Crystal Chemical Relations in the Shchurovskyite Family: Synthesis and Crystal Structures of K2Cu[Cu3O]2(PO4)4 and K2.35Cu0.825[Cu3O]2(PO4)4

Single crystals of two novel shchurovskyite-related compounds, K2Cu[Cu3O]2(PO4)4 (1) and K2.35Cu0.825[Cu3O]2(PO4)4 (2), were synthesized by crystallization from gaseous phase and structurally characterized using single-crystal X-ray diffraction analysis. The crystal structures of both compounds are based upon similar Cu-based layers, formed by rods of the [O2Cu6] dimers of oxocentered (OCu4) tetrahedra. The topologies of the layers show both similarities and differences from the shchurovskyite-type layers. The layers are connected in different fashions via additional Cu atoms located in the interlayer, in contrast to shchurovskyite, where the layers are linked by Ca2+ cations. The structures of the shchurovskyite family are characterized using information-based structural complexity measures, which demonstrate that the crystal structure of 1 is the simplest one, whereas that of 2 is the most complex in the family.


Introduction
The last two decades are marked by the increased interest in mineralogical data from the field of material sciences. Since the discovery of a quantum spin liquid state in herbertsmithite [1,2], the number of mineralogically inspired studies in this field has grown exponentially: from the investigation of magnetic properties of the atacamite-group minerals [3][4][5][6][7], to other Cu minerals such as lindgrenite [8], libethenite [9], dioptase [10,11], volborthite [12], vesigneite [13,14], etc. [15][16][17]. The most important common feature of all these mineral structures is the presence of Cu 2+ cations in variable coordination geometries, a consequence of the Jahn-Teller effect [18][19][20] that results in the existence of at least four most common coordination geometries [21][22][23] with a diversity of transitional forms. Such a flexibility of Cu 2+ -centered coordination polyhedra leads to the occurrence of a multitude of structure types with interesting physical properties tunable through an interplay between structure and chemical composition.
A number of mineral-related structures are characterized by the presence of 'additional' oxygen atoms that do not participate in the formation of strongly bonded "acid residue" complexes (sulfate, vanadate, phosphate, arsenate, selenite groups, etc.). These structures can be described in terms of anion-centered tetrahedra and attract special attention due to their magnetic properties controlled by the local structure of oxygen-based copper polycations [24][25][26]. For example, magnetic studies were performed for such anion-centered-based minerals as ilinskite [27], averievite [28,29], yaroshevskite [30], atlasovite [31], etc.  4 ) were prepared via gas phase crystallization, successfully employed for the simulation of fumarolic mineral formation in a number of previous experiments [30,35,36]. Stoichiometric amounts of copper oxide (CuO, 99%, Vekton, St. Petersburg, Russia), copper pyrophosphate (Cu 2 P 2 O 7 , 99%, Vekton) and potassium chloride (KCl, 99%, Vekton) taken in the 6:2:3 molar ratio were ground in an agate mortar. Due to the hygroscopic nature of potassium chloride [37,38], the resulting mixture was loaded into a porcelain boat and annealed at 250 • C for~24 h in air. The mixture was further loaded into a fused silica ampule, evacuated to 10 −2 mbar, sealed and placed horizontally in a furnace and heated to 800 • C over a period of 6 h. After two days, the furnace was cooled to 350 • C over a period of 72 h and switched off. The resulting sample contained single crystals of K 2 Cu[Cu 3 O] 2 (PO 4 ) 4 (1), K 2. 35 Cu 0.825 [Cu 3 O] 2 (PO 4 ) 4 (2), Cu 5 O 2 (PO 4 ) 2 [39] and copper oxide. All the compounds were found in a source zone of the ampule.

Single-Crystal X-ray Diffraction Study
Single crystals of both compounds were selected for data collection under an optical microscope, coated in an oil-based cryoprotectant and mounted on cryoloops. Diffraction data for 1 were collected using a Bruker APEX II DUO X-ray diffractometer (Bruker Co., Billerica, MA, U.S.A.) operated with a monochromated microfocus MoKα tube (λ = 0.71073 Å) at 50 kV and 0.6 mA and equipped with a CCD APEX II detector. Diffraction data for 2 were collected using a Rigaku XtaLAB Synergy S X-ray diffractometer (Rigaku Co., Tokyo, Japan) operated with a monochromated microfocus MoKα tube (λ = 0.71073 Å) at 50 kV and 1.0 mA and equipped with a CCD HyPix 6000 detector. Exposures were 10 and 74 s per frame for 1 and 2, respectively. CrysAlisPro software [40] was used for the integration and correction of diffraction data for polarization, background and Lorentz effects as well as for an empirical absorption correction based on spherical harmonics implemented in the SCALE3 ABSPACK algorithm. The unit cell parameters (Table 1) were refined using the least-squares technique. The structures were solved by a dual-space algorithm and refined using the SHELX programs [41,42] incorporated in the OLEX2 program package [43]. The final models include coordinates and anisotropic displacement parameters (Tables A1 and A2).

Crystal Structure Descriptions
The crystal structure of 1 contains four symmetrically distinct Cu 2+ cations, three of which (Cu1, Cu2 and Cu3) form the shchurovskyite-type layer as shown in Figure 1a. Considered in terms of the cation-centered polyhedral, the basic unit of the structure is a rod of edge-sharing Cu3O 5 square pyramids (Cu3 · · · Cu3 = 2.856 Å), extended along [100]. The orientation of apical vertices (O ap ) of square pyramids alternates up (U) and down (D) relative to the (010) plane, giving the UDUDUD sequence within the rod, with the Cu-O ap bond distance equal to 2.239 Å (Figure 1c). Each rod is decorated by Cu1O 6 octahedra and Cu2O 5 triangular bipyramids from both sides in the (010) plane. The Cu1O 6 octahedron shows a typical [4+2] distortion with four short (1.887-2.097 Å) and two long (2.706 and 2.768 Å) Cu-O bonds. It is noteworthy that the Cu1 site has one more elongated (2.936 Å) Cu-O distance to the O atom located near one of the apical ligands (O · · · O = 2.500 Å), which corresponds to the edge of the (PO 4 ) 3− tetrahedron. Such a coordination geometry of Cu 2+ cations is rather rare and, as far as we know, among all the natural Cu 2+ -containing oxysalts, it was observed in the crystal structures of cesiodymite, cryptochalcite and saranchinaite, which are the products of fumarolic activity of the Tolbachik volcano [44,45]. The Cu1O 6 octahedron shares a common edge with the Cu2O 5 triangular bipyramid. The equatorial plane of the Cu2O 5 bipyramid is formed by one short (1.944 Å) and two elongated (2.237 and 2.299 Å) Cu-O bonds. The apical Cu2-O ap bond lengths are equal to 1.884 and 1.920 Å. The Cu2O 5 bipyramid is slightly distorted due to the Berry twist mechanism [46,47]: the O ap -Cu2-O ap and O eq -Cu2-O eq angles are equal to 166.6 and 124.4 • , respectively. based layers. The resulting framework has channels filled by K + cations (Figure 1d). There is one symmetrically distinct K atom, coordinated by six oxygen atoms (2.633-2.959 Å), with the <K1 · · · K1> distance equal to 3.865 (3) and 3.732 (3) Å. The calculation of the effective width (e.c.w.) of the channels, by subtracting the ionic diameter of O 2− (2.7 Å) from the shortest and longest O · · · O distances across the channel [48], shows that the channel in the structure of 1 is much smaller than in the structure of shchurovskyite: 1.3 × 4.6 Å 2 in 1 versus 2.8 × 5.9 Å 2 in shchurovskyite. As with all known shchurovskyite-type minerals and compounds, the crystal structure of 1 contains so-called 'additional' oxygen atoms (Oadd), allowing it to be described in terms of anion-centered tetrahedra [24,25]. The structure of 1 contains one symmetrically distinct 'additional' oxygen atom tetrahedrally coordinated by two Cu3, one Cu1 and one Cu2 atoms (Figure 1a). The Oadd-Cu bond lengths are the shortest among all Cu-O bonds and span the range of 1.881-1.913 Å. Two OCu4 tetrahedra share a common Cu3 · · ·Cu3 edge to form a [O2Cu6] 8+ dimer.
The crystal structure description of 2 is far more difficult to describe due to its disordered nature and the enlarged unit cell, which is a consequence of the increased number The rods are linked into the Cu-based polyhedral layer parallel to (010) due to the edgesharing of two adjacent Cu2O 5 triangular bipyramids belonging to the neighboring rods ( Figure 1b). The connection between the layers in the shchurovskyite-related compounds proceeds via the PO 4 tetrahedra. In the crystal structure of 1, each P2O 4 tetrahedron shares common vertices with the Cu3O 5 square pyramid and Cu2O 5 triangular bipyramid of one layer, and with the Cu1O 6 octahedron of the adjacent layer. In opposition, the P1O 4 tetrahedron is located within the layer, and shares common vertices with two Cu2O 5 triangular bipyramids and one Cu1O 5 square pyramid. There is one additional Cu4 site located in between the layers ( Figure 1c) and coordinated by six oxygen atoms, belonging to the PO 4 tetrahedra, to form [4+2]-distorted octahedron with four short (1.977 (×2) and 1.984 (×2) Å) and two long (2.823 (×2) Å) Cu4-O bonds. Two opposite vertices of the equatorial plane of the Cu4O 6 octahedron are common with two Cu3O 5 square pyramids of adjacent Cu-based layers. The resulting framework has channels filled by K + cations ( Figure 1d). There is one symmetrically distinct K atom, coordinated by six oxygen atoms (2.633-2.959 Å), with the <K1 · · · K1> distance equal to 3.865 (3) and 3.732 (3) Å. The calculation of the effective width (e.c.w.) of the channels, by subtracting the ionic diameter of O 2− (2.7 Å) from the shortest and longest O · · · O distances across the channel [48], shows that the channel in the structure of 1 is much smaller than in the structure of shchurovskyite: 1.3 × 4.6 Å 2 in 1 versus 2.8 × 5.9 Å 2 in shchurovskyite.
As with all known shchurovskyite-type minerals and compounds, the crystal structure of 1 contains so-called 'additional' oxygen atoms (O add ), allowing it to be described in terms of anion-centered tetrahedra [24,25]. The structure of 1 contains one symmetrically distinct 'additional' oxygen atom tetrahedrally coordinated by two Cu3, one Cu1 and one Cu2 atoms (Figure 1a). The O add -Cu bond lengths are the shortest among all Cu-O bonds and span the range of 1.881-1.913 Å. Two OCu 4 tetrahedra share a common Cu3 · · ·Cu3 edge to form a [O 2 Cu 6 ] 8+ dimer.
The crystal structure description of 2 is far more difficult to describe due to its disordered nature and the enlarged unit cell, which is a consequence of the increased number of symmetrically distinct positions of all atoms. There are two symmetrically distinct rods of CuO 5 square pyramids in 2. The first rod consists of the Cu3O 5 and Cu4O 5 pyramids, alternating along [010], whereas the alternation of the Cu8O 5 and Cu9O 5 pyramids builds the second rod (Figure 2a,c,e). The equatorial Cu-O eq bond lengths within square pyramids are in the range of 1.898-1.966 Å. The apical oxygen atom of the Cu8O 5 square pyramid is split into two positions, resulting in the Cu8-O ap bond lengths of 2.579 and 2.739 Å; the apical bond lengths in the other square pyramids vary from 2.386 to 2.469 Å. The apical vertices of the square pyramids within the rods are oriented according to the UUDDUU sequence, which is different from the sequence UDUD observed in 1.  The local coordination of the Cu atoms, involved in the orthogonal connection of the polyhedral rods, is different from those observed in the crystal structure of 1: instead of one symmetrically distinct Cu 2+ -centered triangular bipyramid, there are four distinct Cu 2+ polyhedra, forming two types of bridges. The bridge of the first type is formed by the dimer of edge-sharing Cu2O5 and Cu10O5 square pyramids. The average <Cu-Oeq > bond distances are equal to 1.953 and 1.966 Å for the Cu2O5 and Cu10O5 pyramids, respectively, whereas the apical bond lengths are 2.597 and 2.305 Å, respectively. Note that the Cu2O5 square pyramid can be considered as a [4+1+1]-distorted octahedron due to the presence The Cu 2+ -centered polyhedra in 2 form the Cu-based layer parallel to the (001) plane. The comparison with the structure of 1 reveals the significant difference between two structures: instead of the CuO 6 octahedra connecting the layers in 1, the crystal structure of 2 shows an alternation of the Cu and K atoms along [010] (Figure 3c). There are two symmetrically distinct fully occupied Cu12 and K1 sites. The Cu12 site is coordinated by five oxygen atoms to form a [4+1]-distorted square pyramid. Taking into account that positions of two neighboring oxygens in the equatorial plane of the Cu12O 5 polyhedron are disordered, the average < Cu12-O eq > bond length is 1.972 Å. The coordination geometry of the Cu12 site can also be considered as transitional from square-pyramidal to square-planar due to the long Cu12-O ap bond length (2.731 Å). The K1 atoms are coordinated by eight oxygen atoms of the phosphate groups, with five relatively short (2.711-2.857 Å) and three long (3.375-3.318 Å) K1-O bonds.
The enlargement of the unit cell results in the presence of the second symmetrically distinct intra-framework channel. Both types of channels are filled by highly disordered K atoms (Figure 2d). The first channel contains K2 and K3 atoms, each split into two and three symmetrically distinct partially occupied positions, respectively. The displacement of the K atoms, placed in average positions, is similar to that observed in the structure of 1 due to the zigzag arrangement within the channel, with the K2 av ···K3 av and K3 av ···K3 av distances equal to 3.992 and 4.124 Å, respectively. The effective channel width (1.3 × 5.8 Å 2 ) is close to that observed in the crystal structure of shchurovskyite [34]. The content of the second symmetrically distinct channel is significantly different from that observed in any other shchurovskyite-type structures. Herein, along with the disordered K atoms, additional Cu atoms are present. The Cu site within the channel is split into two symmetrically distinct positions, Cu14 and Cu145, with S.O.F. of 0.5 and 0.15, respectively (Figure 3f). While the most occupied Cu14 position exhibits a typical square-pyramidal coordination geometry (2.012-2.735 Å), the Cu15 site shows a different bond distribution, having one short (2.033 Å) and four elongated (2.212-2.490 Å) bonds, a consequence of the low occupancy of the disordered configuration. The K atoms are concentrated near to the center of the channel with the K-O bond lengths in the range of 2.564-3.40 Å. Due to the presence of the additional Cu atoms, the effective width of channels is reduced to 1.5 × 3.0 Å 2 .    The crystal structure of 2 contains four symmetrically distinct 'additional' oxygen atoms, tetrahedrally coordinated by copper atoms, with the O add -Cu bond lengths varying from 1.881 to 1.928 Å (Figure 2b).

Discussion
The crystal structures of shchurovskyite, K 2 Ca[Cu 3 [33,34]. The hetero-polyhedral framework contains channels, filled by K + cations, and one additional position between the copper layers, occupied by Ca 2+ and K + atoms in shchurovskyite and dmisokolovite, respectively. Unlike the structure of both minerals, these additional positions in the crystal structures of 1 and 2 are occupied by Cu 2+ cations, connecting the Cu-based layers, which results in the formation of a Cu-based porous framework, decorated by (PO 4 ) 3− tetrahedra and containing potassium atoms within the channels.
As was mentioned above, all the shchurovskyite-type structures can be described as consisting of Cu-based layers. The simplest way to distinguish the main features of each structure is a topological analysis, which can be performed by means of representation of the connectivity of copper atoms in terms of nets. In order to reduce the influence of chemical composition on crystal chemical comparative analysis, only phosphate members of the shchurovskyite family will be discussed below.
The core of the layers in each structure is a Cu 6 cluster, representing a [O 2 Cu 6 ] dimer of two edge-sharing (OCu 4 ) tetrahedra, with their bases approximately parallel to the planes of the layers. The dimers form linear rods along a in 1, and along b in 2 and other shchurovskyite-type structures, with the shortest Cu···Cu distances between the adjacent dimers varying from 2.866 (in Rb 2 Ca[Cu 3 O] 2 (PO 4 ) 4 ), to 2.908 and 2.933 (in 2), and 2.941 Å (in 1). Figure 3a shows the projection of the Cu-based layer onto the (010) plane in 1, with green lines aligned along terminal Cu atoms of dimers of the neighboring rods. The distance between the lines is 2.202 Å. The rods in the structure of 2 are aligned along two-fold screw axis, which results in the different arrangement ( Figure 3b). Herein, each rod is surrounded by two symmetrically related rods shifted by 1.654 Å relative to each other. The shift is maximal in the crystal structure of Rb 2 Ca[Cu 3 O] 2 (PO 4 ) 4 , where each rod is shifted by 2.820 Å relative to the adjacent rod (Figure 3c).
The results presented above show the highly flexible nature of the shchurovskyite-type structures. Indeed, at least four different structure types are present: triclinic archetype (1), monoclinically distorted 1 × 1 × 1 shchurovskyite and its phosphate synthetic analogue with the C2 space groups, monoclinically distorted 1 × 1 × 2 superstructure of dmisokolovite with the C2/c space group, and monoclinically distorted 2 × 2 × 2 superstructure. Both the archetype (1) and 2 × 2 × 2 superstructure (2) reported herein were obtained in the same experiment, whereas the phosphate analogue of shchurovskyite does not exhibit any significant difference from its parent structure. At the same time, the 1 × 1 × 2 superstructure of dmisokolovite is due to the partial substitution of Cu by Al cations. Thus, the broad variety of shchurovskyite-type structures most likely depends on the flexibility of the Cu-based framework, and the arrangement of the Cu-based rods in particular. We suppose that the flexibility of the Cu-based framework will lead to the discovery of other novel compounds of the series, including novel mineral species.
Another important feature of the shchurovskyite-type structures is the interlayer space that can accommodate different cations, from K + (in the structures of dmisokolovite and 2), to Ca 2+ (in shchurovskyite and Rb 2 Ca[Cu 3 O] 2 (PO 4 ) 4 ) and Cu 2+ (in 1 and 2). The interlayer sites are responsible for the connection of adjacent Cu-based layers, and it can be assumed that the substitution of non-magnetic cations by Cu 2+ will lead to significant changes in the magnetic properties of the respective materials.
The differences between the shchurovskyite-related structure types can be easily demonstrated by information-based measures of structural complexity [49][50][51] (Table 2). In the framework of this approach, the complexity is estimated as the amount of Shannon information contained in a crystal structure according to the following formulas: 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 i th crystallographic orbit, which is: where m i is a multiplicity of a crystallographic orbit (i.e., the number of atoms of a specific Wyckoff site in the reduced unit cell), and v is the total number of atoms in the reduced unit cell. The crystal structure of 1 (archetype) is the simplest one (3.986 bits/atom and 123.58 bits/cell), whereas the crystal structure of 2 is the most complex in the series (5.974 bits/atom and 1493.446 bits/cell) and belongs to the category of very complex structures [52,53]. The complexity parameters of the crystal structures of shchurovskyite and Rb 2 Ca[Cu 3 O] 2 (PO 4 ) 4 are almost as simple as those for the 1 (4.051 bits/atom and 125.58 bits/cell), whereas the crystal structure of dmisokolovite with the doubled c parameter is twice as complex (4.051 bits/atom and 251.16 bits/cell).      (7)