Hidden and apparent twins in uranyl-oxide minerals agrinierite and rameauite: a demonstration of metric and reticular merohedry

Two examples of twinning, by metric and reticular merohedry, in uranyl-oxide minerals demonstrate the care that must be taken during structural studies, and not only of such complex materials. This contribution also demonstrates the possibilities of the Jana2020 program in revealing twinning and in subsequent refinement.

While the UOH sheets in the structure of agrinierite are based on the -U 3 O 8 type, the sheets in rameauite, despite the overall chemical similarity, are based upon the -U 3 O 8 type ( Fig. 1) The close chemical and structural similarities of the two UOHs prompted us to reinvestigate their structures. This revision led us to the conclusion that both structures are affected by twinning. Here we report the investigation of twinning in both minerals and provide a correct description of the agrinierite unit cell and improved structure models.

Samples studied
The studied specimen of agrinierite originates from the type locality: the former Margnac U mine located about 3 km from Compreignac, Haute-Vienne, Nouvelle-Aquitaine, France (Cesbron et al., 1972). The studied sample (8 Â 4 Â 3 mm) is constituted of earthy and massive yellow or orange 'gummite' crosscut by inframillimetre-sized veins covered with well shaped orange UOHs, including agrinierite and acicular uranophane-crystals. In these veins, agrinierite occurs as small (up to 0.8 mm long) pumpkin-orange tabular crystals on {001} pseudo-hexagonal crystals. The sample is preserved in the collection of the Geological Museum of Lausanne, Switzerland (catalog No. MGL 093238). From the same centimetre-sized mineral association, other UOH minerals analyzed utilizing powder X-ray diffraction and energydispersive X-ray spectroscopy reflect the distribution of alkaline and alkaline-earth elements on a millimetre scale: compreignacite (K), becquerelite (Ca) and billietite (Ba) (samples MGL 094375-094378).
Rameauite has been studied by Plá šil et al. (2016) using the specimen originating from Margnac, France.

Chemical composition of agrinierite
Even though agrinierite was discovered and described ca 50 years ago (Cesbron et al., 1972), its chemical composition remains poorly studied. In the original description, Cesbron et al. (1972) provided only one wet-chemical analysis and, for instance, reported a 2.05 wt% of SrO [$0.40 Sr atoms per formula unit (apfu)]. Cahill & Burns (2000) did not provide any chemical data and only gave the composition from the refined structure. The official International Mineralogical Association list of minerals reports agrinierite as K 2 Ca[(UO 2 ) 3 O 3 (OH) 2 ] 2 Á5H 2 O, thus totally neglecting the Sr content in the mineral. In response, we decided to undertake new reliable quantitative chemistry determination by electron microprobe. Crystals of agrinierite were mounted on epoxy resin, polished and carbon-coated to determine their chemical compositions utilizing a CAMECA SX100 electron microprobe. The measurement was performed in wavelengthdispersive mode at 15 kV accelerating voltage, 2 nA beam current and 15 mm beam diameter using the following standards: synthetic UO 2 for U, synthetic SrSO 4 for Sr, wollastonite for Ca and sanidine for K. No other elements were above the detection limit. Regardless of the mild analytical conditions, a systematic decrease of K K X-ray intensity during the analysis was observed. Thus, K was analyzed at the beginning of each measurement; the integration time of K was divided  into four periods and the concentration was calculated from the values of K K intensities extrapolated to time zero. The raw intensities were processed for matrix corrections using X-PHI matrix corrections (Merlet, 1994) involving a stoichiometric amount of H 2 O. The empirical formula was calculated on the basis of 6 U and the amounts of O, OH and H 2 O were derived from the structure and the rule of electroneutrality. Atomic proportions are shown in apfu (atoms per formula unit).

Single-crystal X-ray diffraction
Using single-crystal X-ray diffraction we studied a fragment of the tabular crystal of agrinierite from the Margnac deposit. The crystal of 0.122 Â 0.072 Â 0.020 mm dimensions was examined at room temperature using 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 using binning of 2 Â 2 pixels and a high-gain mode to register even very weak reflections with an acceptable resolution.
Rameauite was studied using the same instrument; details can be found in the paper by Plá šil et al. (2016). Here, we reanalyzed the diffraction data and conducted a new crystal structure refinement. The experimental and refinement details are reported in Table 1.
Subsequently, the structure of rameauite was reinvestigated and tested for twinning presence, following the same procedure as for agrinierite. We used the same reflection file as used in the study by Plá šil et al. (2016), but we reprocessed it with a newer version of the CrysAlis software (version 40.64.67a). We employed a new structure solution and refinement using this reflection file for consistency [we emphasize that by using the original reflection file from the study by Plá šil et al. (2016) and a twin-handling procedure in the current version of the Jana software (Jana2020), several problems occur, which can simply be overcome by using newly processed reflection files from the original diffraction frames]. The unit cell of rameauite, a = 13.947 (3), b = 14.300 (3), c = 13.888 (3) Å , = 118.50 (3) with V = 2434.3 (11) Å 3 , aligns with previous work (Plá šil et al., 2016). The structure was solved using SHELXT in the monoclinic space group Cc (Flack 0.42 by SHELXT output). The structure refinement involved an inversion twin due to merohedry and, in the final stages, also a reticular twin contribution, finally featuring eight twin elements (due to the group > subgroup relationship between tetragonal > monoclinic symmetry groups). As some of the twin-domain fractions returned slightly negative values they were fixed to 0; the rest of the refined twin fractions, mirror in (101) and inversion twin, returned meaningful values. The final refinement converged to R = 4.24% for 2344 unique observed reflections with I > 3(I) and GOF = 1.48. Statistical details for the refinement are given in Table 1. Final atom coordinates and displacement parameters for agrinierite are listed in Table 5, selected interatomic distances in Table 6 and a bondvalence analysis in Table 7. The bond-valence analysis was performed following the procedure by Brown (2002Brown ( , 2009) using bond-valence parameters provided by Gagné & Hawthorne (2015).
Twin contributions for both minerals were evaluated also visually using the reciprocal layer reconstructions retrieved from the diffraction frames (the UNWARP tool within the CrysAlis software) and by computer methods using the program Jana2020 (Figs. 2). We have chosen the best representatives for twinning in both minerals to be displayed. Figs. 2(a) and 2(b) display the h1l layer of the reciprocal space in agrinierite, with apparently all reflections overlapping. This makes the recognition of the twin presence relatively difficult, at least more difficult than in the case of rameauite [Figs. 2(c) and 2(d)]. Although the diffraction intensities are vastly affected by the twin contributions, at least some of the observed reflections that are diagnostic (e.g. Petříček et al., 2016), i.e. warning us of twinning, are 'visible' (i.e. are not completely overlapping as in the case of agrinierite).
For the evaluation of the twin type studied here, it is both necessary and useful to transform the C-centered unit cells into primitive ones. Otherwise, the results of the test for the higher-symmetry cell in Jana2020 will give correct results in terms of the searched cell, but the twin matrices will be applied to the conditions of the cell centering of our choice (and thus could be different from those without the applied conditions for centering and the systematic absences of reflections for the chosen space group). After C!P cell transformation the twin matrix of the mirror element for agrinierite is |1 0 0|0 1 0|1 0 1|, a mirror in (102), and for rameauite is |1/2 1/2 1/2|1/2 1/2 1/2|1 1 0|, a mirror in (111). Therefore, as the twin matrix for rameauite contains non-rational numbers, it appears to be twinned by reticular merohedry with apparent obliquity (diffraction type II). Agrinierite, with a matrix containing only rational numbers, thus appears to be twinned by metric merohedry [diffraction type I; see Petříček et al. (2016) for details]. To conclude, this is also the main reason for the distinct diffraction patterns of agrinierite [Figs. 2(a) Table 4 Bond-valence analysis (all values given in valence units, vu) for agrinierite.
The bond-valence parameters were taken from Gagné & Hawthorne (2015). H -including a contribution of donor-hydrogen bonds; nH -maximum number of possible weak HÁ Á Áacceptor bonds to a particular site. Idealized bond strengths were taken from Brown (2002

The refined structures of agrinierite and rameauite
The current structure model of agrinierite leaves the findings of Cahill & Burns (2000) about structure topology unchanged. Nevertheless, as the correct structure crystallizes in the monoclinic Cm space group, the single M 2+ -interlayer site in the model by Cahill & Burns (2000) is split into two symmetry non-equivalent sites. Moreover, Cahill & Burns (2000) restrained the occupation for Ca and Sr. The current model indicates that, while at one site (designated as M1) Sr is prevailing over Ca, at the second site (M2) Ca is slightly prevailing (Table 2). Therefore, we report the formula of agrinierite comprising two M 2+ sites as K 3.758 (Sr 0.89 Ca 0.11 )-(Ca 0.57 Sr 0.43 )[(UO 2 ) 3 O 3 (OH) 2 ] 4 Á10H 2 O, Z = 2. This formula is not electroneutral, having a 0.121 negative charge surplus; the scattering contribution of the K atoms, namely displacement parameters and occupation factors, is still probably vastly affected by twinning.
The same occurs for the structure model of rameauite, leaving the model proposed earlier by Plá šil et al. (2016) unchanged in general. The fit to the data is better overall, as it can also be documented by the root-mean-squared deviation of the final bond-valence sums of the oxygen atoms within the structure (with the considered contribution of the D-H bonds, equal to 0.8 vu, for the H 2 O and OH groups equally for both rameauite structure models). For the structure model given by Plá šil et al. (2016), this is 0.25 vu, and for the currently presented model it is 0.14 vu. The formula of rameauite, based on refined occupancies and bond-valence calculations, is K 4 Ca 2 [(UO 2 ) 3 O 3 (OH) 2 ] 4 Á12H 2 O, Z = 2. We report the formula based on the same Z as for agrinierite to obtain a better comparison.
(2) Higher residuals. In the case of agrinierite R obs > 6% along with the overestimated fit (S value from SHELX < 1 for the given weighting scheme).
Nevertheless, the handling of the twinned structures might not be as straightforward as for the untwinned structures. The second example, rameauite, is an illustrative case. The twinning features present in the structure (as documented in this study) were simply overlooked by one of the authors (JP). We emphasize that the tolerance limits (for maximal deviations for cell lengths and angles) had to be increased during the test for reticular twinning in Jana2020 for rameauite (up to 0.25 Å for cell lengths and 0.35 for angles). Then the procedure found the supercell of the higher symmetry unambiguously. We recommend doing so for cases of the worst diffraction data quality (and 'worse' fitted unit-cell metrics, which could bias the algorithm). However, the presence has to be then verified every time by a reasonable and meaningful structure refinement. For complicated unusual cases, when ordinary indexing programs (like the algorithms in CrysAlis) for unit-cell search fail, we recommend using the Jana2020 built-in indexing feature, GrIndex. It is a powerful tool, not only for finding the unit cell even from biased data but also for various cell transformations and projections of data.

Figure 2
Single-crystal diffraction patterns of agrinierite and rameauite. (a) Simulated h1l layer of the reciprocal space of agrinierite. Reflections from all domains overlap completely (i.e. 'hidden twinning') due to twinning by metric merohedry and generate an F-centered (pseudo)orthorhombic pattern (the black array corresponds to the unit cell given by the previous structure determination). (b) Reciprocal space reconstruction (UNWARP tool) of the h1l layer from the experimental data for agrinierite. (c) Simulated h1l layer of the reciprocal space of rameauite. Reflections for the two main domains overlap only partially, due to twinning by reticular merohedry. The array corresponds to the supercell. (d) Reciprocal space reconstruction (UNWARP tool) of the h1l layer from the experimental data for rameauite. Table 7 Bond-valence analysis (all values given in vu) for rameauite.
The bond-valence parameters were taken from Gagné & Hawthorne (2015). H -including a contribution of donor-hydrogen bonds; nH -maximum number of possible weak HÁ Á Áacceptor bonds to the particular site. Idealized bond strengths were taken from Brown (2002)