Crystal structure of the uranyl arsenate mineral hügelite, Pb2(UO2)3O2(AsO4)2(H2O)5, revisited: a correct unit cell, twinning and hydrogen bonding

The crystal structure of the uranyl arsenate mineral hügelite is affected by twinning due to reticular merohedry (diffraction type II). This study documents, apart from the correct description of the unit cell and the nature of the twinning, the possibilities of the JANA2006 program in revealing the real nature of twinning even if using published structural data without the original reflection files.

The new find of the rare mineral hü gelite from the small uranium deposit Labská , Krkonoše Mts. (Czechia), prompted us to perform a new diffraction experiment, which revealed that the actual twinning in hü gelite is different from the description presented by Locock & Burns (2003). Here we report on the results of our analysis that might help to understand the nature of the twinning in this mineral, as well as helping in future analyses of similarly twinned crystal structures.

Sample
The hü gelite crystal used in this study was extracted from a specimen collected by Pavel Š ká cha from the Labská uranium deposit. This small uranium deposit is located approximately 5 km to the south of the town of Š pindlerů v Mlý n in the Krkonoše Mountains (Eastern Bohemia, Czechia). Hü gelite forms elongated prismatic crystals apparently flattened on one of the prismatic faces. Crystals reach maximally up to 1 mm across ( Fig. 1). They are dark orange in colour. Hü gelite was found on a few specimens only, associated with more abundant dumontite. Phosphuranylite and saleé ite were also identified in the association.

Single-crystal X-ray diffraction
We studied two tiny crystals of hü gelite from the Labská deposit. While the first crystal (hereafter denoted Labská I) of Table 1 Details of the data collection and refinement for the two different crystals of hü gelite from the Labská deposit.  Figure 1 An aggregate of the tabular yellow crystals of hü gelite from the Labská deposit. Field of view 7 mm (photo by P. Š ká cha). approximate dimensions 0.038 Â 0.013 Â 0.007 mm was later found to be affected by twinning, the second crystal (Labská II), having similar, but somewhat larger, dimensions (0.067 Â 0.018 Â 0.005 mm) was found later on to be untwinned. Diffraction experiments were carried out at room temperature with a Rigaku SuperNova single-crystal diffractometer. The diffraction experiment was carried out using Mo K radiation ( = 0.71073 Å ) from a micro-focus X-ray tube collimated and monochromated by mirror optics and detected by an Atlas S2 CCD detector.
For both experiments, !-rotational scans (of frame width 1 ) were adopted and a full sphere of the diffraction data was collected. For the larger crystal, Labská II, an increased counting time per frame, equal to 840 s (compared to 400 s for Labská I), a high-sensitivity mode of the CCD detector (binning of pixels 2Â2, with a high-gain option) and highredundancy of the data set ($7) were used to reveal even weak reflections.
The diffraction experiment for Labská I, as expected, due to previous results given by Locock & Burns (2003), provided a particularly complicated diffraction pattern, caused by twinning due to reticular merohedry (Petříček et al., 2016). The studied crystal was found to be monoclinic, but with different unit-cell parameters than given by Locock & Burns (2003). Actually, the unit-cell parameters found are a = 7.0189 (7) Å , b = 17.1374 (10) Å , c = 8.1310 (10) Å and = 108.904 (10) , with V = 925.29 (15) Å 3 and Z = 2 ( Table 1). The reticular twin (diffraction type II) was found by the routine implemented in the JANA2006 program (Petříček et al., 2014). The twin operation is a mirror in the [100] direction; the second twin domain can be obtained by the matrix (À1 0 0 | 0 1 0 | 0.75 0 1), simulating a pseudo-orthorhombic supercell, which is eight times larger than a real (sub)cell (a = 7.019 Å , b = 17.137 Å , c = 61.539 Å and = 90.02 ). Therefore, during the data reduction, each twin domain was integrated alone and later imported into the JANA2006 program utilizing the already known twin matrix that helped to define the orientation of each unit cell, thus resolving fully overlapped reflections. Those reflections, present in both data blocks, were included only one time to avoid their multiple occurrences in the refinement. The refinement in JANA2006 including the twin model led to reasonable values of the twin fractions, i.e. 0.877 (1):0.123 (1) ( Table 1); noticeably, the second twin domain is rather weak. The refinement, which took into account twinning, improved/smoothed slightly the difference Fourier; nevertheless, there are still false maxima due to poorly fitted absorption (apparent in the vicinity of the U atoms). The fact that intensities (and namely those of the contributing second domain) are quite weak resulted in the refinement converging to higher R = 7.58% for 2110 reflections with I > 3(I) (GOF = 1.63); noticeably, on first sight, we have also to take into account a different approach to the weighting scheme of the current refinement and a criterion for observed intensities.
Structure solution for the Labská I crystal was carried out using the intrinsic phasing algorithm of the SHELXT program (Sheldrick, 2015); refinement of Labská II was carried out using the model obtained for Labská I. Details of the data collection and refinement for both crystals are given in Table 1, final atomic coordinates and displacement parameters in Table 2, selected interatomic distances and hydrogen-bond parameters in Table 3, and a bond-valence analysis in Table 4. The bond-valence analysis was made following the procedure of Brown (2002Brown ( , 2009) using bond-valence parameters provided by Gagné & Hawthorne (2015). The formula of the crystal studied, based on refined occupancies and bondvalence calculations, is Pb 2 (UO 2 ) 3 O 2 [(As 0.583 P 0.417 )O 4 )] 2 (H 2 O) 5 (Z = 2 and D calc = 5.669 Mg m À3 ).
Twin contributions were evaluated visually using the reciprocal layers (Fig. 2) reconstructed from the CCD frames (UNWARP tool within the CrysAlis software; Rigaku OD, 2019) and by computer methods using the program JANA2006 (Fig. 3). Twinning and the extra reflections due to twinning are easily visible for the Labská I crystal at the h0l and hk2 layers, for instance, while Labská II provided unbiased frames (Fig. 3). The presence of additional reflections can bias the indexing algorithms, because it simulates the larger unit-cell parameter. While the refinement of the Labská I crystal returned the refined twin fractions 0.877 (1) Table 4 Bond-valence analysis (all values given in valence units, v.u.) for hü gelite.
The bond-valence parameters are taken from Gagné & Hawthorne (2015

Figure 2
Twinning in hü gelite, showing the reciprocal space reconstruction for the twinned (Labská I) and untwinned (Labská II) crystals. The twin contribution is easily visible in the case of the h0l layer. The biased intensities are apparent for the hk2 layer.  (Table 1), the second crystal showed a negligible contribution of twinning only when a mirror operation was taken into account, Tw vol1 /Tw vol2 = 0.9994 (5)/0.0006 (5).

Results
Our description of the twinning in hü gelite leaves the structure model proposed by Locock & Burns (2003) unchanged. The structure possesses uranyl-arsenate sheets with a phosphuranylite topology (Burns, 2005;Lussier et al., 2016), with Pb 2+ cations located in the interlayer space between the infinite sheets (Fig. 4).

Twinning in hügelite
The twin operation, i.e. a mirror in [100], leads to a rather large supercell, with V $ 7400 Å 3 . There is a clear relationship between the unit cell derived by Locock & Burns (2003) and the supercell found in our study. The cell of Locock & Burns (2003) is half the volume of the supercell of our choice: our cell thus represents a real cell of hü gelite, while the cell of Locock & Burns is a result of twinning (Fig. 3); the unit cell of Locock & Burns (2003) (a = 30.993 Å , b = 17.159 Å , c = 7.022 Å and = 96.44), when applied a mirror in (001), leads to the same supercell as in the current study. The correct description of twinning in hü gelite confirmed the originally reported unit cell (Walenta, 1979), having a unit-cell volume of $930 Å 3 . The correct unit cell of hü gelite (V $ 930 Å 3 ), when compared to dumontite (V $ 920 Å 3 ), confirms that these two minerals are isotypic As-and P-dominant analogs, respec-tively. The increase of the unit-cell volume towards the As end member (hü gelite), due to the larger effective ionic radius of As 5+ compared to P 5+ , is apparent. It should be noted that the currently investigated crystal of hü gelite is not an end member of the solid-solution series, based on the site-scattering refinement (Tables 1 and 2).

Hydrogen bonding in hügelite
Although hü gelite is a highly absorbing substance, even for Mo X-rays ( = 46.30 mm À1 ), final difference-Fourier calculations revealed few maxima assignable to H atoms around those O atoms that belong, according to the bond-valence analysis, to H 2 O groups. Because it was impossible to freely refine all the parameters of the H atoms, they were refined using restrictions available in JANA2006 for the hydrogenbond geometry. Therefore, the scheme presented should be considered as an approximation at best. We also have to emphasize that the higher BV sums for both H atoms and the donor O atoms resulted from the used restraint on the A-H bond length taken as 0.82 Å as a conservative value for the hydrogen-bond length from X-ray analysis.
The hydrogen-bonding scheme can be deduced from the results of the bond-valence analysis (Table 4). There are three symmetrically independent H 2 O sites (corresponding to O5, O10 and O12), indicating five H 2 O molecules per unit cell for Z = 2. While atom O5 seems to be three-coordinated (one bond from Pb1 and two bonds to H1O5 and H2O5), atoms O10 and O12 are five-and four-coordinated, respectively. According to the terminology introduced by Schindler & Hawthorne (see, for example, Schindler & Hawthorne, 2008), O5 represents the transformer H 2 O group, while O10 represents an inverse transformer and O12 represents a nontransformer H 2 O group. Therefore, the current results are in contrast to the theoretical predictions made by Schindler & Hawthorne (2008), who concluded that hü gelite should contain five inverse transformer (H 2 O) groups, based on the bond-valence approach. The above-mentioned scheme should be taken as a best-available model only. Due to underbonding of the O1 U eq and O2 U eq atoms (with corresponding low BV sums; Table 4), we can speculate about a somewhat different configuration, involving also the two O atoms U eq . Nevertheless, for such a task, employment of advanced theoretical approaches, as used recently for the uranyl phosphate mineral phurcalite (Plá šil et al., 2020), would be necessary.
4. Implications -processing the data using JANA2006 to reveal the nature of twinning Despite the fact that we did not have an original reflection file for the refinement of Locock & Burns (2003), the software we used for the structure analysis, JANA2006, enables us to perform a check for twinning in their structure, based on the available crystallographic information file (CIF). We have to emphasize here that the warning for the hidden translation symmetry in the CIF file of Locock & Burns (2003)   The crystal structure of hü gelite projected down the monoclinic b axis. UO 7 bipyramids are shown in transparent yellow, UO 8 bipyramids are opaque yellow, (As/P)O 4 tetrahedra are green, Pb atoms are dark gray (shown as displacement ellipsoids at the 75% probability level), H atoms are light gray and O atoms are red. The unit-cell edges are outlined with solid black lines. HÁ Á ÁA bonds have been omitted for clarity. checkCIF), returning the B Alert: 'PLAT113_ALERT_2_B ADDSYM Suggests Possible Pseudo/New Space Group P2 1 /m Check Note: (Pseudo) Lattice Translation Implemented'. The entire procedure we followed in JANA2006 is displayed in Fig. 5. The first step involves a calculation of the theoretical reflection file (Mo K, full sphere) based on the atom positions in the CIF of Locock & Burns (2003). The next step involves the calculation of the Patterson map. As the autoconvolution of the electron density itself, it provides important information of the real metrics and can thus reveal the real periodicity features underlying the data. This analysis showed three pronounced Patterson maxima; from them, assuming the omnipresent inversion in the Patterson map, we obtained three translation vectors: (0, 0, 0), (À 1 4 , 0, 1 4 ), ( 1 2 , 0, 1 2 ), ( 1 4 , 0, À 1 4 ). Those were used for the unit-cell transformation by the matrix | 1 4 0 À 1 4 | 0 1 0 | 0 0 1 |. After axis transformation (a!c), we obtained the following cell: a = 7.043 Å , b = 17.30 Å , c = 8.1554 Å , = 90 , = 108.879 and = 90 . During the next step, the creation of the refinement reflection file (even if from the simulated data), there were 24 reflections found that violated the translation symmetry. Nevertheless, they were weak. The structure after the transformation into the smaller cell shows few atoms projected into very close positions (<0.5 Å ). Merging the 24 atoms and refinement of the simulated structure led then to reasonably low R values ($4.2% for 2771 reflections). The test for twinning by reticular merohedry/pseudomerohedry (Petříček et al., 2016) readily revealed an orthorhombic supercell (7.043 Å , 17.302 Å , 61.733 Å , 90 , 89.98 , 90 ), with a unit-cell volume eight times larger than the real cell. This supercell is a result of the twinning that can be described as a mirror in (100) of the a = 7.043 Å , b = 17.302 Å , c = 8.1554 Å , = 90 , = 108.879 and = 90 cell. Fig. 3(a) displays a pattern of the eight times larger cell; from this point of view, the cell choice of Locock & Burns (2003) is reasonable and is due to twinning, which had been present in their crystal without any shadow of a doubt.