research papers
Structural complexity of natural uranyl sulfates
^{a}Department of Crystallography, St. Petersburg State University, University Emb. 7/9, St. Petersburg, 199034, Russian Federation, and ^{b}Institute of Physics ASCR, v.v.i., Na Slovance 2, Praha 8, 18221, Czech Republic
^{*}Correspondence email: plasil@fzu.cz
Uranyl sulfates, including those occurring in Nature (∼40 known members), possess particularly interesting structures. They exhibit a great dimensional and topological diversity of structures: from those based upon clusters of polyhedra to layered structures. There is also a great variability in the type of linkages between U and S polyhedra. From the point of view of complexity of those structures (measured as the amount of Shannon information per unit cell), most of the natural uranyl sulfates are intermediate (300–500 bits per cell) to complex (500–1000 bits per cell) with some exceptions, which can be considered as very complex structures (>1000 bits per cell). These exceptions are minerals alwilkinsite(Y) (1685.95 bits per cell), sejkoraite(Y) (1859.72 bits per cell), and natrozippeite (2528.63 bits per cell). The complexity of these structures is due to an extensive hydrogen bonding network which is crucial for the stability of these mineral structures. The hydrogen bonds help to propagate the charge from the highly charged interlayer cations (such as Y^{3+}) or to link a high number of interlayer sites (i.e. five independent Na sites in the monoclinic natrozippeite) occupied by monovalent cations (Na^{+}). The concept of informational ladder diagrams was applied to the structures of uranyl sulfates in order to quantify the particular contributions to the overall informational complexity and identifying the most contributing sources (topology, real symmetry, interlayer bonding).
Keywords: uranyl sulfates; crystal structure; Shannon information; structural complexity; topological complexity; ladder diagrams.
1. Introduction
Naturally occurring uranyl sulfates are important phases both from the mineralogical and the environmental point of view. Assemblages of uranyl sulfate minerals are common in oxidized parts of uranium deposits worldwide. They form via the oxidation–hydration weathering of primary uranium minerals, mainly uraninite, which interact with acid solutions derived from the decomposition of such as pyrite or chalcopyrite (Finch & Murakami, 1999; Krivovichev & Plášil, 2013; Plášil, 2014). The alteration of primary uranium ores under the low pH generates highly mobile acid solutions, containing dissolved UO_{2}^{2+} as UO_{2}–SO_{4} aqueous complexes, which yields a considerable environmental impact, especially around the old mining sites (Fernandes et al., 1995; Brugger et al., 2003; Johnson, 2003; Johnson & Hallberg, 2005). Uranyl sulfates show a great structural diversity (Krivovichev, 2010; Krivovichev & Plášil, 2013) arising from combinatorial and topological possibilities of linkage of the basic structural elements, uranyl coordination polyhedra and sulfate tetrahedra, which leads to a large variety of topological and geometrical isomers. Herein, we would like to characterize and quantify the topological and structural complexity parameters for one of the most representative groups of supergene uranium minerals – uranyl sulfates. We have used the approach recently developed by S. V. Krivovichev (Krivovichev, 2012, 2013, 2014, 2018), which allows the crystal structures to be characterized in terms of the information content.
2. Natural uranyl sulfates and their crystal structures
Hexavalent uranium in the solid state is most frequently present as a (nearly) linear uranyl ion, UO_{2}^{2+} (Ur), in which the bondvalence requirements of strongly bonded O atoms are almost satisfied (Fig. 1). Therefore, the bonding of additional elements takes place via ligands arranged in the equatorial planes of uranyl coordination polyhedra. In the case of uranyl sulfates, it goes exclusively about the uranyl pentagonal bipyramid, UO_{2}Φ_{7} (where Φ = O^{2–}, OH^{–}, H_{2}O). Sulfur is tetrahedrally coordinated as an SO_{4} tetrahedron and the linkage between U^{6+} and S^{6+} polyhedra is usually monodentate (with exceptions, see below). Polymerization of basic units leads to chain (10) or sheet (23) structures, which prevail over structures. There are fewer structures based upon isolated clusters of polyhedra (5). To date, 38 well characterized uranyl sulfates are known from Nature. Their overview and basic structural and chemical properties are reported in Table 1 as well as displayed in Fig. 2.
3. Complexity calculations
In order to evaluate the influence of various crystalchemical factors (such as dimensionality of the uraniumbearing units and their hydration state) on the structure and symmetry of uranyl sulfate complexes and on the structural architecture of minerals in general, the structural and topological complexity was studied in terms of the informationbased approach developed by Krivovichev (2012, 2013, 2014) and recently used by Cempírek et al. (2016), Gurzhiy et al. (2016, 2017, 2018a, b), Krivovichev et al. (2016, 2017), Majzlan et al. (2018) and Plášil (2018a,b). The structural complexity is quantitatively estimated as a Shannon information content per atom (I_{G}) and per (I_{G,total}). The amount of Shannon information reflects diversity and relative proportion of different objects, e.g. the number and relative proportion of different sites in an elementary of a For a the calculation involves the use of the following equations (Krivovichev, 2012, 2013, 2014):
where k is the number of different crystallographic orbits (independent crystallographic Wyckoff sites) in the structure and p_{i} is the random choice probability for an atom from the ith that is:
where m_{i} is a multiplicity of a (i.e. the number of atoms of a specific Wyckoff site in the reduced unit cell) and ν is the total number of atoms in the reduced unit cell.
The reliable correlation of complexity parameters is possible only for compounds with the same or very close chemical composition (e.g. polymorphs), whereas changes in hydration state could significantly change the complexity values. Analyzing the stability parameters of the minerals and possible mineral evolution trends, it is more reasonable to analyze topological and structural complexity of uranyl sulfate structural units as backbones of crystalline phases, whereas additional cations and water molecules occupying interlayer space can be excluded from the detailed consideration.
4. Topological and structural complexity
The informationbased complexity parameters for the Ubearing units in the structures of uranyl sulfate minerals are given in Table 2. Calculations have been performed in several steps. Firstly, the structural complexity of the structural units has been analyzed, taking into account their real layer (RL) or rod group (RG) symmetries. Secondly, the topological complexity (according to the maximal symmetry group) has been calculated. Complexity parameters for the whole structures have been calculated using the TOPOS (Blatov et al., 2014) package and are given in Table 2 for comparison. It should be taken into account that all calculations were based on the original files from the structural databases (Inorganic Database and American Mineralogist Database) and respective publications. In addition, positions of all H atoms have been assigned manually (if these data were not reported in the original entries) considering the distribution of hydrogenbonding system, which include traditional ranges of bond lengths and angles within the D—H⋯A atoms (here, D is a donor and A is an acceptor; both are O atoms).

The complexity calculations have been undertaken for 38 uranyl sulfate minerals with well defined crystal structures. The most frequent value of structural complexity of the entire structure (including H atoms) is between 500 and 600 bits per cell (with an average of 629.49 bits per cell and a median of 485.84 bits per cell). The distribution of the complexity values is asymmetric, showing a positive skewness (= 2.431) (Fig. 3). The majority of uranyl sulfate structures should be considered as intermediate (100–500 bits per cell) to complex (< 1000 bits per cell). Nevertheless, there are three exceptions, alwilkinsite(Y) (Kampf et al., 2017c), sejkoraite(Y) (Plášil et al., 2011a) and natrozippeite (Burns et al., 2003), that have very complex structures (> 1000 bits per cell) (Table 2). These structures are highly hydrated, either containing highly charged metal cations (Y^{3+} and REE^{3+}) or higher amounts of interstitial metal cations (cf. natrozippeite contains five Na and eight U, while magnesiozippeite contains one Mg and two U). Topological and structural complexities are described and discussed more in detail in the following text.
Crystal structures of belakovskiite, bluelizardite, klaprothite, péligotite and ottohahnite are based on the isolated uranyl sulfate structural units [Figs. 4(a)–4(d)]. The structural unit of belakovskiite contains: one U, four S, two uranyl O, 16 sulfate O, one water O and two H orbits, all with multiplicities of 1 (taking into account its p1 structural symmetry). In total, there are 26 orbits with onefold multiplicity (26 atoms). Structural complexity parameters for the uranyl sulfate unit in the structure of belakovskiite is calculated as I_{G} = 4.700 bits per atom, I_{G,total} = 122.211 bits per cell. In order to calculate the topological complexity parameters for the same unit, its maximal symmetry should be taken into account. The maximal symmetry of this topology is pmm2 (Fig. 4a), i.e. it is higher than the real symmetry. It is possible if sulfate tetrahedra have a mirror arrangement relative to the plane passing through the water molecule and Ur, and if two nonshared O atoms of sulfate tetrahedra are arranged one above another along the c direction, so the mirror plane would pass through the equatorial planes of uranyl bipyramids. In this case, the ν (number of atoms) is 26, but the distribution of orbits will change into another scheme: one U orbit with multiplicity of 1; one S orbit with multiplicity of 4; one O_{Ur} orbit with multiplicity of 2; six O_{S} orbits with multiplicities of 2, 2, 2, 2, 4, 4; one O_{H2O} orbit with multiplicity of 1; one H orbit with the multiplicity of 2. In total, there are two orbits with multiplicities of 1, six orbits with multiplicities of 2 and 3 orbits with multiplicities of 4. The topological complexity parameters for the uranyl sulfate units in the structure of belakovskiite are: I_{G} = 3.470 bits per atom, I_{G,total} = 90.211 bits per cell. Therefore, the structural information for the units in the structure of belakovskiite is higher than the topological information by a factor of ∼ 1.35. The topological symmetry of uranyl sulfate isolated units in bluelizardite is also pmm2 (Fig. 4b) and the structural information is higher than the topological information by the factor of ∼ 1.15. Isolated uranyl sulfate complexes in the structures of klaprothite and péligotite have rather low topological symmetry pm (Fig. 5c) due to the presence of three nonshared vertices at the sulfate tetrahedra transarranged relative to the edgeshared tetrahedra; thus, it is impossible for two mirror planes to be passed through them. The largest isolated complex among the uranyl sulfate minerals has been observed in the structure of ottohahnite (Fig. 4d). Due to the presence of two threeconnected sulfate tetrahedra, two geometrical isomers could be possible. If the fourth nonshared vertices were to arrange up and down relative to the equatorial planes of the uranyl polyhedra as it is in the structure of ottohahnite, the topological symmetry would be . If both vertices were arranged in one direction, topological symmetry would be p2, which in fact wouldn't affect the complexity parameters, since the number of orbits and their multiplicity of 2 will be the same in both cases.
The symmetry of the infinite chains is considered in terms of rod group theory. The structural RG symmetry of all ten minerals, where structures are based on the rarefied (adolfpateraite, fermiite, bobcookite and shumwayite structural types) and dense [alwilkinsite(Y), uranopilite] 1D uranyl sulfate complexes, is rather low and varies from to [Figs. 4(e)–4(j)]. At the same time, the presence of one and twoconnected sulfate tetrahedra allows much higher orthorhombic topological symmetry to be obtained. It is of interest that the maximal symmetry for topologically quite similar chains in the structures of fermiite [, Fig. 4(h)] and bobcookite [, Fig. 4(i)], in which the water molecule is replaced by the oneconnected sulfate tetrahedron, differs as it is impossible to have more than two planes passing through the additional three nonshared tetrahedral vertices. It should be also noted that the lowest topological symmetry [, Fig. 4(f)] among these 1D complexes has the chain in the structure of uranopilite.
The crystal structures of geschieberite, leydetite, magnesioleydetite, strassmannite and wetherillite are based upon the [(UO_{2})(SO_{4})_{2}(H_{2}O)]^{2−} uranyl sulfate layers of the same topological type [Figs. 5(a) and 5(b)]. Being twoconnected, all sulfate tetrahedra could rotate around this edge that result in various possible arrangements, and thus different LGs of symmetry. But all varieties are finally reduced to the maximal c2mm LG. Fig. 5(a) illustrates the real pn symmetry of the uranyl sulfate layer in the structure of geschieberite. In total, there are 16 orbits with the twofold multiplicity (32 atoms in the reduced cell). Structural complexity parameters for the uranyl sulfate layer in the structure of geschieberite is calculated as I_{G} = 4.000 bits per atom, I_{G,total} = 128.000 bits per cell. The highest symmetry could be obtained if both unshared vertices of the sulfate tetrahedra were arranged one above another along the c direction, so that the mirror plane would pass through the equatorial planes of uranyl bipyramids, resulting in twice reduced basecentered cell. In this case, the ν (number of atoms) is 16, and the distribution of orbits is as follows: one U orbit with multiplicity of 1; one S orbit with multiplicity of 2; one O_{Ur} orbit with multiplicity of 2; three O_{S} orbits with multiplicities of 2, 2 and 4; one O_{H2O} orbit with multiplicity of 1; one H orbit with multiplicity of 2. In total, there are two orbits with multiplicities of 1, five orbits with multiplicities of 2 and one orbit with the multiplicity of 4. The topological complexity parameters for the uranyl sulfate layer in the structures of geschieberite, magnesioleydetite and strassmannite are: I_{G} = 2.875 bits per atom, I_{G,total} = 46.000 bits per cell. Another interesting point is the symmetry of uranyl sulfate layer in the structure of wetherillite, which is topologically identical to the structures described above. However, these layered complexes are distinct because of the different arrangement of H_{2}O molecules (Fig. 5c) (see also Krivovichev et al., 2005; Krivovichev, 2008). Although the overall topology is the same, the current geometrical isomer will have another topological symmetry p2_{1}am with twice the number of atoms in the The ideal topology for the geometrical isomers could be different (for details see references cited above).
More complex topology of the uranyl sulfate layer in the structure of beshtauite, with elongated 12membered voids, results in an increased dimensionality of the pbam symmetry (Fig. 5d).
But twoconnected way of tetrahedra arrangement still keeps the high maximalCrystal structures of deliensite, feynmannite, greenlizardite, johannite and meitnerite are based on the layered uranyl sulfate complexes of the same topological type. This type of topology has threeconnected sulfate tetrahedra with the fourth nonshared vertex arranged up or down relative to the plane of the layer. This variability gives rise to geometric isomers with various orientations of the sulfate polyhedra (Krivovichev & Burns, 2003; Krivovichev et al., 2005; Gurzhiy et al., 2015). To identify and classify the isomers of this topological type, their orientation matrices should be determined. According to this approach, the symbols u (up) or d (down) are assigned to each sulfate tetrahedron. As the result, three different geometric isomers have been determined, which has their individual maximal symmetry group. Johannite and meitnerite have the dudu sequence of vertices orientation and c2/m LG symmetry (Fig. 6a). Layers in greenlizardite have the uuuu sequence of vertices orientation and cmm2 LG symmetry (Fig. 6b). Deliensite and feynmannite have the uddu orientation matrix and pmmn LG symmetry (Fig. 6c).
The presence of (VO_{5}) pyramids within the uranyl sulfate layers in the structures of mathesiusite and ammoniomathesiusite stabilizes the LG with the highest p4/n structural and topological symmetries (Fig. 6d) among the natural uranyl sulfates (Table 2). Although the symmetry is high, there is one U orbit with multiplicity of 8, one S orbit with multiplicity of 8, one V orbit with multiplicity of 2, one O orbit with multiplicity of 2 and seven O orbits with multiplicities of 8, which results in ν = 76 and rather high complexity parameters for the uranyl sulfate layers in the structures of mathesiusite and ammoniomathesiusite: I_{G} = 3.353 bits per atom, I_{G,total} = 254.842 bits per cell.
Zippeitegroup minerals can be considered as the most representative group among naturally occurring uranyl sulfates. Additionally, they represent also the trickiest ones due to a variable OH content of the layers and it has to be considered in topological complexity calculations as further discussed in detail. Among the hydroxylfree layers, two groups of minerals could be separated due to geometrical p2/a LG symmetry, which is defined with the topological complexity parameters: ν = 26, I_{G} = 2.777 bits per atom, I_{G,total} = 72.211 bits per cell. Further on, Figs. 7(a) and 7(b) show the real LG symmetry in the structures of magnesiozippeite and pseudojohannite, and the highest topological symmetry for hydroxylfree layers of the currently considered isomer is shown in Fig. 7(c). The second geometrical isomer is represented by the structure of ammoniozippeite and its structural symmetry pbab is equal to the topological (Fig. 7f): ν = 52, I_{G} = 2.777 bits per atom, I_{G,total} = 144.423 bits per cell. While the values of information content per atom are equal for both isomers, information content per is twice as high for the second type due to the twice larger cell, it doubles the amount of atoms in the An appearance of hydroxyl groups strongly affects and reduces the symmetry of the layered complexes. Statistical distribution of H atoms in the structure of zippeite results in a `hydroxylfull', electroneutral [(UO_{2})_{2}(SO_{4})(OH)_{2}]^{0} layer in contrast to the hydroxylfree ones [(UO_{2})_{2}O_{2}(SO_{4})]^{2–}. It appears that occupation of all O atoms shared between three uranyl polyhedra by H atoms will result in the same highest p2/a LG symmetry (Fig. 7d), but slightly higher complexity parameters: v = 30, I_{G} = 2.974 bits per atom, I_{G,total} = 89.207 bits per cell. All intermediate options of hydration could result in structurally and topologically different layers. For instance, Fig. 7(e) shows the uranyl sulfate layer of symmetry in the structure of sejkoraite(Y). The four times larger is a clear structural response to the U:OH ratio equal to 8:1.
that is caused by the shift of Upolyhedra chains along the chain direction. The first isomer group contains magnesiozippeite, plavnoite and pseudojohannite. They have the smallest of the5. Ladders of information
A concept of informational ladders has been introduced quite recently by Krivovichev (2018). This method allows the quantitative estimation of various contributions to the complexity of the whole structure. We have applied this concept in order to evaluate and distinguish informational sources contributing to the complexity of natural uranyl sulfates. Let us consider a few lowdimensional, 0D and 1D structures, including minerals belakovskiite (0D), klaprothite (0D), péligotite (0D), ottohahnite (0D), alwilkinsite(Y) (1D) and uranopilite (1D). We considered three distinct categories contributing to the information content of the entire structure: topological complexity (TOPO), complexity of the desymmetrized structural units (STRU) and the complexity of an interlayer complex, including a hydrogen bonding network (INT). Results of the analysis are given in Fig. 8. Among the abovechosen representatives, the highest topological complexity has the structural unit in ottohahnite [Figs. 2 and 4(d)], which is so far the most complex isolated uranylanion cluster unit (> 300 bits per cell). Interestingly, péligotite and uranopilite show a similar portion of information increase while takes place (STR/TOPO in Fig. 8). Nevertheless, the highest jump in the information content is related to the contribution of the interlayer complex of these minerals. We can distinguish here several factors that contribute to the complexity of the interlayer. Among them the hydration state, i.e. the amount of molecular H_{2}O, is the most crucial factor. The H_{2}O content is closely connected with the presence of highly charged elements [such as Y^{3+} in the case of alwilkinsite(Y)], or due to presence of a large number of interlayer metal cation sites (such as Na^{+} in the cases of ottohahnite and klaprothite). The remarkable informational content in alwilkinsite(Y) is the highest one among the selected group (see INT/SU in Fig. 8), and is a result of the incorporation of highly charged, trivalent yttrium cations.
The extensive role of the interstitial H_{2}O network and its contribution to the overall complexity of the mineral structures containing highly charged cations is well documented in Fig. 9. Among the studied uranyl sulfates it is mostly related to alwilkinsite(Y), Y[(UO_{2})_{3}(SO_{4})_{2}O(OH)_{3}](H_{2}O)_{14} (Kampf et al., 2017c), bobcookite, NaAl(UO_{2})_{2}(SO_{4})_{4}(H_{2}O)_{18} (Kampf et al., 2015a), leydetite, Fe(UO_{2})(SO_{4})_{2}(H_{2}O)_{11} (Plášil et al., 2013a), magnesioleydetite, Mg(UO_{2})(SO_{4})_{2}(H_{2}O)_{11} (Kampf et al., 2018d) and strassmannite, Al(UO_{2})(SO_{4})_{2}F(H_{2}O)_{16} (Kampf et al., 2018d).
As it was mentioned above mathesiusite, ammoniomathesiusite and zippeite possess structures with the highest content of information with regard to their topological complexity (Fig. 9). In the cases of mathesiusite and ammoniomathesiusite, it is due to incorporation of VO_{5} polyhedra of the high pointgroup symmetry (C_{4v}). In the case of zippeite, it is due to distribution of the OH^{−} groups within the uranyl sulfate sheet.
6. Conclusions
The complexity of the uranyl sulfate structural units varies significantly and it is highly dependent on the
of the layer (chain or cluster), which in turn depends on the connectivity of U and S polyhedra: the more connectivity within the layer, the higher density is; and the larger complexity parameters attributed to such structures.The twoconnected arrangement of the sulfate tetrahedra makes the rotation of these groups, which should make the structure less stable. In contrast, the threeconnected arrangement has fewer _{2}O molecules arranged in the interlayer space.
and thus it is more stable. The distribution of the complexity parameters confirms this observation. The majority of considered minerals have the real symmetry of the Ubearing layers, chains and isolated clusters much lower than the topological symmetry, which means that the complexity of the structural units is determined by the cations and HAcknowledgements
We are indebted to referees for their constructive reviews that helped to improve this article.
Funding information
The following funding is acknowledged: This research was partially supported through the project Ministry of Education, Youth and Sports National sustainability program I of the Czech Republic (project No. LO1603 to JP); and through the grant of Russian Science Foundation (grant No. 181700018 to Vladislav V. Gurzhiy).
References
Blatov, V. A., Shevchenko, A. P. & Proserpio, D. M. (2014). Cryst. Growth Des. 14, 3576–3586. Web of Science CrossRef CAS Google Scholar
Brugger, J., Burns, P. C. & Meisser, N. (2003). Am. Mineral. 88, 676–685. CrossRef CAS Google Scholar
Burns, P. C. (2001). Can. Mineral. 39, 1139–1146. CrossRef CAS Google Scholar
Burns, P. C., Deely, K. M. & Hayden, L. A. (2003). Can. Mineral. 41, 687–706. CrossRef CAS Google Scholar
Cempírek, J., Grew, E. S., Kampf, A. R., Ma, C., Novák, M., Gadas, P., Škoda, R., VašinováGáliová, M., Pezzotta, F., Groat, L. A. & Krivovichev, S. V. (2016). Am. Mineral. 101, 2108–2117. Google Scholar
Fernandes, H. M., Veiga, L. H. S., Franklin, M. R., Prado, V. C. S. & Taddei, J. F. (1995). J. Geochem. Explor. 52, 161–173. CAS Google Scholar
Finch, R. J. & Murakami, T. (1999). Uranium: Mineralogy, Geochemistry and the Environment, edited by P. C. Burns and R. J. Finch, in Reviews in Mineralogy, Vol. 38, pp. 91–179. De Gruyter. Google Scholar
Gurzhiy, V. V., Kovrugin, V. M., Tyumentseva, O. S., Mikhailenko, P. A., Krivovichev, S. V. & Tananaev, I. G. (2015). J. Solid State Chem. 229, 32–40. CrossRef CAS Google Scholar
Gurzhiy, V. V., Krivovichev, S. V. & Tananaev, I. G. (2017). J. Solid State Chem. 247, 105–112. CrossRef CAS Google Scholar
Gurzhiy, V. V., Tyumentseva, O. S., Britvin, S. N., Krivovichev, S. V. & Tananaev, I. G. (2018a). J. Mol. Struct. 1151, 88–96. CrossRef CAS Google Scholar
Gurzhiy, V. V., Tyumentseva, O. S., Krivovichev, S. V., Krivovichev, V. G. & Tananaev, I. G. (2016). Cryst. Growth Des. 16, 4482–4492. CrossRef CAS Google Scholar
Gurzhiy, V. V., Tyumentseva, O. S., Krivovichev, S. V. & Tananaev, I. G. (2018b). Z. Kristallogr. 233, 233–245. CrossRef CAS Google Scholar
Johnson, D. B. (2003). Water Air Soil Pollut. 3, 47–66. CrossRef CAS Google Scholar
Johnson, D. B. & Hallberg, K. B. (2005). Sci. Total Environ. 338, 3–14. CrossRef CAS Google Scholar
Kampf, A. R., Kasatkin, A. V., Čejka, J. & Marty, J. (2015a). J. Geosci. pp. 1–10. CrossRef Google Scholar
Kampf, A. R., Olds, T. A., Plášil, J., Marty, J. & Perry, S. N. (2018c). Mineral. Mag. DOI: 10.1180/mgm.2018.117. Google Scholar
Kampf, A. R., Plášil, J., Čejka, J., Marty, J., Škoda, R. & Lapčák, L. (2017c). Mineral. Mag. 81, 895–907. CrossRef CAS Google Scholar
Kampf, A. R., Plášil, J., Kasatkin, A. V. & Marty, J. (2014). Mineral. Mag. 78, 639–649. CrossRef CAS Google Scholar
Kampf, A. R., Plášil, J., Kasatkin, A. V. & Marty, J. (2015b). Mineral. Mag. 79, 695–714. CrossRef Google Scholar
Kampf, A. R., Plášil, J., Kasatkin, A. V., Marty, J. & Čejka, J. (2017b). Mineral. Mag. 81, 753–779. CrossRef CAS Google Scholar
Kampf, A. R., Plášil, J., Kasatkin, A. V., Marty, J. & Čejka, J. (2015cb). Mineral. Mag. 79, 1123–1142. Google Scholar
Kampf, A. R., Plášil, J., Kasatkin, A. V., Marty, J., Čejka, J. & Lapčák, L. (2017a). Mineral. Mag. 81, 273–285. CrossRef CAS Google Scholar
Kampf, A. R., Plášil, J., Kasatkin, A. V., Nash, B. P. & Marty, J. (2018d). Mineral. Mag. DOI: 10.1180/mgm.2018.118. Google Scholar
Kampf, A. R., Plášil, J., Nash, B. P. & Marty, J. (2017e). Mineral. Mag. 82, 401–411. CrossRef Google Scholar
Kampf, A. R., Plášil, J., Nash, B. P. & Marty, J. (2018a). Mineral. Mag. DOI: 10.1180/mgm.2018.112. Google Scholar
Kampf, A. R., Plášil, J., Nash, B. P. & Marty, J. (2018e). Eur. J. Mineral. 30, 999–1006. CrossRef Google Scholar
Kampf, A. R., Plášil, J., Olds, T. A., Nash, B. P. & Marty, J. (2018b). Can. Mineral. 56, 235–245. CrossRef CAS Google Scholar
Kampf, A. R., Sejkora, J., Witzke, T., Plášil, J., Čejka, J., Nash, B. P. & Marty, J. (2017d). J. Geosci. 62, 107–120. CrossRef Google Scholar
Krivovichev, S. V. (2008). Structural Crystallography of Inorganic Oxysalts, p. 308. Oxford University Press. Google Scholar
Krivovichev, S. V. (2010). Eur. J. Inorg. Chem. 2010, 2594–2603. CrossRef Google Scholar
Krivovichev, S. (2012). Acta Cryst. A68, 393–398. Web of Science CrossRef IUCr Journals Google Scholar
Krivovichev, S. V. (2013). Mineral. Mag. 77, 275–326. Web of Science CrossRef CAS Google Scholar
Krivovichev, S. V. (2014). Angew. Chem. Int. Ed. 53, 654–661. Web of Science CrossRef CAS Google Scholar
Krivovichev, S. V. (2018). Z. Kristallogr. 233, 155–161. CrossRef CAS Google Scholar
Krivovichev, S. V. & Burns, P. C. (2003). Z. Kristallogr. 218, 683–690. CAS Google Scholar
Krivovichev, S. V., Kahlenberg, V., Tananaev, I. G. & Myasoedov, B. F. (2005). Z. Anorg. Allg. Chem. 631, 2358–2364. CrossRef CAS Google Scholar
Krivovichev, S. V., Hawthorne, F. C. & Williams, P. A. (2017). Struct. Chem. 28, 153–159. CrossRef CAS Google Scholar
Krivovichev, S. V. & Plášil, J. (2013). In: Uranium: From Cradle to Grave, edited by P. C. Burns and G. E. Sigmon. MAC Short Courses series, Vol. 43, pp. 15–119. Mineralogical Association of Canada. Google Scholar
Krivovichev, S. V., Zolotarev, A. A. & Popova, V. I. (2016). Struct. Chem. 27, 1715–1723. CrossRef CAS Google Scholar
Majzlan, J., Dachs, E., Benisek, A., Plášil, J. & Sejkora, J. (2018). Eur. J. Mineral. 30, 259–275. CrossRef CAS Google Scholar
Mereiter, K. (1982). TMPM Tschermaks Mineral. Petrogr. Mitt. 30, 47–57. CrossRef CAS Google Scholar
Pekov, I. V., Krivovichev, S. V., Yapaskurt, V. O., Chukanov, N. V. & Belakovskiy, D. I. (2014). Am. Mineral. 99, 1783–1787. CrossRef Google Scholar
Plášil, J. (2014). J. Geosci. 59, 99–114. Google Scholar
Plášil, J. (2018a). Eur. J. Mineral. 30, 237–251. Google Scholar
Plášil, J. (2018b). Eur. J. Mineral. 30, 253–257. Google Scholar
Plášil, J., Dušek, M., Čejka, J. & Sejkora, J. (2014c). Mineral. Mag. 57, 1249–1263. Google Scholar
Plášil, J., Dušek, M., Novák, M., Čejka, J., Císařová, I. & Škoda, R. (2011a). Am. Mineral. 96, 983–991. Google Scholar
Plášil, J., Fejfarová, K., Škoda, R., Dušek, M., Marty, J. & Čejka, J. (2013c). Mineral. Petrol. 107, 211–219. Google Scholar
Plášil, J., Fejfarová, K., Wallwork, K. S., Dušek, M., Škoda, R., Sejkora, J., Čejka, J., Veselovský, F., Hloušek, J., Meisser, N. & Brugger, J. (2012c). Am. Mineral. 97, 1796–1803. Google Scholar
Plášil, J., Hauser, J., Petříček, V., Meisser, N., Mills, S. J., Škoda, R., Fejfarová, K., Čejka, J., Sejkora, J., Hloušek, J., Johannet, J.M., Machovič, V. & Lapčák, L. (2012b). Mineral. Mag. 76, 2837–2860. Google Scholar
Plášil, J., Hloušek, J., Kasatkin, A. V., Novák, M., Čejka, J. & Lapčák, L. (2015a). J. Geosci. 60, 113–121. Google Scholar
Plášil, J., Hloušek, J., Kasatkin, A. V., Škoda, R., Novák, M. & Čejka, J. (2015b). Mineral. Mag. 79, 205–216. Google Scholar
Plášil, J., Hloušek, J., Veselovský, F., Fejfarová, K., Dušek, M., Škoda, R., Novák, M., Čejka, J., Sejkora, J. & Ondruš, P. (2012a). Am. Mineral. 97, 447–454. Google Scholar
Plášil, J., Kampf, A. R., Kasatkin, A. V. & Marty, J. (2014a). J. Geosci. 59, 145–158. Google Scholar
Plášil, J., Kampf, A. R., Kasatkin, A. V., Marty, J., Škoda, R., Silva, S. & Čejka, J. (2013b). Mineral. Mag. 77, 2975–2988. Google Scholar
Plášil, J., Kasatkin, A. V., Škoda, R., Novák, M., Kallistová, A., Dušek, M., Skála, R., Fejfarová, K., Čejka, J., Meisser, N., Goethals, H., Machovič, V. & Lapčák, L. (2013a). Mineral. Mag. 77, 429–441. Google Scholar
Plášil, J., Mills, S. J., Fejfarová, K., Dušek, M., Novák, M., Škoda, R., Čejka, J. & Sejkora, J. (2011b). Can. Mineral. 49, 1089–1103. Google Scholar
Plášil, J., Škácha, P., Sejkora, J., Kampf, A. R., Škoda, R., Čejka, J., Hloušek, J., Kasatkin, A. V., Pavlíček, R. & Babka, K. (2017). Eur. J. Mineral. 29, 117–128. Google Scholar
Plášil, J. & Škoda, R. (2015). Mineral. Mag. 79, 649–660. Google Scholar
Plášil, J., Veselovský, F., Hloušek, J., Škoda, R., Novák, M., Sejkora, J., Čejka, J., Škacha, P. & Kasatkin, A. V. (2014b). Am. Mineral. 99, 625–632. Google Scholar
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