zr 2 (OH) 2 (SeO 4 ) 3 ·4H 2 O was unknown up to now. This structure type is further reported for Ce 2 (OH) 2 (SO 4 ) 3 ·4H 2 O [5].

Results and discussion
Selected individual and mean bond lengths and angles as well as bond valences ν (calculated according to [20]) of the four title compounds are listed in Table 1. Details about the hydrogen bonds are compiled in Table 2.

Zr 2 (OH) 2 (XO 4 ) 3 ·4H 2 O (X = S, Se)
The zirconium atoms in the isotypic compounds Zr 2 (OH) 2 (XO 4 ) 3 ·4H 2 O (X = S, Se) are coordinated by eight oxygen atoms arranged in distorted tetragonal antiprisms. The ligands are represented by the oxygen atoms of two hydroxyl groups (O h 1) and two H 2 O molecules (O w 8, O w 9), as well as by four oxygen atoms of XO 4 tetrahedra (O2, O4, O5, O6). Each two ZrO 8 polyhedra are edgeconnected to form dimers. The common O h 1-O h 1 edges are shortened to ~ 2.34 Å in both compounds due to repulsion of the two tetravalent central atoms. These dimers are corner-linked with two crystallographically different XO 4 tetrahedra (Fig. 1); one has the point symmetry 2, the other is centered on a general position. The oxygen atoms O3 and O7 belong to the XO 4 tetrahedra only; furthermore they act as acceptor atoms of three respectively two hydrogen bonds ( Table 2). The hydrogen bond lengths D-H···A are ~ 2.7 Å for the H 2 O molecules but somewhat longer for the hydroxyl groups (2.84 and 2.96 Å for X = S and Se, respectively). Without considering the contributions of hydrogen atoms, the bond valences amount to ~ 1.5 and 1.6 v.u. for the atoms O3 and O7, respectively [20]. The proposed model complies well with calculated bond valences.
Topologically, the crystal structure is formed by Zr 2 (OH) 2 [9,10,14]. For Zr(SeO 4 ) 2 ·4H 2 O the presence of a maximum in the residual electron-density (9.7 e Å −3 ) was observed at the special position 8a (at 1/8 5/8 5/8) [1]; it was attributed to a partially occupied site Zr2 going along with the formation of vacancies at the Zr1 position [8b, at 5/8 5/8 5/8]. The occupation factors for the Zr1 and Zr2 atoms were refined to 0.960(1) and 0.040(1), respectively, indicating a slight site disorder [1]. In the present study on Zr(SO 4 ) 2 ·4H 2 O, the highest residual electron density amounts 2.2 e Å −3 ; it again occurs at the 8a position. This slightly enhanced electron density is not considered to be  [10]. In β-Ce(SO 4 ) 2 ·4H 2 O (space group Pnma) the respective layers are puckered. For detailed discussions, comparisons, and illustrations of the differences and similarities of these two structure types see [10].
A further modification, i.e. γ-Ce(SO 4 ) 2 ·4H 2 O, was described in literature [16] in space group C2/c. However, already in Ref. [10] the authors note that "The packing features adopted by the monoclinic form are very similar to the one adopted by the α-form", and the respective structure layers were compared in their Fig. 3, but not further discussed in detail. A transformation of the unit-cell parameters listed by [16] for the space group C2/c according to [1/3 0 2/3 / 0 1 0 / 1/3 0 -4/3] results in the cell parameters a = 11.988, b = 5.633, c = 26.614 Å, α = 90.00, β = 90.03, γ = 90.00°; they fit with those given by [10] for the orthorhombic modification of α-Ce(SO 4 ) 2 ·4H 2 O, a = 5.6587(1), b = 12.0469(2), c = 26.7201(3) Å. Applying the same transformation to the atomic coordinates of the two Ce and three S atom positions results in overlapping Ce···Ce distances < 0.009 Å and S···S distances < 0.015 Å. For the O atoms the situation is not that clear as obviously some misprints occur already for the atomic coordinates published in space group C2/c [16]: e.g. O16···O16 (1.21 Å), O13···O18 (2.13 Å), O18···S2 (1.95 Å), although the published H atom positions are conspicuous (see also comments to Figs. 2 and 3). As a consequence, the existence of the structure type of γ-Ce(SO 4 ) 2 ·4H 2 O must be doubted. Very likely, the phase investigated by [16] actually is the modification α-Ce(SO 4 ) 2 ·4H 2 O. This close similarity is evident also in our Figs. 2 and 3a, 3b. In the light of the present investigations on the crystal structure of Zr(SO 4 ) 2 ·4H 2 O with its remarkable twinning behavior (see chapter on single-crystal X-ray diffraction in the experimental part), it seems very likely that crystals of α-Ce(SO 4 ) 2 ·4H 2 O might be twinned in the same way as described herein, thus simulating a monoclinic C-centered Table 2 Selected data for hydrogen bond systems in Zr 2 (OH) 2 (XO 4 ) 3 ·4H 2 O (X = S, Se) and Zr(SO 4

Zr(SeO 3 ) 2
The atomic arrangement in Zr(SeO 3 ) 2 consists of isolated ZrO 6 octahedra, sharing all corners with trigonal pyramidal selenite groups as illustrated in Fig. 4. Four-and six-membered rings consisting of alternating Zr atoms and selenite groups are formed, linked to tubes running parallel to [100]. The Se atoms of the selenite groups point into these tubes to give space for the lone-pair electrons. The compound is isotypic with Ti(SeO 3 ) 2 [18], Pb(SeO 3 ) 2 , and β-Sn(SeO 3 ) 2 [19], a comparison is given in Table 3. It has to be noted that the unit cell volumes of Zr(SeO 3 ) 2 and Pb(SeO 3 ) 2 are rather similar, while the mean Zr-O bond length resembles more closely that of the SnO 6 polyhedron. Actually, based on the single-crystal data, the mean M 4+ -O bond lengths in this group obey a strict linear correlation with their respective ionic radii. The comparatively high cell volume of Zr(SeO 3 ) 2 could be induced by the clearly extended M-O-Se angles, which in turn are negatively correlated with the octahedral bond angle distortion σ oct 2 ( Table 3). As outlined in the section on X-ray powder diffraction, a previous description of Zr(SeO 3 ) 2 with orthorhombic symmetry (space group Pmmm) from powder data [17] and the respective ICDD entry 50-0336 have to be revised.

Analysis of structural similarities
The title compounds and isotypic analogues were geometrically analyzed with the program COMPSTRU as summarized in Table 4 (for details see [16] is shown with dashed lines for compari-son. Note: to comply at least approximately with the bond lengths and figures given in [16], the coordinates of O16, O18, H7, H8, H11, and H12 had to be corrected 0.160 Å). Again, the smaller shift of the S2 atom is notable. In case of the α-M(XO 4 ) 2 ·4H 2 O structure type (space group Fddd), the smallest degree of lattice distortion and the closest structural similarity are verified between the Zr-and Hf-sulfates. For the selenites M(SeO 3 ) 2 (M = Zr, Sn, Ti, Pb) the M atoms are strictly localized due to their point symmetry mmm, but a pronounced shift and rotation of the selenite group is observed. Compared to Zr(SeO 3 ) 2 , the lattice distortion is large for the Ti-compound but consistently smaller for the Sn-and Pb-representatives; however, the ratios of the corresponding lattice parameters are inverse proportional.  'monoclinic γ-Ce(SO 4 ) 2 ·4H 2 O' according to [16] in a projection onto ( 2 0 1). Note: to comply at least approximately with the bond lengths and figures given in [16], the coordinates of atoms O16, O18, H7, H8, H11, and H12 had to be corrected C-centered cell. By analogy, we postulate that the previously proposed γ-modification of Ce(SO 4 ) 2 ·4H 2 O (space group C2/c [16]) is most probably identical with α-Ce(SO 4 ) 2 ·4H 2 O. Finally, Zr(SeO 3 ) 2 is monoclinic (space group P2 1 /c) and belongs to the structure type known for Ti(SeO 3 ) 2 , Pb(SeO 3 ) 2 , and β-Sn(SeO 3 ) 2 . A previous indexing of Zr(SeO 3 ) 2 with orthorhombic symmetry (space group Pmmm) from powder data [17] and the respective ICDD entry 50-0336 have to be revised.

Conclusion
At the time we started our investigations of zirconium oxysalts [1], more than a dozen of purely inorganic zirconium sulfates, but no selenates or selenites had been structurally described in the literature. In the course of our studies [1][2][3] and present work, we were as yet able to synthesize and characterize seven zirconium sulfates as well as seven zirconium compounds containing [SeO 4 ] and/or [SeO 3 ] anions with interesting stereochemical properties. Currently, in continuation of our research program, the investigation of eight new zirconium oxysalts is in progress. Usually, respective Zr-sulfates and -selenates were found to be isotypic. Besides, the rare element hafnium, substituting zirconium in nature (it is found e.g. as a solid solution with Zr in the mineral zircon, ZrSiO 4 ) is also expected to form isotypic compounds as reported for zirconium. While a series of respective hafnium sulfates are listed in the ICDD database, no hafnium selenates or selenites are evident so far. It is most likely that a thorough study on this class of compounds will be promising, too.  respectively, and a few tenths of a cm 3 water filled in Teflon-lined steel vessels of about 5 cm 3 volume (filling level ≤ 25%). The autoclaves were heated up to a maximum of 220 °C within several hours, kept at this temperature for one week and finally cooled down slowly to room temperature.
In case of Zr 2 (OH) 2 (XO 4 ) 3 ·4H 2 O (X = S, Se) and Zr(SO 4 ) 2 ·4H 2 O colorless crystals up to several tenth of a mm formed; they were separated from the remaining liquid, washed in methanol, dried, and embedded in silicone grease. Zr(SeO 3 ) 2 was obtained mainly as a very finegrained white powder, only occasionally crystals with up to 10 µm were obtained; the largest one found was used for the single-crystal X-ray investigation. By variation of reaction conditions (ratio of precursor reagents, temperature, cooling rate, pH value) no significant effect on the grain size of the precipitate could be achieved. In literature, the formation of zirconium selenite only as nanoparticles or microcrystals [21,22] by reaction of ZrO(NO 3 ) 2 ·H 2 O and SeO 2 at room temperature has been described.

Single-crystal X-ray diffraction data and structure refinement
Selected fragments of Zr 2 (OH) 2 (XO 4 ) 3 ·4H 2 O (X = S, Se), Zr(SO 4 ) 2 ·4H 2 O, and a tiny chip of Zr(SeO 3 ) 2 were prepared for single-crystal X-ray investigations. Data collections were performed on a Bruker APEXII diffractometer equipped with a CCD area detector, an Incoatec Microfocus Source IµS (30 W, multilayer mirror, Mo-K α ), and an Oxford Cryosystems Cryostream 800 Plus LT device; the crystal-detector distance was 40 mm. Zr(SeO 3 ) 2 was studied at room temperature, all other samples at 200 K to avoid decomposition and improve the location of the hydrogen atoms. Several sets of phi-and omegascans with 2° scan-width were combined to achieve respective full-sphere data. For data handling including integration and absorption correction (evaluation of multi-scans) the Bruker Apex3 suite was used [23]. For Zr 2 (OH) 2 (XO 4 ) 3 ·4H 2 O (X = S, Se) the atomic coordinates reported by [4] were taken as starting parameters and the crystal structures were refined by full-matrix least-squares techniques (Shelxl [24]). The positions of the hydrogen atoms were revealed from final difference Fourier maps. Crystal parameters as well as a summary on the data collections and structure refinements are given in Table 5, final atomic positions are compiled in Table 6.
It has to be noted that for Zr(SO 4 ) 2 ·4H 2 O standard indexing of the 'single-crystal' reflex positions led to a monoclinic C-centered unit cell (a = 34.815 (5) At a first glance, the refinement gave a reasonable result (R1 = 0.028). However, an evaluation of the refined atomic arrangement (via the ADDSYMM tool implemented in the program PLATON [25]) revealed the presence of "nonspace group" translation vectors. A further analysis of the collected data with the program CELL_NOW [26] indicated the tentative presence of a twinned crystal with F-centered orthorhombic unit cell. A transformation of the atom coordinates formerly obtained in space group C2/c by the transformation matrix [1/3 0 2/3 / 0 1 0 / 1/3 0 −4/3] resulted in the hitherto known unit cell and an atomic arrangement based on space-group symmetry Fddd, also known for α-Ce(SO 4 ) 2 ·4H 2 O [10]. Finally, the observed reflection pattern is best described by an orthorhombic unit cell (a = 5.498, b = 11.618, c = 25.893 Å, Z = 8) and assuming a twinning (twin matrix [1 0 0 / 0 2/3 1/3 / 0 -5/3 2/3]). The conclusive structure refinement, starting with the atomic positions given in [1,10], is based on a new processing of the measured reflection intensities of both orthorhombic twin components (Bruker APEX3 program suite [23], a reflection file in format HKLF5 from program TWINABS [27]). The orthorhombic crystal-structure model was refined satisfactorily to R1 = 0.027 with twin components of 73(1) and 27(1)%.
For the refinement of Zr(SeO 3 ) 2 (see also next section) the unit-cell setting and the atom labelling scheme were chosen in accordance to literature on the isotypic compounds M(SeO 3 ) 2 with M = Ti, Sn, and Pb [18,19].
Furthermore, the title compounds and isopointal analogues were geometrically analyzed with the program COMPSTRU [28,29]. It allows a comparison between the configurations of crystal-structure pairs by the degree of lattice distortion (S), the maximal displacement between the atomic positions of the paired atoms (d max ), the arithmetic mean of the displacement between the atomic positions (d av ), and the similarity as a function of the differences in atomic positions and the ratios of the corresponding lattice parameters (Δ). The results are compiled in Table 4. The atom labels for the structure types under discussion refer to those given in Table 6.

Powder X-ray diffraction work
Microcrystalline powder of Zr(SeO 3 ) 2 was studied at ambient conditions on a Bruker D8-Advance Eco diffractometer system, equipped with a CuKα-optimized LynxEye XE-T position sensitive detector with an angular opening of 3.29° 2θ, primary Ni-filter, fixed divergence slit (FDS = 0.3°), 2.5° soller slits for primary and secondary beam path, a fixed anti-scatter knife edge improved by an in-house variable anti-scatter screen and sample φ-spinning (15 min −1 ). Sample diameter and FDS setting avoided beam spill in the angular range of the first occurring peak at ~ 17° 2θ. Data were collected from 5 to 125° 2θ with ~ 0.01° 2θ step size and an overall measurement time of 200 min (equivalent to an accumulated step counting time of 330 s), thus leading to an I max of ~ 35,000 counts. The ambient temperature within the Eco-system enclosure was about 30(2) °C. Identification and characterization of crystalline phases was undertaken using the program EVA [30]. Consecutively, the advanced qualitative data treatment based on indexing [31], whole powder pattern decomposition [32], and structure refinement [33] was done with the program TOPAS [34]. The atomic coordinates of the isotypic compounds M(SeO 3 ) 2 with M = Ti, Sn, and Pb [18,19] were used as starting structural parameters.
For the preliminary data evaluation, a Pawley refinement based on the orthorhombic unit cell given in literature [17] was performed, clearly demonstrating a misfit of Table 5 Relevant crystal data and details of the single-crystal intensity measurements and structure refinements for Zr 2 (OH) 2 (XO 4 ) 3 ·4H 2 O (X = S, Se), Zr(SO 4 ) 2 ·4H 2 O, and Zr(SeO 3 ) 2   Table 6, the final Rietveld plot is shown in Fig. 5. X-ray powder-diffraction data are listed in Table 7.